Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Glacially-induced scaling relations in mountain drainage basins Brardinoni, Francesco 2006

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-ubc_2006-199442.pdf [ 33.12MB ]
Metadata
JSON: 831-1.0092947.json
JSON-LD: 831-1.0092947-ld.json
RDF/XML (Pretty): 831-1.0092947-rdf.xml
RDF/JSON: 831-1.0092947-rdf.json
Turtle: 831-1.0092947-turtle.txt
N-Triples: 831-1.0092947-rdf-ntriples.txt
Original Record: 831-1.0092947-source.json
Full Text
831-1.0092947-fulltext.txt
Citation
831-1.0092947.ris

Full Text

GLACIALLY-INDUCED SCALING RELATIONS IN MOUNTAIN DRAINAGE BASINS by F R A N C E S C O B R A R D I N O N I M . S c . The University of British Columbia, 2001 Diploma di Laurea, Universita' C a ' Foscari di Venezia, 1999 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R OF P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Geography) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A M a y 2006 © Francesco Brardinoni, 2006 Abstract In glaciated British Columbia, Canada, Quaternary climate changes are responsible for profound spatial reorganization of earth surface processes. These changes have left a landscape characterized by topographic anisotropy associated with a hierarchy o f glacial troughs. The evolution of formerly glaciated landscapes is examined by considering a set o f scaling relations and assessing their departures from known unglaciated trends. Ultimately, the magnitude of these departures should provide a measure of the state of landscape recovery (transience) from glacial disturbance. The set o f scaling dependences studied includes slope-area relations, for assessing geomorphic process domains; landslide magnitude-frequency ( L M F ) and yield-area relations, for evaluating landslide-driven sediment dynamics; and the spatial organization of channel-reach morphology. In addition, along channel long-profiles the scaling between drainage area and channel cross-sectional variates (downstream hydraulic geometry), coarse grain-size fraction, and stream power indices are examined. The methodological approach couples extensive field surveys, GIS-based topographic analysis, air photo interpretation, and multivariate statistical analysis. Slope-area analysis reveals generalized process-form disequilibrium with a mismatch between topographic signatures and currently active geomorphic process domains. A t the landscape scale of "source" colluvial channels, the glacial/paraglacial signature commonly overrides that produced by contemporary debris flows. Along the axis of former ice flows, relict glacial cirques introduce a "hanging" fluvial domain at contributing areas as small as 8*10" k m and produce complex channel long-profiles similar to those observed for rivers responding to tectonic forcing. The concept of process domains appears to hold; however, some major glacially-forced modifications in the alluvial-colluvial transition are observed and the definition of a depositional colluvial sub-domain is proposed. Direct spatial scale linkages and generalized departure from unglaciated scaling relations are observed at all levels of investigation. Glacial macro-forms, by imposing local channel gradient and degree i i of colluvial-almvial coupling, dictate the spatial distribution of process domains, which in turn affect L M F relations, landslide yield, channel-reach morphology, downstream hydraulic geometry, and stream power. The combination of glacial and post-glacial fingerprints and the effects of ongoing earth surface processes generate a complex landscape whose glacial signatures may persist until the onset of the next ice age. i i i Table of Contents Abstract i i Table of Contents iv Lis t o f Tables v i i List o f Figures x Acknowledgements xv Dedication x v i C H A P T E R 1 - Introduction 1 1.1 A i m s 1 1.2 Thesis Structure Overview 2 C H A P T E R 2*- Literature Review and Research Questions hi Formerly Glaciated Mountain Settings 3 2". 1 Mountain Geomorphic Systems 3 2".2~Uhglaciated" Mountain Settings 6 2.2.1 Topographic Units and Geomorphic Process Domains 6 2~.2'.2"Sediment SourcesandMagnitude-Frequency Relations 9 2~.2:3"Channel Morphology 10" 2".2".4'Downstream Hydraulic Geometry 12 2.3 GlaciatedMountaih Settings 14 2.3". 1 Geomorphic Process Domains 14 2.3^2" Sediment Sources and Magnitude-Frequency Relations 16" 2.33* Channel Morphology 19 2.3.4 Downstream Hydraulic Geometry 20 C H A P T E R 3 - GlaciaFErosion, River Long-Profiles, and Process Domains in Mountain Drainage Basins of Coastal British Columbia 22" 3.1 Introduction . .> 22 3.2" Study Areas 26" 3.3 Data Collection 4 26 3.4 Results 27 3.4.1 Val ley Walls and'Cirque Walls 28" iv 3:4:2"Glacially-lMuced'S"addle 31 3.4:3" GlacialTroughs 31 3.4.4 Process Domains 35 3.4.5 Field- Versus GIS-Measured Data 38 3.5 Discussion 41 C H A P T E R 4 - ' Characterization o f Sediment Sources 45 4.1 Introduction 45 43" Study Area .' 49 ' 4.3 Data Collection 54 4.4 Results , 58 4.4.1 Landslide Type 59 4.4.2 Landslide Position at Initiation 62 4.4:3" Landslide Terminus and Delivery 64 4:4:4 The Significance o f Hollbw-RelatedSlbpe Failures to Sediment Production 66 4:4.5"Effects o f Litholbgy on the SpatiarDistributibn o f Sediment Sources... 6T 4.4.6 Land Use, Litholbgy, and "the Temporal Variability of Landslide Activi ty 72 4.4.7Xandslide Magnitude-Frequency Relations 77 4:4:8" Tsitilca-Eve Versus Capilano 84 4:4.9Xandslide-Driven Dynamics across Process Domains and Sediment Y i e l d 87 4.5 Discussion 94 C H A P T E R 5 - ChanneL-Reach Morphology 105" 5.1 Introduction 105 5:2" Study Areas 108" 5.3 Data Collection I l l 574 SpatiarDistributibn o f Channel-Reach" Morphology in the Slope-Area Context 115 5T5"Channel'-ReacH Morphology, Available Energy, andTlbw Resistance 125 576 Channel-Reach Morphology, ChannelSize, and Grain Roughness 128 v 5.TMultivariate Prediction of "Channel :Reach Morphology 133 5.7.1 P C A for Variable Reduction 134 5[772"Multivariate Discriminant Analysis 136 5.8 Discussion 142 C H A P T E R ? 6 - Downstream Hydraulic Geometry in Glaciated Mountain Streams and" Implications for Charmer Width Prediction 147 6.1 Introduction 147 6 X . T Downstream Hydraulic Geometry in Mountain Streams 148 6.1.2 Prediction of Bankfull Channel Width 151 6:2" Objectives 153" 6.3" Study Areas 153" 6/4 Data Collection and"Analysis 153 6.5 Results ; 155 67571 Transverse Transect: Ground Measurements Versus Reach Averages... 155 6.572"Uongimdihal Transects: ChannelWidtK 159 67573" LongitudihalTransects: ChannelDepth 164 6.574 ITongitudihal Transects: Coarse Grain-Size Fraction 169 67575XongitudiharTfansects: Stream Power 170 6.5.6 Prediction of Bankfull Channel Width 173 6.6 Discussion 177 C H A P T E R 7 - Conclusions 186 R E F E R E N C E S 192 A P P E N D I X A - Sediment Sources 211 A P P E N D I X B - Multivariate Statistical" Analysis: Testing the Assumptions 223 A P P E N D I X C - Total Stream Power 247 v i List of Tables Table 3 . 1 - Field data for the transverse transects 29 Table 3.2 - Fielddata for the longitudihal'transects 34 Table 373"- Error analysis o f "GIS-measured "slopes performedagaihst field-measured" slopes 41 Table 4~. 1 - Land-use history across lithologies in TsifiKa and Eve watersheds 54 Table 4.2 - Landslide types and sediment production in the Tsitika-Eve River basins... 55 Table 4 3 - Landform at landslide initiation point 55 Table 4.4- Landslide terminus andsediment delivery to channels 57 Table 4.5"- Descriptive statistics of landslide types across land use categories 60 Table 4.6 - Descriptive statistics of landslides categorized by land "use andihitiatibn position 62 Table 4.7"- Sediment delivery to channels 65 Table 4.8 - Landslide source-to-sihk pathways 67 Table 4.9 - Descriptive statistics of landslide types across land use and litholbgy 68 Table 4.10 - Descriptive statistics of landslides categorized by landuse, initiation, and litholbgy 70" Table 4.11 - Sediment delivery to channels by litholbgy 71 Table 4.12"- Temporal'variability of annuallandslide density for the pe r iod ! 930-2003 72" Table 4.13" - Temporal" variability of landslide yield'for the period"1930-2003" 72 Table 4.14 - Landslide density and yieldratios for the pe r iod ! 930-2003" 76 Table 4.15"- Drainage density anddescriptive statistics o f slope gradient 86 Table 4 ! 6 - Gross volume erodedand deposited by landslides across process domains 89" Table 4.17 - Percent volumes eroded and deposited by landslides categorized by land use and by type of material'mobilized expressedas percent of the total 91 Table 5 ! - Transformations of reach-variables 133 Table 572"- Eigenvalues o f the correlation matrix 135" Table 5"3"- Eigenvectors of the first four principal components 136 Table 5.4 - Univariate test statistics 137 v i i Table 575"- Canonicaf discriminant analysis: likelihood test ratio 137 Table 5.6 - Total Canonical Structure 138 Table 577"- Jackknife-validated membership classification results: 7 variables, 5 classes 138 Table 578"- Jackknife-validated membership classification results: 3"variables (S", x, D957d), 5"classes 139 Table 579 - Cross-validated membership classification results: 2" variables (S", D957d), 5"classes. Training dataset: Capilano River sub-basins (Pacific Ranges); validation dataset: Elliott Creek (Insular Ranges) 140 Table 5710 - Jacldcnife-validatedmembership classification results: 3" variables (ST, T, D"95/d), 4 classes 141 Table 5711 - Cross-validated'membership classification results: 2"variables (S~ D95/d), 4 classes. Training dataset: Capilano River sub-basins; validation dataset: Elliott Creek 142" Table 5712 — Stepwise selection summary 142 Table 6.1 - Hydraulic geometry relations in HeskethlOO Cr.: fielddata points versus reach averages 156 Table 612"- Barikfuirchannerwidth as a function of "contributing area across process domains 160 Table 6.3- B~aiildM"channerdepth as a function of contributing area across process domains 165 Table 6.4 - D95 as a function of contributing area across process domains 169" Table 6'S- Root Mean Squared'Error of bankfulfwidth 174 Table 6.6- Exponents of DHG" relations for the study basins 183" Table 6.T- Dimensibnarratibs of driving force (fl)'to substrate resistance (D95) 183 Table A . l - Volume of materiarmobilized"(m 3) categorized by initiation site, landslide type, andlanduse 212 Table A . 2 - Volume of materiarmobilized (m 3) in natural terrain, categorized by terminus andlandslidetype 213" Table A .3 - Volume of material mobilized (m ) in clearcut terrain, categorized by terminus andlandslide type 214 v i i i Table A . 4 - Volume of material mobilized (m 3) at road-related locations, categorized" by terminus andlandslide type 215 Table A . 5"- Landslide geometry by litholdgy 217 Table A . 6 - NaturalTandslide geometry by position at initiation 218 Table A . 7 - Landslide geometry by landslide type 221 ix Listof Figures Figure 2". 1 - Idealized"structure of an unglaciated"second :order drainage basin 7 Figure 2.2"- Schematic representation of process domains and topographic signatures in an imglaciated mountain landscapes at steady state 8 Figure 2" 3 - Idealized "process-based classification of a mountain channel, concave up, long profile; (b) Slope-area plot o f channel reaches in a "simple" unglaciated basin . . . . 11 Figure 2~4 - Scale relations for channel width and depth versus flow 13 Figure 2.5"- Generalizedgeomorpholbgicarzonation of the southern Coast Mountains 15" Figure 2.6 - Landslide magiumde-frequency relation for the Capilano River basin, British Columbia 18 Figure 3 ! - Map of "the Capilano River basin indicating the location of "the ground-surveyed streams 25 Figure 3.2 - Slope-area plots (a-g) along debris-flow dbmihatedchannels and "(h) at a glacially-ihducedsaddle 30 Figure 3.3 - Slope-area plots along the direction of formerly active ice flows 33" Figure 3.4 - (a) Process domains based'on field :measured"slbpes plotted "in slope-area space, (b) Process domains based on DEM-measured slopes 36 Figure 3.5 - Contour map of Hesketh Creek and Eembke Creek showing the spatial configuration of "sediment sources, colluvial channels and alluvial channels 37" Figure 3.6 - Scatter plots comparing: (a) field slopes vs. D E M "slopes, and "(b) field slopes vs. digitized slopes 39" Figure 3.7 - Box plots o f field'slbpes, digiiizedslbpes, a n d D E M "slopes across channel types 40 Figure 3.8 - Schematic representation o f "(a) lbngitudinalprofile and"(b) corresponding area-based process domains and topographic signatures in a glaciatedstudy basin of" coastal British Columbia 43 Figure 4 . 1 - Map of "the Tsifika and Eve River basins indicating the mapped channel network and" the drainage divides 49 Figure 4.2- Tsitika-Eve elevation frequency distribution by litholbgy 50" x Figure 4i3~- Lithology map of the Tsitika and Eve River basins 51 Figure 4.4 - Relative frequency distribution of slope gradient across lithology types in: (a) natural terrain, and (b) logged terrain 52 Figure 4.5 - Map of land use history in the Tsitika and'Eve River basins for the period" 1961-2003 53 Figure 4.6 - (a) Examples of landslide positions at initiation in Thursday Creek. (b) Sidewall slope failures 56 Figure 4.7 - Landslide area vs. depth for 96 ground:measured~events in the Tsitika River basin , 58 Figure 4.8 - Size distribution of landslide types in naturar(unlbgged) terrain 61 Figure 4.9 - Landslide size distribution categorized by types across land use classes . . . 61 Figure 4.10 - Landslide size distributions grouped by initiation position across land : use classes > — 6 3 Figure 4.11 - Landslide size distributions categorizedby sediment delivery to channels across land-use classes 65 Figure 4.12 - Box-whisker plots o f landslide size distributions comparing litholbgies across (a) land uses, (b) failure types in natural terrain (c) failure types in clearcuts (d) initiation positions in clearcuts (e) initiation positions in natural terrain, and "(f)" land uses and sediment delivery classes 69 Figure 4A3- Annual landslide density for the period 1930-2003: (a) bedrock and debris movements in natural terrain, and "(b) debris movements in natural and logged terrain 73 Figure 4 T 4 - Landslide sediment yield for the period 1930-20031 (a) bedrock and debris movements in naturaLterraih, and"(b) debris movements in natural and logged terrain 74 Figure 4.15 - Landslide activity for the pe r iod ! 930-2003"adjusted for post-logging recovery: a) annual "landslide density, and (b) landslide sediment yield 75" Figure 4.16 - Landslide magnitude-frequency relations: (a) considering all landslides together; and (b) separating landslide by lithology 78 Figure 4.17 - Magnitude-frequency relation of: (a) landslide length; and (b) average landslide width 79 x i Figure 4 . 1 8 - Magnitude-frequency relations of natural and logging-related landslides 81 Figure 4.19 - L M F relations plotted by movement style 82 Figure 4.20 - L M F relations categorized by position at initiation point 83" Figure 4.21 - LMF'relations categorized by terminus/run-out type 84 Figure 4.22 - LMF'relations for Capilano and Tsitika-Eve watersheds 8 5 ' Figure 4.23 - Percent frequency distributions in Capilano andTsitika-Eve drainage basins of "(a) elevation, and (b) slope gradient 86 Figure 4.24"- Examples showing the methodology usedto estimate landslide sediment transfer within and between geomorphic process domains 87"" Figure 4.25"- Slope-area plots for the API : based landslide inventory of the Tsifika and Eve River basins: (a) initiation points; and (b) end of transportatibn/beginnihg of deposition zones 88 Figure 4.26 - Slope-area plots for landslides in naturalterraih classified by type of materialmobilized: (a) initiation points; and~(b) endof transpoitation/begihiiihg o f deposition zones. Slope-area plots for debris mobilizing landslides in logged terrain: (c) initiation points; and"(d) endof fransportatibn/begihnihg o f deposition zones 90 Figure 4.27"- (a) Specific landslide sediment yieldas a function of contributing area for the Tsitika-Eve landslide inventory, (b) Landslide-relatedsediinent yield and cumulative sediment yield expressed as percent of the totalflux 92" Figure 4.28 - Landslide and'fluviarspecific sediment yieldas functions of drainage area 94 Figure 5 T — Map indicating the location o f recent (< 20 yr-old) and old"(>55 yr-old) cutblocks in (a) the Capilano River Basin; and (b) Elliott Creek 110" Figure 5.2 - Channeltypes encompassedih the study basins: (a) bedrock-controlled reaches in Elliott Creek; (b) riffle-pools in Hesketh Creek; (c) colluvial channel i n Hesketh Creek; (d) boulder-cascades in Elliott Creek; (e) rapids reaches in Lembke Creek; and "(f)" step-poolmorpholbgy in Elliott Creek 113 Figure 5.3 - (a) Poorly defihedchannelat the headwaters o f Hesketh Creek; (b) Interlocked boulder structures in Hesketh Creek; (c) Hanging valley seen from the apex of the paraglacial fan (Lembke Creek); and'(d) Step-pools in Hesketh Creek 115 x i i Figure 5.4 - Hesketh Creek: (a) longitudinal profile showing glacial macroforms, area-based process domains, and dominant channel-reach morphology; and (b) slope-area plot of channel reaches 117 Figure 5.5 - Elliott Creek: (a) longitudinal profile showing glacial macroforms, area-based process domains, and dominant channel-reach morphology; and (b) slope-area plot of channel reaches 118 Figure 5.6 - Lembke-Sisters Creek: (a) longitudinal profile showing glacial macro-forms, area-based process domains, and dominant channel-reach morphology; and (b) slope-area plot of channel reaches 120 3 Figure 5.7 - East Cap Creek: (a) longitudinal profile showing glacial macro-forms, area-based process domains, and dominant channel-reach morphology; and (b) slope-area plot of channel reaches 121 Figure 5.8 - Slope-area plot of channel reaches in the study headwater basins 123 Figure 5.9 - Box-plot of channel-reach slope categorized by dominant channel morphology 124 Figure 5 . 1 0 - Reaches plotted by area versus (a) specific power, and (b) total power . . . 126 Figure 5.11 - Channel-reach morphology plotted by drainage area vs. (a) shear stress, (b) total stream power-D95 ratio, and specific stream power-D95 ratio 127 Figure 5.12 - Channel types plotted by slope versus (a) relative roughness, (b) width-to-depth ratio, (c) coarse grain-fraction, (d) bankfull channel width, and (e) bankfull channel depth •„.-.• 129 Figure 5.13 - (a) Bankfull width, (b) bankfull depth, (c) coarse grain-size fraction, (d) width to depth, and (e) relative roughness, plotted as functions o f drainage area 130 Figure 5 . 1 4 - Flowchart showing the multivariate analytical framework 134 Figure 5 . 1 5 - The broken-stick plot 135 Figure 6.1 - Plots of channel width vs. drainage area showing the lack o f systematic hydraulic geometry relationship for drainage areas below 1 and 10 k m 2 in: (a) Deton Creek (Oregon); and (b) Pojaque River (New Mexico) 148 Figure 6.2 - Width versus depth for different dominant channel substrates 152 Figure 6.3 - Width-to-depth ratio across channel types 154 x i i i Figure 6.4 - Scaling relations in Hesketh 100 Creek, based on all field data points and reach averages, o f contributing area with (a) bankfull channel width, and (b) bankfull channel depth and D95 157 Figure 6.5 - Bankfull channel width as a function o f contributing area for: (a) Hesketh Creek, (b) Elliott Creek, (c) Lembke-Sisters Creek, and (d) East Cap Creek 162 Figure 6.6 - Bankfull channel depth and D95 as a function of contributing area for: (a) Hesketh Creek, (b) Elliott Creek, (c) Lembke-Sisters Creek, and (d) East Cap Creek ... 166 Figure 6.7 - Elliott Creek: (a) rapids morphology in the headmost hanging valley; and (b) boulder-cascade morphology along the secondary valley step 168 Figure 6.8 - Unit stream power as a function of drainage area for: (a) Hesketh Creek, (b) Elliott Creek, (c) Lembke-Sisters Creek, and (d) East Cap Creek 171 Figure 6.9 - Comparison of measured bankfull width and channel width modelled using two variants of equation (6.4) in: (a) Hesketh Creek, (b) Elliott Creek, (c) Lembke-Sisters Creek, and (d) East Cap Creek 175 Figure 6.10 - Schematic representation of (a) area-width and (b) area-depth scaling relations with specific reference to channel slope and colluvial load variability 18! Figure 6 . 1 1 - Ratio of Q/D95 plotted for the study basins 183 Figure A . l - Landslide length-area plots categorized according to (a) land-use type, (b) initiation position, (c) lithology in logged terrain, (d) lithology in natural terrain, (e) landslide type in natural terrain, (f) landslide type in logged terrain, (g-h) selected landslide types in natural terrain 219 Figure A . 2 - Landslide area as a function o f elevation in natural terrain: (a) at initiation point; and (b) at deposition point 222 Figure C . l - Unit and total stream power as functions of drainage area for: (a) Hesketh Creek, (b) Elliott Creek, (c) Lembke-Sisters Creek, and (d) East Cap Creek 247 x iv Acknowledgements Many people have crossed my life since January 2002, when I had no idea of how many days of field, but especially of deskwork were awaiting me; I here wish to thank all of them, even though I may be forgetting someone. I shall begin with my supervisor (and true friend), Marwan Hassan, for having to deal with my fiery temper in more than a situation, for being hyper-supportive, and for granting me complete freedom on how to conceive and materialize this research project. Olav Slaymaker and Michael Church have been always provocative, available for discussion, and patient to proofread my writing; the course on directed studies taken under their guidance has been a critical turning point at the beginning of this endeavor. Thanks to Terry Rollerson and Denny Maynard; without their support and collaboration on the Tsitika-Eve landslide inventory, chapter 4 would not be part of this dissertation. Thanks to the ideal field assistant (Jason Rempel), and the not quite so (Mike Hurwitz)... no need to say more. Thanks to Derek Bonin and Dave Dunkley, for allowing access to the GVRD watersheds and for sharing their field experience; I always felt very welcome. Robert Hudson provided fundamental logistical support in northern Vancouver Island. Garry Clarke, David Montgomery, Colin Stark, and Kelin Whipple stimulated exciting discussions on glaciology, geomorphic process domains, landslide magnitude-frequency relations, and the evolution of transient landscapes. A special thanks to Garry Clarke, who in an eight-hour marathon, reviewed with me an earlier draft of chapter 3, challenging every single sentence I had written; I am still amazed by his passion for teaching and supporting ideas. Thanks to Hans Schreier, for genuinely appreciating my research efforts. Insightful reviews by the external examiner Bill Dietrich and UBC examiners Rob Millar and Dan Moore are greatly acknowledged. A sincere "grazie" to Sally and Chris Hermansen, for being so close to me, especially during the hard times I went through. Muchas gracias to cheerful Jose Aparicio, who never became tired of rescuing me from my perennial map projection amnesia. A hug to my graduate buddies Humberto, Emre, Raul, Liz, Dorna, Ydko, Alberto, Mark H., Mark M., Ivette, Chiaki, Hakan, Pinar, Kenji, Ali, Uli, and Aliye, with whom I have shared great times outside school. Without the love and support of my parents, Eugenio and Vilma, I would not have completed this effort within reasonable time. xv A mio padre Eugenio per I 'amore e la stima incondizionati la forza e la fede incrollabili I 'equilibrio e la gioia di vivere xv i CHAPTER 1 Introduction 1.1 Aims Research in unglaciated drainage basins documents that river networks define specific scaling relations in the landscape. Accordingly, critical area for channel initiation sets hillslope length [Horton, 1945; Montgomery and Dietrich, 1989] which, in turn, to some extent controls landslide magnitude-frequency relations and maximum landslide size [Hovius et al., 1997]. Contributing area scales with local slope gradient, generating distinct geomorphic process domains [Montgomery and Foufoula-Georgiou, 1993; Ijjaz-Vasquez and Bras, 1995], hence determining local rates o f erosion. Channel reaches exhibit a continuum of bed-forms as contributing area increases downstream [Montgomery and Buffington, 1997]. Down the river long profile, channel cross-sectional variables (i.e., width, depth, and mean velocity) scale with water discharge, generating the so called downstream hydraulic geometry relations [Leopold andMaddock, 1953]. In currently glacierized environments, glaciers and ice sheets possess distinctive geomorphic erosion and transport laws [e.g., Hallet, 1989; MacGregor etal., 2000; Anderson etal., 2006] which likely disturb pre-glacial landscape structure and superimpose "glacial" scaling dependences. O n such a premise, it is hypothesized that formerly glaciated environments at present exhibit transient scaling dependences that deviate significantly from those well documented in unglaciated analogues. In fact, the systemic effects o f Quaternary glacial activity on contemporary geomorphic forms and processes i n mountain drainage basins are virtually unknown. Similarly, the magnitude and rate o f modification o f glaciated landscapes are also poorly understood. 1 In this context, the present work aims to verify the existence of glacially-induced scaling departures and quantify their magnitudes, to determine which geomorphic variables and what spatial scales are involved, and to explain the patterns associated with such departures. The ultimate goal is to document the magnitude and rate o f post-glacial transition, hence to understand the effects o f Quaternary glacial forms, on the present structure and functioning o f glaciated, mountain drainage basins which, in this dissertation, are regarded as fundamental geomorphic entities. Accordingly, research objectives are tackled at the drainage basin scale in a systemic framework whose components include (i) contemporary geomorphic process domains (i.e., hillslope, colluvial, and fluvial); (ii) dominant sediment sources (i.e., shallow rapid failures) and their magnitude-frequency relations; (iii) relict glacial macro-forms (e.g., troughs, hanging valleys, and valley steps); (iv) channel types; and (v) downstream hydraulic geometry, including downstream patterns of stream power indices and coarse grain-size fraction (i.e., D95). The list is not meant to include all possible hydro-geomorphic proxies that could help to achieve the objectives o f this study; rather, it represents a parsimonious set of qualitative and quantitative indicators (see section 2.1 for more details). Finally, the existence o f potential between-scale causal linkages is examined. Study basins are drawn from the Coast Mountains o f southern British Columbia. Given these objectives, a brief review o f the relevant geomorphic components is reported in chapter 2. The review begins by introducing the concept of geomorphic process domains and their spatial organization, proceeds with the characterization o f sediment sources and their spatial sphere o f influence, and ends by summarizing current knowledge on channel type sequencing, on downstream trends of channel cross-sectional variables and coarse grain-size fraction. Unglaciated drainage basins are presented first, as most o f the relevant research comes from such environments, then research gaps in glaciated settings are identified and research questions are formulated. Throughout this dissertation, the terms glacierized, glaciated, and unglaciated refer respectively to a given landscape that is presently covered by ice, was subjected to glacial erosion during the last ice age, and never came into direct contact with glaciers or ice sheets. 1.2 Thesis Structure Overview This thesis is composed o f seven chapters. Chapter 2 provides a literature review o f the four main geomorphic components selected to characterize glaciated mountain drainage basins. 2 Owing to the greater progress achieved in the understanding o f unglaciated mountain basins, these settings are considered first (section 2.1), and are regarded as equilibrium prototypes against which to evaluate the effects o f the glacial palimpsest. There follows a review of current knowledge in glaciated mountain settings (section 2.2), in which research gaps are identified and corresponding research questions are formulated. Open research questions are addressed in chapters 3 to 6. Each o f these chapters is composed o f an introduction, description of the study areas and methods, presentation o f the results, and discussion. For the benefit o f the reader, since each research component was based on specific combinations of study sites, and given the broad range of methods for data collection and analysis, study areas and methodologies were not pulled together into a dedicated chapter. Lastly, comprehensive conclusions on glacially-induced scaling dependences, including emergent causal linkages across spatial and temporal scales, are detailed in chapter 7. Chapter 3, which I consider to be the keystone o f this dissertation, addresses the question of process domains in glaciated mountain drainage basins. The effects o f relict glacial macroforms on the organization of currently active geomorphic process domains, topographic signatures, and the structure of channel long-profiles are examined. Analysis relies on sloperarea plots obtained from D E M s , contour-based topography, and field measurements. In an effort to assess potential DEM-based automated landscape classifications, the quality o f D E M - and contour-based topographic data is also evaluated against field measurements. This chapter has been recently published in the Journal of Geophysical Research and should be referenced as: Brardinoni F. , and M . A . Hassan (2006), Glacial erosion, evolution o f river long-profiles, and the organization of process domains in mountain drainage basins o f coastal British Columbia. Journal of Geophysical Research, 111, F01013, doi: 10.1029/2005JF000358. Chapter 4 deals with the general issue of characterizing dominant sediment sources in space and time. The spatial characterization is undertaken in respect o f a series o f landslide and terrain attributes including land use, mass movement type, landscape position at initiation, and terminus type. Subsequently, the effect o f lithology is evaluated. The second half o f the chapter defines the temporal scales, and turns on the question o f what controls the shape of 3 landslide magnitude-frequency relations. Accordingly, before dealing directly with magnitude-frequency plots a series o f preparatory aspects are analysed including (i) landslide geometry, to assess causal linkages between landslide shape and environmental factors; and (ii) history o f landslide activity, to try separating land-use, lithologic, and Quaternary effects. Finally, landslide sediment inputs as a function of contributing area are examined within the contexts o f geomorphic process domains and fluvial suspended sediment yield. To what degree and how does the inherited organization of the landscape affect the spatial distribution of channel-reach morphology in mountain drainage basins? The answer, which is provided in chapter 5, takes advantage of information gathered in chapter 3. Accordingly, the effects o f a number o f channel variates on channel-reach morphology are evaluated graphically. In order to generate prediction criteria for channel-reach morphology, a multivariate statistical analysis is conducted. The investigation includes principal component analysis ( P C A ) , followed by multivariate discriminant analysis ( M D A ) . Glacially-induced dependences in downstream hydraulic geometry ( D H G ) are tackled in chapter 6. Variates considered i n the analysis include channel width, depth, and coarse grain-size fraction (i.e., D95). D H G relations are evaluated within the contexts o f geomorphic process domains, geomorphic coupling, and relict glacial macro-forms. Finally, implications of glacially-induced D H G relations are discussed and two variants o f a model for the prediction of bankfull width are examined. The model is based on the Manning equation and basic mass conservation principles. 4 CHAPTER 2 Literature Review and Research Questions in Formerly Glaciated Mountain Settings 2.1 Mountain Geomorphic Systems Mountain drainage basins are complex systems due to the variety of Earth surface processes, the complexity o f their interactions at different spatial and temporal scales, and the confounding influences o f tectonic setting and past episodes of climate change. For analytical purposes hydro-geomorphological complexity may conveniently be reduced. Specifically, Earth systems may be classified as process-response systems [Chorley and Kennedy, 1971] which contain and combine time-independent assemblages o f morphological units (static systems; e.g., topography, substrate) and dynamic components (process or cascades systems; associations o f hydro-geomorphic processes). Such systems are concerned with the effects of one or more processes on the static components (forms and materials would be static without the intervention o f processes) through time and vice versa [e.g., Ahnert, 1998]; Applying this thinking, any given mountain drainage basin can be seen as a mosaic of topographic units through which mass is detached, transported, and/or temporarily stored. In this view, the rationale for having selected the five geomorphic components listed above becomes more apparent. Accordingly, the landscape partition into geomorphic process domains by means of slope-area plots (Sections 2.2.1 and Chapter 3) - the central component o f the present framework - allows the definition o f spatial scales for channel initiation, landsliding, colluvial deposition, and fluvial reworking. The examination of sediment sources accounts for sediment production and delivery to landscape components, yet allows analysis of within-colluvial and -alluvial variability via characterization o f source-to-sink sediment pathways and patterns o f hillslope-chanrtel coupling. Landslide magnitude-5 frequency relations [e.g., Hovius et al, 1997] should serve to link explicitly sediment volumes to time, for assessing erosion rates in relation to biogeoclimatic controls and channel catastrophic disturbance. In fact, channel morphology at one location is a qualitative expression o f the competition between water/sediment supply and transport capacity [e.g., Montgomery and Buffington, 1997] and, as such, is profoundly affected by the spatial organization of process domains and that o f sediment sources. These same effects may be evaluated in a quantitative way by examination of channel cross-sectional size, coarse grain-size fraction, and indices o f stream power. Finally, all o f the above components need be considered within a broader context, beyond drainage basin divides and beyond contemporary time scales. In the case o f coastal British Columbia, factors such as tectonic and climate history should be carefully considered, as these dictate the first order structure o f the landscape [e.g., Ryder, 1981] which may impart characteristic arrangements to geomorphic process domains. 2.2 Unglaciated Mountain Settings Mountain drainage basins of the Pacific R i m have been the focus of intensive and interdisciplinary studies [e.g., Swanson et al, 1982; Beschta et al, 1987; Hogan et al, 1998; Marutani et al, 2001]. For example, on the Northwest coast o f North America, research efforts in the past four decades have been fuelled by the need for sustainable management that could balance the interests o f forest industries and the conservation o f the habitat for anadromous fish species. Since research campaigns in unglaciated settings o f the Pacific Northwest span al l critical hydro-geomorphic components this study aims to address (section 1.1), and have achieved a superior understanding o f such settings, unglaciated systems w i l l be used as the main reference (this section) against which to evaluate current knowledge and progress made in glaciated ones (section 2.3). 2.2.1 Topographic Units and Geomorphic Process Domains The relative availability o f water and sediment, primarily controlled by topography and substrate erodibility, leads to a range of geomorphic processes which transfer material and shape the Earth's surface. In this context, Hack and Goodlett [1960] provide the first example of landscape partition (in the "ridge and ravine" landscape of the Central Appalachians) according to topographic properties, where mountain terrain is subdivided into noses, side slopes, hollows, channelways and footslopes (Figure 2.1). Such features reflect 6 the curvature pattern of contour lines, which regulates the rate of water runoff received by each unit and ultimately controls the range and intensity o f processes available for material detachment and transport. In this view, different landscapes are composed of different arrangements o f building blocks such as ridges, rock walls, hillslopes, zero-order basins, channels, fans, talus slopes, and floodplains. This apparent simplification o f the landscape dissolves somewhat when one takes into account that each fundamental unit has a number of attributes (e.g., bedrock geology, exposure, nature of surficial materials, and vegetation cover) that vary across drainage basins [e.g., Montgomery, 1999], or even along a given hillside. Indeed, the variability of each attribute influences the functioning and the way i n which each unit interacts (receives, stores, and delivers material) with adjacent elements. In addition, the sequence in which various landscape elements are combined alters mutual interactions, while the position within the channel network - up-slope/stream contributing area, and degree o f geomorphic coupling [Brunsden and Thornes, 1979] - is l ikely to influence the cumulative effects of landscape assemblages on channel processes and transport rates at the drainage basin scale (which may be summarized in the sediment delivery ratio [Walling, 1983; Lu et al, 2005]). However, the actual response of a channel also depends on the ability o f the channel to transmit or resist the imposed impulse o f disturbance {Brunsden and Thornes, 1979; Montgomery, 2001a]. Figure 2.1. Idealized structure o f an unglaciated second-order drainage basin (after Hack and Goodlett [1960], from Benda et al. [2005]). 1st order channel: (ephemeral or seasonal) 2nd order channel: (bedrock or, colluvial) Zero order basin (bedrock hollow) 1 1 si order channel: (bedrock or colluvial) A s for process-based landscape zonation, a fairly complete picture o f the geomorphic process domains that are active in steep, unglaciated, mountain drainage basins has been 7 drawn in a series of studies [e.g., Montgomery and Dietrich, 1988; 1989; 1992; and 1994a; Montgomery and Foufoula-Georgiou; 1993; Stock and Dietrich, 2003]. The term process domain is commonly used at the drainage basin scale to define spatial associations of geomorphic processes where, within a set time frame, one particular process prevails in terms of material detached and/or transported. Customarily, the delineation of process domains is accomplished by plotting the logarithms o f local slope gradient vs. contributing drainage area [e.g., Montgomery and Foufoula-Georgiou, 1993; Ijjaz-Vasquez and Bras, 1995] (Figure 2.2). Slope and area represent first order approximations to the physical conditions at which processes are active and can be readily extracted from Digital Elevation Models (DEMs) . Slope is indicative o f mass wasting initiation and deposition thresholds as well as of channel-reach morphology. Area is a proxy for discharge and sediment supply. Process domains for steep, unglaciated, equilibrium landscapes are: (i) hillslope, (ii) colluvial (or debris-flow), and (iii) fluvial. The boundaries of these domains are marked by inflections and/or reversals in slope-area plots, and by distinctive geomorphic features in the field: (i) channel heads, which set the scale of landscape dissection [Montgomery and Dietrich, 1988; 1989; 1994a; Dietrich and Dunne, 1993], (ii) debris flow fans, which form along channels at the colluvial-fluvial transition [e.g., Stock and Dietrich, 2003], and (iii) fluvial terraces and floodplains that testify to fluvial transport dominance [e.g., Montgomery and Foufoula-Georgiou, 1993; Tucker and Bras, 1998]. 10" 3 10 _ 1 10 1 10 3 Area (km2) Figure 2.2. Schematic representation of process domains (dashed boundaries) and topographic signatures (solid lines) in an unglaciated mountain landscapes at steady state (after Montgomery and Foufoula-Georgiou [1993]). 8 Starting from the headwaters and proceeding downstream, the analytical framework of geomorphic process domains and its first-order representation via slope-area plots provide applications for the spatial characterization and modelling of sediment sources [Montgomery and Dietrich, 1994a; 1994b], channel-reach morphology [Montgomery and Buffington, 1997; Montgomery and Bolton, 2003], and for the examination of downstream trends in channel width and median grain size [Brummer and Montgomery, 2003]. Different process domains are associated with different styles of natural disturbance (e.g., debris flow run-out, bank erosion, freeze-thaw induced solifluction, and river avulsions) and different rates of background sediment production and mobilization. That is, different zones o f the landscape have specific mtrinsic thresholds to external disturbances [Schumm, 1973] and specific sensitivity to environmental change [e.g., Brunsden, 1993]. In this context, anthropic activities can affect the range of landscape partitions in specific ways, including the potential for shifting their spatial extent [e.g., Strahler, 1956; Roberts and Church, 1986; Swanston and Marion, 1991; Montgomery, 1994; Brardinoni et al, 2003a]. For these reasons, the recognition and spatial delineation of geomorphic process domains is an extremely valuable tool for projects concerned with land management, environmental restoration, and habitat conservation. 2.2.2 Sediment Sources and Magnitude-Frequency Relations Characterizing the spatial organization of sediment sources means identifying which portions o f the landscape are principal sites of sediment production in a given time window. Probably, the best documented example in the literature is that of bedrock hollows and their cycle of periodic evacuation and recharge [Dietrich and Dunne, 1978; Reneau and Dietrich, 1991]. Hollows are regarded as primary sites of sediment production in the humid, unglaciated, active orogens that border the Pacific plate [Tsukamoto, 1973; Dietrich and Dunne, 1978; Reneau and Dietrich, 1987; 1991; Crozier et al, 1990]. According to the topographic zonation by Hack and Goodlett [1960], hollows are unchanneled areas with contour concave outward (Figure 2.1), the spatial distribution o f which appears to be integrated with the drainage network ("zero-order basins" [Tsukamoto, 1973]), as often hollows constitute the topographic continuation of first-order channels. In these mountain environments, shallow landsliding and debris flows are the dominant mechanisms by which material is delivered from steep slopes to slope base [e.g., Swanson 9 and Swanston, 1976; Swanson et al, 1982; Sidle et al, 1985] and exert major control on the development of valley floor landforms and channel morphology. Wi th the purpose o f providing scientists and practitioners useful tools for hazard assessment, landscape evolution, and land management, a myriad o f landslide prediction models has been developed. Within the context of process domains and topographic units, a physically-based, distributed model for the topographic control o f shallow landsliding has been proposed by Montgomery and Dietrich [1994b]. The model expresses instability conditions, commonly stated in terms o f critical slope angle in the infinite slope equation, in terms o f critical soil wetness, critical contributing area, and finally as critical rainfall. More recently, hollow instability potential has been expressed and simulated as a function o f hyetograph characteristics [D'Odorico et al, 2005]. Many other models have been proposed [e.g., Wu and Sidle, 1995; Pack et al, 1998], al l o f which function best at the hillslope or headwater basin scale. A broader review of such modelling techniques is beyond the scope of this section. In the past decade, studies on landslide magnitude-frequency ( L M F ) relations, which appear to exhibit a power-law scaling [Hovius et al, 1997; Stark and Hovius, 2001], have explicitly incorporated a temporal dimension into hillslope processes, providing the basis to scale up landslide-driven sediment dynamics from the headwater level to the regional scale. L M F power-law scaling holds implications and useful applications in hazard assessment [Hungr et al, 1999; Guzzetti et al, 2005], and landscape evolution models [Benda et al, 1998; Burbank, 2002]. A t present, L M F relations are solely explained by the concept o f self-organized criticality, although some authors have suggested that morphometric and substrate characteristics may exert prominent controls. 2.2.3 Channe l Morpho logy Geomorphic processes that are directly connected to the drainage network affect the local and systematic downstream spatial organization of channel reach morphology [e.g., Church, 1992; 2002; Montgomery and Buffington, 1997; Montgomery and Bolton, 2003]. Understanding the processes driving both landscape evolution and geomorphological influences on ecological systems in mountain drainage basins requires knowing spatial patterns and linkages between channel morphology and process domains [Montgomery, 1999]. In general terms, the morphology o f channel reaches - discrete stretches of channel with a relatively consistent morphology over spatial scales many times the width o f the 10 channel - results from: (i) the volume and timing of water supplied from upstream; (ii) the sediment supply delivered to the channel; (iii) nature o f the materials through which the river flows; and (iv) the geo-climatic history of the riverine landscape. Other drainage-basin-scale factors that influence channel morphology include (i) annual precipitation regime, (ii) nature of riparian vegetation, and (iii) land-use [Church, 1992]. Such a long, yet incomplete, list o f controls testifies to the difficulties associated with a purely deterministic prediction o f channel reach morphology per se. Debris flows a) initiation *4 • socur deposition Large woody debris largely mobile: acts as sediment diffusion dominated debris flow dominated fluvial Figure 2.3. (a) Idealized process-based classification of a mountain channel, concave up, long profile; (b) Slope-area plot o f channel reaches in a "simple" unglaciated drainage basin: Finney Creek, Washington (from Montgomery andBuffington [1997]). b) 10u I 10- colluvial A bedrock A colluvial • pod-rtHle O plane-bed H step-pool • cascade 10 10' 10° 10" 10' 10° 10' drainage area (m2) Montgomery and Buffington [1997] proposed an idealized model for channel morphology in unglaciated mountain drainage basins based on systematic process-derived variation in channel-reach morphology. Their classification is based on process linkages and disturbance 11 cascades within the channel network. Accordingly, headwater channels in steep terrain are typically dominated or heavily affected by mass wasting processes such as debris flows and debris slides. These channels are strongly coupled to hillslope processes and are termed colluvial channels. Proceeding downstream, as drainage area increases slope gradient, bed material grain size, degree of geomorphic coupling and stream power generally decrease, whereas channel width, valley width and sinuosity increase and sediment has greater opportunities for in-channel storage. A t increasingly large drainage areas (and lower slopes) debris flows lose erosive power; fluvial processes become prevalent at drainage areas >1-10 k m 2 [Brummer and Montgomery, 2003; Stock and Dietrich, 2003], and channel reach morphology grades from chaotic, boulder-strewn cascades to step-pool and riffle-pool reaches (Figure 2.3a). The strong coupling o f channel morphology to channel slope [e.g., Rosgen, 1985; 1994; Montgomery and Buffington, 1997; 1998] leads to the typical downstream sequence of channel types along an idealized concave river profile in mountainous terrain. Despite the numerous influences on channel form, drainage area and slope are primary controls on channel-reach morphology in mountain drainage basins (Figure 2.3b) to the extent that such controls are not overwhelmed or overprinted by disturbances or processes that impose stochastic variability. 2.2.4 Downstream Hydrau l i c Geometry Channel size is thought to be controlled by the amount of water flowing through it. Specifically, in self-formed alluvial channels cross-sectional variables (i.e., width, depth, and mean velocity) appear to vary systematically downstream i n response to changes in water discharge at bankfull according to specific power-law relations [Leopold and Maddock, 1953], known as downstream hydraulic geometry (DHG) . It should be noted that although mean annual floods are customarily regarded as the bankfull, "channel forming flows", no universally systematic correlation has been found between flood frequency and bankfull or geomorphic change [Williams, 1978]. General consensus on this matter is still missing. Accordingly, in many studies, due to the lack o f gauging stations, water discharge is replaced by contributing area [e.g., Miller, 1958; Church and Mark, 1980; Brummer and Montgomery, 2003; Montgomery and Bolton, 2003], assuming that discharge scales approximately linearly with drainage area. Notwithstanding these controversies and limitations, compilations o f 12 worldwide datasets testify that power-law D H G relations possess well-defined, empirical, exponents (see Figure 2.4 and chapter 6 for details) [e.g., Church, 1992]. 10* 101 10u 10" 10" I Brahmacutra » Amazon • -• • • • • - • [ppj o 0 e * o io • * 3 32-108 •* i OO e o 10s 10 n e 103 I I 102 101 10° 10 1 102 103 DISCHARGE, m3 s' 1 10" Figure 2.4. Scale relations for channel width and depth versus flow (from Church [1992]). A long an idealized concave alluvial longitudinal profile, non-alluvial geomorphic processes directly connected to the drainage network have the potential to alter "standard" D H G relations. A s explained earlier, in large portions of mountain streams, fluvial erosion is perturbed and overwhelmed by non-alluvial/colluvial processes. D H G studies in unglaciated mountain drainage basins are scarce [e.g., Thornes, 1970; Wohl, 2004b], and mainly consider channel width only [Montgomery and Gran, 2001; Brummer and Montgomery, 2003; Montgomery and Bolton, 2003; Snyder et al, 2003; Duvall et al, 2004]. In this context, studies appear to yield contradictory results. In some cases: X i n g u and Araguaya Rivers (Mato Grosso, Brazil) [Thornes, 1970], Deton Creek (Oregon) and Pojoaque River (New Mexico) [Montgomery and Bolton, 2003], fourteen small drainage basins in Northern California [Snyder et al, 2003]; headmost tributaries (Drainage area < 1 km 2 ) and river main-stems have distinct D H G relations. Specifically, headwater streams display significant departures from the accepted alluvial standards. In others [e.g., Brummer and Montgomery, 2003: four case studies from Washington State], channel width-contributing area relations do not change across process domain transitions. Brummer and Montgomery [2003] examine network-wide patterns of D H G variates (i.e., bankfull width) in conjunction with other 13 parameters that may control the development of D H G relations (i.e., Wohl [2004a] (see section 2.3.4 and chapter 6 for details), such as median bed material grain size (D 5o), and stream power indices. Their results indicate that geomorphic process domains control downstream systematic variations of D 5 0 and stream power, but not channel width. Specifically, D 5 0 and stream power increase monotonically along debris-flow dominated channels (colluvial domain), attaining maximum values in proximity o f debris flow fans, then decreasing further downstream (reversal in area-Dso and area-power trends), where fluvial transport prevails. Bankfull width increases systematically downstream, regardless of transitions in process dominance. 23 Glaciated Mountain Settings In the geomorphological literature, far less information exists on glaciated mountain drainage basins and, where studies have been conducted, little effort has been made to interpret quantitative results in the glacial palimpsest context. Similarly, even though great progress has been achieved in glaciology, where quantitative models o f glacial erosion have been useful in suggesting explanation of glacial morphologies such as U-shaped valleys and overdeepenings [e.g., Hallet, 1989; Hooke, 1991; Harbor, 1992; Braun et al, 1999; MacGregor et al, 2000], insufficient research has been conducted on the implications o f relict glacial morphometry with respect to contemporary process domains. 2.3.1 Geomorphic Process Domains Limited information is available on contemporary process domains [Slaymaker and McPherson, 1977; Ryder, 1981; Dadson, 2000; White, 2002]. Slaymaker and McPherson [1977] present a zonation o f geomorphic activity o f the Canadian Cordillera based on relief and sediment availability, where each region (three in total) has distinctive landform assemblages, hence peculiar arrangement o f process domains. A t the sub-regional scale, Ryder [1981] proposes an altitudinal zonation of geomorphic processes of the Pacific Ranges, southern coastal British Columbia (Figure 2.5). Today the result of the tectonic and Quaternary glacial history is a vertically zoned landscape, where an organised pattern o f distinctive geomorphic processes reflects the altitudinal distribution o f materials (bedrock, colluvium and till) , and the gradients of slope and climatic variables (e.g., temperature, water availability). Accordingly, glacial and nival processes dominate mountain summits; a range of episodic slope instability processes - debris slides and flows on soil-mantled slopes, 14 rockslides and falls on steep rock faces - dominates hillslopes and low order streams; more continuous fluvial processes selectively rework glacial materials and colluvium in the valleys. The first quantitative analysis of process domains implied from slope-area plots was conducted by Dadson [2000]. The work completely relies on data extracted from a 25-m DEM of the Capilano River basin. Accordingly, common hillslope-channel threshold occurs at about 2,000 m2, whereas no mention of the second inflection point (debris-flow related) is made. Dadson [2000], following the methodology proposed by Veneziano and Iacobellis [1999] according to which fluvial and hillslope processes would be responsible for topography of different fractal dimensions, uses the variogram method (structure function analysis). Results confirm that subdividing the landscape into fluvial and hillslope domains can result in topographies with homogeneous fractal dimension; more importantly, some landscape features were found not to fit this classification. These were headmost channel systems and scars of deep-seated bedrock failures. However, no direct comment was made on the possibility that past glacial carving may be the cause of such fractal inconsistencies. Landform Mountain summits, r i d 9 e s \ all gradients Debris slopes, \ 70% avajanche, slide Y . r eeWne Colluvium. glacial y \ 3 5 % drift, fluvial and i t w n t » n e X debris, flaw fans fore^_^_ Landslide deposits f t»r«* u Glacial deposits, fluvial deposits Sediment transfer mechanisms glacial and nival processes mass wasting wi th frost snow avalanche Figure 2.5. Generalized geomorphological zonation of the southern Coast Mountains (from Church [1998], and after Ryder [1981]. mass wasting, debris flow, fluvial 20% dominantly fluvial Sedimentation in lakes and ocean At the watershed scale, White [2002] provides the first and to date only attempt to characterise process domains by means of field-based slope-area plots in headwater systems of the same watershed studied by Dadson. The study detects a "headmost fluvial" domain and identifies two different thresholds for channel incision. Thresholds seemed to depend on the process by which the channel is maintained: mass wasting for incised reaches and fluvial transport for unincised channels. In contrast with the interpretation by Stock and Dietrich [2003], White [2002] identifies a slope-area break at the transition between the headmost fluvial and the debris-flow domains. Is this break due to past glacial carving? Is it the result 15 of a regional configuration o f landscape units? The type of data collected - no information on surficial materials, on relict macro-forms such as glacial cirques, and limited GIS-based topographic analysis - did not allow White [2002] to draw definitive conclusions. Open Research Question: What are the effects of glacial history on the organization of currently active geomorphic process domains, topographic signatures, and the structure o f channel long profiles? 2.3.2 Sediment Sources and Magnitude-Frequency Relations Formerly glaciated landscapes may present peculiar spatial distributions o f sediment sources due to a long history o f glacial activity. Information on this research topic is scarce. In general terms, glaciations have promoted oversteepening o f major valley walls, scouring o f high frequency topographic features (hollows), and have left large amounts of glacially derived sediments on hillslopes that in places have buried pre-existing stream networks. Johnson et al. [2000] provide an instructive example of how glacial basin morphometry can affect the spatial sphere o f colluvial activity, hence the magnitude of sediment sources. The study plots landslide runout lengths vs. corresponding change in elevation and compares data from unglaciated terrain o f Oregon and California, with data from glaciated mountains in Prince o f Wales Island (Alaska). Results indicate that glaciated topography is associated with higher average runout slope (23°), compared to unglaciated settings (14°). Runout o f landslides appeared to be affected by the structure of the drainage network; in fact a trellis-like organisation, typical o f glaciated terrain in southeast Alaska, seemed to induce deposition in first- or second-order channels in principal U-shaped valleys, leaving main stem channels unaffected. Conversely, the headwaters o f glaciated basins, but also the dendritic unglaciated drainage systems, showed longer runouts and a lower average depositional slope. Interestingly enough, different network organisations affect the run out behaviour of debris flows, which in turn determines the downstream extent of the colluvial domain [Montgomery and Buffington, [1997]. In terms o f sediment source characterization, Johnson et al. [2000] report initiation of landslides to be closely associated with landforms and t i l l was the primary material mobilised. They selected a random sample of 45 air photo-inventoried slope failures (in old growth, second growth, and clearcuts), and conducted detailed field measurements on the sample. Forty of 45 o f the failures initiated in bedrock hollows (meta-sedimentary 16 mudstone); the remainder occurred on planar slopes. The small number of observations, and the different types o f land use involved, clearly do not allow definitive conclusions to be drawn on where landslides preferentially initiate. In the terrain of the Alexander Archipelago (Alaska), Swanston [1989] reports that 87 percent of natural failures (n=1374), inventoried by Helmers (unpublished data) before 1963, initiated on open slopes or ridges not associated with permanent stream courses. Almost al l these failures originated in shallow, linear depressions oriented perpendicularly to the contour lines. The remaining 13 percent were debris torrents triggered by the rapid deposition of debris from adjacent hillslopes into gullies and canyons during periods of storm flow. In the Wellington Region (New Zealand), an area that experienced intense Quaternary periglacial activity, Crozier et al. [1990] report that colluvium-filled bedrock (greywacke) depressions are the major source o f failures. Evidence shows that pre-existing low order streams have been affected by periglacial mass movements and subsequently covered by Pleistocene deposits during the last periglacial episode (fossil gullies). In fact, there appears to be a bimodal population (n=80) of colluvium-filled bedrock depression ages: recent hollows that have experienced landslides within the last 150 years as a result o f European deforestation and ancient ones that store periglacial deposits from the last glacial maximum. Crozier et al. [1990] conclude that hollows' "behaviour cannot be considered to be entirely self-regulating within the Wellington Region and modifications in the external morphogenic regime, including the vegetation component, appear to exercise an important control". The mountain landscape o f coastal British Columbia, when compared to that of the unglaciated Pacific Northwest, appears to have coarser texture, lower drainage density, higher local relief, longer slopes with large amounts o f glacial deposits, and steeper gradients. Specifically, the "ridges and ravines" pattern is replaced by rather planar slopes drained by rectilinear gullies. Interestingly, in places the presence o f gullies does not seem to alter the overall plan curvature o f the slope. This could be due to the fact that gullies are incised into thick surficial materials underlain by quartz- and granodiorite, the depth of surficial material limiting the lateral expansion of gully incision. In this physiographic context, headmost channels (gullies) are important features draining large portions o f the landscape. They are strongly coupled systems and, as such, regarded as the most active sites o f sediment production [e.g., Rollerson, 1992; Millard, 1993; Bovis et al., 1998; Millard et 17 al, 2002; Jakob et al, 2005]. Gullies are relatively steep, low order, ephemeral channels, typically 3 to 30 metres deep, with a V - or U-shaped cross section. They can act as an important temporary reservoir for sediment delivered from adjacent hillslopes [Slaymaker and McPherson, 1977]. A t this landscape scale, the sediment flux through the headmost part of the drainage network depends on the storage characteristics of the channel and the magnitude and frequency o f debris slides and debris flows [e.g., Bovis et al, 1998; Bovis and Jakob, 1999]. Studies on landslide magnitude-frequency ( L M F ) relations conducted in coastal British Columbia, have clarified that the shape of the relation itself (Figure 2.6) is i n part affected by A P I undersampling [Brardinoni and Church, 2004; Guthrie and Evans, 2004] o f small slides. Nevertheless, this circumstance must be insufficient, as a distinct inflection point is observable at about 4,000m 3 (Figure 2.6). This might have to do with some other environmental factor overwhelming self-organized criticality. Generally speaking, the effects o f topography, as well as any other bio-geo-climatic control (i.e., lithology, surficial material, land use, landslide type), on L M F relations are virtually unknown. In other words, the spatial organization o f sediment sources has not been incorporated into L M F relations regardless o f landscape history (i.e., unglaciated and glaciated settings). 0.010 f - Freq = 0.017*Vol & c a) 2 0.001 A-. •+-• \ s r OJOI :o o i ! ;0 N \ \ o i r b! m i i i i i N m 11! Freq = 1 .7*10"* V o l ' 3 5 mwrv O API API & ground 10 100 1000 Landslide volume (m3) 10000 Figure 2.6. Landslide magnitude-frequency relation for the Capilano River basin, British Columbia. " A P I " and "ground" stand respectively for aerial photo interpretation and fieldwork. Note the difference caused by API-undersampling, and the break at 4,000 m 3 which is not controlled by API-related limitations (from Brardinoni and Church [2004]). 18 A s previously stated, L M F studies have the potential to answer questions of sediment dynamics at the regional scale. In fact, in British Columbia it is not clear whether the sediment yield disequilibrium, due to the Holocene remobilization of large amounts o f glacially-derived sediments stored along river valleys [Church and Slaymaker, 1989], extends to basins smaller than 10 k m 2 (mass wasting-dominated). Slaymaker [1987] reports that at this scale fluvial sediment yield measured in basins o f the Pacific Ranges seems to be of the same order o f magnitude as the estimated denudation rates of contemporary colluvial processes. However, data on colluvial denudation were limited at the time and so they are today. In this context, progress in L M F relations may resolve such uncertainty; specifically by plotting landslide sediment yield vs. contributing area, geomorphic process domains and landslide sediment flux may be linked, and landslide yield may be evaluated against fluvial yield. Open Research Questions: (i) What are the dominant sites of sediment production in glaciated mountain basins o f coastal British Columbia? (ii) Is the glacial signature able to mask the influence of bedrock geology in controlling contemporary shallow landslide activity? (iii) What controls scaling relations in landslide magnitude-frequency plots? 2.3.3 Channe l Morphology The generalized downstream trend in channel types described for unglaciated environments (Figure 2.3) may be altered by disturbance history or landscape features such as where streams cross geologic contacts between rocks o f different erosion resistance; where there are strong local controls on sediment supply, such as large accumulations o f wood debris or bedrock channels; where there are gradients in rock uplift rates; across discontinuities imposed by the specific tectonic or glacial history o f the landscape; or where there is spatial variability in sediment supply. In the glaciated setting of British Columbia, channel slope is often the result o f subglacial excavation and paraglacial deposition so that, in terms o f channel bed characteristics, slope may be considered as an imposed variable that influences reach-scale channel architecture. A s a result, the sequencing o f channel-reach morphology, may exhibit characteristic spatial arrangements in relation to the fact that the landscape has not recovered from glacial disturbance since deglaciation occurred. 19 Sediment mixtures in primary and tributary valleys are largely dominated by late Pleistocene Glaciation drift and paraglacially-derived colluvium. Glacial t i l l and rock walls have chronically delivered large amounts of keystones to form channel bed architecture. A s a result, step-pool and boulder-cascade channel types are prevalent in formerly glaciated mountain settings [Halwas and Church, 2002] and greatly contribute to stabilize the structure o f these streams [Zimmerman and Church, 2001]. In this context, Zimmerman and Church [2001] have estimated that, although during a median annual flood the largest stones in the bed can theoretically be moved, the channel stays substantially stable thanks to the interlocking arrangement of step-forming boulders (increased resistance to entrainment). In mountain streams o f Vancouver Island, Halwas and Church [2002] detect channel bedforms (units) associated with significantly higher slope ranges compared to previous studies conducted in unglaciated settings [e.g., Bisson et al., 1981; Sullivan, 1986; Grant et al, 1990]. Those authors attribute the discrepancy to channel geometry, hence potential stream power. However, no GIS-topographic analysis was conducted on these study basins, so the sequencing of channel types was not assessed. To my knowledge, no study has documented the effects o f the glacial legacy on the sequence o f bed morphologies along a river longitudinal profile. Open Research Question: To what degree and how does the glacially-induced organization of the landscape affect the spatial distribution o f channel-reach morphology in mountain drainage basins? 2.3.4 Downstream Hydrau l i c Geometry For the same reasons enunciated above, the glacial geomorphic legacy may affect downstream hydraulic geometry (DHG) . Many studies have examined D H G relations in drainage basins that were affected by partial [e.g., Brummer and Montgomery, 2003; Wohl, 2004a; Wohl et al, 2004; Wohl and Wilcox, 2005] or complete [e.g., Coates, 1969; Day, 1969; Ponton, 1972; Cenderelli, 1998] ice cover in the Quaternary. These studies have yielded contrasting results, in some instances relations appear to deviate from unglaciated trends [e.g., Ponton, 1972; Wohl et al, 2004], in some others relations conform to self-formed alluvial standards [e.g., Day, 1969; Wohl and Wilcox, 2004]. According to Wohl [2004a], such dichotomy can be explained by a characteristic threshold (i.e., the average ratio between total stream power (Q) and coarse grain-size fraction (D&4) has to be greater than 20 10,000 kg/s 3), above which D H G relations would be well-developed in a given basin. However, the method does seem to be rather arbitrary and not satisfactory: first because D H G are assumed to be well-developed when R 2 is greater than 0.5 for two out of three cross-sectional variates, and second because in that study glaciated and unglaciated settings are confounded. While the impact o f glacially-inherited topography is often mentioned as one o f the potential causes for D H G misbehaviour due to transient environmental conditions [e.g., Ponton, 1972; Wohl, 2004a], to my knowledge no study has ever examined this question in causal and quantitative terms. A s a result, in glaciated mountain basins a detailed consideration o f the impacts brought about by geomorphic process domains and/or relict glacial macro-forms (where applicable) is missing. Open Research Questions: (i) Does the spatial organization of glacial macro-forms affect downstream hydraulic geometry? (ii) What are the implications o f such glacially-induced effects ( i f any) for landscape evolution modelling? 21 CHAPTER 3 Glacial Erosion, River Long-Profiles, and Process Domains in Mountain Drainage Basins of Coastal British Columbia 3.1 Introduction Drainage basins are complex systems, due to the variety of Earth surface processes at work, the complexity o f their interactions at different spatial and temporal scales, and the confounding influences o f tectonic activity and past episodes of climate change. They comprise unchanneled terrain (hillslopes) dominated by diffusive surface erosion and/or mass wasting, and of stream channels where debris flows and fluvial processes prevail [e.g., Horton, 1945; Jackli, 1957]. Process domains are defined as regions within which one or a collection of Earth surface processes prevails for the detachment and transport o f mass. Plots o f the logarithms of local slope gradient (S) vs. contributing drainage area (A) [e.g., Montgomery and Foufoula-Georgiou, 1993; Ijjaz-Vasquez and Bras, 1995; Tucker and Bras, 1998] can be used to delineate process domains (Figure 2.2). Slope and area represent first order approximations to the physical conditions at which processes are active. In environments assumed to be at steady state, where topographic change is merely the product of contemporary Earth surface processes, slope and area have been used to identify process-specific topographic signatures. Steady state conditions require that the rate o f local erosional lowering (E), limited by sediment transport capacity Q c (E = Q c = kS " A m ) , keeps pace with local rock uplift rate (U) while all other factors such as tectonic and climatic forcing are invariant, so that elevation 22 does not change through time. In an idealized soil-mantled (transport-limited) equilibrium landscape, when local erosion and local uplift are balanced, local slope can be expressed as a power function of drainage area (Figure 2.2): S = (U/K)'/nA(1-m)/n, (3.1) where K , m, and n are constants. The coefficient K expresses lithologic, climatic, and discharge variability; m and n are functions o f active dominant processes [e.g., Montgomery, 2001b]. Domains for unglaciated equilibrium landscapes are: (i) hillslope, (ii) colluvial (or debris flow), and (iii) fluvial. The boundaries of these domains are marked by kinks in slope-area plots and by transitional geomorphic features in the field: (a) channel heads, that separate unchanneled and channeled portions o f the topography, and (b) debris flow fans, which form at the transition o f colluvial channels (sensu Montgomery and Buffington [1997]) and (c) fluvial reaches, where contemporary fluvial terraces form [e.g., Montgomery and Foufoula-Georgiou, 1993; Sklar and Dietrich, 1998; Stock and Dietrich, 2003] (Figure 2.2). Research in long-term landscape evolution has made substantial use of slope-area plots, particularly for modeling fluvial erosion in bedrock channels [e.g., Seidl and Dietrich, 1992; Sklar and Dietrich, 1998; Whipple, 2001] as well as for assessing relevant controls exerted by lithology [Duvall et al., 2004], tectonic activity [e.g., Whipple et al., 1999; Snyder et al., 2000; Kirby and Whipple, 2001; Schoenbohm et al., 2004], and vegetation [e.g., Istanbulluoglu and Bras, 2005]. In such models o f fluvial erosion, slope can be empirically expressed as a function of drainage area: S = kA'°, (3.2) where k s is the channel steepness index, and 0 is the channel concavity index. It has been suggested that k s is dependent and 0 is independent o f tectonic uplift rates [e.g., Sklar and Dietrich, 1998; Whipple and Tucker, 1999]. Note that in a detachment-limited (bedrock-covered) landscape equation (3.1) becomes S = ( U / K ) 1 / n A " m / n , where m/n corresponds to 0 only when the study area is at steady state and local bedrock uplift, climate, and lithology are uniform in space. Process domains, their boundaries (i.e. channel heads and debris flow fans), and channel long profiles are dynamic entities that respond to variations in hydro-climatic regime [e.g., Ryder, 1971; Dunne, 1991; Montgomery, 1999], yet limited quantitative research has been 23 conducted on the topic [e.g., Tucker and Slingerland, 1997; Whipple et al., 1999]. Recent studies o f transient conditions due to the regional Quaternary pattern o f uplift and climate change in unglaciated mountain systems [e.g., Schoenbohm et al., 2004] report slope-area relations with multiple kinks and discontinuities that are in clear contrast with systems in steady state. However, unglaciated terrains, in or out of equilibrium, do not represent the full range o f conditions that one can observe in mountain environments. In fact, a number of orogens are currently glacierized or have been glaciated in the Quaternary but, because of their intrinsic complexity, these environments have received less attention and therefore merit closer study [e.g., Hooke, 1991; Whipple et ah, 1999; MacGregor et al., 2000; Montgomery, 2002; Tomkin and Braun, 2002]. Glaciated environments are transient and contain "fingerprints" of glacial erosion that are progressively erased by post-glacial processes. The objectives of this chapter are to evaluate the effects of glacial history on the organization o f currently active geomorphic process domains and topographic signatures, to determine how these compare to previous conceptual models proposed for unglaciated analogues; and to characterize the structure o f channel long-profiles. In addition, aims include evaluating whether or not GIS-based measurements are sufficient and suitable to address research questions about landscape evolution and watershed management. To pursue these goals slope-area relationships were determined for five basins in coastal British Columbia using equation (3.2) and k s and 9 values were inferred through linear regression of the model on field and GIS measurements of their topographic relief. To address the question of GIS-data suitability, field-measured slopes were used to evaluate the error associated with GIS-measured slopes and assess in what measure this affects the discrimination o f process domains. In British Columbia, repeated episodes of glacier advance and retreat during the Quaternary have left a profound geomorphic legacy in terms o f sediment dynamics and morphology [e.g., Church and Ryder, 1972; Church and Slaymaker, 1989]. In terms o f morphology, ice flows have introduced a strong topographic anisotropy and created a variety o f features at different landscape scales including glacial cirques, hanging valleys, valley steps, and over-steepened valley walls. A s a result, geomorphic processes have acquired a characteristic spatial organization: fluvial processes preferentially dominate along the longitudinal axis of 24 relict glacial troughs; on the valley walls, transverse to this axis colluvial processes dominate fe.g., Ryder, 19811. +— Debris-flow dominated channel J on valley walls Creeks flowing through glacially carved saddle Creeks flowing along ice flow axes 1. LembkeOI 2. Lembke02 3. Lernbke03 4. LembkeW 5. Slide 6. SistenOI 7. StiachanOI 8. Stmehan02 9. rteskethlOOl 10. Rapid 11. Eas«Cap120 12. EastCsplOOL 13. HeskethOI 14. Hesketti02 1 15. Sistera02 16. Sister* Pm Figure 3 .1. Map of the Capilano River basin indicating the location of the ground-surveyed streams. The inset shows locations of Elliott Creek and Radium Creek. In view o f this anisotropy, slope-area transects were conducted along relict glacial troughs (Figure 3.1, white lines) and along their adjoining valley walls (Figure 3.1, black lines). For the former component one seeks to document the effects o f valley modification by glacial activity; for the latter, the aim was to verify the existence of debris flow-induced topographic signatures, particularly to assess the state of landscape recovery from glacial disturbance. 25 Collectively, the longitudinal and transverse transects present a picture o f glaciated terrain structures and process domain arrangements. 3.2 Study Areas The physical environment o f coastal British Columbia is the result o f a series o f geo-climatic processes, which in chronological order include diastrophism, glaciations, and paraglacial sedimentary dynamics [Ryder, 1981; Muhs et al, 1987]. Accordingly, the landscape contains elements of three phases of evolution. First order landforms resulted from the orogeny that took place during the Tertiary period. These features have undergone repeated episodes o f profound glacially-induced modifications in the Quaternary period (Pleistocene Epoch) leading to second order landforms that still dominate the morphology o f the landscape today. Finally, third order features developed as local modifications of the glacially-derived landforms, through accelerated mass wasting processes on valley sides and downstream accumulation of fluvial sediment on valley floors, during deglaciation at the end of the Pleistocene [Ryder, 1981] about 14,000 years ago [Kovanen and Easterbrook, 2002]. A l l study basins are located on homogeneous intrusive lithologies, largely granodiorite and quartz diorite [Roddick, 1965; Muller et al, 1974; Monger, 1989]. The study basins are Lembke Creek, Hesketh Creek and East Cap Creek, tributaries of the Capilano River in the Pacific Coast Ranges; Elliott Creek in the Northern Insular Ranges; and Radium Creek in the Northern Cascades (Figure 3.1). 3.3 Data Collection The methodologies adopted in this study include air photo interpretation (API), GIS-based topographic analyses, and field surveys. A P I yielded a preliminary delineation o f the downstream boundary o f the "debris-flow domain" via identification o f debris-flow fans, fluvial terraces, and evaluation o f geomorphic coupling from hillslope sediment inputs. The term coupling is used in geomorphology [e.g., Brunsden and Thornes, 1979; Caine and Swanson, 1989] to indicate the degree o f connectivity between hillslope and fluvial processes. Specifically, coupled systems exhibit direct colluvial-alluvial interaction, as opposed to decoupled (or buffered) systems, where colluvial sediment inputs do not reach the channel network. Evaluation of degree of coupling is fundamental to drainage basin sediment dynamics as it controls (i) sediment and process-disturbance cascades, and (ii) in what 26 proportion hillslope denudation rate contributes to sediment storage and yield respectively [e.g., Roberts and Church, 1986; Reid and Dunne, 1996]. GIS-based analysis was used to derive and compare slope-area plots of two kinds for main-trunk streams: (i) automatically-extracted from a 25-m gridded D E M and, (ii) hand-digitized along the channel network from 1:20,000 digital topographic maps. In the DEM-based analysis standard procedures were used [e.g., Montgomery and Foufoula-Georgiou, 1993; Ijjaz-Vasquez and Bras, 1995], slope gradient was computed using the steepest descent algorithm and contributing area by the D8 single-flow accumulation algorithm [O'Callqghan and Mark, 1984; Garbrecht and Martz, 1997]. For the contour-based map analysis, the procedure adopted by Stock and Dietrich [2003] was replicated. This second procedure was employed to eliminate algorithm-related artifacts that were observed in the drainage network extracted from D E M grids. The D8 flow algorithm is certainly not the most appropriate solution for modeling flow-divergent surfaces (hillslopes) where instead multiple-flow algorithms mimic real hydrologic conditions more closely. To test this limitation, D8-derived contributing areas were compared with values obtained by the multiple outflow algorithm D -inf [Tarboton, 1997] at a number of GPS-recorded locations (n=88) with drainage area ranging between 3.15*10"3 k m 2 and 1.7*102 k m 2 . Results reveal discrepancy between D- in f and D8 that lies within the uncertainty associated with D E M resolution. Field surveys involved mapping as well as measurement and description o f morphologic features (e.g., channel heads, debris-flow fans, landslide tracks, and strath terraces) that were identified or misinterpreted during A P I . Depending on site accessibility, slope gradients were measured by means o f a hand held clinometer or laser theodolite. In order to ensure appropriate comparison with GIS-measured slopes, field measurements were taken at a length scale equal to the local channel width (up to a maximum of 25 m). Field measurements are considered the true values from which the error associated with the contour-based and D E M slope estimates was calculated (cf. section 3.4.5). In order to overlay and compare the different types of measurements, positioning information was gathered via G P S devices and orthorectified air photos. 3.4 Results Results are ordered by system size (drainage area), starting from streams located on valley walls, progressing to incipient hanging valleys, and ending with fully developed glacial 27 troughs. A s w i l l become clear, system complexity increases with system size. In slope-area plots this is matched by increasing complexity o f the graphs. For the simplest cases a single power-law is adequate. For the most complex cases the graphs are multisegmented. I then consider how well geomorphic process domains are resolved in the slope-area space by plotting all field transects together, and finally analyze the error associated with GIS-measured slope gradients. 3.4.1 Valley Walls and Cirque Walls Slope-area transects o f unglaciated debris-flow (colluvial) dominated channels are typically fit by a single power law (e.g., Stock and Dietrich [2003] and Figure 2.2). For debris-flow dominated channels in formerly glaciated landscapes the situation is more complex. Some of the study slope-area transects are fit by a single power-law relation (Figure 3.2a, 3.2b, and 3.2g), while others, even though debris-flow dominated for their entire length, require a double power-law fitting (Figure 3.2c-3.2f and Table 3.1). One could attribute the slope break o f the latter plots to progressive loss o f erosive power as the debris flow travels downstream and fluvial processes become more important. However, the kink observed in most slope-area plots o f the study debris-flow channels casts doubt on this interpretation. Specifically, the kink occurs within a broad range o f slope gradients, between 0.48 and 1.01, values that are undoubtedly too high (i) to justify a debris flow loss o f power, and (ii) to allow formation of fluvial terraces (diagnostic landforms of dominant fluvial activity). For reference, Stock and Dietrich [2003] reported kinks occurring at slopes between 0.04 and 0.40 for unglaciated granitic basins and interpreted trend differences, such as the presence and/or location o f the kink and variation in the shape of the curvature, in terms of system size (drainage basin area). In particular, they recommended using sufficiently large basins to define fluvial trends, hence deviations due to debris flow scouring. In the present Work, single vs. double power-law trends cannot be explained as an effect o f system size because basins o f comparable drainage area display different trends. For example, single power-law relations yield excellent fits for Rapid Creek, HeskethOl and LembkeOl, whereas double power-law relations are required for HeskethlOO, Slide Creek, and Lembke03 (Table 3.1). A careful look at the geomorphology of the study basins suggests that the shape of the slope-area relations is imposed by glacially-induced local topography rather than controlled by differential erosive power associated with dominance of colluvial and fluvial processes. 28 Table 3.1. Field data for the transverse transects Stream channel Basin Area (km2) Surficial Materials 3 Slope (m/m) Kink Area (km2) e k s StrachanOI 0.055 M 0.51 6 n.a. 0.301 12.7 Strachan02 0.048 M 0.54 b n.a. 0.089 1.5 SistersOl 0.072 M 0.53 b n.a. 0.118 2.2 Slide 0.210 M 0.56 - 0.65 0.051-0.110 0.098 1.8 Slide lower R.C 0.30 n.a. 0.727 2*103 LembkeOI 0.056 M 0.21 n.a. 0.546 224.6 Lembke02 0.062 R 0.50 - 0.77 0 .036-0.039 -0.122 0.2 Lembke02 lower C M 0.16 n.a. 0.495 92.7 Lembke03 0.081 C/R 0.62 - 0.78 0.037 - 0.041 0.233 7.7 Lembke03 lower C 0.23 n.a. 1.780 2*108 Lembke04 0.029 C/M 0.23 n.a. 0.192 4.2 HeskethOI 0.190 R/C 0.21 n.a. 0.380 34.3 Hesketh02 0.100 R n.a. n.a. 0.423 55.4 HeskethlOO 0.320 R.C 0.48 - 0.57 0 .093-0.185 0.129 2.6 Hesketh 100 lower GF/M 0.23 n.a. 1.889 5*109 EastCaplOO 0.068 R/C 0.72 - 0.85 0 .019-0.029 - 0.248 0 ! EastCaplOO lower R 0.42 n.a. 1.052 4*104 East Cap120 0.057 R 0 .74-1.01 0 .010-0.022 -0.179 0.2 East Cap120 lower C 0.27 n.a. 1.071 3.5*104 Rapid 0.750 R.C 0 .25-0 .35 0.531 -0.651 0.320 21.9 Rapid lower C/R 0.27 n.a. 2.351 1*1013 Sisters02 1.780 M 0 .19-0 .23 0.622-0.851 -0.027 0.1 Sisters02 mid C/R 0.31 - 0.40 1.203-1.461 -1.679 2*10"11 Sisters02 lower /CM n.a. n.a. 3.834 1*1023 Sisters Pass 1.010 C R 0.32 0.092-0.134 0.596 325.9 Sisters Pass mid M/C 0.52 0.291 - 0.403 -0.865 9*10"6 Sisters Pass lower F n.a. n.a. 1.334 2*107 M=morainal till, C=colluvium, R=bedrock, GF=glaciofluvial, F=fluvial. (.=components are approx. in equal proportions; / = the left hand side component is more extensive;7CM=till partially covered by colluvium). b Truncated fan. In this context, morphometric parameters, namely valley bottom width, valley wal l profile curvature and steepness, and the way these are connected through the presence or absence o f paraglacial fans (see Ryder [1971] for details) and cones seem to play a prominent role. Applying this thinking, one can explain the slope-area plots for al l the debris-flow dominated channels. StrachanOI, Strachan02 (Figure 3.2a), Lembke04, and SistersOl Creeks (Figure 3.2b) flow down steep, till-blanketed, planar valley walls, which form non-buffered V -shaped valleys: this explains why they exhibit single power-law relations and possess low concavity index (0.089 < 0 < 0.301, Table 3.1). In contrast, the higher concavity indices for LembkeOI, HeskethOI and Hesketh02 Creeks (0.380 < 0 < 0.546) are due to more concave valley walls which form buffered U-shaped hanging valleys. 29 Turning to systems that display a double power-law relation, the kinks in the Slide Creek graph (Figure 3.2c) and Hesketh 100 graph (Figure 3.2d) correspond to the apex o f paraglacial fans. For Lembke02, Lembke03, EastCaplOO (Figure 3.2e), and EastCapl20 (Figure 3.2f) the kinks correspond to a transition from the bedrock/colluvium-dominated upper slopes to the till-blanketed base slopes. Rapid Creek (Figure 3.2g) is an extreme example of the sharp transition from a rocky planar valley wall (0 = 0.320) to a paraglacial fan (0 = 2.351) that protrudes into the Capilano River valley. Most of the plot fits a single power-law, but to fit the right limb one requires the largest 0 value o f any in the study. 10' 10° 10"' 10* .10 3 10 4 to5 106103 10 4 10 5 10° 10" CL o CO 10° 10" 10^ 10" a) Strachan 02 o Field slopes + 25m DEM ^ A Digitized data 0 = 0.089 r i 11 1 1 — i — i — i i ' r i [ 1 1 1—i i i i 11 1 1—i— i i l i i . b) Sisters 01 4, Channel head \ 1* Debris flow fan 0.118 1 1 1 c) Slide V 0 - 0.089 1 0.727 1 , d) Hesketh 100 0129 1 o + '. , 1 1.889 e) EastCaplOO 1 i X 0 =-0.248 1 1.052 1 f) EastCap 120 ••• 1 1 + -0179 U.071 1 1 10 1 g) Rapid A A A 4 d A 1 1 \ 0 = 0.320 lo 2.351 . i *t h) Sisters Pass j 1 1 1 1 0.596 l - O ^ S r 1 * ^ 1.333 101 10° 10" 10" 10" 10° 10" 10 10° 10" 1 0 4 10* 106103 1 04 1 05 1 06 Area ( m 2 ) Figure 3.2. Slope-area plots (a-g) along debris-flow dominated channels and (h) at a glacially-mduced saddle. Numbers indicate concavity indices defined between the dished lines usmg field-measured slopes (cf. Table 3.1) 30 3.4.2 Glacially-Induced Saddle The glacially-induced saddle of Sisters Pass (Figure 3.2h) illustrates the breakdown of the foregoing power law characterization. Sisters Pass and Sisters02 Creeks (Figure 3.1, dashed lines) illustrate an intermediate case between valley walls and glacial troughs. Both stream channels originate from a glacially carved saddle (Sisters Pass), then flow into an incipient hanging valley before intersecting a major glacial trough (Lembke Creek and Capilano River). Ice flow through Sisters Pass has created a higher degree of plan-view curvature on both sides of the saddle compared to that of adjacent streams (HeskethlOO and Rapid Creek). Sisters Pass and Sisters02 Creeks possess morphologies that are characteristic of intermediate stages of valley development by glacial activity; hanging valleys are not fully developed and channel main stems are not completely decoupled from hillslope sediment inputs nor longimdinally scoured by debris flows. In slope-area terms, this translates into plots having two distinct kinks of opposite sign, which bound a portion of stream channel characterized by negative concavity index (-1.679 < 8 < -0.865, Table 3.1; positive slope-area relation). For unglaciated basins such a trend has been defined at very small drainage areas as diagnostic of unchanneled topography, where hillslope diffusive styles of sediment transport are dominant (Figure 1.2, [e.g., Montgomery and Foufoula-Georgiou, 1993; Tucker and Bras, 1998]). For the study of glaciated basins, transient topography clearly alters the slope-area relations that are accepted for unglaciated environments at steady state. 3.4.3 Glacial Troughs The terrain structure along glacial troughs presents much more composite configurations than what observed in valley walls and therefore it requires a more detailed description. Hesketh Creek (Figure 3.3a) originates from an unchanneled saddle (H) followed by a poorly defined colluvial channel (CI, 9=0.817) which degrades into a spoon-shaped hanging valley (HF1, 0=n.a., not available, due to the presence of a kink in the slope-area relation within the domain boundaries) characterized by a poorly defined channel. The hanging valley terminates abruptly into a steep and incised colluvial channel (C2, 0=0.885) dominated by large boulders commonly interlocked in massive jammed structures. Here material is transferred preferentially via debris flows into the principal decoupled hanging valley (HF2, 0=3;892), which presents typical riffle-pool morphology. Downstream, the channel reacquires a colluvial and confined character (C3, 0=n.a) with step-pool and boulder-cascade 31 morphologies, sediment being supplied by near-bank failures. Gentler slope gradients (F, 0=4.607) and riffle-pool morphology reappear i n the distal reaches where Hesketh Creek intersects the Capilano glacial trough (Figure 3.1). This sequence o f "building blocks" (hillslope-colluvial-fluvial-colluvial-fluvial-colluvial-fluvial) applies with some variations to the structure of al l other basins studied (see Figures 3.3b-e). Due to the formation o f cirques and hanging valleys, transient situations such as those observed in Sisters Pass and Sisters02 Creeks are here developed to a further stage, with increased relative relief, longer valley walls, and wider valley floors. Longitudinal profiles exhibit a stepped topography which, in slope-area plots, yields multiple sequences o f kinks or discontinuities, extreme positive limbs (0 « 0), lower minima for hanging valleys and, in some cases extremely high negative slope coefficients for confined colluvial channels (0 > 3.9). During glaciation transient topography likely evolved to a stable "glacial equilibrium state" that produced fully developed glacial troughs that today are associated with drastically decreased channel gradient variability (e.g., zone F Figure 3.3d). A long relict glacial troughs, the contemporary riverine valley floor, which was termed distal fluvial sub-domain, is permanently decoupled from hillslope sediment inputs and differs from the hanging fluvial sub-domain, typically found in correspondence o f relict glacial cirques. Similarly to what is seen for transverse transects, the presence of kinks within single process domains (e.g., zone C2 in Figure 3.3a, and zones H F 2 and C3 in Figure 3.3b, Table 3.2) requires the use of double power-law fitting. Figure 3.3. (Next Page) Slope-area plots along the direction o f formerly active ice flows. The following notation applies: B=bedrock canyon; C=colluvial domain, typically having chaotic, cascade or step-pool morphology; F=fluvial and HF=hanging fluvial domains, commonly with rapids or riffle-pool morphology; and H=hillslope domain. Numbers indicate field-based concavity indices (cf. Table 3.2). Hesketh Creek (a) is the prototype for the description o f the other basins (see text for explanation), (b) Elliott Creek (C1=0, HF1=0.623, C2=-1.479, HF2=n.a., C3=n.a., F=41.429) exhibits the same domain sequence o f Hesketh Creek, (c) Lembke Creek has a simple structure with a hanging valley (HF=n.a.) that separates two colluvial channels (C1=0.277, C2=0.303), and no distal fluvial domain, (d) East Cap Creek originates as a colluvial channel (CI =0.136) that flows into a hanging valley (HFl=n.a.), hence through a relict melt water channel (bedrock canyon, B=1.368). Downstream, the primary hanging valley is replaced by a glacial trough (C2=1.368 and F=0.086). (e) Radium Creek exhibits the same domain sequence as o f Elliott Creek (Cl=0.346, HFl=n.a. , C2=4.732, HF2=0.835, C3=n.a., F=n.a.). 32 i o - 10 -2 10' 10u 10' 102 10* 10" -2 10 10" 10' : '• o Field slopes ; + 25m DEM A Digitized data 1 1 1 I I I I I | • — r * ° * + A 1 !o i i i i 1 1 11 1— ,—1—1 1' 1 1 1 1 1 1 1 r ] 1 p—I I ( I I I . a) Hesketh Creek , , , , , , ,i i i -0 •£ , , 1 1 , 0 a % ! , , , 1 , 1 , LL. 1 < 10" 10"' ,0 F 10" 10 +8A fl $ X 1 u - J l ' ' i i i i U i i 1.1 u j , i i i i i i + J i A - I 1 P ? I b) Elliott Creek 10 10": 10° ,-2 1 0 <>r+-1^0 10"' ,-1 8. o 10 • I t 10c 10" 1 U S o u _ i l _ + A ± A OA c) Lembke Creek 66 o' a 10u 10 ,-l ,-2 IO"2 10° A 6 + + + | A + ^ A + A A,+ $ CO I I I I I A+ (N . L> 1 i i . i _ d) East Cap Creek 10 10° ^ l O " 10 -1 10" + + A I I. I I I A+ A . A 4 A * + ' I J. I A I A l l i i l l i I I I I I I N I e) Radium Creek _ j i • • * , 11, i , i _ .1.1 10" 10° r2 10 r1 i o - io-ri 10 ,-2 10u 10' 102 Area (krrr) Table 3.2. Field data for the longitudinal transects Stream Basin area Process Landscape Dominant channel Domain upstream limit e ks channel (km2) Domain macro-form morphology Slope (m/m) Area (km*) Hesketh 5.5 C1 Cirque wall Chaotic 0.594 0.016 0.817 4*10* HF1 Hanging valley Rapids 0.114 0.154 n.a. n.a. C2 Valley step Cascades; Step-pools 0.649 0.231 0.885 4*104 HF2 Hanging valley Riffle-Pools; Rapids .0.190 0.604 3.892 9*10 2 2 C3 Valley step Cascades; Step-pools 0.091 3.200 n .a . c n.a. 1 F Glacial trough Riffle-pools; Rapids 0.069 5.300 4.607 6*10 2 9 Elliott 10.4 C1 Open saddle Step-pools 0.364 0.012 -0.005 0.2 HF1 Hanging valley Rapids; Riffle-pools 0.095 0.805 0.623 589.9 C2 Valley step Step-pools; Bedrock 0.221 2.027 -1.479 6*10"11 HF2 Hanging valley Riffle-pools 0.060 4.171 n .a . c n.a. C3 Valley step Cascades; Step-pools 0.113 7.575 n.a.° n.a. F Glacial trough Step-pools; Rapids 0.138 10.162 41.429 5*10 2 8 9 Lembke 22.3 C1 Cirque wall Chaotic; Bedrock 0.783 0.003 0.273 8.7 HF Hanging valley Riffle-pools; Rapids 0.090 0.211 n . a . c n.a. C2 Valley step/trough Step-pools; Cascades 0.149 1.083 0.233 3.6 East Cap 40.7 C1 Cirque wall Chaotic 0.670 0.004 0.136 1.9 HF Hanging valley Rapids; Bedrock 0.100 0.088 n .a . c n.a. B Relict meltwater ch. Bedrock 0.364 0.388 1.368 3*107 C2 Glacial trough Chaotic; Step-pools 0.126 1.022 1.368 3*107 F Glacial trough Rapids; Riffle-pools 0.060 1.989 0.086 0.237 EastCap 1 1 0 a 1.3 C1 Colluvial fan Chaotic; Step-pools 0.520 0.103 0.762 4*103 HF Hanging valley Riffle-pools 0.072 0.807 n . a . c n.a. C2 Valley step Step-pools; Cascades 0.129 1.043 -3.411 4*10"22 F Glacial trough Rapids 0.076 1.167 9.691 5*105 7 Radium" 10.1 C1 Cirque wall 0.857 0.011 0.346 25.59 HF1 Hanging valley 0.194 0.566 n .a . c n.a. C2 Valley step n .a . b 0.563 1.307 4.732 4*10 2 8 HF2 Hanging valley 0.156 2.086 0.835 2*103 C3 Glacial trough 0.180 3.573 n .a . c n.a. F Glacial trough 0.180 8.054 n.a.° n.a. a Not shown in Figure 4." GIS-measured data (digitized). c Presence of a kink within the domain that prevents from using a single power-law fit. 3.4.4 Process Domains B y plotting together al l field-based transects of the study basins (Figure 3.4a) I seek to illustrate how well geomorphic process domains are resolved in slope-area space, and therefore gain a better understanding o f the causal linkages connecting processes active in different morphological units o f the glaciated landscape. Specifically, this should allow testing of Montgomery and Foufoula-Georgiou''s [1993] idealized conceptual model (Figure 2.2), originally proposed for unglaciated environments on the basis of DEM-der ived data. Results are encouraging: hillslope, colluvial and fluvial domains exhibit good separation. The two alluvial sub-domains (hanging and distal) overlap substantially, due to the topographic anisotropy created by formerly active ice flows. Accordingly, the landscape scale (drainage area) at which slope gradients characteristic of purely alluvial reaches occur is controlled by the length of cirque walls for hanging fluvial channels and that o f valley walls for distal fluvial channels, which appear to be o f comparable size. However, the position of the colluvial domain in the slope-area space deviates significantly from what has been proposed for unglaciated environments [Montgomery and Foufoula-Georgiou, 1993; Sklar and Dietrich, 1998]. In particular, the transition from colluvial to alluvial channels occurs at a systematically decreasing slope beyond drainage areas larger than 1 k m 2 (Figure 3.4a). Interestingly, 1 k m is the characteristic spatial scale of valley step and glacial trough initiation (cf. contributing area values of C2 zones in Figure 3.3 and Table 3.2), which might imply some sort o f dependence on valley morphometry. Examination o f the spatial distribution and of the magnitude-frequency relations o f sediment sources in the Capilano River basin [Brardinoni et al., 2003; Brardinoni and Church, 2004] confirm that the typically glacial, trellis-like structure of the channel network and stepped nature o f the topography affect debris flow trajectories and run-out distances. Consequently, it was decided to classify the study colluvial channels into two sub-categories, depending on how these are spatially connected to debris flows: source and sink colluvial channels (Figure 3.5). Source colluvial channels are very steep, first- and second-order streams, typically located on valley walls and cirque walls. Distinctively, they are longitudinally scoured by debris flows and may receive colluvial lateral inputs (e.g., debris slides and avalanches) from open-slope locations. Sink colluvial channels are moderately steep second- and higher-order streams, typically flowing along valley steps and glacial troughs whose floor is not wide enough to 35 prevent lateral colluvial inputs from impacting the stream main stem. They receive exclusively lateral colluvial inputs (as opposed to colluvial imputs from upstream), including debris flows at tributary junctions. 0.001 0.01 0.1 1 10 100 1000 Area (km2) Figure 3.4. (a) Process domains based on field-measured slopes plotted in slope-area space, (b) Process domains based on DEM-measured slopes. Solid lines are the schematic boundaries of process domains for unglaciated drainage basins sketched by Montgomery and Foufoula-Georgiou [1993]. Dashed line is the "glacially-forced" colluvial-alluvial transition detected in this study. 36 Figure 3.5. Contour map o f Hesketh Creek and Lembke Creek showing the spatial configuration o f sediment sources, colluvial channels and alluvial channels. Open circles indicate initiation points of sediment sources (debris slides and debris flows) identified via A P I within a 30-year time window. Sediment sources were mapped during extensive field surveys conducted to establish the reliability o f API-based landslide inventories (for details see Brardinoni et al. [2003]). The source-sink stratification reveals that the inflection point of the colluvial-fluvial transition corresponds to a shift i n colluvial sub-category. The source colluvial-fluvial transition occurs at a roughly constant slope of 0.2 for all drainage areas, a value typical of debris flow fans in glaciated British Columbia [e.g., Hungr et al, 1984; Van Dine, 1985, Fannin and Roller son, 1993]. The sink colluvial-fluvial transition decreases with increasing 37 drainage area and is associated with channels flowing along coupled glacial troughs. The declining trend of the transition - its gradient, onset, and length - appears to be forced by the glacially-induced topography. Along relict glacial troughs, as contributing area increases so does relative relief and length of valley walls. As a result, increasingly large debris flows intersect stream channels which possess gradients otherwise typical of alluvial environments. This spatial configuration of processes explains the deposition of a colluvial blanket at channel gradients as low as 0.06 and a drainage area at least as large as 20 km2. One expects the colluvial-alluvial boundary to stop declining (and potentially reverse its trend) at a scale where glacial troughs are wide enough to decouple lateral colluvial inputs and/or valley walls become considerably less prone to the initiation of shallow rapid failures. 3.4.5 Field- Versus GIS-Measured Data Typically, GIS-based calculation of local slope gradient for the purpose of analyzing channel long profiles and process domains has relied upon 90 m [e.g., Schoenbohm et al, 2004], 30 m [e.g., Wolinsky and Pratson, 2005], or 10 m [e.g., Montgomery, 2001] DEMs, rarely on high-resolution (meter-scale) topography (e.g., some catchments in Stock and Dietrich [2003]). The extensive field surveys of this study allow to use field-measured slopes to (i) evaluate the error associated with GIS-measured slopes and (ii) assess the reliability of an "automated" DEM-based delineation of geomorphic process domains/signatures. Comparison of field-measured slopes with those calculated using GIS data (contour-based and gridded DEM) exhibits a high degree of scatter (Figure 3.6a and 3.6b). GIS-measured slopes nearly all plot within +/- 100% error; exceptions are field slopes smaller than 0.27, which in places are overestimated by more than 100%. Furthermore, slope discrepancies seem to vary between process domains. Respectively, GIS slopes underestimate field slopes on actively eroding, steep, highly dissected terrain (i.e., source colluvial channels) and overestimate field slopes on dominantly depositional environments characterized by a less rugged topography (i.e., hanging valleys and sink colluvial channels). These trends are visually confirmed by the box plots of Figure 3.7. Process domains may be ranked in terms of increasing root-mean-square (RMS) residual error of GIS-measured slopes relatively to field-measured slopes as follows (Table 3.3): distal fluvial < sink colluvial < hanging fluvial < source colluvial 38 Digitized slope (m/m) DEM slope (m/m) Figure 3.6. Scatter plots comparing: (a) field slopes vs. D E M slopes, and (b) field slopes vs. digitized slopes. In addition, evaluation of treatment effect (field, D E M , and digitized) within process domains was conducted. Accordingly, one-way A N O V A followed by Bonferroni post-hoc tests shows that along sink colluvial channels the mean of field-measured slopes is significantly smaller than those calculated with GIS (Table 3.3). Since slopes are not normally distributed within process domains Kruskal-Wallis tests were also performed. These tests yield virtually identical results to those o f the Bonferroni procedure. Figure 3.4b shows that D E M data are markedly inferior for delineating process domains in the slope-area space. DEM-based domains are not wel l resolved. Specifically, while sink and source colluvial stay well separated, the source colluvial lower boundary is shifted up to a gradient value greater than 0.3. More importantly, fluvial and hanging fluvial reaches tend to plot within the sink-colluvial domain. l . O i 0.8h 0.6 h 8. o 0.4 h 0.2 h Bedrock canyon Colluvial (source) * Colluvial (sink) Distal fluvial Mean • ±SE I ±SD Hanging fluvial "J" " ~ jjpjni e & nBal EEEO • 1 i ^ 1 "5» ch 5 S 2 2 " Q E d Q ch S 2 2 "2 £ I CD O 2 "2 2 2 u. *j3 Q u. o Figure 3.7. B o x plots of field slopes, digitized slopes, and D E M slopes across channel types. Overall, I think that a semi-automated mscrimination of process domains and topographic signatures is more appropriate than a fully automated one. This is because: (i) inflection points in slope-area relations do not always correspond to a transition o f process dominance, (ii) bias (under- or over-estimation) is not uniform between different process domains, (iii) some complex features located at relatively small drainage areas (i.e., H F in East Cap Creek) 40 may not be captured by a 25 m D E M , and (iv) process domains are not well discriminated in the slope-area space (Figure 3.4b). The semi-automated assessment procedure would entail coupling DEM-based slope-area plots to some A P I analysis. Table 3.3 Error analysis o f GIS-measured slopes performed against field-measured slopes RMS residual error Statistical significance Bonferroni Kruskall-Wallis Digitized D E M Digitized D E M Digitized D E M Bedrock canyon 0.105 0.074 a ns ns ns ns Colluvial (source) 0.114 0.127 ns ns ns ns Colluvial (sink) 0.056 0.056 0.002 0.009 0.001 0.017 Distal fluvial 0.017 0.012 ns ns ns ns Hanging fluvial 0.114 0.113 0.091 0.068 0.059 0.085 ns = not significant at the 0.05 level. 3.5 Discussion Debris-flow dominated channels, which typically initiate as steep, rectilinear streams, degrade to gentler gradients towards the base o f valley walls, where till-mantled slopes and paraglacial fans and cones provide sedimentary linkages between valley walls and valley bottoms. In process-related terms these have been zones o f transition between colluvial- and fluvial-dominated environments in the early Holocene epoch. Today, active debris flow fans in the area are typically located at the terminus of paraglacial fans. In slope-area terms, the presence of paraglacial fans imposes a kink in the relation which, at this landscape scale, is otherwise controlled by the valley wall and bottom bedrock geometries carved by past ice flows. It is concluded that in debris-flow dominated channels o f coastal British Columbia the glacial/paraglacial signature commonly overrides that produced by contemporary debris flows. Operationally, this result complicates the identification o f the debris flow transition zone (the kink does not always correspond to a change in process dominance) from area-slope plots, hence from automated GIS analysis (cf. section 3.4.5). Along the direction o f formerly active ice flows, hanging valleys that originated from relict cirques are the most striking features. Their peculiar morphology imposes low channel 41 gradients and isolates sediment inputs delivered from bordering cirque walls. A s a result, in steep glaciated mountain environments relict glacial cirques enclose distinctive hanging fluvial domains. In contrast to steep unglaciated drainage basins, where the degree of coupling progressively weakens downstream until colluvial reaches grade to fluvial analogues, decoupled hanging valleys separate strongly coupled channel reaches that together produce stepped long profiles. Therefore, the glacially imposed variations in valley long profiles impart substantial variability to process domain sequencing in individual watersheds (Figure 3.3). In terms o f slope-area relations this translates into fragmented, "saw-tooth" patterns with hanging valleys and steep colluvial channels corresponding to slope relative minima and maxima respectively (Figure 3.8b). The well-established slope-area relations for unglaciated environments do not apply in glaciated environments. In these environments, slope-area relations have the following features: (1) segments with positive slope-area relations occur at the transition between the downstream end o f hanging valleys (or saddles) and the inception of colluvial reaches, and (2) high negative concavity indices are associated with colluvial channels. Positive slope-area relations are also observed in unglaciated orogens [e.g., Snyder et al, 2000] and have been explained as a transient response to tectonic forcing [e.g., Schoenbohm etal, 2004]. In strictly fluvial geomorphology terms, the inherited Quaternary geomorphology imposes local channel gradient and degree o f coupling (Figure 3.8a), which in turn at the channel reach scale control hydraulics, unit stream power, channel morphology and in-channel habitat characteristics. A t the watershed scale this influences hydrologic response, downstream variation of stream power, as well as material transfer dynamics (e.g., wood and sediment cascades) and the transmission o f impulses o f any kind along the system (cf. "transmission resistance" in Brunsden and Thornes [1979]). In summary, the glacially-inherited topography induces a peculiar degree of geomorphic coupling (connectivity) between hillslope and channel processes. This in turn has a major impact on the delineation o f process domains in slope-area plots by generating a transitional process domain (sink colluvial) whose boundary with alluvial environments is an inverse function o f local slope and contributing area. One expects to see different colluvial-alluvial 42 transition trends in different glaciated landscapes, depending on pre-glacial litho-topographic properties and style of glaciation. a) 1100 900h c o 700H 500h-g 300 1000 2000 3000 Distance (m) 4000 5000 Figure 3.8. Schematic representation of (a) longitudinal profile and (b) corresponding area-based process domains and topographic signatures (solid lines) in a glaciated study basin of coastal British Columbia. Degree of coupling and relevant glacial macro-forms are reported in brackets. Arrows indicate apex of paraglacial fans. The presence of a relict glacial cirque imposes a "hanging fluvial" domain between colluvial domains, which translates into a multi-fragmented slope-area sequence. Note that kinks (reversal and inflection points) do not necessarily correspond to change in process dominance. 43 In watershed analysis, GIS is an extraordinarily valuable tool for quantifying topographic spatial variability and for integrating field- and remotely-sensed data. From a watershed management standpoint, assessing how well topographic signatures and process domains may be captured solely from DEM-extraction is very critical. In slope-area plots of transverse transects (Figure 3.2) GIS-derived slopes ( D E M and digitized) exhibit considerably higher scatter than field data, making the identification o f inflection points more difficult. A long longitudinal transects (Figure 3.3) inflections and reversals observable in field-based slope-area relations are reproduced reasonably wel l by those extracted with GIS. The hanging valley at East Cap Creek headwaters is an exception and is not appropriately captured. I attribute such a discrepancy to the presence o f two (about 20 m long) relict meltwater channels and their associated morphological jumps. 44 CHAPTER 4 Characterization of Sediment Sources 4.1 Introduction In glaciated mountain environments o f the Pacific Northwest coast, shallow landsliding and debris flows are the dominant mechanisms of sediment supply [Slaymaker and McPherson, 1977] and take part in the development o f valley floor landforms and channel morphology in the headmost portions of these systems. In this context, headwater streams play a prominent role. They are important features draining large portions of the landscape and having distinctive process geomorphology: according to field [e.g., White, 2002] and remotely derived data [e.g., Dadson, 2000] they set the transition zone between hillslope and fluvial process domains (strongly coupled systems, see chapter 3 for details). In fact, headmost channels display an ephemeral hydrologic regime that cannot be defined as exclusively fluvial. Residence times of sediment can approach the order of centuries and sediment transfer is episodic. A t this landscape scale mass wasting dominates over fluvial processes, hence justifying the term "colluvial channels" introduced by Montgomery and Buffington [1997]. Accordingly, headwater systems are important temporary storage sites for landslide-derived material [Slaymaker and McPherson, 1977]. It follows that sediment dynamics through the colluvially-dominated part of the drainage network depend on sediment recharging rates, storage capacity of the channel, and frequency of debris flows [Bovis et al, 1998; Bovis and Jakob, 1999; Jakob et al, 2005]. Within the research framework o f glaciated scaling relations detailed in chapter 1, the main objective o f this chapter is to characterize dorninant sources o f sediment production in steep terrain o f coastal British Columbia. Four research questions are considered: (i) what are the dorninant sites o f sediment production? (ii) Is the glacial signature able to mask the influence 45 of bedrock geology in controlling landslide activity? (iii) What controls scaling relations in landslide magnitude-frequency plots? A n d (iv) H o w is the landslide sediment flux distributed across geomorphic process domains? In consideration o f the potential multiple sources o f confounding which may hamper the understanding of actual landslide processes, research questions are listed by increasing degree of complexity. Accordingly, addressing the first research question requires separating terrain attributes (topography and land use) and landslide attributes (type of motion and nature o f material mobilized). The second question is a logical follow up, and adds complexity to the picture by considering geological effects on landslide activity in different topographies, land uses, and landslide types. The answer to the third question builds upon findings gained from addressing prior questions; specifically, it considers issues of landslide geometry (scaling between landslide area, width, and length, see Append ix A ) , and combines al l outcomes together into landslide magnitude-frequency plots. Finally, evaluation of the colluvial sediment budget across geomorphic process domains is accomplished by slope-area analysis o f landslide initiation and deposition points. Today, owing to the long history of glacial erosion and to the contemporary impacts associated with forest practices, topographic and land use effects are confounded in many mountain settings o f coastal British Columbia. A number of studies have focused on gullies as primary sources o f sediment [e.g., Rollerson, 1992; Bovis and Dagg, 1992; Bovis et al, 1998; Millard, 1993; 1999; Oden, 1994; Brayshaw, 1997; Millard et al, 2002]. Since most o f these projects aimed to assess terrain response to forest management, little research has been conducted on the functioning of gully (headwater) systems and the spatial distribution of shallow rapid failures in undisturbed settings. In relation to poor experimental control, it is still unclear to what extent timber harvesting - besides affecting landslide frequency - alters the location at which landslides preferentially initiate and deliver sediment. The picture gains even more complexity when lithologic variability is added to those associated with topography, land use, and Quaternary deposits. The role o f geology in shallow landslide production is a fascinating and complex question, especially in a province like British Columbia, that is extensively blanketed by t i l l . A number o f studies have tackled this issue, yielding contrasting results. Some researchers claim that landslide frequency reflects the relative erodibility o f bedrock lithology [e.g., VanDine and Evans, 1992; Guthrie and Van der Flier-Keller, 1998; Guthrie and Evans, 2004; Sterling and Slaymaker, in press], 46. while others are unable to document lithologic effects [Rood, 1990; Jakob, 2000; Martin et al., 2002; Rollerson et al, 2002; Brardinoni et al, 2003a]. The latter group interprets this outcome as part o f the glacial/paraglacial legacy that manifests itself through the spatial variability o f glacial macro-forms and glacially-derived surficial deposits. The fact that large landslides (i.e., rock slides, rock fall-avalanches and rock slumps) exhibit the effect o f lithology rather clearly [VanDine and Evans, 1992] does not automatically solve the problem o f what controls shallow landslides. Similarly, conclusions from Guthrie and Van der Flier-Keller [1998] are based on a small sample o f relatively large open-slope landslides (26 events of area larger than 10,000 m 2 ) . Considering that fifteen of these occurred in moraine deposits (which cover only 27% of the watershed) either at the weathered-unweathered t i l l interface or at the bedrock-till contact, they confirm the prominent role that Quaternary deposits play. In the Brooks Peninsula (northwestern Vancouver Island), Guthrie and Evans [2004] show that pristine forest on West Coast Crystalline Complex (quartz diorite, agmatite, amphibolite, and gneiss) is associated with higher landslide rates than Island Plutonic Suite (granitic intrusive). According to the authors, the former would be more unstable because it remained ice-free during the last glacial maximum, and therefore was exposed to longer weathering, which nowadays translates into higher rates o f landsliding. However, the study fails to document sufficient experimental control because it considers only open-slope failures, and does not examine the topographic variability (e.g., slope frequency distributions) across lithological types. In a study conducted in Clayoquot Sound (western Vancouver Island), Jakob [2000] reports data that disagree substantially with Guthrie and Evans' conclusions. High landslide frequencies (0.63-0.80 #LS/km 2 ) occur in the Quatsino Formation (sedimentary), Sicker Group (mainly extrusive), and Island Plutonic Suite (intrusive), whereas significantly lower frequencies (0.31-0.44 #LS/km 2 ) for the West Coast Crystalline Complex and the Karmutsen Formation. Even though unsupported by actual D E M analysis, Jakob speculates that confounding between bedrock geology and topography cannot be ruled out as a plausible explanation for these counterintuitive lithologic effects. Similarly, Rood [1990] and Martin et al. [2002] find landsliding rates not to be affected by rock type in the Queen Charlotte Islands, suggesting instead that Quaternary deposits may play a more prominent role. 47 Roller son et al. [2002], in southwestern Vancouver Island, indicate the Leech River formation (phyllite) as the most unstable unit; at the same time they report that clearcut terrain units on Island Intrusions (quartz diorite and granite) tend to fail more often than clearcut units on Karmutsen volcanics. In summary, Rollerson et al. [1998; 2002] state that colluvial and bedrock-dominated landforms tend to be very stable, while landforms dominated by morainal and glaciolacustrine materials are less stable and show greatest landslide likelihood. These last findings were confirmed by Brardinoni et al. [2003b] in the Capilano River basin, where till-blanketed terrain exhibited landslide-yield one order o f magnitude higher than colluvium-mantled and bedrock (quartz diorite) hillslopes. Summarizing, there is little doubt that rates o f rock-mobilizing slides are directly affected by bedrock erodibility [e.g., Evans and VahDine, 1992]. However, owing to the large number of factors involved and to poorly-controlled experimental designs, there appears to be confusion as to how geology controls shallow rapid failures for which the effect of Quaternary deposits may still today be dominant. Little is known about the third research question - what controls landslide magnitude-frequency ( L M F ) relations. Understanding L M F relations is very important, because these processes likely affect the morphology and the geometry of mountain streams and, more importantly, because such relations can provide scientists and practitioners with predictive tools for the assessment of long-term landscape evolution, and the rapid evaluation o f sediment budgets and geomorphic hazards. The issue is complex for the same reasons stated before: interactions between multiple environmental factors, which make difficult achieving any satisfactory experimental control. To answer this question, I w i l l use al l information gathered while addressing the first two research problems. This should allow substantial clarification on the eventual existence/magnitude of land use, lithologic, and topographic controls. Before considering L M F relations directly, in order to gain additional insights on the effects caused by such biogeoclimatic factors, an analysis o f landslide geometry w i l l be performed. Study basins are the Tsitika and Eve Rivers, located in the Insular Ranges o f north-eastern Vancouver Island. This choice is justified by (i) a well documented land use history (1930-2003), that is, cutblock characteristics and land use partitions can be quantified via GIS; (ii) the existence of a qualitative landslide inventory, reporting initiation points of landslides 48 across five sequential aerial photosets [Maynard and Golder, 2004]; (iii) available 25-m D E M for documenting the topographic variability; and (iv) a peculiar lithologic configuration which allows contrasting extrusive (covers 72% o f total study area) with intrusive lithologic effects. M6'40' 126°30' 126°20' 126°10'W Figure 4.1. Map o f the Tsitika and Eve River basins indicating the mapped channel network and the drainage divides. The inset shows locations o f the study sites within British Columbia. 4.2 Study A r e a The study area (612 km ) includes the entire Eve River and most of the Tsitika River basin on the central north coast of Vancouver Island (Figure 4.1). The headwaters and upper reaches o f the Tsitika River that lie within the Canadian Forest Products Ltd. operating area were not included in the original inventory conducted by Denny Maynard Associates Ltd. and Golder Associates Ltd. [2004]. The basins lie in the Vancouver Island Ranges, a 49 physiographic region that is part of the northwest to southeast-trending Insular Ranges [Holland, 1964]. Most of the area is characterized by deeply dissected and moderately rugged terrain [Holland, 1964; Howes, 1981]. Elevations range from sea-level to 1800 m (Figure 4.2). Val ley patterns tend to closely follow major joints, faults and lineations within the underlying bedrock. Areas o f gently undulating topography are found in the northeastern portions o f the study area and east o f Tsitika River. A s a result of intense glacial erosion, the main valleys, and in particular that of Tsitika River, are deeply scoured, typical U-shaped glacial valleys that slope gently into Johnstone Strait. Topography is bedrock-controlled, and surficial materials are thin on middle to upper slopes. Thick sequences of glacial drift (ti l l , glacio-fluvial and glacio-marine sediments) are limited to major valley floors [Maynard and Golder, 2004]. 0.16 0.14 -I 0.12 S 0.1 o o 0.08 a p £ 0.06 0.04 0.02 0 Extrusive Intrusive Combined 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Elevation (m) Figure 4.2. Tsitika-Eve elevation frequency distribution by lithology A wide range of landslide types [Varnes, 1978; Hungr et al, 2001] is active in the study area including falls, slumps, slides, avalanches, flows, and complex movements resulting from various combinations o f these processes. Colluvial cones and fans are found at the base o f avalanche and debris flow tracks. Blocky talus slopes are common along the base o f cliffs. The study area is covered with old-growth and second-growth conifer forests of the Coastal Western Hemlock and Mountain Hemlock Biogeoclimatic Zones [Krajina, 1969]. The former is prevalent from sea level up to about 900 m elevation. It is considered one of the 50 wettest and most productive forest zones in British Columbia, with annual precipitation varying with location between 1650 and 6650 mm [Krajina, 1969]. The Mountain Hemlock Biogeoclimatic Zone occupies higher elevations (i.e., 900-1800 m) and has a significantly lower capability for forestry [Meidinger and Pojar, 1991]. W6'4V 126°30' 126'2tr 126°10'W Figure 4 3 . Lithology map o f the Tsitika and Eve River basins (modified from Muller et al., [1974]; Geological Survey o f Canada M a p 1552A, original scale 1:250,000). The Karmutsen Formation includes basalt lava, p i l low lava, volcanic breccia, tuff, greenstone, limestone; the Pacific R i m Complex is a melange o f quartz diorite, granodiorite, quartz monzonite, and quartz feldspar porphyry. Most of the study area (444.5 km 2 ) is underlain by extrusive rocks of the upper Triassic Karmutsen Formation (Figure 4.3). The middle of the study area (167.6 km 2 ) is underlain by younger intrusive rocks of the Jurassic Island Intrusions of the Pacific R i m Complex [Muller, 51 1977]. Widespread faulting has produced areas where the bedrock is strongly fractured or sheared. Prior studies have hypothesized that locally high frequencies o f both natural and post-logging landslide activity may be a result o f this faulting [Sterling, 1997; Guthrie and Van der Flier-Keller, 1998]. The topography o f pristine forested terrain is steeper in extrusive (median slope = 0.595) than in intrusive lithologies (median slope = 0.411) (Figure 4.4a). Similarly, relative frequency o f logged steep terrain is higher in extrusive (median slope - 0.339) than in intrusive lithologies (median slope = 0.239) (Figure 4.4b). a) 6 b) 10 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 8 >. o c 8 3 6 £ c 4 <0 a. Slope (m/m) • Logged Intrusive • Logged Extrusive J l l b f U l f i f u w , 0.0 0.2 0.4 1.2 1.4 1.6 0.6 0.8 1.0 Slope (m/m) Figure 4.4. Relative frequency distribution o f slope gradient across lithology types in: (a) natural terrain, and (b) logged terrain. 52 Oldest documented cutblocks date to 1969 and are located in the lower portion of Eve River watershed. Forest clearing and road building progressed constantly throughout the rest o f the century and still continues today (cf. Table 4.1 and Figure 4.5). In 2003 a cumulative area o f 155 k m 2 was logged since 1969, corresponding to approximately 25% o f the whole study watersheds. 126°40' 126-30' 126°20' 126°10'W Drainage divide Figure 4.5. Map of land use history in the Tsitika and Eve River basins for the period 1961-2003 (data provided by Weyerhaeuser Ltd.). 53 Table 4.1. Land-use history across lithologies in Tsitika and Eve watersheds Land Use Lithology -Time period 1961-68 1969-79 1980-87 1988-94 1995-03 Logged Area (km?) Intrusive Extrusive 0 0 4.4 32.4 15.8 20.1 12.7 21.4 22.8 25.4 Total 0 36.8 35.9 34.1 48.2 Cumulative Intrusive 0 4.4 20.2 32.9 55.7 (33.2)* Logged Area (km?) Extrusive 0 32.4 52.5 73.9 99.3 (22.3)* Total 0 36.8 72.7 106.8 155 (25.3)* Natural Area (km2) Intrusive Extrusive 167.6 444.5 163.2 412.1 147.4 392 134.7 370.6 111.9 345.2 Total 612.1 575.3 539.4 505.3 457.1 * Cumulative percent logged area for the period 1969-2003 reported in brackets 4.3 Data Collection The Tsitika-Eve landslide inventory was initially compiled by Terry Rollerson and Denny Maynard v ia stereoscopic inspection of sequential aerial photosets. Five sets of air photos were examined. Photosets were flown in 1961, 1977-79, 1987, 1994, and 2003, and range in nominal scale from 1:15,000 to 1:20,000. Landslide locations were marked and numbered on the air photos beginning with the oldest air photos first and progressing to the most recent, ensuring that individual landslide locations were recorded only once. Initiation points were then imported in digital format onto the 2003 ortho-photo mosaic so that GIS analysis and further data integration could be conducted. For each landslide a number of attributes were recorded including photo year, land use, landslide type (Table 4.2), the morphologic landform present at the apparent landslide initiation point (Table 4.3), and a characterization of the landslide terminus/run-out zone (Table 4.4). Landslide type information is important to separate movements involving bedrock from those mobilizing surficial materials, therefore to separate lithologic from glacially-inherited effects. Surface expression o f landslide initiation is critical to address the question of dominant topographic sites of sediment production. Classification of landslide termini allows evaluating where and in what proportions the material eroded is redistributed in the landscape for theoretical and applied considerations (e.g., landscape evolution models, sediment budgets, and habitat/water quality). Together, landslide type, land use, lithology, initiation morphology, and terminus are expected to aid understanding the hierarchy and interactions o f those factors controlling landslide magnitude-frequency relations. A total o f eighteen mass movement types was recognized during aerial photo interpretation (API) , and then grouped into 8 categories (Table 4.2). Initiation sites were classified into 54 seven classes (Table 4.3 and Figure 4 . 6 ) including: escarpment faces of two types (gullied and unchanneled), headwater basins (API-visible zero-order basins/hollows), gully channels, gully headwalls, gully sidewalls, and open-slope locations. Landslide termini and sediment deliverability are listed in Table 4 . 4 . Table 4.2. Landslide types and sediment production in the Tsitika-Eve River basins Landslide Type (code) Number of Events Mobilized Volume ( m 3 ) -Debris avalanche (da, dadf, dsda) 75 (10.0)a 988,354 (38.2) Debris flow (df, dsdfj 390(52.0) 1,023,388 (39.5) Debris slide (ds) 174 (23.2) 108,822 (4.2) Deep-seated (DSIs) 1 (0.1) 8,009 (0.3) Movement of bedrock and debris mixtures (rfds, rfrsdf, rsda, rsdadf, rsdf, rsds, rsdsdf) 93 (12.4) 423,616 (16.4) Rock movements (rfrs, rs, rsra) 9 (1.2) 32,015 (1.2) Slump (u) 8 (1.1) 4,726 (0.2) Total 750 2,588,930 a. Percentages of total mobilized volume are reported in brackets Table 4 .3. Landform at landslide initiation point Initiation Position (code) Number of Events Mobilized Volume (m3) Headwater basin / Hollow (ch) 6 1,9641 (0.8)a Gullied escarpment (eg) 15 9,439 (0.4) Unchannelled Escarpment (es) 89 65,704 (2.5) Gully channel (gc) 10 36,020 (1.4) Gully headwall (gh) 117 399,908 (15.4) Gully sidewall (gs) 234 299,901 (11.6) Open slope (os) 279 1,758,318(67.9) Total 750 2,588,930 a. Percentages of total mobilized volume are reported in brackets Subsequently, the writer reviewed and re-elaborated the landslide inventory. In particular, A P I was re-assessed independently, landslide tracks were digitized on orthophotos, and a series o f GIS operations was performed so that landslide attributes (i.e., area, landslide length, lithology, and slope, elevation, and contributing area at initiation and deposition locations) could be obtained for each event. Specifically, landslide area includes the initiation and the transportation zones, but not the deposition zone. A P I is a convenient technique for the rapid detection o f landslides in steep, forested terrain. However, the methodology has limitations. Landslide depth cannot be quantified; as a result o f vegetation cover, photo scale, and terrain ruggedness, a population of small landslides remains undetected. In addition, in some instances it is not possible to discern whether a landslide scar is the product o f a single or multiple (recurrent) events at a location within the time interval considered. Limitations of 55 landslide inventories based on API have been discussed extensively in other studies [e.g., Robison et al, 1999; Brardinoni et al., 2003b; Malamudet al, 2004]. Figure 4.6 (a) ^ Examples o f landslide positions at initiation in Thursday Creek (north-easthern Tsitika River basin; see Table 4.3 for explanation of codes). Figure 4.6 (b) Sidewall (GS) slope failures. In the bottom left, note a sidewall landslide (ds) that develops into debris flow (dsdf). Two sub-populations o f sidewall landslides are identified: (i) low-magnitude events, whose size resembles that o f escarpment-related landslides (cf., Figure 4.6a); and (ii) high-magnitude events, whose size approaches that typical of open-slope and headwall landslides (see Figure 4.21, and section 4.6 for discussion). 56 Table 4.4 Landslide terminus and sediment delivery to channels T . . . , a Number of Landslides Terminus (code) No Delivery Partial Delivery Delivery cone (co) 35 connected tributary (ct) 65 connected tributary and floodplain (ctfl) 1 escarpment (es) 3 fan (f) 22 fan and connected tributary (fct) 7 fluvial level/terrace (fit) 26 fan and main channel (fmc) 2 gully channel (gc) 301 gully channel/connected tributary (gcct) 1 gully channel/fan (gcf) 29 gully sidewall (gs) 13 lake (Ik) 1 lower slope (Is) 2 main channel (mc) 16 mid slope (ms) 117 road (rd) 26 toe slope (ts) 72 toe slope and main channel (tsmc) 1 upper slope (us) 6 unconnected tributary (ut) 4 Total 287 365 98 a. See Appendix A for definitions of termini Estimation of landslide depth deserves special attention. Ninety-six landslides were measured on the ground [Maynard, 1991] in the Tsitika watershed. The average depth for the initiation and transportation zones was equal to 0.72 m (± 0.05 m; standard error). However, this value includes landslides ranging in size from about 8 m 3 to 30,000 m 3 . A s such it considers small failures that do not appear in aerial photography and it is l ikely to underestimate on average the actual depth o f air photo detected landslides. In fact, API-visible landslides (23 out o f 96) exhibited an average depth of 1.15 m (± 0.13 m). Landslide depth seems to increase slightly with landslide area (Figure 4.7); however, the relation shows too high scatter (R = 0.29) to be conveniently used for predicting landslide volume. Therefore, 1 m was adopted as average slide depth in the calculations o f landslide volumes from air photos. This value is regarded as appropriate for shallow rapid failures according to extensive field experience elsewhere in coastal British Columbia [e.g., GVRD, 1999; Brardinoni and Church, 2004], but likely underestimates the depth of bedrock-related tracks. 57 0.1 -I 1 — I 1 — i 1 — 1 — 1 1 1 — i 1 10 100 1000 10000 100000 Landslide Area (m2) Figure 4.7. Landslide area vs. depth for 96 ground-measured events [Maynard, 1991] in the Tsitika River basin. Note that the scaling exponent becomes 0.65 when adjusted for functional regression [Mark and Church, 1977]. In the Tsitika-Eve inventory the aerial photo year represents the minimum age for each landslide. In fact, some landslides w i l l have occurred several years before the air photo date. Vegetation regrowth on landslide scars in this area can occur fairly rapidly. To have an idea o f the temporal imprecision associated with landslide occurrence the reader should consider that with the exception of the 1961 photoset, taken 16 years before the 1977 set, sequential records are separated approximately by 9-year intervals. Earlier work conducted in coastal British Columbia [e.g., Smith et al., 1983, 1986; Rood, 1984; Brardinoni, 2001] indicates that identification on the air photos o f landslide tracks older than 30 years is unreliable, and rare in the case o f failures older than 40 years. O n the other hand, slides younger than 30 years can be detected reliably on the basis o f surface visibility and/or serai vegetation signature. Applying this reasoning, the API-based inventory represents landslides that occurred between the early 1930's and the summer o f 2003, hence covering a time window o f approximately 70 years. 4.4 Results Landslides are considered in terms o f number o f events and o f associated mobilized volume. Landslide activity w i l l be expressed as landslide density (n/km 2), annual landslide density (n/km 2/yr), denudation (m 3 /km 2 ) , and yield (m 3 /km 2 /yr). Results are presented as follows: 58 first, the spatial characterization of sediment sources is examined in respect o f a series o f landslide and terrain attributes including land use, mass movement type (section 4.4.1), landscape position at initiation (section 4.4.2), and terminus type (section 4.4.3). In section 4.4.5 the effect o f lithology on the spatial distribution of sediment sources is evaluated. Landslide geometry (i.e.,'landslide area and landslide length) is considered in section A . 2 (Appendix A ) . Section 4.4.6 deals with the temporal variability o f landslide activity with the purpose of separating land-use, lithologic, and Quaternary effects. Section 4.4.7 covers the study o f landslide magnitude-frequency relations, also in light o f results obtained in prior sections. In section 4.4.8, the Tstitika-Eve landslide magnitude frequency relation is compared to that o f the Capilano River. Finally, section 4.4.9 analyzes landslide sediment inputs as a function of contributing area within the contexts of geomorphic process domains and of fluvial suspended sediment yield. In all subsections the characterization o f sediment sources is first analysed in pristine settings, then in logged terrain (roads and cutblocks); likewise, landslide distributions are first considered in respect to number o f landslides, then in terms of mobilized volume. In the long-term landscape evolution context, logging may be regarded as surrogate for other types of natural disturbance (e.g., climatic variability) that might have affected sediment dynamics since deglaciation occurred. 4.4.1 Landslide Type In natural terrain, debris slides that develop into debris flows constitute the majority (dsdf = 59.7%) o f mass movement events (Table 4.5); other significant typologies are debris slides (ds = 11.9%), rock-debris-slide-flow sequences (rsdsdf = 8.4%), and debris slides that develop into avalanches (dsda = 5.1%). Translated into terms o f mobilized volumes (Table 4.5), debris slide-flows are still dominant, even though they drop to 39.1%, debris slide contributions become negligible (2%), and the relative importance o f rsdsdf does not change appreciably (8.6%). B y contrast, avalanche-related contributions, negligible in terms of landslide count, stand out and account for 38.2% o f mobilized volume (da = 13.3%; dadf = 7.1%; dsda = 17.8%) thus indicating that avalanches are generally larger than other movement types (Table 4.5). This observation becomes apparent in Figure 4.8, where dsda and rsda plot above the other landslide types (medians are reported instead of means because, as w i l l become clear in section 4.9, landslides are not normally distributed across types). 59 In logged terrain landslide typology is significantly simplified. N o bedrock movements are observed, and only six landslide categories are represented, of which three are dominant (i.e., ds, dsda, dsdf, Table 4.5). Specifically, the number of road-related landslides is almost equally distributed among ds (34%), dsda (28%), and dsdf (30%); in cutblocks debris slides represent over 50% o f all events, followed by dsdf (34.4%) and dsda (10.6%). In terms of landslide volume, contributions are shifted towards dsda and dsdf, at the expense o f debris slides (ds) which account respectively for 26.3% and 14.3% of the total in clearcut and road-related locations. Table 4.5. Descriptive statistics of landslide types across land use categories Landslide Type Number of Landslides Percent Number Total Percent -Volume Landslide Volume (m3) Land Use Volume (m3) Mean Median Std Error Natural da 2 0.4 307990 13.3 153995 153995 na dadf 8 1.6 162841 7.1 20355 15141 6719 df 1 0.2 1500 0.1 na na na ds 61 11.9 45347 2.0 743 432 124 dsda 26 5.1 410558 17.8 15791 11210 3339 dsdf 305 59.7 902002 39.1 2957 1402 276 DSIs 1 0.2 8009 0.3 na na na rfds 1 0.2 2799 0.1 na na na rfrs 6 1.2 16867 0.7 2811 3138 800 rfrsdf 2 0.4 1103 0.0 551 551 na rs 2 0.4 10695 0.5 5147 5147 na rsda 15 2.9 126674 5.5 8445 5673 1776 rsdadf 1 0.2 24824 1.1 na na na rsdf 16 3.1 35675 1.5 2230 1602 373 rsds 15 2.9 46170 2.0 3078 2630 548 rsdsdf 43 8.4 197322 8.6 4589 3433 638 rsra 1 0.2 4453 0.2 na na na u 5 1.0 2482 0.1 496 628 141 total 511 100 2296352 100 4514 1623 431 Clearcut da 2 1.1 3377 1.9 1688 1689 na df 3 1.6 2515 1.4 838 544 401 ds 96 50.8 47452 26.3 494 348 70 dsda 20 10.6 48502 26.9 2425 1645 501 dsdf 65 34.4 76127 42.2 1171 828 136 u 3 1.6 2244 1.2 748 381 457 total 189 100 180224 100 953 496 91 Road da 1 2 3105 2.8 na na na dadf 2 4 5273 4 7 2636 2636 na df 1 2 600 0.5 na na na ds 17 34 16023 14.3 942 406 283 dsda 14 28 46708 41.6 3336 3013 639 dsdf 15 30 40645 36.2 2710 1733 1205 total 50 100 112354 100 2247 1422 431 60 1E5 10000 o > 3 1000 100 Median 25%-75% 10%-90% o Outliers ds dsda dsdf rsda rsdf rsds rsdsdf Figure 4.8. Size distribution o f landslide types in natural (unlogged) terrain. 1E5 10000 > i a 1000 100 Median 25%-75% 10%-90% o Outliers Clearcut Natural Road dsda dsdf ds dsda dsdf ds dsda dsdf Figure 4.9. Landslide size distribution categorized by types across land use classes. Only movement types with comparable number of observations are considered. 61 Box plots in Figure 4.9 consider landslide types that possess a comparable number o f events across land use categories (i.e., n > 10). Landslide styles show consistent patterns throughout land-use types: debris slides plot within the low-magnitude spectrum, debris slide-avalanches tend to be larger, and debris slide-flows exhibit somewhat intermediate sizes. Interestingly, debris slide-avalanches are markedly larger in natural terrain than on logged hillslopes. These emerging trends highlight the importance o f looking at landslides as disturbance cascades [e.g., Nakamura et al, 2000] of composite movement mechanisms controlled by material coherence (e.g., bedrock or debris) and water content (e.g., slide, avalanche, and flow). 4.4.2 Landslide Position at Initiation Sites o f landslide initiation, as interpreted from aerial photographs, have been subdivided into seven classes (Table 4.6 and Figure 4.6). In natural terrain, landslides initiate preferentially at gully-sidewall (gs = 33.9%) and open-slope (os = 35%) locations, with gully headwalls (gh) and escarpments (esc) accounting for respectively 21.3% and 6.7% o f the total number Table 4.6. Descriptive statistics of landslides categorized by land use and initiation position Land Use Landslides Total Percent Volume Landslide Volume (m3) Initiation Position Number Percent Volume (m3) Mean Median Std Error Natural Headwat Basin (ch) 6 1.2 19641 0.9 3274 1936 1562 Gullied Escarp (eg) 1 0.2 195 0.01 na na na Escarpment (esc) 34 6.7 38134 1.7 1122 587 367 Gully Channel (gc) 9 1.8 34667 1.5 3852 3759 683 Gully Headwall (gh) 109 21.3 389622 16.9 3575 2515 348 Gully Sidewall (gs) 173 33.9 266236 11.6 1539 609 165 Open Slope (os) 179 35.1 1547857 67.4 8647 3285 1843 Total 511 100 2296352 100 4494 1623 667 Clearcut Headwat Basin (ch) 0 0 0 0 na na na Gullied Escarp (eg) 14 7.5 9244 5.1 660 550 117 Escarpment (esc) 44 23.4 21390 11.8 486 388 55 Gully Channel (gc) 1 0.1 1353 0.8 na na na Gully Headwall (gh) 6 3.3 8713 4.8 1452 1321.5 298 Gully Sidewall (gs) 57 30.3 29123 16.2 511 251 134 Open Slope (os) 67 35.4 110401 61.3 1648 1239 195 Total 189 100 180224 100 954 496 91 Road Headwat Basin (ch) 0 0 0 0 na na na Gullied Escarp (eg) 0 0 0 0 na na na Escarpment (esc) 11 22.0 6180 5.5 562 404 110 Gully Channel (gc) 0 0 0 0 na na na Gully Headwall (gh) 2 4.0 1573 1.4 786 786 75 Gully Sidewall (gs) 4 8.0 4542 4.0 1135 1074 552 Open Slope (os) 33 66.0 100060 89.1 3032 2207 608 Total 50 100 112354 100 2247 1422 431 62 of observations. The proportions shift towards open-slope dominance (67.4%) when mobilized volumes are considered (Table 4.6); the escarpment contribution becomes negligible (1.7%), that of sidewall sites drops to 11.6%, and the proportion of headwall-related movements decreases slightly (17%). Such discrepancies in proportions between number of events and percent volumes indicate that open-slope movements are largest, followed by gully-headwall failures, and then by escarpment and gully-sidewall landslides. These last two categories have virtually identical median values (i.e., ~ 600 m , see Table 4.6 and Figure 4.10), nearly one order o f magnitude smaller than open slope- (3285 m 3 ) and headwall-related movements (2515 m ). Landslide Fbsition at Initiation esc gh gs os esc gh gs os esc gh gs os Figure 4.10. Landslide size distributions grouped by initiation position across land-use classes In logged terrain, open-slope movements remain fairly prevalent over the other initiation categories; 66 % o f road-related landslides initiate at open-slope locations and contribute 89 % of the total volume. In cutblocks, the number of landslides is equally distributed among escarpment, gully-sidewall, and open-slope locations, which account for 61.3 % o f the volume mobilized. Overall, initiation positions seem to affect landslide size in a similar way 63 across land-use types (Figure 4.10), the only exceptions being road-related gully headwalls and sidewalls, whose values however have likely been affected by the limited number of observations (i.e., n gh = 2; n g s = 4; Table 4.6). 4.4.3 Landslide Terminus and Delivery Landslide terminus/run-out types have been classified into 21 categories and subsequently grouped into three broader sediment-delivery groups (Table 4.4 and Table 4.7). Groups include sediment delivered to (i) unchanneled topography (no delivery to channels), (ii) to gullies (indirect delivery), and (iii) to permanent streams (direct delivery). This partition, even i f accurate in geomorphic principle, l ikely suffers high imprecision due to aerial-photo resolution and density of forest cover and, therefore, represents only a first order approximation of where material is redistributed and/or stored throughout landscape components for assessing sediment dynamics/budgets [e.g., Campbell and Church, 2003]. In pristine terrain, sediment sources deliver material to gully channels preferentially, then ranked by decreasing importance, to main channels, mid- and toe-slopes, tributaries, and colluvial cones (gc > mc > ms > ts > ct > co) (see Appendix A , Table A2) . One open-slope debris avalanche in Claude-Elliotf sub-basin delivered about 300,000 m to a lake, which belongs to the "main channel" category. In clearcuts, the highest volumetric proportion of material is delivered for storage to toe slopes (ts) and, in decreasing order o f importance, to mid slopes (ms), roads (rd, rdms, rdts), and gully channels (gc) (Table A2) . Lastly, within the road-related hierarchy o f landslide termini, connected tributaries (ct) occupy the highest rank, followed by toe slope (ts) and mid slope (ms) locations (Table A4) . The comparison o f sediment delivery groups in natural terrain reveals that gullies receive the highest number o f landslides, followed by unchanneled slopes, and permanent streams, which collect the lowest proportion (Table 4.7). The natural landslide volume is equally distributed among hillslopes (36%), ephemeral/seasonal (31%), and permanent streams (32%). Stream connectivity for cutblock-related landslides appears to decrease both in terms o f landslide count and mobilized volume. In fact, respectively 52% o f movements and 69% of total mobilized volume is deposited in unchanneled topography. Conversely, roads seem to promote strong sediment delivery to channels [e.g., Montgomery, 1994] as 30% of road-related failures (34% o f mobilized volume) are connected to permanent streams. 64 Table 4.7. Sediment delivery to channels Land use Sediment Landslides Total Volume (m3) Percent Landslide Volume (m3) Delivery To Number Percent Volume Mean Median Std Error Natural Permanent Streams 62 12.1 837026 36.5 13500 1262 5177 Gullies Unch. Slopes Total 290 159 511 56.8 31.1 100 715869 743457 2296352 31.2 32.4 100 2469 4676 4494 1113 2837 1623 200 443 667 Clearcut Permanent Streams Gullies Unch. Slopes Total 21 69 99 189 11.1 36.5 52.4 100 14836 40845 124543 180224 8.2 22.7 69.1 100 706 592 1258 954 468 309 768 496 119 119 144 91 Road Permanent Streams 15 30 37659 33.5 2511 626 1289 Gullies Unch. Slopes Total 6 29 50 12 58 100 10111 64587 112357 9.0 57.5 100 1685 2227 2247 2085 1734 1422 499 345 431 1E5 Msdian • 25%-75% 7: 10%-90% o Outliers 10000 8 e Road Clearcut o > J3 1000 100 Natural H PS G H PS G H P S G Figure 4.11. Landslide size distributions categorized by sediment delivery to channels across land-use classes ( H - hillslope, PS = permanent streams, G = gullies). In terms of landslide size, the median of not-connected landslides is consistently largest across land-use categories i f one excludes road-related gully-connected failures (for which only six observations are available). Overall, sediment delivery classification seems to oversimplify the situation, in that it does not provide a good means for separating landslide sizes (note the high degree o f overlapping within natural and road-related delivery categories in Figure 4.11). This finding should not surprise; for example a near-bank slump mobilizing just a few hundred cubic meters would belong to the same class as debris flows scouring an entire valley wal l before hitting a main-trunk channel (order o f 10,000 m 3 and more). 4.4.4 The Significance of Hollow-Related Slope Failures to Sediment Production Hollows [Hack and Goodlett, 1960] are unchanneled topographic depressions (also termed zero-order basins) located immediately upstream o f channel heads, whose surficial expression is often not detectable in the field [Reneau and Dietrich, 1987]. They are regarded as dominant loci o f sediment production across unglaciated mountain ranges and periglacial environments o f the Pacific R i m [e.g., Tsukamoto, 1973; Dunne and Dietrich, 1978; Crozier et al, 1990]. Regionally in coastal British Columbia, hollow-like features are termed "gully headwalls". Remotely-based identification of hollows in the Tsitika and Eve watersheds is hampered by air-photo resolution, topographic texture, and forest cover. A series o f selection criteria has been used to identify hollow-related shallow failures from A P I . Specifically the following landslides have been excluded: (i) landslides initiating as bedrock movements, (ii) landslides initiating at escarpment, gully-sidewall, and gully-channel positions, and (iii) landslides delivering material to unchanneled topography (see Table 4.4; e.g., escarpment faces, mid slopes, and toe slopes). Accordingly, it follows that potentially hollow-related failures are debris-mobilizing landslides (i.e., df, ds, dsdf, dadf) that initiate at gully headwall, open-slope, and headwater-basin locations have a confined or unconfined transportation zone, and deliver material to cones, fans, gullies and stream channels. Applying these criteria, topographic hollows mobilize 18.8 ± 7.4% and 10.1 ± 6.0% of the total volume o f sediment in natural and logged terrain respectively. The uncertainty is due to the use o f liberal selection criteria, and relates to the proportion (none or all o f them) o f open-slope initiation sites that are in fact hollows. 66 Table 4.8. Landslide source-to-sink pathways Initiation Position Volume (m3) Cone Gully M id& Main channel Fan & channel Toe slope & tributary fluvial terrace Gully Total 57,033 235,666 25,420 34,595 46,253 headwall Percent 2.20 9.10 0.98 1.34 1.79 Gully Total 17,491 248,963 5,921 1,117 25,374 sidewall Percent 0.68 9.62 0.23 0.04 0.98 Open slope Total 25,188 136,159 644,096 563,392 345,088 Percent 0.97 5.26 24.88 21.76 13.33 Escarpment Total 0 3,534 6,210 41,292 21,621 Percent 0 0.14 0.24 1.59 0.84 Combining logged and natural terrain, potential hollow landslides mobilize 16.9 ± 8.2% of the total volume. I f al l open-slope failures considered originate from hollows indeed, these failure types would account for 1/4 o f the total, which translates into about 650,000 m . A t best, in the all-open-slope-are-hollow scenario, the significance o f the hollows is important but not dominant in the context of source-to-sink pathways that landslides can take across the terrain o f the Tsitika and Eve basins. In fact, open-slope failures delivering sediment to unchanneled topography (i.e., mid- and toe-slopes) have identical impact (24.9%) in the sediment dynamics o f the study area (cf. Table 4.8). Gully-sidewall failures delivering to gully channels are also relevant (9.6%) to the overall sediment input to channels. 4.4.5 Effects of Lithology on the Spatial Distribution of Sediment Sources In this section the spatial distribution of sediment sources is analyzed in relation to lithology. For this purpose, the same landslide and terrain attributes examined in section 4.5 w i l l be considered. Figure 4.12 shows landslide size distributions stratified by bedrock lithology, but only for landslide types that have comparable numbers o f observations in extrusive (Ext) and intrusive (Int) lithological units (Table 4.9). Quartiles of extrusive and intrusive natural landslides exhibit a great degree o f overlap (Figure 4.12a) suggesting that the range o f natural landslide size in Tsitika-Eve is not affected by lithology. This pattern does, not change significantly or systematically when landslide types are compared (Figure 4.12b) and the number of observations is limited (Table 4.9; Ext-ridadf = 5, Int-rtdadf = 3). B y contrast, clearcut and road-related landslides are generally smaller in intrusive than in extrusive lithology (Figure 4.12a) and a similar lithologic control is observed when considering landslide types in cleared terrain o f different lithology. Specifically, the extrusive debris-slide 67 population plots above (is larger than) the intrusive median value, and 50% of extrusive debris slide-flows plot above the corresponding intrusive population (Table 4.9 and Figure 4.12c). Table 4.9. Descriptive statistics o f landslide types across land use and lithology Land Use Landslide Type Landslides Total Percent Volume Landslide Volume (m3) Lithology Number Percent Volume (m3) Mean Median Std Error Natural da Extrusive 1 0.2 3755 0.2 na na na Intrusive 1 1.1 304236 42.0 na na na dadf Extrusive 5 1.2 82451 5.2 16490 13673 6147 Intrusive 3 3.4 75890 10.5 25297 12956 16655 ds Extrusive 43 10.2 31772 2.0 739 449 143 Intrusive 18 20.2 13574 1.9 754 365 251 dsda Extrusive 18 4.3 309402 19.6 17189 10382 4697 Intrusive 8 9.0 101158 14.0 12645 11814 2615 dsdf Extrusive 260 61.6 746619 47.4 2872 1283 305 Intrusive 45 50.6 149429 20.7 3321 1748 565 rsdsdf Extrusive 36 8.5 168239 10.7 4673 3569 751 Intrusive 7 7.9 29083 4.0 4155 2914 731 total Extrusive 422 100 1575127 100 3733 1518 338 Intrusive 89 100 721225 100 8104 2448 3466 Clearcut ds Extrusive 76 48.7 42245 25.9 556 411 87 Intrusive 20 60.6 5211 31.0 261 165 55 dsda Extrusive 19 12.2 44671 27.3 2351 1634 523 Intrusive 1 3.0 3830 22.8 na na na dsdf Extrusive 55 35.3 70323 43.0 1279 973 156 Intrusive 10 30.3 5808 34.5 581 576 89 total Extrusive 156 100 163402 100 1047 548 105 Intrusive 33 100 16822 100 510 269 121 Road ds Extrusive 14 29.8 15041 13.6 1074 522 335 Intrusive 3 100 983 100 328 354 53 dsda Extrusive 14 29.8 46709 42.3 3336 3013 639 Intrusive 0 0 0 0 na na na dsdf Extrusive 15 31.9 39646 35.9 2643 1339 1209 Intrusive 0 0 0 0 na na na total Extrusive 47 100 110374 100 2348 1512 454 Intrusive 3 100 983 100 328 354 53 Figure 4.12. (Next page) Box-whisker plots o f landslide size distributions comparing lithologies across a) land uses, b) failure types in natural terrain c) failure types in clearcuts d) initiation positions in clearcuts e) initiation positions in natural terrain, and f) land uses and sediment delivery classes. 68 Landslide Volume (m3) 100 RRTT— 1000 CC-esc-Ext -CC-esc-Int -CC-gs-Ext H" K H IH C c W |Q}H CC-os-Ext CC-os-Int H K 10,000 —i—i—mm H 100 1— 1000 NF-Ext -NF-Int -RD-Ext -RD-Int 10,000 CC-Ext - | — | | | fn» c c - l n 4 K Z O H ° H Z K Z T K • H4* •~<4 H o o 100 1000 10,000 100,000 dadf-NF-Ext dadf-NF-Int ds-NF-Ext ds-NF-Int dsda-NF-Ext dsda-NF-Int dsdf-NF-Ext dsdf-NF-Int rsdsdf-NF-Ext rsdsdf-NF-Int C M 1 1 r - L T H i—l l H ° \—LZHH I—I I I F* 8 r z H o -tZLT-H> n i & 100 1000 10,000 ' I 111 j 1 ooo H I I—i I I H K ~ n—i H I I P u n z H o H I I KXP r - a z z H i-cz I 1 1 ~1 |O0305 H I I—I C D I 1 I >-l o H I a •\ I H 69 In terms of mobilized volume, landslide-type hierarchies in natural terrain differ between extrusive (dsdf > dsda > rsdsdf > dadf) and intrusive (da > dsda > dsdf > dadf) lithologies. On extrusive lithology, debris slide-avalanches (dsda) and debris slide-flows (dsdf) together account for about 70% of the mobilized volume, as opposed to 40% in intrusive terrain, where one single debris avalanche contributes 42% o f the total (Table 4.9). It appears important to highlight that bedrock-related failures (i.e., rsdsdf) mobilize a higher proportion o f volume in extrusive lithology (~ 11%) than in intrusive lithology (4%). A t first glance, this observation may indicate the presence o f a lithologic effect promoting higher landslide activity in softer extrusive terrain (see section 4.4.6 for extended analysis of lithologic effects). Table 4.10. Descriptive statistics o f landslides categorized by land use, initiation, and lithology Land Landslide Lithology Landslides Volume Percent Landslide Volume (m3) use position Number Percent (m3) Volume Mean Median Std Er Escarp. Extrusive 21 5.0 31420 2.0 1496 677 578 Intrusive 14 15.7 6909 1.0 494 321 131 Gully Extrusive 9 2.1 34667 2.2 3852 3759 683 Channel Intrusive 0 0 0 0 na na na ural Gully Extrusive 93 22.0 322545 20.5 3468 2478 362 ural Headwall Intrusive 16 18.0 67077 9.3 4192 2591 1112 CO Gully Extrusive 145 34.4 207872 13.2 1434 606 176 z Sidewall Intrusive 28 31.5 58464 8.1 2088 1143 446 Open Extrusive 150 35.5 972437 61.7 6483 3047 855 Slope Intrusive 29 32.6 575421 79.8 19842 4620 10384 Total Extrusive 422 100 1575127 100 3733 1518 338 Intrusive 89 100 721225 100 8104 2448 3466 Escarp. Extrusive 40 25.6 21243 13.0 531 401 61 Intrusive 18 54.5 9391 55.8 522 424 95 Gully Extrusive 6 3.8 8713 5.3 1452 1322 298 —I Headwall Intrusive 0 0 0 0 na na na learci Gully Extrusive 46 29.5 27030 16.5 588 326 163 learci Sidewall Intrusive 11 33.3 2093 12.4 190 156 41 c_> Open Extrusive 63 40.4 105063 . 64.3 1668 1248 202 Slope Intrusive 4 12.1 5338 31.7 1335 678 854 Total Extrusive 156 100 163402 100 1047 548 105 Intrusive 33 100 16822 100 510 269 121 Escarp. Extrusive 8 17.0 5197 4.7 3002 1948 610 Intrusive 3 100 983 100 650 610 139 Gully Extrusive 2 4.3 1573 1.4 328 354 na Headwall Intrusive 0 0 0 na na na T J CO Gully Extrusive 4 8.5 4542 4.1 787 787 75 O DC Sidewall Intrusive 0 0 0 na na na Open Extrusive 33 70.2 99062 89.8 1136 1074 552 Slope Intrusive 0 0 0 na na na Total Extrusive 47 100 110374 100 2348 1512 454 Intrusive 3 100 983 100 328 354 53 70 In cutblocks, differences in landslide-type volume contributions across lithologies are minimal (Table 4.9). Conversely, the 44 (out o f 47) road-related failures that have occurred in extrusive terrain - even considering that intrusive logged terrain is gentler than the extrusive (Figure 4.4) - seems to indicate that the Karmutsen formation is more sensitive to road building than intrusions of the Pacific R i m Complex, as one would expect from all knowledge o f these rocks. Box-whisker plots of landslide size categorized by position at initiation point yield a somewhat complex situation with respect to lithology. Landslides initiating at logged gully-sidewalls and natural escarpment faces are smaller in intrusive than in extrusive lithology; in contrast, natural open-slope failures are larger in intrusive than in extrusive terrain (Table 4.10, and Figures 4.12d-e). In terms o f volumetric contributions, the hierarchy o f natural initiation position (os > gh > gs) is identical across lithologies and open-slope movements dominate. In clearcuts, open slopes are still important, however, volume contributions from Table 4.11. Sediment delivery to channels by lithology Land Sediment Landslides Volume Percent Landslide Volume (m J) use Delivery To Litnoiogy n % (m 3) Volume Mean Median S t d E r Permanent Extrusive 42 10.0 406291 25.8 9674 3202 2594 Streams Intrusive 20 22.5 430735 59.7 2870 391 15205 ural Gullies Extrusive 244 57.8 583865 37.1 2393 958 222 ural Intrusive 46 51.7 132004 18.3 21537 1747 451 ro Unchannel. Extrusive 136 32.2 584972 37.1 4301 2683 459 Slopes Intrusive 23 25.8 158486 22.0 6891 4222 1355 Total Extrusive 422 100 1575127 100 3733 1518 338 Intrusive 89 100 721225 100 8104 2448 3466 Permanent Extrusive 14 9.0 9288 5.7 663 425 158 Streams Intrusive 7 21.2 5548 33.0 793 807 180 Gullies Extrusive 56 35.9 38017 23.3 679 346 144 Clearci Intrusive 13 39.4 2828 16.8 218 169 39 Clearci Unchannel. Extrusive 86 55.1 116097 71.0 1350 824 158 Clearci S lopes Intrusive 13 39.4 8446 50.2 650 317 278 Total Extrusive 156 100 163402 100 1047 548 105 Intrusive 33 100 16822 100 510 269 121 Permanent Extrusive 12 25.5 36676 33.2 3056 738 1584 Streams Intrusive 3 100 983 100 328 354 53 Gullies Extrusive 6 12.8 10111 9.2 1685 2085 499 TJ CO Intrusive 0 0 0 0 na na na o oc Unchannel. Slopes Extrusive Intrusive 29 0 61.7 0 63587 0 57.6 0 2193 na 1643 na 346 na Total Extrusive 47 100 110374 100 2348 1512 454 Intrusive 3 100 983 100 328 354 53 71 escarpments stand out and become prevalent (-56%) in intrusive terrain. Given the small number o f road-related failures i n intrusive terrain, no comment can be made on the inter-lithologic variability o f landslide initiation position for such land use (Table 4.10). In summary, in the study area sediment deliverability seems to vary with lithology. Volume delivered to streams in intrusive lithology is consistently higher than in extrusive terrain across land use categories (Table 4.11). Specifically, in natural intrusive terrain, 60% o f the total volume mobilized reaches permanent channels as opposed to 25% in extrusive terrain, where the remaining 75% is equally redistributed between unchanneled topography and ephemeral streams (gullies). In clearcut terrain, sediment delivered to streams accounts for 21% and 9% of the total volume mobilized respectively in intrusive and extrusive lithology. 4.4.6 Land Use, Lithology, and the Temporal Variability of Landslide Activity In this section landslide activity is analysed through time in terms o f annual landslide density (n/km 2/yr) and associated annual sediment yield (m 3 /km 2 /yr). To this purpose, the lithologic (intrusive and extrusive) and land-use (natural and logged) effects are separated and examined across five sequential photosets (from 1961 to 2003; time window = 1930-2003). In order to isolate lithologic from Quaternary effects, landslides are classified according to the type o f material (bedrock or surficial deposit) mobilized in the initiation zone. Table 4.12. Temporal variability o f annual landslide density for the period 1930-2003 • Annual Landslide Density (n/102km2/yr) Land use Natural Logged Lithology Intrusive Extrusive Intrusive Extrusive Material Debris Bedrock Combined Debris Bedrock Combined Debris Debris 1930-61 1.25 0.18 1.43 2.04 0.58 2.62 0 0 e 1962-77 0.34 0.10 0.44 0.61 0.09 0.70 18.18 15.12 S 1978-87 0.08 0 0.08 0.22 0.10 0.32 5.57 18.33 > 1988-94 0.32 0 0.32 0.12 0.12 0.23 7.52 14.84 1995-03 0 0 0 0.13 0.03 0.16 0.31 7.83 Table 4.13. Temporal variability o f landslide yield for the period 1930-2003 Annual Landslide Yield (m3/km2/yr) Land use Natural Logged Lithology Intrusive Extrusive Intrusive Extrusive Material Debris Bedrock Combined Debris Bedrock Combined Debris Debris 1930-61 95.8 13.1 108.9 67.9 24.2 92.1 0 0 £ 1962-77 29.1 3.4 32.5 31.2 3.3 34.5 56.0 201.3 g 1978-87 10.0 0 10.0 4.7 10.0 14.7 30.2 200.9 ^ 1988-94 65.7 0 65.7 0.4 7.6 8.0 33.6 203.5 1995-03 0 0 0 7.8 0.2 7.9 1.0 153.2 72 Results show that in natural forest, landslide annual density is generally higher in extrusive than in intrusive lithology for both bedrock- and debris-related events (Figure 4.13a and Tables 4.12 and 4.14). In logged terrain landslide density increases between 20 and 82 times regardless o f lithologic characteristics (Figure 4.13b and Tables 4.12 and 4.14). a) 0.025 0.000 b) 0.200 0.150 0.100 0.050 0.000 Natural Forest • bedrock-lntr H debris-lntr bedrock-Extr • debris-Extr WW i d 1930-61 1962-77 1978-87 1988-94 1995-03 • Nf-lntr E3Nf-Extr • Lg-lntr • Lg-Extr 1930-61 1962-77 1978-67 1988-94 1995-03 Year Figure 4.13. Annual landslide density for the period 1930-2003: (a) bedrock and debris movements in natural terrain, and (b) debris movements in natural and logged terrain. N f = natural forest; L g = logged; Intr = Intrusive lithology; Extr = Extrusive lithology. 73 a) 1 0 0 Natural Forest • bedrock-lntr B debris-lntr bedrock-Extr • debris-Extr AZZX 1930-61 1962-77 1978-87 1988-94 1995-03 b) 250 • Nf-lntr E3 Nf-Extr • Lg-lntr • Lg-Extr 1930-61 1962-77 1978-87 1988-94 1995-03 Year Figure 4.14. Landslide sediment yield for the period 1930-2003: (a) bedrock and debris movements in natural terrain, and (b) debris movements in natural and logged terrain. N f = natural forest; L g = logged; Intr = Intrusive lithology; Extr = Extrusive lithology. The picture in terms o f annual sediment yield is more complex (Figure 4.14a-b). In natural terrain, bedrock-related yield is always higher in extrusive than in intrusive litho-types (from 1.84 times to infinitely greater). Conversely, intrusive debris-related yield is virtually identical (1930V1977) or markedly higher (2.17 to 100 times, between 1978 and 1994) to that recorded in extrusive terrain (Figure 4.14a and Tables 4.13 and 4.14). Such results need 74 be examined in relation to the frequency distribution o f slope gradient across lithologies. Given that natural topography is steeper in extrusive (median slope = 0.595) than in intrusive lithologies (median slope = 0.411) (see Figure 4.4a), higher basaltic rock-related landslide activity cannot be attributed to lithologic effects alone. Taking into account the peculiar litho-topographic arrangement (steeper-extrusive terrain vs. gentler-intrusive terrain), intrusive hillslopes appear to be more active in terms of debris mobilization. 0.200 1930-61 1962-77 1978-87 Year 1988-94 1995-03 Figure 4.15. Landslide activity for the period 1930-2003 adjusted for post-logging recovery (see text): (a) annual landslide density, and (b) landslide sediment yield. N f = natural forest; L g = logged; Intr = Intrusive lithology; Extr = Extrusive lithology. 75 Table 4.14. Landslide density and yield ratios for the period 1930-2003 Land use Natural Logged/Natural Lithology Extrusive/Intrusive Intrusive Extrusive Material Debris Bedrock Combined Debris Debris n/km*/yr 1930-1961 1.63 3.23 1.83 na na 1962-1977 1.78 0.92 1.59 53.41 24.93 1978-1987 2.63 . > a 4.00 65.67 82.13 1989-1994 0.36 > 0.72 20.47 71.88 1995-2003 » > > > 28.68 m'VknrrVyr 1930-1961 0.71 1.84 0.85 na na 1962-1977 1.07 0.98 1.06 1.92 6.45 1978-1987 0.46 1.47 3.01 43.09 1989-1994 0.01 » 0.12 0.44 322.58 1995-2003 > > » > 9.30 a. > infinite ratio due to denominator equal to zero, the numerator is equal to or less than 1. b. » ... the numerator is greater than 1. In logged terrain, the effect o f lithology on debris-related yield is unequivocal. Specifically, yield increases between 6 and about 300 times (Table 4.14) as a result o f forest clearing and road building in the Karmutsen formation, whereas it remains at undisturbed, natural levels (logged-natural ratio varies between 0.44 and 3) in the Island Plutonic Complex (Figure 4.14b and Table 4.14). Again, such values need be considered in light o f the different slope distributions (intrusive median = 0.239, extrusive median = 0.339; see Figure 4.4b). Interestingly, sediment yield on cleared slopes underlain by extrusive lithology starts decreasing somewhere between 1987 and 1994, about 20 years after logging began in 1969. To test the hypothesis according to which hillslopes logged 16-25 years earlier do not contribute significantly to the contemporary denudation rate, sediment yields were calculated for the periods 1987-94 and 1994-2003 dividing sediment production only by terrain cleared in the prior 20 years. Figure 4.15a-b shows that logging-related sediment yield is still sustained in 1987-94 and in 1994-2003 (cf , with Figures 4.13b and 4.14b), suggesting that hillslopes harvested more than 20 years earlier had recovered from disturbance, at least in terms of landslide activity. The same temporal response, however, is not quite observed for landslide logging-related activity in intrusive terrain. Reasons for such behaviour w i l l be discussed in section 4.5. This last case provides one more example ( i f any other was needed) of how complex the question of hillslope response to logging may be. 76 4.4.7 Landslide Magnitude-Frequency Relations Many studies have shown that landslide magnitude-frequency ( L M F ) relations have a power-law (fractal) scaling [e.g., Hovius et al, 1997; Hovius and Stark, 2001; Guzzetti et al. 2002; Brardinoni and Church, 2004]. Such behaviour, by analogy with the self-organized criticality of an ideal sand-pile model [Bak et al, 1987, 1988], has been interpreted as resulting from the existence o f critical, metastable, intrinsic thresholds for landsliding [Noever, 1993]. In these studies, however, landslide magnitude-frequency relations are customarily treated with a rather abstract (black box) approach and little reference to bio-geo-climatic factors such as lithology, surficial materials, land use, landscape history, and climate that could affect terrain characteristics and styles o f mass movement, as i f self-organized criticality would overwhelm all other potential controlling factors. Seeking to advance current understanding o f landslide processes at the watershed scale, and hypothesizing that self-organized criticality applies to strictly simple systems (i.e., sand-pile, bean-box) I am going to examine the potential controls that bio-geo-climatic and anthropogenic factors may exert on the fractal behaviour of landslide distributions. Figure 4.16a describes the "black box" landslide magnitude-frequency relation for the Tsitika-Eve study area, that is, without consideration for any anthropogenic and environmental factor. The relation may be approximated by a three-segment power-law expression of the form: F = cAb (4.1) where A is the area o f the slide and, F is the frequency o f landslides occurring in the study area within a set time window o f interest; c and b are constants. Landslide frequency increases monotonically (b - 1.13) for areas smaller than about 500 m 2 , remains about constant (b = -0.01) for areas between 500 m 2 and 4,000 m 2 , and declines monotonically (b = -1.39) for areas larger than 4,000 m 2 (Figure 4.16a). Such scaling relations are matched by similar landslide length (Figure 4.17a) and average width (Figure 4.17b) power-law trends. Stratification of landslides by bedrock geology is instructive (Figure 4.16b). The extrusive L M F relation, owing to the large proportion o f surface occupied (73%) and to the higher landslide densities (compared to intrusive standards), controls the combined L M F relation at low and medium/high landslide sizes (Figure 4.16a). For these same reasons - low landslide density and limited study area: 167 k m 2 - the intrusive relation exhibits a high degree o f 77 scatter, allowing only tentative interpretations. Notwithstanding this limitation, the L M F relation plots at relatively uniform low frequencies across spatial scales, characteristically generating a less pronounced inflection between medium and large-size events, which occurs at approximately 7,000 m ; the intrusive relation appears to dominate the high-magnitude end (Landslide area > 20,000 m 2 ) . 0.01 0.00001 a) o o o o & F = 2.27 A " 1 3 9 O 100 1000 10000 100000 1000000 0.01 0.00001 4 b) Extrusive Intrusive X 100 1000 10000 100000 1000000 Area (m2) Figure 4.16. Landslide magnitude-frequency relations: (a) considering all landslides together; and (b) separating landslide by lithology. Dashed line indicates high-magnitude power-law relation; solid line marks inflection point at approximately 4,000 m 2 . 78 0.01 0.001 4 E cr 0.0001 0.00001 0.01 —1 I ' 1 • ' 1 cr 0.001 0.0001 0.00001 10 100 1000 Landslide length (m) 10000 : b) . 1 , — , — i • • i—,—,— i 1 — i — ' i i 1 1 1 10 100 1000 Average landslide width (m) Figure 4.17. Magnitude-frequency relation of: (a) landslide length; and (b) average landslide width. Solid lines mark thresholds at which relations start declining monotonically. Threshold values are approximately 200 m and 20 m for landslide length and landslide width respectively. In Figure 4.18 are reported landslide distributions categorized by land use. A s stated in section 4.3, landslide frequencies are calculated over five sequential photosets across which natural terrain decreases and logged terrain increases. To account for the dynamic evolution of land cover (statistically speaking one is dealing with five replications over time) and to examine the impact o f land use on landslide activity, the following procedures have been used to calculate landslide densities and volume yield over time: 79 i) For natural landslides two densities were calculated, one considering all the study area pristine (i.e., 1961 photoset, see Table 4.1) which yields a "minimum" natural frequency distribution; the other considering the 2003 photoset when natural area is lowest, which yields a "maximum" frequency distribution (Figure 4.18). Landslide densities are then divided by the evaluated time window, which encompasses a period o f about 72 years (i.e., the 1961-2003 period and the antecedent 30 years). i i) For logging-related landslides I took advantage of the regular spacing between photosets (about 9 year interval, see Table 4.1), also considering that logging began in 1969, and assuming that all landslides in cleared terrain occurred within the 9-year post-logging period. The assumption seems appropriate at the drainage basin scale considering that total reinforcement by live and dead roots is estimated to reach a minimum within 7-11 years after logging [Sidle et al., 1985], even though at a finer scale the "window o f vulnerability" created by forest cutting can last much longer due local patches of poor vegetation recovery [Schmidt et al. 2001]. The application o f this thinking, makes the repeated (five times) landslide densities comparable. Accordingly, the total number of landslides for the period 1930-2003 was divided by the total area logged and further divided by the time window (i.e., 9 years). In order to assess the sensitivity o f this temporal framework, a 20-year time window was also tested, a scale within which prior studies from coastal British Columbia and central Japan [e.g., Brardinoni et al., 2003a; Campbell, 2005; R. Sidle, pers. comm., 2006] have found landslide activity to resemble pre-logging conditions. Results show that the natural landslide distribution changes little after altering the total area of natural terrain (cf., M I N and M A X relations in Figure 4.18). Interestingly, logged and natural relations have similar shapes (i.e., three-segment power-law relations). In fact, within the 200-2,000 m region landslide frequency in logged terrain (9-year window) plots approximately one order of magnitude higher than in natural forest. The comparison between the 9- and 20-year time windows highlights that (i) landslides occur mostly within 9-years after logging; and that (ii) root reinforcement is efficient over limited landslide sizes (i.e., < 6,000 m 2 in Figure 4.18; ~ 360 m X 17 m (length and width obtained from relations in Table A . 5 in Appendix A)) . Note that the 20-yr logged relation plots as a virtual continuation of the natural relation, hence suggesting that such a time interval is sufficient to capture al l logging-related landslides [Sidle et al., 1985]. 80 Even though both high-magnitude relations (natural and logged) show exponents identical to that of the "combined" landslide distribution (b = -1.39), the declining magnitude-frequency Natural (MAX) Natural (MIN) 0.00001 100 1000 10000 100000 1000000 Area (m2) Figure 4.18. L M F relations o f natural and logging-related landslides. Dashed lines indicate high-magnitude power-law relations; solid lines mark inflection points at approximately 2,000 m 2 (logged) and 4,000 m 2 (natural). Landslide frequency of events smaller than about 6,000 m 2 increases considerably due to forest clearing, and the slope of the falling limb does not change with land use. Double and triple lines mark A P I landslide visibility thresholds in recent cutblocks (< 15 yr-old) and in old-growth forest/mature plantations (>50 yr-old) (from Brardinoni et al. [2003b]; see section 4.4.8). trends start at different landslide areas. A kink is observed at about 2,000 m 2 in logged terrain, and at 4,000 m 2 in natural terrain which, after substitutions according to length-area scaling relations (Table A.5) , correspond to length scales equal to 165 m and 235 m respectively. Interestingly, the low-magnitude kinks in recently logged (-200 m 2 ) and natural/old plantation (-650 m ) relations appear to match the visibility thresholds previously identified by Brardinoni et al. [2003b] in the Capilano River basin, therefore revealing the existence o f API-related undersampling dependences [Brardinoni and Church, 2004]. In Figure 4.19 L M F relations are categorized by landslide style. Results are striking, specifically high-magnitude limbs for debris slides, debris slide-flows, and rock movements 81 have the same slope (b = -1.39), identical to that o f the combined landslide distribution. Landslide frequencies start decreasing at 500 m for debris slides, at 4,000 m for rock movements (DSls-rfds-rfrs-rfrsdf-rs-rsda-rsdadf-rsdf-rsds-rsdsdf-rsra), and for debris slide-flows. Similar to the appearance for land-use effects, such behaviours suggest the existence of style-specific critical thresholds for landsliding that depend on water content and stream connectivity (debris slides vs. debris slide-flows), as well as material type (bedrock vs. debris). Note that, since rock movements are not related to logging activities, their reversal at 4000 m 2 cannot be ascribed to effects related to vegetation reinforcement. Movements o f the avalanche group (da-dadf-dsda) which, owing to the limited number o f each single typology, combines a series o f complex mechanisms, do not exhibit a distinctive power-law scaling behaviour; avalanches are important in that they control the combined distribution of largest events (greater than 30,000 m 2 ; Figure 4.19). 0.01 \ \ \ 0.00001 -I 1—1—1— i 1 1—1— i —1 1—1—' i 1 1 1 j—>—i—»_i—i—i i i 1 1 100 1000 10000 100000 1000000 Area (m2) Figure 4.19. L M F relations plotted by movement style. Dashed lines indicate high-magnitude power-law relations; solid lines mark inflection points at approximately 500 m 2 (debris slides), 4,000 m 2 (rock movements and debris slide-flows). Note that the combined magnitude-frequency scaling is the result o f underlying mechanism-specific scaling relations. The plot o f L M F categorized by initiation position (Figure 4.20) is in agreement with the size continuum identified in the box-plot representations. Accordingly, gully-sidewall and 82 escarpment failures dominate the low-magnitude movements, gully-headwall slides occupy intermediate scales, and open-slope failures prevail in the intermediate/high magnitude range. A l l initiation categories, except the escarpment that starts declining at about 1,000 m , appear to decline systematically for sizes between 4,000 m and 5,000 m . Interestingly, the gully-sidewall category contains exactly the escarpment and gully-headwall ranges; an outcome that would intuitively match the organization o f initiation types (e.g., Figure 4.6). O f all initiation classes, only the headwall high-magnitude falling l imb exhibits the same slope as the combined relation (b = -1.39), the other relations are not so well defined. The interpretation of such distributions, hence o f any potential control driven by morphometric properties o f the landscape, remains difficult at this stage. 0.01 T *- . , 0.00001 -I 1—1 1 •—1 * 1 1 1 1 11 '— >x 1 100 1000 10000 100000 1000000 A r e a (m 2) Figure 4.20. L M F relations categorized by position at initiation point. Dashed line indicates high-magmtude power-law relation; solid line marks inflection point at approximately 4000 m 2 . Note that sidewall landslides seem to cover the magnitude-frequency range of escarpment and headwall-related movements (see Figure 4.6). Landslide magnitude-frequency relations categorized by terminus type (Figure 4.21) do not reveal any obvious high-magnitude power-law trend, perhaps with the exception o f gully-connected failures, whose distribution somewhat mirrors the shape of the overall magnitude-frequency curve. Interestingly, the 4000-m 2 kink in the overall (combined) distribution 83 occurs simultaneously for gully-related and mid-slope termini. The high-magnitude range (>25,000 m 2 ) is dominated by stream-connected landslides which, not surprisingly, cover the whole spectrum of magnitudes from near-bank slumps to headwall-related debris slide-flows that travel down a whole valley wal l . Similar to the appearance for initiation positions, the general lack of terminus-specific power-law relations indicates some confounding effects brought about by this type o f categorization (see discussion). Therefore, one does not expect that terminus type categories per se would impart any detectable threshold for landsliding. 0.01 TC « 1 1 0.00001 -I — ' — ' 1 ' i i , • i , . |— r » | 100 1000 10000 100000 1000000 Area (m2) Figure 4.21. L M F relations categorized by terminus/run-out type. Dashed line indicates high-magnitude power-law relation for the combined distribution; solid line marks inflection point at 4000 m 2 . The inflection point o f the combined distribution matches the inflections in gully-connected and mid-slope termini. 4.4.8 Tsi t ika-Eve Versus Capi lano In this section the Tsitika-Eve L M F distribution is compared to that of the Capilano River, located in the North Shore Mountains o f the Vancouver area. The main purpose o f the Capilano landslide inventory was to assess the reliability of API-based studies (see Brardinoni et al. [2003b] for details). The inventory was constructed from interpretation of two photosets (1992 and 1996, nominal scale ranging between 1:12,000 and 1:15,000) coupled with extensive fieldwork conducted in the summers o f 2000 (12.6 k m 2 surveyed) and 2003-04 (9 k m 2 surveyed) covering a total area o f 21.6 k m 2 , approximately 11% o f the total basin area (198 km ). Among other findings, the study by Brardinoni et al. [2003b] yielded an API-visibi l i ty threshold of 650 m (equal to 1,700 m , see Figure 5a in Brardinoni and Church [2004] and Figure 4.22). 1 0.1 0.01 0.001 0.0001 4 0.00001 Visibility threshold -©-• -B— Tsitika-Eve (API) • Capilano (API) • Capilano (API + field) F= 4.2 V II \ •1.58 G> F = 2 . 3 V <•> (V o 1.39 10 100 1000 10000 Volume (m 3) 100000 1000000 Figure 4.22. L M F relations for Capilano and Tsitika-Eve watersheds. Both relations start decreasing monotonically between 4,000 m 3 and 5,000 m 3 (single solid line). Power-law tails are not significantly different in terms o f slope. Double solid line marks the A P visibility threshold established by Brardinoni et al. [2003b] for the Capilano watershed. Even though frequencies are an order o f magnitude apart (Figure 4.22), L M F relations in Capilano and Tsitika-Eve are similar in many respects. They have similar high-magmtude falling limbs (the two expressions are not significantly different at the 95% confidence level), which initiate between 4,000 m 3 and 5,000 m 3 . In addition, the frequency o f intermediate-size landslides tends to remain constant (b ~ 0). Overall, i f one applies to Tsitika-Eve the visibility threshold established in Capilano - a threshold that according to other studies conducted in coastal British Columbia [e.g., Roller son et al, 2001] should not vary dramatically - the shapes of the two distributions are very similar, the main difference being that in Capilano landslides are one order o f magnitude more frequent across sizes. Such observations raise the question o f what causes the one order difference between the landslide specific frequencies o f the two study areas. In fact, logging disturbance has affected comparable proportions o f the two study basins: 21.7% in Capilano and 25.3% in Tsitika-Eve 85 Table 4.15. Drainage density and descriptive statistics of slope gradient Basin Drainage Slope Density a Median Mean Std. Dev. No. of obs. Range Skewness Tsitika-Eve 2.48 0.481 0.538 0.363 979382 6.840 0.473 Capilano 3.86 0.561 0.600 0.370 308140 5.640 0.313 a. Drainage density values were obtained from TRIM vector digital data (1:20,000). 0.12 ^ — 0 200 400 600 800 1000 1200 1400 1600 1800 Elevat ion (m) 0.14 T — — , Slope (m/m) Figure 4.23. Percent frequency distributions in Capilano and Tsitika-Eve drainage basins o f (a) elevation, and (b) slope gradient. (Table 4.1); topographic relief is also comparable (Figure 4.23a). However, the Capilano River is relatively steeper and more dissected (rugged) than the Tsitika-Eve system. Specifically, slopes steeper than 0.5 occupy a larger portion o f Capilano (median slope = 0.56) than Tsitika-Eve (median slope = 0.48; see Figure 4.23b and Table 4.15). In addition, 86 Capilano drainage density (13.86 km/km 2 ) is 1.6 times higher than in Tsitika-Eve (2.48 km/km 2 ) (see Table 4.15). Completion of the surficial material mapping for Tsitika-Eve is scheduled for early 2006, so this type o f information is still missing. On the basis o f currently available data (i.e., higher landslide frequency, median slope, and drainage density in Capilano), one would expect to observe in Capilano a higher proportion o f steep terrain (e.g., > 30°) covered by glacial t i l l than in Tsitika-Eve. Reasons to support such a hypothesis are inferred from previous work conducted in Capilano [Brardinoni et al, 2003b] documenting order o f magnitude discrepancies in sub-basin landslide activity owing to differences in drainage density, and distributions of slope frequency and surficial materials (see section 4.5 for discussion). 4.4.9 Landslide-Driven Dynamics across Process Domains and Sediment Yield This section considers landslide sediment transfer in the context of the geomorphic process domains previously delineated in the Capilano and Tsitika river basins (chapter 3), and the specific fluvial suspended sediment yield for drainage basins o f British Columbia [Church and Slaymaker, 1989; Church etal, 1989; 1999; Church, 2002]. j Figure 4.24. Examples showing the methodology used to estimate landslide sediment transfer within and between geomorphic process domains. In one case (larger scar), the landslide transfers material from a colluvial to a fluvial channel; in the other, material remains in storage within the source colluvial domain. Dashed line delimits process domain boundaries. Gray dots mark landslide initiation points, black dots mark end of transportation zone/beginning o f deposition zone. 87 Landslide sediment transfer within and between process domains (as outlined in Figure 3.4) is analysed as follows: first, slope-area plots are constructed for landslide initiation and landslide deposition points (Figures 4.25a and 4.25b); second, the assumption o f full delivery is made between the initiation arid the deposition (end o f transportation) points o f a given landslide (see Figure 4.24). This assumption implies that within each process domain total sediment input and output are approximated respectively by the total volumes associated with landslide deposition and initiation points; and the landslide driven sediment budget is closed. Finally, gross sediment aggradation or degradation within each process domain is estimated by subtracting total landslide output (initiation) from total sediment input (deposition) (see Tables 4.16 and 4.17). In this computation the respective proportions o f colluvial material deposited and/or subsequently reworked by stream flow are unknown. Figure 4.25. Slope-area plots for the API-based landslide inventory of the Tsitika and Eve Paver basins: (a) initiation points; and (b) end o f transportation /beginning o f deposition zones. Slope and drainage area values are extracted from a 25-meter D E M . Recall that DEM-based slopes are underestimated in comparison to field-measured values in steep actively eroded surfaces (hillslopes and source colluvial channels) and overestimated in depositional environments (sink colluvial and fluvial channels) (cf, Figure 3.7). E 1 i o (0 0.01 0.001 Deposi t ion points Source Colluvial Channels 0.001 Area (km2) 1000 88 The distributions of landslide initiation (Figure 4.25a) and deposition (Figure 4.25b) points in the slope-area space match reasonably well the definitions of geomorphic process domains provided in chapter 3, that is, virtually no slides initiate in fluvial and sink colluvial channels, while deposition becomes significant in these process domains. In quantitative terms (Table 4.16), during the seventy years examined planar hillslopes and source colluvial channels are by far the most active domains in the landscape. Respectively, 99% and 81% of the overall landslide volume is detached and redeposited in such domains. A s a result, planar slopes and source colluvial channels are currently degrading, whereas significant aggradation is observed in unchannelled valleys, sink colluvial channels, and in fluvial reaches. Table 4.16. Gross volumes eroded and deposited by landslides across process domains Process Domain Erosion Deposition Storage m % m % m % Hillslope 1,322,903 51.1 1,071,106 41.4 -251,797 -9.7 Unchannelled Valley 24,180 0.9 167,181 6.5 143,001 5.5 Source Colluvial 1,237,883 47.8 1,025,941 39.6 -211,942 -8.2 Sink Colluvial 520 0 153,414 5.9 152,894 5.9 Fluvial (Hanging + Distal) 3,444 0.1 171,288 6.6 167,844 6.5 Total 2,588,930 100 2,588,930 100 0 0 Categorization of the Tsitika-Eve landslide dataset by type of material mobilised (Figure 4.26 and Table 4.17) reveals interesting insights. Bedrock landslides, which only occur in natural terrain (see section 4.4.1), produce a distinct initiation cluster in the slope-area space (Figure 4.26a); they initiate exclusively in hillslope and source colluvial domains, at gradients higher than 0.5 and drainage areas smaller than 0.05 k m 2 . Similarly, the mobility o f bedrock landslides across domains appears to be significantly limited in comparison to debris-mobilizing events (Figure 4.26b). These outcomes, in conjunction with elevation-area plots (see Figure A . 2 in Appendix A ) identify a bedrock-landslide domain located on the higher slopes of the landscape, chiefly above the tree line (cf., Figure 2.5). In quantitative terms (Table 4.17), bedrock landslides contribute greatly to the degradation o f planar slopes ( - 24.4%), do not interact with unchanneled valleys, and deposit excess material in source colluvial channels; in contrast, debris-mobilizing landslides promote aggradation in unchannelled valleys and significant degradation in source colluvial channels (-12.2%). One 89 Figure 4.26. Slope-area plots for landslides in natural terrain classified in Tsitika-Eve basins by type of material mobilized: (a) initiation points; and (b) end of transportation/beginning of deposition zones. Slope-area plots for debris mobilizing landslides in logged terrain: (c) initiation points; and (d) end of transportation^eginning o f deposition zones. 90 could speculate that the excess volume of material delivered to source colluvial channels by bedrock landslides is transferred further downstream via debris slides and flows (13.7%). Table 4.17. Percent volumes eroded (negative) and deposited (positive) by landslides Process Domain Natural Clearcut Road L o g g e d 8 Debris Bedrock Combined Debris Hillslope -7.7 -24.4 -11.1 -9.2 18.1 1.2 Unchannelled Valleys 6.3 0 5.0 11.6 6.5 9.6 Source Colluvial -12.2 13.7 -6.9 -7.0 -36.7 -18.4 Sink Colluvial 6.7 5.2 6.4 1.4 3.2 2.1 Fluvial (Hanging + Distal) 6.9 5.5 6.6 3.3 8.9 5.4 a. Logged = Clearcut + Road Classification of landslides by land use shows that events initiating in harvested terrain occupy the lower portion o f the natural slope-area envelope (Figure 4.26c). Logging effects are more apparent in depositional terms, where a significantly greater number o f landslides deliver mass to unchannelled valleys (Figure 4.26d). Specifically, in comparison to natural terrain logging promotes higher degradation in source channels (-18.4%), as well as higher storage on unchannelled valleys and planar slopes (Table 4.17). Overall, the combined logging effects (Table 4.17) agree with findings outlined in section 4.4.3, according to which such activities tend to favour delivery to unchannelled topography. While clearcut failures impart the same degradation/aggradation trends observed in natural terrain, road-related slides accentuate erosion on planar slopes and deposition in source colluvial channels. Landslide specific sediment yield (Y , Figure 4.27) is expressed in Mg/km 2 /day ( M g = mega grams = 10 6 g) so to make it comparable to previous data of fluvial suspended sediment yield (i.e., Figure 4.28). To calculate yield, contributing area was first calculated at the end o f the transportation zone o f each landslide, to associate each landslide volume with the landscape scale at which it is released; then, landslide mobilized volume was summed across logarithmically equally spaced contributing area bins (10 bins per order o f magnitude). Finally, mass values were obtained after multiplying landslide mobilized volume (m 3) by a bulk density o f 2,000 kg/m 3 . This value seems appropriate considering that shallow rapid failures in the area mobilize preferentially glacial t i l l , for which bulk density values between 1,850 and 2,150 kg/m 3 are typically reported [Bell, 1981; Williams, 1982]. The same bulk density was adopted by Campbell and Church [2003] for landslides located on the upper slopes o f Lynn Creek, a montane stream adjacent to the Capilano River. 91 0.1 a ) 0.01 4 I 0.001 0.0001 0.00001 100 b) 90 80 4 j • Landslide Input -• o Landslide Cumulative Input • ; j » ^ ^ • \ • oc^ T • • i • i • ^^NL • I s • \ C • OO • • j • f • • ceo ! -hillslope 1 | 1 I I I I I I L. hillslope & source colluvial source colluvial; & hanging fluvial ; sink colluvial > & hanging & distal fluvial ; — i i i — 1 1 1 1 1 1 — i — i — 1 1 1 distal fluvial TJ > 9 a. > a E o 70 60 50 40 30 20 10 0 0.0001 hillslope hillslope & source colluvial source colluvial & hanging fluvial distal fluvial sink colluvial & hanging & distal fluvial -Cumulative % % S 0.1 I 2 3 c % < 01 3 i t a >< Q. ID f 8 s o cr N I 0.01 20 18 16 14 12 10 8 6 4 2 0 -2 a> | -< Q. 0.001 10 100 1000 0.01 0.1 1 Contributing Area (km2) Figure 4.27. (a) Specific landslide sediment yield as a function of contributing area for the Tsitika-Eve landslide inventory. Sol id lines enclose a potential yield-area trend. Dashed lines separate area-based geomorphic process domains identified in Capilano and Tsitika watersheds (see chapter 3 for details); (b) Landslide-related sediment yield and cumulative sediment yield expressed as percent o f the total flux. 92 The landslide yield-drainage area scaling exhibits high scatter (Figure 4.27a), which testifies to the stochastic nature of mass wasting processes at the drainage basin scale [e.g., Benda and Dunne, 1997; Benda et al, 1998]. Nevertheless, the pattern of the landslide yield envelope can be explained by the area-based geomorphic process domains previously delineated. Accordingly, yield is maximum in unchanneled topography (0.1 < Y < 0.01), decreases at the scale o f source colluvial channels (0.02 < Y < 0:005), and does not change appreciably (0.02 < Y < 0.002) for drainage areas where source colluvial and hanging fluvial domains overlap. Landslide yield starts declining consistently beyond areas larger than 0.6 k m 2 , where fluvial environments (hanging and distal) are still coupled i n places to colluvial processes (sink colluvial domain). Finally, along relict glacial troughs, which are virtually decoupled from colluvial inputs, landslide yield plots below 0.001 M g / k m /day. A s one would expect, landslide-driven cumulative yield decreases systematically down-stream (Figure 4.27a-b); particularly sharp are the kinks occurring at 0.002 k m 2 (hillslope-source colluvial transition) and 0.6 k m (source-sink colluvial transition), this last being the scale of trough initiation where colluvial inputs become increasingly decoupled. In figure 4.27b, landslide yield is expressed as percentage o f the total daily flux mobilized in Tsitika-Eve watershed system. This representation is useful in that it allows quantifying the degree o f sediment redistribution at different landscape scales. Remarkably, 40% o f the total landslide yield is released into the system at a contributing area of about 2000 m 2 . This figure increases steadily downstream, so that at the scale o f hanging valley floors (~ 0.02 km 2 ) it already exceeds 60%, and at 1 km reaches about 90%. U p to this landscape scale, material is delivered (i) to talus slopes and hanging valleys, where it remains decoupled and continuous aggradation occurs; and (ii) to steep low-order streams, where it is then reworked via debris flows. Only beyond 20-50 km does fluvial remobilization appear to become effective (in accordance with colluvial and alluvial scales detailed in chapter 3). Abrupt transitions between landscape scales and the corresponding glacial relict macro-forms (hence process domains) are clearly visible in the non-cumulative percent yield (Figure 4.27b). From the landscape evolution standpoint figure 4.28 holds important implications. A t a drainage area comprised between 5 and 50 k m 2 landslide yield (0.005 < Y < 0.0001) plots below the fluvial suspended sediment yield, which in turn varies between 0.05 and 0.1 M g / k m /day. Despite the potential underestimation of landslide yield due to under-sampling, 93 error that may be estimated between 10% and 20% [Brardinoni et al, 2003b], at this landscape scale the fluvial processes ( B C fluvial main trend) appear to re-mobilize more material than what is currently supplied by colluvial processes (Tsitika-Eve trend, Figure 4.28). It follows that drainage basin sediment dynamics are not in steady-state conditions and degradation occurs. This study, by showing that glacial and paraglacial disturbances overwhelm drainage basin sediment dynamics at scales smaller than 10 k m 2 complements the work by Church and Slaymaker [1989]. 10 •a 2 0.1 i > 0.01 •* c • £ co u co 0.001 0.0001 (total Tsitika-Eve Landslide Tmnd 0.00001 - I — ' ' ' — — ' — ' " i — — — — ' i — — "'i 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 1000000 Contributing Area (km2) Figure 4.28 Landslide and fluvial specific sediment yield as functions o f drainage area. A t the landscape scale where fluvial and colluvial data coexist, landslide sediment yield in the Tsitika-Eve system plots systematically below the regional fluvial suspended trend for British Columbia [shaded trend; from Church and Slaymaker, 1989]. 4.5 Discussion Spatial Characterization of Landslides In natural forested terrain of the Tsitika-Eve system, debris slide-flows (dsdf) are by far the most frequent mechanisms of sediment production, followed by debris slides (ds) and by rock slides that develop into debris flows (rsdsdf), these three categories account for about 80% o f the total number o f events. In terms o f mobilized volume, even though debris slide-flows remain dominant; combined with ds, and rsdsdf, they constitute less than 50% o f the total. Instead, movements o f the avalanche type become increasingly important, accounting for about 44%. It follows that avalanche movements are generally larger but less frequent (high-magnitude low-frequency) than the rest, and that debris slides and debris slide-flows dominate the low-magnitude high-frequency spectrum. In particular, a continuum is observed across landslide types in respect to median size: ds < dsdf < rsdf < rsdsdf < rsda < dsda < da. These emerging relations testify o f the importance o f considering colluvial processes as disturbance cascades [e.g., Nakamura et al, 2000] of composite movement mechanisms across the landscape, which are regulated by material coherence (bedrock or debris) and water content (slide, avalanche, and flow). Landslides preferentially initiate at open-slope, gully sidewall, and headwall locations; open-slope failures mobilizing about 2/3 o f the total volume. In this context, open-slope and gully headwall categories are high-magnitude but also high-frequency events; the low-magnitude range being occupied by gully sidewall and escarpment-related events (Figure 4.6). Gul ly channels receive the largest number o f landslides, followed by unchanneled slopes and river channels; corresponding volumes of material detached and transported by colluvial processes, however, are distributed in equal proportions among the three categories. Apparently, logging disturbance alters the significance o f various source-to-sink pathways, and the type o f colluvial mechanisms involved in the sediment cascade. Accordingly, the variety o f landslide types is drastically reduced to three categories (i.e., ds, dsda, and dsdf); in part, owing to the lack o f rock mobilizing slides, as forest practices tend to avoid rocky and highly dissected sites. In agreement with prior studies [e.g., Sidle et al, 1985; Rood, 1990; Brardinoni et al, 2003a], logging-related movements are markedly smaller than those in natural forest. Reasons are likely related to (i) the position and size of cutblocks that limit landslide magnitude; and (ii) that with root decay smaller masses have a sufficient gravitational component to fail. Similar to natural forests, landslides show consistent patterns throughout land-use categories, that is, debris slides are smallest, debris slide-avalanches tend to be largest, and debris slide-flows plot at intermediate magnitudes. Logging disturbance also simplifies the diversity o f initiation sites. Specifically, open-slope landslides become more frequent, while events at gully headwalls disappear (likely due to the recommendation to avoid timber harvesting at such locations [e.g., BC Ministry of Forests, 1995]) and are replaced by initiations at escarpment faces. Not surprisingly, logging-related 95 changes in landslide style and initiation position are transmitted downslope/stream. It follows that the distribution o f landslide terminus/run-out types, and so basin-wide sediment delivery ratios, become profoundly altered. In general, the bulk of logging-related sediment load (volume) is delivered in increasingly greater proportions to unchanneled topography. This is particularly true for in-cutblock slides, which stop preferentially at toe slope and mid slope locations, and to a lesser extent for road-related slides. In volumetric terms, landslides that initiated in clearcuts and in proximity o f roads deliver to streams 32% and 25% volume less than i f they had occurred in natural forest. The road network, and the system o f culverts and ditches that comes with it, does ensure a relatively stronger geomorphic coupling [e.g., Montgomery, 1994]. Overall, in logged terrain o f the Tsitika and Eve River basins, gullies lose their prominent role o f temporary storage sites, where fine sediment is washed out by fluvial processes and coarse material is removed periodically by debris flows. In fact, colluvial processes remain for the most part disconnected from the drainage network, and so landslide deposits are placed for longer-term storage on unchanneled hillsides. The combined analysis of sediment sources, terminus types, and sediment delivery to streams, allows an estimation of the role o f bedrock hollows in the context o f glaciated mountain sediment dynamics. Even though bedrock hollows may have no surface expression and may occur on planar or convex topographies [Reneau and Dietrich, 1987; Crozier et al, 1990], source-to-sink pathways, as classified from A P I , indicate that hollows are important but not dominant loci o f sediment production. Specifically, hollow-related landslides, account for about 19% and 10% of the total volume mobilized in natural and logged terrain. In this respect, those open-slope failures that deliver material to unchanneled topography appear to be more prevalent (~25% of total volume). The Role of Bedrock Geology on Landslide Spatial Organization In old-growth forest, bedrock geology seems to affect the hierarchy of movement types in a subtle, indirect but significant way. O n one hand the range of natural landslide size does not suggest any lithologic dependence, and movements of the avalanche type (i.e., da, dsda, dadf) produce the bulk of sediment flux regardless o f bedrock nature; on the other, some indication of geology control is observed, as two distinct landslide types are responsible for most o f sediment transfer within each bedrock typology; debris slide-flows (dsdf) dominate in extrusive terrain, and debris avalanches (da) prevail in intrusive terrain (observation also 96 made by Sterling [1997]). Even more supportive o f expectations linked to bedrock relative credibility: rock-related failures (i.e., rsdsdf) in extrusive lithology mobilize a proportion of volume which is as much as three times that displaced in intrusive lithology. Last but not least, data collected in the Tsitika and Eve River basins indicate that bedrock geology does not affect the distribution o f landslide initiation positions. In terms o f interactions between forest operations and bedrock type, logging seems to amplify lithologic effects in respect to landslide size and sensitivity to road building. Accordingly, slope failures are significantly smaller in intrusive than in extrusive terrain, and road-related failures are extremely rare events in the former. In addition, the nature o f litho-types appears to influence sediment volumes delivered to streams, which in proportion are much higher in intrusive (21-60%) than in extrusive terrain (9-25%) across land use types. Reasons may be due to the higher permeability o f soils developed oh intrusive than on extrusive terrain [e.g., Sterling, 1997], or to peculiar bedrock-surficial material arrangements. Landslide Density and Volume Yield The analysis of annual landslide density and sediment yield across sequential photosets ensures better separation, hence understanding, of the effects associated with spatial variability in bedrock geology, surficial materials, and land-use. Indications noted in earlier sections are confirmed, and additional insights are gained. It turns out that looking exclusively at landslide density can be misleading; for example, annual landslide density i n natural forest supports the "lithology-control" hypothesis; accordingly, landslide density is systematically highest in terrain underlain by extrusive lithology. However, examination of annual sediment yield provides a critical and more geomorphically relevant insight. Specifically, while bedrock-related yield is consistently highest in extrusive litho-types, debris-related yield from intrusive terrain is either identical to, or higher than (2.17 to 100 times) the corresponding extrusive figure. Such inverse dependence is even more apparent i f one considers that natural topography is steeper in extrusive than in intrusive lithologies. This outcome corroborates the hypothesis according to which the Quaternary signature, by means o f type and distribution o f surficial materials (e.g., glacial t i l l , colluvium, glacio-lacustrine), overwhelms the effects of different bedrock lithologies. A n explanation that agrees with field observations made in mountainous terrain on Northern Vancouver Island, according to which glacial t i l l blankets are often more 97 continuous on the smoother and uniform slopes underlain by granitic bedrock. On the Karmutsen (extrusive) terrain the steeper average slopes usually occur on cliff-and-bench morphology where high, steep rock cliffs have little, if any, surficial cover and the till blankets are mainly confined to the benches. Therefore, the distribution of surficial materials combined with slope morphology, which is partially determined by the type of bedrock, is likely an important factor in landslide occurrence and sedimentation behavior [D. Maynard and T. Rollerson, pers. comm., 2005]. Incidentally, this interpretation provides a reasonable explanation for the different degrees of connectivity to streams associated with each litho-type, as previously noted. In logged terrain, landslide density, which includes only debris-mobilizing events since rocky slopes are not harvested, increases between 1 and 2 orders of magnitude. Again, landslide density alone does not indicate any obvious lithologic control, which instead becomes unequivocal when sediment yield is examined. Through the years, the increase of landslide yield in Karmutsen formation is about one order of magnitude higher than that observed in the Island Plutonic Complex. In terms of geo-biological temporal dynamics, the analysis reveals that logging-related sediment yield in extrusive terrain tends to reset at undisturbed rates after about twenty years since harvesting operations ceased. Such a time-window for hillslope recovery matches results from previous studies conducted in coastal British Columbia [Brardinoni et al, 2003a; Campbell, 2005] and in Japan [R. Sidle, pers. comm., 2006], and agrees with experimental data on the recovery of root strength [e.g., Sidle et al, 1985; Schmidt et al., 2001]. Interestingly, the same response to logging is not observed in intrusive terrain. This might have to do with (i) the fact that the intrusive terrain logged between 1987 and 2003 (i.e., in Figure 4.5 note the flat topography Akan Creek, logged between 1995 and 1997) was less sensitive (i.e., less steep) than those cleared prior to 1987; and (ii) the consistently low logging-related yields observed in intrusive terrain, so that actual changes are more difficult to detect from API. Landslide Geometry Landslide length is positively allometric with respect to landslide area (Figure A . l in Appendix A). The relation is positive for all land-use types, and for all lithology-land use combinations. In this context, logging-related landslides on intrusive terrain constitute the 98 exception; there the exponent in the power-law relation is not significantly different from 0.5. In other words, in intrusive lithology logging-related landslides are self-similar, natural landslides are not, and tend to become relatively more elongated as they grow larger (travel farther). This is an important finding, considering that the vast majority of the Coast Mountains in British Columbia is underlain by granitic (intrusive) lithology, and holds significance from the standpoint of assessing long-term impacts of anthropogenic disturbance in landscape evolution modelling. The landslide length-area relation with respect to initiation position does yield some statistically significant insights. While the intercept is not significantly different among position types, the exponents in gully-sidewall and gully-headwall relations are significantly higher than in open-slope landslides, and therefore they are more elongated. This behaviour may be explained by the recurrent nature of gully-related failures, which initiate as unconfined and become confined during transport along gully channels, where water content increases (hence potentially longer run-out zones) and width is limited by channel size; conversely, open-slope landslides are episodic, unconfined events, whose width is controlled by bedrock-structural and surficial material properties (hence potentially wider events). In natural terrain, the geometry of rock slides and rock falls is within self-similar boundary conditions; all other landslide types, which are increasingly elongated as they become larger, have almost identical exponents (-0.8), hence describe a continuum in the length-area space (Figure A.lg, appendix A). In logged terrain, all typologies display positive allometry. Specifically, debris slide geometry diverges (is less elongated) from that of debris slide-flows at average hillslope lengths equal to 80-90 m (Figure A.If), which is interpreted as an indicative minimum threshold length for coupling between diffusive- (unconfined) and channelized-colluvial (debris flows) processes to occur (see section 4.4.7). Landslide Magnitude-Frequency Relations In consideration of the API-related landslide visibility thresholds [Brardinoni et al, 2003b; Figure 4.19], the combined LMF shape in the Tsitika-Eve area is substantially identical to that in the Capilano River [Brardinoni and Church, 2004] (Figure 4.23). Both LMF relations may be approximated by two power-law segments, a low-magnitude high-frequency domain, characterized by an exponent not different from zero, and a high-magnitude low-frequency domain with negative exponent. The transition between the two relations occurs at 99 approximately 4,000 m 2 . Notwithstanding such similarities, landslide frequencies are systematically higher in Capilano, by one order of magnitude. This could be explained by considering that in Capilano the slope frequency distribution is shifted to steeper gradients, and that drainage density is 1.5 times higher than in Tistika-Eve. Unfortunately, owing to insufficient information on the spatial distribution o f surficial materials in Tsitika-Eve, where mapping is still under way, it is not possible to provide a completely quantitative comparison between these two study areas. In this context, prior research conducted in Capilano [Brardinoni et al., 2003b] proved that landslide activity in Sisters Creek (Dd = 3.6 km/km 2 ) was one order of magnitude higher than in East Cap Creek (Dd = 2.2 km/km 2 ) as a result o f higher drainage density, relatively steeper slopes, and a greater proportion o f class-5 t i l l -mantled terrain polygons. Inter-basin comparison (i.e., Capilano vs. Tsitika-Eve) o f surficial material distributions relative to terrain steepness w i l l be the subject o f further study as soon as such data become available. The writer expects the spatial distribution of surficial materials to exert a certain control on maximum landslide length relatively to hillslope length (cf., F igure 2.5), by affecting the contributing area at which debris-movements can initiate. Wi th the available information on bedrock geology, land use, landslide type, and initiation and terminus positions, a number of insights have been gained on L M F controls. Forest practices (i.e., 20-year time window) appear to shorten the low-magnitude, "constant-frequency" segment, which is also shifted to significantly higher (up to one order of magnitude) frequencies. In fact, the inflection occurs at about 2,000 m 2 (-165 m x 12 m); as opposed to 4,000 m 2 (-235 m x 17 m) in natural forest, with total root reinforcement progressively losing importance up to 6,000 m 2 (~ 360 m x 17 m), beyond which its effect becomes null. L ike ly , landslide magnitude upper limit (i.e., 20,000 m 2 ) is imposed by cut-block size and by its position on a given hillslope. Because o f the landscape structure o f coastal British Columbia [Ryder, 1981; Figure 2.5], where upper slopes are generally rocky, steeper than 70% hence unstable and unproductive, cutblocks are located far away from drainage divides. Such results provide an indirect measure o f root strength contribution to hillslope stability and testify to the existence o f vegetation-specific thresholds affecting both landslide frequency and length scale (hence size). The plotting o f L M F relations stratified by landslide type clarifies a number o f aspects, otherwise not discernible. The combined L M F relation appears to be the result of underlying 100 style-specific scaling relations, whose falling l imb has a slope that does not change appreciably with landslide style. In particular, debris slide-flow events determine the overall shape o f the combined distribution; debris slides and avalanches exert moderate influence respectively in the low- and high-magnitude sub-spectra. Inflection or reversal points occur at different landslide size (area) for different movement types: at 500 m 2 for debris slides, at 4,000 m 2 for rock-mobilizing slides and debris slide-flows. B y analogy to the observed land-use effects, these parallel and declining trends are interpreted as expression of specific threshold length scales for landsliding that are regulated by water content (drainage area), and so stream connectivity, as well as by material type (bedrock vs. debris). In this context, particularly instructive is the case o f debris slides (ds) and debris slide-flows (dsdf), where the ds distribution is centred at areas one order o f magnitude smaller than dsdf. This gap likely reflects the distribution o f hillslope lengths that a typical debris slide has to travel in order to intersect a high energy, low-order stream before transforming itself into a debris flow. The same critical length for rock slide/falls is highlighted by the rsdsdf distribution; specifically, the high-magnitude limb of the rock-related L M F , which encompasses a range o f mechanisms (i.e., DSls-rfds-rfrs-rfrsdf-rs-rsda-rsdadf-rsdf-rsds-rsdsdf-rsra), is apparently controlled by rsdsdf (Figure 4.20). When landslide frequencies are calculated within uniform lithologies it becomes clear that the extrusive relation is almost identical to the overall landslide distribution. B y contrast, the intrusive distribution exhibits a rather scattered power-law trend, likely due to the limited portion o f intrusive terrain (167.6 km 2 ) that covers a relatively gentler portion o f the whole study area (612.1 km 2 ) . The hypothesis according to which bedrock geology would affect the shape of L M F relations cannot be dismissed. In fact, intrusive landslides seem to play a prominent role in the high-magnitude spectrum and, although at a purely speculative level, a declining trend in the relation may be identified for landslides larger than 7,000 m 2 (Figure 4.17b). Such a trend is less steep than that described by extrusive landslides. L M F categorized by initiation position highlight interesting scaling relations for understanding and connecting the geometric controls of gully-headwall, gully-sidewall, and escarpment movements. Specifically, in the L M F plot the sidewall domain contains escarpments, headwalls and the transition zone (500 m and 2,000 m ) between these two typologies. B y inference two sidewall populations can be discriminated: i) debris slides that 101 2 2 impact steep stream channels and develop into debris flows (from 500 m to 20,000 m ), from ii) debris slides that do not develop into debris flows either because they do not reach a channel or because the impact angle does not allow propagation o f disturbance [e.g., Benda and Cundy, 1990], from 100 m 2 to about 2,000 m 2 ; cf. Figure 4.6b). In general, initiation-specific relations have higher scatter than those associated with land use and landslide type categorizations. This makes the interpretation of the results rather difficult, including the identification of landslide thresholds that are controlled by hillslope geometry. The stratification by terminus type highlights the importance o f gully channels as temporary storage sites in mountain basins; accordingly, the distribution of gully-connected sediment sources appears to control large portions o f the entire size spectrum, except the high end o f the scale, which is regulated by stream-connected events. Every terminus type covers three of the four orders o f magnitude, and likely contains events as small as near-bank slumps up to "slope clearing landslides" [Densmore et al, 1997]. Overall, terminus-specific distributions don't seem to indicate any obvious high-magnitude power-law trend, suggesting that terminus variability does not affect significantly the shape of the combined L M F distribution. Landslide-Driven Dynamics across Process Domains and Landslide Sediment Yield The high percentage of volume (~40% of total mobilized; Table 4.8), delivered from open slope locations to seasonal or perennial channels, testifies o f high channel network instability and its ongoing re-organization after glacial disturbance. Accordingly, i f one considers the landscape as a mosaic o f sediment reservoirs, then Quaternary natural disturbance can be seen as a phase o f recharge (rejuvenation), where headwater systems have in places been filled up with exceptional amounts o f glacial deposits. It is expected, though this has not been demonstrated, that such reservoirs are still today degrading by delivering down the system the "inherited" extra sediment [Church and Slaymaker, 1989; Church, 2002]. From this perspective, it is reasonable to assert that the headmost drainage network has developed from the rather smooth terrain surface left behind by the retreat o f the Cordilleran Ice Sheet [e.g., Campbell and Church, 2003]. Initial randomly spaced perturbations (open-slope mass movements) would have generated subtle depressions whose formation can be explained as a result of (i) differential weathering due to variations in hydro-geotechnical properties of the substrate, and/or (ii) underlying topographic discontinuities [Dunne, 1998]. Like ly , gullying, landsliding, and debris flows have been continuously active along the principal axis of the 102 depressions up to the present time, deepening the surface and setting the stage for further flow convergence, weathering and recurrent failure, but more importantly, developing an organized ephemeral drainage system. Notwithstanding the heavy assumption o f landslide full delivery, colluvial sediment dynamics derived from slope-area plots (Figures 4.26 and 4.27) indicate that planar hillslopes and source colluvial "reservoirs" are currently degrading, and that such glacially-inherited sediment load is delivered to unchannelled valleys, sink colluvial channels, and fluvially-dominated reaches, where aggradation is inferred. One expects that colluvial material delivered to unchannelled valleys w i l l be remobilized by diffusive processes such as soil creep and further landsliding, and that material delivered to sink colluvial and fluvial channels w i l l be selectively remobilized by fluvial transport. In this context, bedrock landslides, which typically dominate the sediment dynamics on ridgetops and uppermost hillslopes, appear to trigger the overall disturbance cascade. Specifically, bedrock slides chiefly erode from planar upper slopes and deliver to source colluvial channels, in which material is remobilized further downslope by debris slides, avalanches and flows. Logging operations alter the colluvial sediment cascade across process domains in a significant way. In comparison with the undisturbed setting, increased proportion of degradation is observed in source colluvial channel (gullies), which corresponds to augmented sediment delivery to unchannelled topography. The scaling relation between landslide yield and contributing area is directly related to the topographic delineation of geomorphic process domains. Owing to the spatial heterogeneity of environmental factors, including the stochastic nature o f mass wasting processes and locally morphometric-forced run-out distances, high scatter within each process enclave is observed. Undeniably, however, both the non-cumulative and cumulative percent sediment yields indicate that about 90% of the total colluvial load reaches the landscape at the scale where landslides and debris flows are most active [Slaymaker, 1987]. The remaining 10% is deposited along glacially-induced coupled troughs (-1-50 km 2 ) , the sink-colluvial domain. Given the scales o f colluvial and alluvial prevalence detailed in chapter 3, and the combined plot o f landslide (Tsitika-Eve) and suspended fluvial (entire British Columbia) sediment yields, three main regions can be identified (Figure 4.28). The region located at drainage areas smaller than about 5 k m 2 , which represents the scale of colluvial footslope, colluvial 103 fan, and alluvial fan accumulation, corresponds to the sites where most o f aggradation is occurring today in the glaciated landscape o f British Columbia [e.g., Church and Ryder, 1972]. The region comprised between 5 and 50 k m 2 is a broad geomorphic transition zone, where one expects the contribution o f fluvial yield to increase systematically with drainage area, and there probably is an increasing, unmeasured bedload yield as well . A t this landscape scale, suspended sediment yield is notably higher than the landslide sediment load that is, fluvial transport re-mobilizes more material than is currently supplied by colluvial processes, and a pattern o f degradation is inferred. Degradation continues for areas larger than about 50 k m 2 , where relict trough floors are permanently decoupled, fluvial processes act undisturbed, and suspended sediment yield increases with drainage area. This trend, which contradicts the general notion of aggrading riverine environments [Schumm, 1977], indicates the presence of transport-limited conditions and it has been interpreted as expression of glacially-inherited sediment surplus [Church and Slaymaker, 1989]. Specifically, fluvial processes are currently remobilizing the excess sediment load stored along large valley floors of British Columbia. In other words, the landscape is still responding to the natural perturbation brought about by Quaternary glacial activity and the front of the sedimentary disturbance, which is today located at landscape scales comprised between 10 4-10 5 k m 2 (maximum yield in Figure 4.28), has still to approach the distal most reaches of the system [Church, 2002]. To summarize, the novel approach employed in this section has allowed assessing global sediment dynamics by means o f API-derived data. The analysis, even though limited to a restricted area, has provided encouraging insights that complement results presented by Church and Slaymaker [1989] in the context of regional sediment dynamics. Particularly relevant is the finding that contemporary fluvial processes mobilize more material than what is currently mobilized by mass movement processes for drainage areas comprised between 5 and 50 k m . In other words, at this scale landscape sediment dynamics are not in steady-state conditions, and glacial and paraglacial disturbances still overwhelm current sediment dynamics. Last but not least, since the landslide yield is representative o f only a small portion of British Columbia, one should consider the foregoing discussion on local colluvial and regional fluvial sediment yields only at an indicative level. 104 CHAPTER 5 Channel-reach morphology 5.1 Introduction Mountain drainage basins are complex systems owing to the nature and interaction of hydrologic, biologic, and geomorphic processes at different spatial and temporal scales, coupled with the effects o f tectonic activity and landscape history. In this context, both the local and systematic downstream spatial variability of channel forms and types is affected by the processes that are directly connected to the drainage network [e.g., Church, 1992; Montgomery and Bolton, 2003]. Understanding the spatial pattern of geomorphic processes and channel characteristics is fundamental for problems o f landscape evolution, aquatic ecology, conservation biology, and river restoration. Consequently, the ability to confidently predict spatial variation in reach-scale channel morphology would be valuable for a wide range of applications [Montgomery, 1999]. The morphology o f a channel is customarily described by classification o f characteristic organized structures of sedimentary particles, termed channel units or bedforms [e.g., Grant et al., 1990]. In essence, channel units express the ability o f particles to withstand the stream flow by virtue of structural arrangements. A s such, in coarse-grained streambeds they constitute a relevant component (form roughness) o f the boundary resistance to flow, sometimes greater than that exerted by particle calibre (grain roughness) [Prestegaard, 1983; Griffiths, 1989; Knighton, 1998]. For example, form resistance can constitute up to 80% of total resistance in step-pool and boulder-cascade morphologies [Canovaro et al, 2004]. Channel units that characterize mountain streams include bedrock and boulder cascades, steps, rapids, chutes, glides, pools and bars [e.g., Grant et al, 1990; Church, 1992; Halwas and Church, 2002]. 105 In an attempt to control for the effects of local anomalies (e.g., forest cut-blocks, erratic stones, lithologic contacts, and bedrock knickpoints) o f channel-unit morphology that may confound natural patterns driven by currently active hydro-geomorphic processes, stream channels are subdivided into reaches. A reach is a subjectively defined channel stretch that contains a sequence of channel units along which, due to the influence of uniform governing conditions, channel morphology is relatively homogeneous [e.g., Grant et al, 1990; Church, 1992; Montgomery and Buffington, 1997, 1998; Wohl, 2000]. In this way the within-reach variability is assumed negligible compared to the between-reach variability, which then becomes the only source of variation. Channel reaches of at least 10 to 20 channel widths in length define a useful scale over which to relate stream morphology to channel processes, response potential, and habitat characteristics [e.g., Montgomery and Buffington, 1997]. In general terms, along an idealized concave-up channel long profile in mountainous terrain, proceeding downstream from the headmost reaches, as drainage area increases slope gradient, bed material grain size, degree o f geomorphic coupling and stream power decrease, whereas water runoff, channel width, valley width and sinuosity increase and sediment has greater opportunities for in-channel storage [Church, 1992]. These systematic changes correspond to a shift in hydro-geomorphic process dominance. Several studies have inferred a transition zone within the 1-10 km region, in which colluvial processes become less efficient and are replaced by fluvial counterparts [e.g., Slaymaker, 1987; Brummer and Montgomery, 2003; Stock and Dietrich, 2003]. These same studies have shown that slope-area analysis can provide insights into the spatial distribution of different channel types. In particular, Montgomery et al. [1996; 2003] showed that bedrock and alluvial channels could be discriminated for drainage basins in the unglaciated drainage basins in coastal mountains of Oregon and Washington. Montgomery and Bolton [2003] further showed that channel reaches with different alluvial reach-scale morphologies plotted in different zones on area-slope plots based on field surveys in unglaciated basins. Montgomery and Buffington [1997] developed a scheme for channel morphology classification in unglaciated mountain basins that relies upon deterministic process-controlled heterogeneity in channel-reach morphology (Figure 2.3). This framework is based on process interactions and disturbance propagation along the channel network, and provides a basis for (he zonation of the channel network into reaches of distinct transport regime. In this perspective, channel morphology in one reach is 106 considered as the qualitative expression of the competition between water/sediment supply, and transport capacity (cf., classification proposed by Church [1992]). Accordingly, a continuum of channel types situated immediately downstream of colluvial channels (transport-limited) is proposed, which includes boulder-cascade, step-pool, rapids, and p o o l -riffle channel reaches (Figure 2.3). Transport capacity, which is regarded as being maximum in bedrock reaches and boulder-cascades (supply-limited), decreases progressively across the bedform spectrum, and is in approximate balance with sediment supply in rapids (plane-bed) reaches; riffle-pool and colluvial morphologies constitute the opposite end-member and are expression of transport-limited conditions. In particular, while riffle-pools are transport-limited chiefly because local slope is extremely low, colluvial channels exhibit excess sediment storage for lack of flow. This idealized downstream continuum o f channel types, however, may be modified by land-use history or litho-topographic features such as where streams cross geologic contacts between rocks of different credibility; where there are strong local controls on sediment supply, such as large wood loads or bedrock-controlled morphological jumps; where there are spatial gradients in rock uplift rates; across discontinuities imposed by the specific tectonic or Quaternary history of the landscape; or where there is spatial variability in sediment supply. In glaciated drainage basins of coastal British Columbia results o f slope-area analyses coupled to field investigations o f channel properties depart significantly from prototypes originally developed for unglaciated systems (see chapter 3). In these mountain settings, hanging valleys are aligned along the direction o f formerly active ice flows that originated from relict cirques. Their peculiar morphology imposes low channel gradients in some headwater channels and decouples sediment inputs delivered from bordering cirque walls. A s a result, relict glacial cirques enclose distinctive "hanging" fluvial valleys at contributing areas smaller than 0.1 k m and produce non-uniform channel long-profiles . In contrast with Schumm's [1977] prototype of the fluvial system, where the degree of slope-channel coupling generally weakens downstream until colluvial reaches grade to fluvial reaches, decoupled hanging valleys are associated with stepped long profiles that separate strongly 1 A similar landscape configuration may be observed in plateau-like regions (unglaciated or glaciated), except that the headmost colluvial domain, separating hillslope and fluvial enclaves, would be missing. 107 coupled channel reaches. The glacially imposed variations in valley long profiles impart substantial variability to process domain sequencing in individual watersheds. To summarize, work conducted in glacially-shaped topography reveals a peculiar degree of geomorphic coupling (connectivity) between hillslope and channel processes. This in turn has a major impact on the delineation of process domains in slope-area plots by generating a transitional process domain (sink colluvial) whose boundary with alluvial environments is an inverse function of local slope and contributing area. On such geomorphic premises, and considering that most work concerned with slope-area relations in the context of channel type classification has focused on unglaciated drainage basins (e.g., coastal Oregon) or in unglaciated portions of basins with limited alpine glaciation (e.g., Olympic Mountains), an obvious follow-up question arises: how and to what extent does the glacially-induced organization o f geomorphic process domains affect the spatial distribution of channel-reach morphology in formerly glaciated mountain drainage basins? The specific objectives of this chapter are (i) to examine the impact of process domains, hence that of Quaternary inherited topography, on the spatial distribution of channel-reach' morphology and its sequencing down the channel long profile, (ii) to assess what type of controls ( if any) are exerted by parameters relating to channel cross-section, bed material, and resistance to flow on channel-reach morphology, and ultimately (iii) to determine a parsimonious set of variables for predicting channel-reach morphology. The first objective is pursued v ia examination o f channel long-profiles and slope-area plots. Subsequently, in order to examine interactions between controlling factors, channel types are examined by plotting series of variable pairs. Finally, all factors are considered together in a comprehensive multivariate statistical analysis. 5.2 Study Areas Study basins are tributaries of the Capilano River (East Cap Creek, Hesketh Creek, and Lembke Creek) and the Tsitika River (Elliott Creek). The former lies within the Pacific Ranges of the Coast Mountains; the latter belongs to the Insular Ranges [Holland, 1964]. Rugged topography characterizes the Capilano and Tsitika valleys, with slopes typically steeper than 35° and steepness generally increasing with elevation. The typically stepped landscape is the result o f the combined effects o f tectonic uplift, rock strength, but chiefly glacial erosion. Gentle and moderate slopes, especially at mid to low elevations, are mantled 108 by glacial t i l l , which is the most extensive surficial material and constitutes the primary source o f fine sediments. Surficial materials deposited on hillslopes in post-glacial time consist primarily of colluvium. Bedrock in Capilano consists primarily o f intrusive igneous rocks - granodiorite, quartz diorite, diorite, and lesser amounts of gabbro and migmatite. Limited metamorphic-dominated formations are present in places (i.e., Gambier Group and Twin Islands Group; [Roddick, 1965]) and do not occur within the study tributaries. Similarly, Elliott Creek is underlain by intrusive lithologies o f the Jurassic Island Intrusions o f the Pacific R i m Complex (quartz diorite, granodiorite, quartz monzonite, and quartz feldspar porphyry) [Muller, 1977]. The climate in the Pacific and Insular Ranges exhibits a typically prolonged winter wet season from October through May , followed by a much drier summer regime. A t the outlet o f Capilano Lake about 80% of the annual precipitation falls during the wet season. Convergence in valleys and topographic uplift tend to increase precipitation abruptly north o f the Fraser River flood plain, where fronts intersect the North Shore Mountains. Annual precipitation ranges from 2,000 mm at Cleveland Dam (157 m) to about 3,000 mm at Hollyburn Ridge (930 m) and M t Seymour (823 m) stations, and in places at the head of passes through the mountains ((Mt. Hollyburn (1325 m) and M t . Strachan (1454 m)) is estimated to approach 5,000 mm [Schaefer and Nikleva, 1973]. Elevation also affects the snowfall proportion o f total precipitation. Measurements from snow courses show that at elevations of around 1000 m the normal maximum water equivalent in the snow pack is at least 1,600 mm [GVRD, 1999]. In the Tsitika River climatological data coverage is poor. According to published data from stations located in Northern Vancouver Island [Atmospheric Environment Service, 1995], annual total precipitation appears to decline eastward, from about 3,500-4,000 mm on the west coast to less than 2,000 mm on the east coast. Specifically, precipitation records along the east coast (i.e., Alert Bay (63 m) and Chatham Point (23 m), located respectively 25 k m west and 40 k m east of the Tsitika mouth), indicate total annual amounts ranging between 1,600 and 2,200 mm. Similar to Capilano, orographic effect in conjunction with topographic convergence along relict glacial troughs w i l l undoubtedly generate higher precipitation values at the headwaters of tributary streams. The actual total figures are presently unknown 109 Figure 5.1 Map indicating the location of recent (< 20 yr-old) and old (>55 yr-old) cutblocks in (a) the Capilano River Basin; and (b) Elliott Creek. 110 at such locations; average annual precipitation over the area is estimated to be less than 2,500 mm [Stirling, 1997]. Elevation in Elliott Creek lies between 230 m, at the confluence with the Tsitika River, and 1557 m at the M t . Elliott summit, on the southwest side o f the basin. Elliott Creek (10.3 km 2 ) was selected among al l Tsitika tributaries for its relatively easy access, the intrusive lithology, but especially for the highly pristine nature (Figure 5.1b). Specifically, timber harvesting affects about 12 % (1.3 k m 2 , all conducted between 1991 and 1996) of the basin, in flat terrain of the primary hanging valley, and along the adjacent valley step. A t these locations, direct impacts on channel bed morphology and natural cross-sectional characteristics are minimized ( if not neutralized), as buffers o f undisturbed forest were left in proximity o f the channel main stem. Accordingly, no logging-related landslides were detected in Elliott Creek during aerial photo interpretation (see section 4.3) and field surveys (see section 5.3). Similar arguments can be made for the study tributaries o f the Capilano River, where forest harvesting in the last 50 years has been conducted in gentle terrain with "careful", well-defined, and documented techniques: clearcut and partial cutting (helicopter) followed by grapple, highlead, or skyline full-suspension yarding [D. Bonin, G V R D , pers.comm., 2001]. Here, recent cutblocks (< 20 yr-old) cover respectively 9.4% (0.65 km 2 ) of the total basin area in East Cap Creek, 17.2% (0.89 km 2 ) in Hesketh Creek, and 2.4% (0.40 km 2 ) in Lembke-Sisters Creek (Figure 5.1a). In addition, about 17.6% (3 km 2 ) o f the Lembke-Sisters system examined had been harvested more than 55 years ago (hereafter referred as old logging land use category). It is reasonable to assume that the old logging legacy today does not affect channel size and bed morphology to a significant extent; in fact, no apparent local evidence o f logging-related disturbance (e.g., landslides, stump-made logjams, in-cutblock channel avulsions) could be found during field visits. 5.3 Data Collection Field surveys of the study streams involved measuring local slope (S), bankfull width (w), bankfull depth (d), and D95 (i.e., medial axis of the five largest stones, then averaged), as well as delineating channel reaches. Reaches were defined and classified according to dominant channel bed morphology, which comprises the following categories: bedrock-controlled, chaotic (colluvial), boulder-cascades, step-pools, rapids, and riffle-pools (Figure 5.2). In order to avoid confusion with sandTbed terminology, the term rapids [Grant et al, 1990], as opposed to plane-bed [Montgomery and Buffington, 1997], was preferred for describing 111 gravel bedforms arranged into transverse ribs that partially emerge at low and intermediate flows [e.g., Hassan et al, 2005]. Bankfull level in the field was judged from the presence of rooted vegetation, stain lines, channel morphology, and flow-deposited organic debris [Montgomery and Buffington, 1997; Wohl and Wilcox, 2005]. Bankfull width and the intermediate axis o f the five largest stones were measured with a metric tape; slope gradient was measured with a clinometer (except in the distal-most reaches of the Capilano River, where a laser theodolite was used); depth measurements at bankfull were taken with a metric rod at three locations across each channel cross-section. Owing to the high number o f slope measurements taken over a large study area, and the difficult access of the study streams, with at times extremely unstable channel beds, the use o f a higher precision surveying instrument would have entailed rather risky and onerous logistics. For the same reasons, the number of stones measured in proximity (i.e., within one channel width distance in the active bed) of the exact point where bankfull width and depth were measured in was limited to five. Field measurements were taken at a length scale equal to twice the local channel width. Field measurements were then averaged across channel reaches (averages are weighted by the distance between points o f measurement). A s a consequence, Dx (the diameter at which X per cent of the material is finer), which is a measure of the size o f roughness elements for each reach, is calculated over at least 30 stones. In poorly-sorted channel beds, in order to account for the large proportion of flow resistance exerted by large particles, D$4, D90, and D95 are commonly adopted [Knighton, 1998]. In the present study it is assumed that the five largest stones approximate the D95. Resistance to flow was approximated by associating a Manning's roughness coefficient (n) to every channel reach; specifically, this step was achieved by visual comparison with representative reaches [Hicks and Mason, 1991] and is supposed to incorporate the undifferentiated effects of all types of resistance (e.g., form and grain roughness). Unit stream power ( « ) was calculated at the reach scale from the product of mean water velocity (5.1) with total shear stress (r) (5.2): v = (R2/s S,/2)/n « (d23 Sl/2)/n (5.1) r=pgdS (5.2) co = rv (5.3) Finally, total stream power (Q) was calculated by multiplying unit power by width: 112 Q = co w (5.4) A number of assumptions and simplifications stand behind such calculations, mainly because the expressions listed above have been empirically developed in large flood plain rivers (purely alluvial). First, the hydraulic radius R is approximated by bankfull depth; second, one should note that the Manning equation (5.1) is valid only for turbulent flow; and third, that equation (5.2) applies to steady, uniform flow, hence should be seen as an approximation for obtaining average resistance to flow. Since discharge data were not available in the study basins, and owing to the lack of hydrologic information in small streams of the Coast Mountains the relation between water discharge and drainage area is unknown for basins smaller than 50 km [Eaton et al, 2002], in the remainder of this dissertation (i.e., chapters 5 and 6) drainage area (A) will be considered as a proxy for bankfull discharge ( 0 . Specifically, it is assumed that bankfull discharge varies linearly with drainage area (A = gQ*; with g = 1 and h = 1), an assumption that in humid environments of coastal British Columbia appears to be reasonable [e.g., Ponton, 1972; Brummer and Montgomery, 2003]. Figure 5.2. Channel types encompassed in the study basins: (a) bedrock-controlled reaches (i.e., bedrock chute) in Elliott Creek (zone C2); (b) riffle-pools in Hesketh Creek (zone HF2). (Next Page): (c) colluvial (chaotic) channel in Hesketh Creek (zone C2); (d) boulder-cascades in Elliott Creek (zone C2); (e) rapids (or plane-bed) reaches in Lembke Creek (zone HF); and (f) step-pool morphology in Elliott Creek (zone C3). 113 114 The layout o f the results matches the sequential order of the objectives. Accordingly, section 5.4 deals with the spatial distribution and sequencing of channel-reach morphology associated with process domains. Channel types are subsequently analysed in relation to available energy and its ratio with coarse-grain fraction (section 5.5.), channel cross-sectional variables, and grain roughness (section 5.6). Finally, multivariate statistical techniques are used to establish the best set of predictors for automated channel-reach morphology classification (section 5.7). 5.4 Spatial Distribution of Channel-Reach Morphology in the Slope-Area Context For the study o f channel-reach morphology, combining the use of longitudinal profiles (linear scale) and slope-area plots (logarithmic scale) is both analytically and visually effective. When aiming to illustrate glacial macro-forms, the shapes of longitudinal profiles are undoubtedly more intuitive and immediately understood than slope-area plots. On the other hand, slope-area plots are superior to longitudinal profiles in that they (i) provide greater detail o f process domains active at small contributing areas (note that C I , H F 1 , and C2 had to be collapsed together in Figure 5.4a), (ii) enhance changes in topographic curvature and therefore facilitate the identification of confluence effects and second-order landforms (e.g., HF1 zones in Figures 5.4a and 5.4b), and (iii) indicate slope ranges for different channel types (morphologies). Hesketh Creek (Figure 5.4a) originates from a glacially-carved saddle. It is a poorly defined channel flowing through a relatively steep spoon-shaped hanging valley (HF1 in Figure 5.4b) characterized by chaotic (CH) channel morphology with evident signs of nivation (Figure 5.4a). The hanging valley terminates abruptly into a steep and incised colluvial channel dominated by large boulders commonly interlocked in massive jammed cascades (Figures 5.2c and 5.2b). A t this location material is transferred preferentially via debris flows into the principal decoupled hanging valley (through a dissected paraglacial fan), whose morphology is at first that typical o f a debris-flow run-out zone, and then degrades to rapids and riffle-pool bedforms (Figure 5.2b). Right at the edge of the hanging valley, where the gradient increases abruptly, the channel reacquires a colluvial and confined character with Figure 5.3. (Next page), (a) Poorly defined channel at the headwaters of Hesketh Creek; (b) Interlocked boulder structures in Hesketh Creek (zone C2); (c) Hanging valley seen from the apex o f the paraglacial fan (Lembke Creek); (d) Step-pools in Hesketh Creek (zone C3). 115 116 a) 1 1 0 0 1000 900 g" 800 J 700 ra > • 600 500 400 300 CH ! C A - S P ; RD RP ; C A - S P RD Cirque Hanging Valley Glacial Wall Valley j Step \ Trough (C1-HF1-C2) (HF2) (C3) N V (F) 1000 2000 3000 4000 5000 Distance (m) b) £ 0 . 1 CD O-o CO 0.01 X X A X chaotic A cascade O rapids + step-pool X riffle-pool X + C1 HF1 C2 10 0.01 0.1 1 Drainage area (km2) Figure 5.4. Hesketh Creek: (a) longitudinal profile showing glacial macroforms, area-based process domains (in parenthesis), and dominant channel-reach morphology ( C H = chaotic; C A = boulder-cascade; SP = step-pool; RD = rapids (or plane bed); RP = riffle-pool) arrow marks apex of paraglacial fan; and (b) slope-area plot of channel reaches; slope values are channel-reach weighted averages (weighted by distance) of field measurements. 117 a) 1300 1200 1100 1000 -p 900 c o i > Ul b) fo.1 Q. 0 CO 0.01 700 600 500 400 300 200 CA-SP RD-RP BR-CA-SP RP : i i i i CA-SP RP Cirque Hanging Valley ^^ ^^  • i i Hanging j V a l l e y ^ v Glacial - Wall Valley Step Valley Step >^ Trough - (CI) (HF1) (C2) 1 1 (HF2) i 1 1 1 1 r>— (C3) (C3) 1000 2000 3000 4000 5000 Distance (m) 6000 7000 8000 A A + + + 4 + + C1 HF1 C2 X X HF2 C3 • bedrock A cascade O rapids X riffle-pool + step-pool 0.01 0.1 1 10 100 Drainage area (km2) Figure 5.5. Elliott Creek: (a) longitudinal profile showing glacial macroforms, area-based process domains (in parenthesis), and dominant channel-reach morphology ( C A = boulder-cascade; SP = step-pool; R D = rapids (or plane bed); RP = riffle-pool) arrow marks apex of paraglacial fan; and (b) slope-area plot of channel reaches; slope values are channel-reach weighted averages (weighted by distance) of field measurements. step-pool and boulder-cascade morphologies (Figure 5.3d), sediment being supplied by near-bank failures that remobilize large boulders from banks cutting through glacial outwash 118 deposits and till-mantled slopes. Finally, gentler slope gradients, and so rapids morphology, reappear in the distal reaches, where Hesketh Creek intersects the Capilano main valley (Figure 5.1a). Elliott Creek long profile (Figure 5.5a) mirrors closely that of Hesketh Creek. It originates as a well-defined step-pool channel (CI in Figure 5.5b), which gradually decouples into a hanging valley characterized by rapids and riffle-pool channel morphology. The stream flows abruptly into a steep colluvial channel, which receives chronic debris flow inputs at tributary junctions and presents a typical boulder-cascade (Figure 5.2d) and step-pool morphology alternating with short bedrock reaches ( B R - C A - S P in Figure 5.5). Downstream, at a drainage area of about 4 k m 2 , Elliott Creek flows into a wide, flat hanging valley and assumes riffle-pool-bar channel morphology. Subsequently, as channel gradient increases at the hanging-valley/valley-step transition (the valley step links Elliott hanging valley to Tsitika glacial trough, Figure 5.1b) riffle-pools are replaced by step-pools (Figure 5.2f) and boulder-cascades in colluvial and confined reaches, coupled in places to near-channel failures. Elliott Creek flows through purely alluvial reaches as it enters the Tsitika main valley and the glacially-imposed gradient becomes very gentle. In the case of Elliott Creek it is apparent that bedrock reaches are located at high transport capacity sites and not necessarily at the headmost portion o f the channel, where slope gradient is high, but water flow (contributing area) does not have the competence to transport all available sediment supply and debris flows are not active (sink colluvial channel, see chapter 3 for definition). Lembke Creek (Figure 5.6) presents the simplest structure of all study basins. It flows from a flat, unchannelled saddle, at an abrupt channel head (landslide headscarp), into a steep and incised colluvial channel. The channel is periodically scoured to bedrock by debris flows (source colluvial channel) and strongly coupled to chronic lateral sediment inputs delivered from gully walls. A t these locations, channel morphology varies from chaotic (CH) to boulder-cascades ( C A ) and bedrock (BR) stretches in places. A paraglacial fan separates Lembke Creek from a wide U-shaped hanging valley, which exhibits rapids (Figure 5.2e) and riffle-pool morphology (Figure 5.3c). A t the downstream end o f the hanging valley sit a series of ponds characterized by high content of organic matter. The last pond in particular formed as a result o f lateral debris-flow damming. Immediately downstream, the valley 119 exhibits a narrow V-shaped profile and Lembke Creek assumes the form of a high-gradient, strongly-coupled colluvial channel. Due to the asymmetric structure of the cirque morphome-a) c o CO > UJ 1200 1100 1000 900 800 700 600 500 400 300 200 BR-CA RP-RD BR-CA-SP Non-torrented > v tributary S P - Sisters Creek confluence _ Cirque Wall (C1) Hanging Valley (HF1) i Valley Step (C3) G l a c i a l " ^ — Trough " (C3) ' • 1000 2000 3000 Distance (m) 4000 5000 6000 b) E — 0 1 o. o CO X non-torrented tributary • bedrock X chaotic A cascade O rapids -I- step-pool X riffle-pool C 1 H F 1 0.01 0.001 Sisters Creek confluence 0.01 10 100 0.1 1 Drainage area (km2) Figure 5.6. Lembke-Sisters Creek: (a) longitudinal profile showing glacial macroforms, area-based process domains (in parenthesis), and dominant channel-reach morphology ( C H = chaotic; C A = boulder-cascade; SP = step-pool; R D = rapids (or plane bed); R P = riffle-pool); and (b) slope-area plot of channel reaches; slope values are channel-reach weighted averages (weighted by distance) o f field measurements. Ar row marks apex o f paraglacial fan. Note confluences of Lembke Creek with a non-torrented tributary and with Sisters Creek, which is torrented. 120 a) 1600 c .2 ta > 1000 2000 3000 Distance (m) 4000 5000 b) f 0.1 Q. O CO 0.01 X C1 + HF B 44 i 1 i • bedrock X chaotic A cascade o rapids + step-pool C2 0.01 0.1 1 10 100 Drainage area (km2) Figure 5.7. East Cap Creek: (a) longitudinal profile showing glacial macroforms, area-based process domains (in parenthesis), and dominant channel-reach morphology ( C H = chaotic; C A = boulder-cascade; SP = step-pool; RD = rapids (or plane bed)); and (b) slope-area plot of channel reaches; slope values are channel-reach weighted averages (weighted by distance) of field measurements. 121 try [e.g., Evans, 2005], Lembke Creek receives debris flows from the southeast facing valley wall and rock avalanches from the opposite side. Channel morphology is dominated by step-pool, boulder-cascade morphologies alternating in places with short chaotic stretches and a 70-m long bedrock reach; channel bed and banks are formed by colluvial interlocking clasts. A non-torrented tributary junction at approximately 2.5 k m 2 characterized by rapids and riffle-pool morphology produces a relative minimum in the slope-area plot (Figure 5.6b). A t a drainage area of about 10 k m 2 Lembke Creek joins Sisters Creek, whose valley long-profile overwhelms that of Lembke Creek (Figure 5.6b). Lembke-Sisters valley-trunk, a "second order" relict glacial trough with significantly higher relief and valley amplitude, maintains a high degree of geomorphic coupling due to debris-flow inputs from lateral tributaries (Slide Creek, SistersOl Creek) as well as material derived from the actively eroding glacio-fluvial terraces. The headwaters of East Cap Creek (Figure 5.7) have a pronounced rocky character. East Cap Creek originates as a poorly-defined colluvial channel (CI in Figures 5.7a and 5.7b) characterized by chaotic assemblages of boulders. The channel flows into a hanging valley with lake (rapids, step-pool and bedrock reaches) then through a long narrow canyon, the result o f a relict melt-water channel occupying the valley step between the hanging valley and East Cap glacial trough. Down to this distance from the channel head, all reaches are heavily affected by rock falls and rock avalanches. The rocky canyon opens into East Cap main valley, which is initially coupled to upstream debris-flow inputs and exhibits dominant step-pool morphology. Downstream, the channel becomes decoupled and step-pool systems are composed o f sequences of low steps (<0.4 m) and long pools and glides (>7 m), which often degrade to rapids morphologies. East Cap Creek slope-area plot (Figure 5.7b) has high scatter within all process domains. Along the bedrock canyon (B) steep reaches alternate with relatively gentle stretches. In terms of channel bedforms, rapids are well separated in the slope-area space (Figure 5.7b) from all other channel types (i.e., chaotic and bedrock reaches, boulder-cascades, and step-pools), whose ranges exhibit general overlap. A l l study reaches are plotted together in slope-area space (Figure 5.8). In order to provide a more complete representation of distal fluvial reaches, the distal-most reaches of East Cap Creek (A ~ 40 k m 2 , data from White [2002]) and two purely alluvial reaches o f the Capilano River (A ~ 180 k m ) located just upstream of the reservoir are also reported. In figure 5.8, 122 for drainage areas smaller than 10 k m 2 , all data points plot below an empirical threshold power-law 2 relation (exp = -0.25). Differently from what is observed in unglaciated basins of Washington State [Montgomery and Buffington, 1997; Brummer and Montgomery, 2003], no obvious colluvially-imposed inflection point can be detected at contributing areas comprised between 1 and 10 k m 2 (cf., Figure 2.3b). Reasons for this have to do with the complex glaciated topography o f the study basins. In fact, the distinct sequences of relict glacial macro-forms observed in different study basins impart peculiar threshold slopes at different spatial scales, so that basin-specific slope-area lacunae (topographic signatures) are erased in the combined plot. 0.1 £ £ Q. O to 0.01 0.001 0 A • bedrock X chaotic A cascade O rapids -I- step-pool X riffle-pool 001 0.01 0.1 1 Drainage Area (km2) 10 S = 0.21 A -0.25 X X 100 1000 Figure 5.8. Slope-area plot o f channel reaches in the study headwater basins. Note that the plot reports also the distal-most reaches of East Cap Creek (A ~ 40 k m 2 , data from White [2002]) and the purely alluvial reaches of the Capilano River (A ~ 170 km 2 ) upstream of the reservoir. Dashed line marks an empirical slope-area threshold described by the study reaches, and serves as benchmark for comparison with results from an idealized concave-up, unglaciated longitudinal profile. 2 The presence of an inflection point at 10 km2 cannot be excluded; however, the number of data points beyond this landscape scale is rather small to justify such an interpretation. 123 Bedrock and chaotic reaches follow closely the threshold trend; note that the two bedrock reaches that plot at considerable lower slope are located within a relict melt-water channel (zone B in East Cap Creek), a steep narrow canyon in which are present some relatively gentle and wider stretches. Interestingly, step-pools depict a power-law threshold trend similar to that described by bedrock reaches but characterized by a lower intercept. B y contrast, alluvial reaches (i.e., rapids and riffle-pools) describe horizontal domains in the slope-area space (slope in upper and lower boundaries is constant). Finally, boulder-cascade reaches exhibit high slope scatter at drainage area smaller than 1 k m 2 but are contained between 0.1 and 0.2 slopes at larger landscape scales. 1.0 0.1 Median 25%-75% 10%-90% bedrock chaotic cascade step-pool rapids rif lie-pool Figure 5.9. Box-plot o f channel-reach slope categorized by dominant channel morphology. Overall, the combined slope-area representation of all study reaches yields a reasonable discrimination of channel morphologies. Given the satisfactory slope-based discrimination of channel types, it was decided to examine the slope factor alone, by plotting relevant distributions o f channel reaches categorized by morphological types (Figure 5.9). In 124 agreement with Figure 5.8, the corresponding box-plot reveals a good degree of separation among channel types (Figure 5.9). Separation is not complete; however, median values plot on an idealized log-linear trend that starts from riffle-pool morphology (median = 0.02), and continues with rapids (0.06), step-pool (0.1), boulder-cascade (0.13) and chaotic morphologies (0.5). Specifically, inner quartiles (25-75%) of chaotic, boulder-cascade, step-pool, rapid, and riffle-pool types do not overlap. B y contrast, bedrock channels (median = 0.22) exhibit the widest slope range, which completely contains the chaotic and boulder-cascade domains. The slope-based hierarchy and the separation between channel types is very similar to those reported elsewhere in unglaciated settings [Buffington, 1995; Montgomery et al., 1995; Montgomery and Buffington, 1997]; however, slope spectra are significantly higher. 5.5 Channel-Reach Morphology, Available Energy, and Flow Resistance Flow resistance is a first-order component of stream channel self-organization, for it connects bed material characteristics, sediment transport regime, and dissipation o f energy [Knighton, 1998]. A s stated in section 5.1, channel morphology in gravel-bed rivers is considered a primary element o f boundary flow resistance. In order to gain additional insights into what controls the spatial organization of channel-reach morphology a number of variables, expressive of available energy and single-grain resistance, are examined. These variables include unit stream power (of), total stream power (£2), total shear stress (r), and driving force to substrate resistance ratios that are estimated as total power and specific power relative to the coarse-calibre fraction (0/D95 and Q/D95). Graphical comparisons reveal that discriminatory efficiency o f slope across spatial scales (Figure 5.8) remains unsurpassed in comparison with specific (Figure ,5.10a) and total power (Figure 5.10b); virtually no separation of channel types is achieved by means o f Q/D95 (Figure 5.11b) and C0/D95 (Figure 5.1 lc ) . One would expect such similar behaviours; in fact Q and co were calculated from the Manning's equation (see section 5.3), so the four variables are highly correlated. On the contrary, the shear stress-based graph (Figure 5.11a) yields good discrimination between purely fluvial channel types (i.e., rapids and riffle-pools). A s previously observed for slope-area plots, generalized overlapping is noted between bedforms situated on highly disturbed colluvial (i.e., bedrock and chaotic reaches, and 125 boulder-cascades) and semi-alluvial reaches (sensu Halwas and Church [2002], i.e., bedrock and step-pools). 10000 I 1000 o a. o » a. eo 100000 c-10000 L . as <S o a. 3 P 1000 100 A X + • bedrock X chaotic A cascade © rapids + step-pool X riffle-pool A 0.001 0.01 0.1 1 10 Drainage area (km2) X X 100 1000 Figure 5.10. Channel reaches plotted by drainage area versus (a) specific power, and (b) total power. Note that in both cases the degree of discrimination between channel types is much poorer than that associated with channel gradient in figure 5.8. Figure 5.11. (Next page) Channel-reach morphology plotted by drainage area vs. (a) shear stress, (b) total stream power-D95 ratio, and (c) specific stream power-D95 ratio. 126 0.001 0.01 0.1 10 100 1000 a ) 10000 E 1000 CO CO CO n 2 100 co 10 -100000 A X A • bedrock X chaotic A cascade O rapids + step-pool X riffle-pool X 0.001 0.01 0.1 1 10 Drainage area (km2) X X 100 1000 127 5.6 Channel-Reach Morphology, Channel Size, and Grain Roughness In this section, bedform heterogeneity and corresponding form roughness are examined with respect to the self-organization of channel size [e.g., Rodriguez-Iturbe et al, 1992] and grain roughness. A i m s include looking for (i) dependences between cross-sectional variables and channel-reach morphology; and (ii) interactions between grain and form roughness. To these purposes, the following variables are considered: bankfull depth (d), bankfull width (w), coarse grain fraction (D95), relative roughness (Dgs/d), and width-to-depth ratio (w/d). Specifically, these variables are graphically evaluated against slope and contributing area in an attempt to achieve a channel-type discrimination superior to that obtained via slope-area analysis (Figure 5.8). Among the slope-based representations contained in Figure 5.10, the slope-relative roughness relation (Figure 5.12a) seems to yield the best discrimination among channel morphologies. The relation describes a broad rollover-shape, so that relative roughness increases greatly for small slope increments across hanging-fluvial riffle-pool (D/d < 1) and rapids reaches attaining a maximum at about 0.1 slope V v i t h i n the step-pool domain, and declines gently for higher slope values in bedrock and cascade-dominated reaches (4 > D/d > 1). Owing to the correlation between variables, the relative-roughness trend is mirrored in the corresponding slope-based plots o f D95 and bankfull depth (Figures 5.12c and 5.10e). However, a major dissimilarity stands out: riffle-pool reaches are wel l discriminated from rapids in the slope-Dpj space (Figure 5.12c), but not in the slope-depth space (Figure 5.12e). Channel slope and width-to-depth ratio (alpha = a - w/d) describe a weak inverse relation with no apparent rollover (Figure 5.12b), indicating that as water flows through gentler topography channel cross section tends to stretch along its horizontal axis (channels are shallower and wider). Overall, this graphical representation does not yield any apparent discrimination between channel morphologies. Inspection of slope-depth (Figure 5.12e) and slope-width plots (Figure 5.12d) suggests that channel width (which as noted before describes a non-linear trend) controls the slope-alpha relation to a greater extent than channel depth. In this context, particularly well-defined is the slope-width relation for bedrock channel-reaches (Figure 5.12d) which, in agreement with previous studies [i.e., Finnegan et al, 2005], appear to be narrower as they become steeper. 128 0.001 10 0.01 * 1 XI -a D a) £ 1 a Q 0.1 e) ~i—i—r-TT-n r-0.1 1 0.001 100 0.01 0.1 -1—i—i—r-r-0 + O * E 510 5 b) • X x ; • bedrock X chaotic A cascade + step-pool O rapids X riffle-pool + 0.01 0.1 Slope (m/m) Figure 5.12. Channel types plotted by slope versus (a) relative roughness, (b) width-to-depth ratio, (c) coarse grain-fraction, (d) bankfull channel width, and (e) bankfull channel depth. Dashed circle encloses the distal-most reaches o f the Capilano River. 0.001 0.01 0.1 Slope (m/m) 129 0.001 100 a) 510 b) £ 1 a. & 0.1 10 c) 1 + 0.1 0.01 1 — I I I I 1 1 I • bedrock X chaotic A cascade + step-pool O rapids X riffle-pool 0.1 10 100 1000 i * S 4 k X A w = 6 A 0.32 d = 0.5 A 0.16 A * 0.001 0.01 / ' x \ 100 1000 0.1 1 10 Drainage area (km2) Figure 5.13. (a) Bankfull width, (b) bankfull depth, and (c) coarse grain-size fraction, plotted as functions of drainage area. Dashed circle encloses distal-most reaches o f Capilano River. Dashed lines are best fit regressions based on least-squares. Arrows mark the scale of valley steps, where departure from the general trend seems to occur. 130 0.001 100 d) E £ 10 X I 5 e) 10 ' 0.01 0.1 10 —1 1 1—I I ' M ! 1 1 1 1 I ! I I | 1 1 1 1—r T I T ] r— 100 1000 •: x • bedrock X chaotic A cascade O rapids + step-pool X riffle-pool £ 1 X i i A A • X • X ; 0.1 -I—1— 1— 1— — ' 1—1 1 1 1 1 1 11— 1— I 0.001 0.01 0.1 1 10 100 1000 Drainage area (km 2) Figure 5.13. (d) Width to depth, and (e) relative roughness, plotted as functions of drainage area. Dashed circle encloses distal-most reaches o f Capilano River. Interestingly, in all graphs in figure 5.12 riffle-pool distal-most reaches of the Capilano River (enclosed by dashed circle) define a cluster away from the population o f riffle-pools associated with decoupled hanging valleys. The distal riffle-pool reaches exhibit significantly higher bankfull depth, bankfull width, and D95, which clearly impart higher relative roughness and width-to-depth ratio. In figure 5.13 variables related to channel cross-sectional (d, w, and w/d) and bed material (D95 and Dgs/d) characteristics are expressed as functions of contributing area (A). This type 131 of representation is presented with the intent to identify additional causal linkages between channel types and geomorphic process domains. Bankfull width scales with contributing area 0 32 (Figure 5.13a) according to a general power-law relation (least-squares method: w = 6A , R 2 = 0.68) with a functional exponent equal to 0.39±0.05 ( a = 0.05). Even though subject to high scatter, the relation appears to exhibit a steeper gradient (i.e., exp > 1, between arrows in figure) for drainage areas between 3 k m 2 and 10 k m 2 (the scale of valley steps) indicating that one simple power-law expression might not be sufficient to fit al l the data range. A similar area-based general scaling is observed with respect to bankfull depth (least-squares method: d = 0.5 A016, R 2 = 0.37; Figure 5.13b) with an exponent equal to 0.26±0.07 ( a = 0.05) after adjustment for functional analysis. Segmentation lies within the data scatter in the case of depth (Figure 5.13b) and width-to-depth ratio (Figure 5.13d), and is not at all discernible in terms o f coarse-grain fraction (Figure 5.13c) and relative roughness (Figure 5.13e). Overall, scaling relations in Figure 5.13 exhibit poor separation between morphology types, riffle-pools in hanging valleys being the exception, as these have significantly lower D95 and relative roughness. In this chapter, the study of downstream hydraulic geometry (DHG) relations is limited to their ability to help discriminating between channel types. For further analysis on the downstream pattern of hydraulic geometry see chapter 6. Notwithstanding such poor area-based discriminatory representations, some important insights are gained from a process domain perspective. Riffle-pool reaches (purely fluvial) show smaller bankfull width than colluvial and semi-alluvial reaches (i.e., step-pool, cascade, and chaotic) at a given contributing area (Figure 5.13a), Bankfull depth and the coarse grain-size fraction behave in similar way. The former exhibits a maximum fluvial value o f 1.2 m at 180 k m 2 , which is exceeded in colluvial (or semi alluvial) reaches at contributing areas as small as 5 k m (Figure 5.13b). Similarly, a D95 equal to 1.8 m at a contributing area of 180 k m 2 , the largest particle size measured in fluvial reaches, is also recorded in colluvial reaches at about 20 k m (Figure 5.13c). To summarize, these results altogether hint at the existence of process-driven scaling dependences with respect to channel cross-sectional and bed material variables. Specifically, the spatial scales associated with a given bankfull depth, bankfull width, and D95 are significantly reduced where colluvial and alluvial processes are coupled, in comparison to purely alluvial geomorphic conditions, and therefore may underlie the existence o f distinct regime types. 132 5.7 Multivariate Prediction of Channel-Reach Morphology The objective o f this section is to determine a parsimonious set of variables for predicting channel-reach morphology in complex glaciated topographic settings. The procedure entails Principal Component Analysis ( P C A ) applied to the original dataset, to reduce the number o f predictor variables; subsequently, Multivariate Discriminant Analysis ( M D A ) is applied to the PCA-reduced dataset to assess success rates o f the corresponding channel type classification (see flowchart in Figure 5.14). Normality Tests Principal Component Analys is (Correlation limit = 0.35) Canonica l Discriminant Analysis: - Homogeneity of Var iance test - Bonferroni's test - Total Canonica l Structure (Correlation limit = 0.5) - Principle of Pars imony (Minimum Error Rate) Cross-validation: - Jackknife - G r o u p splitting Figure 5.14. Flowchart showing the multivariate analytical framework Table 5.1. Transformations o f reach-variables Reach variable (string) String Transformation Normality achieved Length (m) J length Natural logarithm Statistical tes t D Contributing area (km 2) contr_area Natural logarithm Histogram 0 Slope gradient (m/m) avg_slope Natural logarithm Histogram Bankfull width (m) avg_width Natural logarithm Statistical test Bankfull depth (m) avg_depth Natural logarithm Statistical test Mean velocity (m/s) Shear stress (N/m ) mean_yel Natural logarithm Statistical test shstress Natural logarithm Histogram Number of wood pieces (#) woodcount Natural logarithm Statistical test Specific stream power (W/m 2) unipower Natural logarithm Statistical test Total stream power (W) totpower Natural logarithm Statistical test D 9 5 ( m ) 8 avg_d95 Not transformed Statistical test Relative roughness (m/m) D_d Square root Statistical test Width-to-depth ratio (m/m) w_d Square root Statistical test co/D9 5 (W/m 3) omega_D Natural logarithm Statistical test Q/D95 (W/m) Gmega_D Natural logarithm Statistical test a. Grain diameter at which 95 per cent of bed material is finer. b. Normality is significant (a = 0.05) according to Shapiro-Wilk, Kolmogorov-Smimov, Cramer-von Mises, and Anderson-Darling. c. Normality is not statistically significant; quasi-normality has been graphically evaluated in histogram. 133 5.7.1 P C A for Var iab le Reduct ion The original dataset is composed o f fifteen variables and 98 reaches (Table 5.1), which in part were collected during field surveys (D95, depth, length, slope, width, wood, Manning's coefficient), and in part were obtain through algebraic calculations (mean velocity, specific power, and total power); drainage area was extracted from D E M s v ia GIS analysis (see section 5.3). This initial set of variables is first analyzed for reduction via P C A , as a predictive model with fifteen variates seems too data intensive (hence costly), difficult to handle and, l ikely, redundant. In P C A , when the analysis is used descriptively to summarize the relationships in a large set o f variables, assumptions regarding the distributions o f variables are not critical. However, multivariate normality is assumed when statistical inference is used to determine the number of components [Tabachnick and Fidell, 2001; p. 588]. Multivariate normality states that al l variables and all linear combinations of variables are normally distributed. This is not an easily testable hypothesis; in fact most available tests are too strict; however, the likelihood of multivariate normality is greatly increased i f the variables are all normally distributed [Tabachnick and Fidell, 2001; p. 180]. This last condition is what P C A has been tested for. Only one variable (D95) is normally distributed; for the other variables several transformations were tried. In the end al l variables have been successfully normalized by using natural-logarithm or square-root transformations (see Table 5.1 and Append ix B l for details on normality tests). P C A takes the original variables that are correlated and finds components (linear combinations o f variables) that are uncorrelated. In particular, through elimination o f redundancies in the data P C A aims to reduce the original number of variables to a smaller number o f components and obtain a model with simple structure. In order to eliminate any potential bias deriving from different units of measurement (see Tab le 5.1) the correlation matrix was used. Accordingly, each "real value" was scaled (or standardized); that is, the corresponding variable mean was first subtracted from each matrix element, and the result was divided by the variable standard deviation. Among the stopping rules available for deciding component retention the Kaiser-Guttman (or latent root) method was considered at an exploratory level, that is, to establish the maximum number o f components to keep [McGarigal et al, 2000]. Further, the broken-stick criterion 134 was applied: an objective, conservative and reliable method [e.g., Jackson, 1993; McGarigal et al, 2000] that advises on the minimum number o f non-trivial components. Accordingly, the latent root method indicated to retain the first four components (90%. o f variance explained, see Table 5.2), the broken-stick criterion (Figure 5.15) suggested keeping the first three components (82% of variance explained, see Table 5.2). The final decision on the number o f components to retain was based on the cumulative-variance explained and on the existence of redundancies (i.e., one variable being significant in more than one component). Component number Figure 5.15. The broken-stick plot. This method suggests retaining all components whose eigenvalue surpasses that o f the ideal random distribution. Table 5.2. Eigenvalues o f the correlation matrix Component Eigenvalue Difference Proportion Cumulative 1 5.64308724 0.97618866 0.3762 0.3762 2 4.66689858 2.61435473 0.3111 0.6873 3 2.05254384 0.88781908 0.1368 0.8242 4 1.16472476 0.66115723 0.0776 0.9018 5 0.50356753 0.08133472 0.0336 0.9354 6 0.42223281 0.06953674 0.0281 0.9635 7 0.35269607 0.19522518 0.0235 0.9871 8 0.15747089 0.12690004 0.0105 0.9975 9 0.03057085 0.02573844 0.0020 0.9996 10 0.00483240 0.00345744 0.0003 0.9999 11 0.00137497 0.00137491 0.0001 1.0000 12 0.00000006 0.00000006 0.0000 1.0000 13 0.00000000 0.00000000 0.0000 1.0000 14 0.00000000 0.00000000 0.0000 1.0000 15 0.00000000 0.0000 1.0000 135 Table 5.3. Eigenvectors of the first four principal components Variable Prin1a Prin2 Prin3 Prin4 lnlength -.041405 0.327590 0 177867 0.333409 lncontr_area -.224959 0.324429 0. 158725 -.175779 lnw_avg_slope 0.370365 -.047538 - 261619 0.195289 lnavgjuddth -.081814 0.441259 0 084540 -.083080 lnshstress 0.368412 0.136269 - 241264 0.013355 lnwoodcount 0.076461 0.154393 0 270174 0.678208 lnavgdepth 0.056530 0.404317 0 002650 -.375827 avg_d95 0.001982 0.390151 - 310034 -.135959 lnunipower 0.411631 0.085251 - 042583 -.037048 lntotpower 0.319356 0.296729 0 005248 -.074258 sqrtD_d -.008580 0.111554 - 584291 0.300219 sqrtw_d -.210262 0.285962 0 148926 0.280142 lnmean_vel 0.235282 -.086285 0 433027 -.125894 lnomega_D 0.391218 - .120166 0 174347 0.011264 lnGmegaJ) 0.367315 0.144725 0 238584 -.039386 Eigenvectors greater than 0.35 are entered in underlined bold font Specifically, a 0.35 threshold was adopted for variable selection in the eigenvector table (Table 5.3). Since bankfull depth appeared significantly correlated in components number 1 and number 4 (see Table 5.3), and considering 82% a sufficient proportion of variance explained, a total o f three components (out o f 15) were retained for further analysis. The first component, which obviously explains the largest portion of variance (Table 5.2), contains variables highly correlated to channel gradient, the second component summarizes relative spatial scaling, and the third component expresses inverse resistance. The forth component, which is not retained, expresses the transient effect played by wood load. In summary, ten variables in total were retained (indicated in underlined bold in Table 5.3). 5.7.2 Multivariate Discriminant Analysis A first M D A was performed on the PCA-reduced dataset (ten variables). M D A relies on two basic assumptions, that data are multivariate normal, and that within-group covariance matrices are homogeneous. The former was already tested in P C A ; Bartlett's test shows the latter assumption is not satisfied (Appendix B2) and so covariance matrices could not be pooled together. To circumvent this limitation, linear discriminant functions were replaced by quadratic functions. Multiple A N O V A tests revealed that bankfull width was not significant at the 0.05 level (bold underlined in Table 5.4), and as such was discarded from the predictive model. Specifically, since ten means were pair-wise compared simultaneously; according to Bonferroni's procedure the critical significance level becomes 0.005. 136 Table 5.4. Univariate test statistics T o t a l Pooled Between R-Square F Value Labe l Standard Standard Standard R-Square / (1 -RSq) (4, 93) P r > F D e v i a t i o n D e v i a t i o n D e v i a t i o n lnw_avg_slope 0.8917 0 4929 0.8344 0. 7086 2^4318 49.85 <.0001 l n s h s t r e s s 0.9623 0 4578 0.9472 0 . 7842 3.6340 74.50 <.0001 lnraean_vel 0.4274 0 3712 0.2518 o. 2808 0.3904 8.00 <.0001 lnavg_depth 0.4292 0 3916 0.2166 0 . 2062 0.2597 5.32 0.0007 lnavg_width 0.6352 0 6070 0.2540 0. 1294 0.1486 3.05 0.0215 lnunipower 1.1055 0 7331 0.9365 0. 5807 1.3850 28.39 <.0001 sqrtD_d 0.2246 0 1860 0.1470 0 . 3466 0.5305 10.87 <.0001 lnGraega_D 1.0263 0.8707 0.6390 0 . 3137 0.4571 9.37 <.0001 lnomega_D 1.0965 0 9087 0.7160 0. 3451 0.5270 10.80 <.0001 avg_d95 0.4196 0 3708 0.2359 0. 2557 0.3435 7.04 <.0001 Table 5.5. Canonical discriminant analysis: likelihood test ratio Can g E igenva lue D i f f e r e n c e P r o p o r t i o n Cumulat ive L i k e l i h o o d R a t i o b Approx F Va lue Num DF Den DF Pr > F 1 7.7455 7.2002 0.9078 0.9078 0.05916400 11.48 32 318.75 <.0001 2 0.5453 0.3486 0.0639 0.9717 0.51741649 3.08 21 250.37 <.0001 3 , 0.1967 0.1516 0.0231 0.9947 0.79954462 1 .74 12 176 0.0627 4 0.0451 0.0053 1.0000 0.95682359 0.80 5 89 0.5503 a . E igenva lues of Inv(E)*H = CanRsq/(1 -CanRsq) b. Test of HO: The c a n o n i c a l c o r r e l a t i o n s i n the cu r ren t row and a l l t ha t f o l l o w are zero A second Discriminant Analysis (i.e., Canonical Discriminant Analysis) was performed on the nine-variable dataset. Note that, since the eigenvalue of C a n l is much larger than the others (Table 5.5), most of the sample differences likely w i l l be explained by the first discriminant function alone. Not surprisingly, likelihood-ratio tests (Table 5.5) indicate that the first two discriminant functions (out of four; i.e.j C a n l and Can2) are significantly different from zero, and as such they have to be considered when interpreting the total canonical structure. With a critical correlation value set to 0.5, the total canonical structure of the first two canonical functions indicates that bankfull depth and D95 can be dropped from the discriminant model (Table 5.6). The model now contains seven variables: slope, shear stress, Dgs/d, specific power, mean water velocity, a/Dgs, and Q/D95. The fact that D95 and specific power enter in three and two predictors respectively, indicates the presence of redundancies within the predictive model. M D A performed with these seven variables yielded a total Error Rate (ER) o f 0.141 which became a disappointing 0.457 after cross-validation (jackknife procedure). In essence, according to the cross-validated output more than 4 out of 10 channel reaches went misclassified (Table 5.7). 137 Table 5.6. Total canonical stracture Variable Cam Can2 Can3 Can4 lnw_avg_slope 0.846236 0.464406 -0.164114 -0.112489 lnshstress 0.914476 0.311872 0.173123 -0.063658 lnmean_vel -0.182874 0.850035 -0.018240 -0.071321 lnavg_depth 0.305651 -0.259580 0.729033 0.089799 lnunipower 0.714860 0.600947 0.141745 -0.082664 sqrtD_d 0.571805 -0.249548 -0.303577 0.575096 lnGmega_D 0.428189 0.660992 0.359911 -0.058088 lnomega_D 0.382873 0.816826 -0.043851 -0.296631 avg_d95 0.449932 -0.295923 0.532383 0.430193 Not satisfied with a 55 % success rate and aware of the redundancies in the dataset, by invoking the principle of parsimony, on the basis o f mmimum, cross-validated, total E R , the number of significant variables was reduced to three. Specifically, the best model includes slope (S), shear stress (r), and relative roughness (Dgs/d); it has a total E R equal to 0.202 and a cross-validated E R of 0.248, which translates into approximately 76 % success rate (Table 5.8). Examination o f bedform-specific misclassifications reveals that the greatest part o f the error occurs in boulder-cascade reaches, where 43 % o f the observations were misclassified as step-pool morphologies (Table 5.8). Bedrock reaches exhibit a success rate o f about 67 %, Table 5.7. Jackknife-validated membership classification results: 7 variables, 5 classes Number of Observations and Percent Classified into chtype From chtype BEDROCK CASCADE SP RAPIDS RP Total BEDROCK 2 4 1 2 0 9 22.22 44.44 11.11 22.22 0.00 100.00 CASCADE 3 10 8 0 0 21 14.29 47.62 38.10 0.00 0.00 100.00 SP 1 10 27 1 0 39 2.56 25.64 69.23 2.56 0.00 100.00 RAPIDS 2 1 3 7 2 15 13.33 6.67 20.00 46.67 13.33 100.00 RP 0 0 0 2 12 14 0.00 0.00 0.00 14.29 85.71 100.00 Total 8 25 39 12 14 98 8.16 25.51 39.80 •12.24 14.29 100.00 Error Count Estimates for chtype BEDROCK CASCADE SP RAPIDS RP Total Rate 0.7778 0.5238 0.3077 0.5333 0.1429 0.4571 Priors 0.2000 0.2000 0.2000 0.2000 0.2000 138 which partly reflects the limited number of observations (n = 9) and the great influence exerted by the anomalous, relict melt-water canyon in East Cap Creek. A l l other channel types have success rates higher than 79 %, with a peak of 100 % for riffle-pool morphologies (located either in hanging valleys or in relict glacial troughs). Table 5.8. Jackknife-validated membership classification results: 3 vars (S, T, D95M), 5 classes Number of Observations and Percent Classified into chtype From chtype BEDROCK CASCADE SP RAPIDS RP Total BEDROCK 6 2 1 0 0 9 66.67 22.22 11.11 0.00 0.00 100.00 CASCADE 3 9 9 0 0 21 14.29 42.86 42.86 0.00 0.00 100.00 SP 2 4 31 2 0 39 5.13 10.26 79.49 5.13 0.00 100.00 RAPIDS 0 0 1 13 1 15 0.00 0.00 6.67 86.67 6.67 100.00 RP 0 0 0 0 14 14 0.00 0.00 0.00 0.00 100.00 100.00 Total 11 15 42 15 15 98 11 .22 15.31 42.86 15.31 15.31 100.00 Error Count Estimates for chtype BEDROCK CASCADE SP RAPIDS RP Total Rate 0.3333 0.5714 0.2051 0.1333 0.0000 0.2481 Priors 0.2000 0.2000 0.2000 0.2000 0.2000 Every statistical model is typically developed on a specific set o f data (calibration set), and is tested on an independent dataset (validation set). Jackknife is a one-at-a-time cross-validation technique, where one observation is held out as a single-element validation set, and all other observations serve as calibration set; the procedure continues until all observations have been involved in the validation re-substitution. In order to account for location effect (i.e., physiographic region), it was decided to run a further M D A , using the three Capilano sub-basins as calibration dataset and Elliott Creek on Vancouver Island as validation dataset. The best model turns out to be simplified. Specifically, the model includes only slope and Dgs/d, yet yielding a validation E R equal to 0.272 (Table 5.9). Considering that success rate associated with random membership allocation of expected class (n = 5) is 20 %, this 73 % 139 discriminatory success seems to be encouraging. In accordance with earlier discussion, boulder-cascade reaches tend to fall wi lhin the step-pool category. Table 5.9. Cross-validated membership classification results: 2 variables (S, D95M), 5 classes. Training dataset: Capilano River sub-basins (Pacific Ranges); validation dataset: Elliott Creek (Insular Ranges) Number of Observations and Percent Classified into chtype From chtype BEDROCK CASCADE SP RAPIDS RP Total BEDROCK 1 1 0 0 0 2 50.00 50.00 0.00 0.00 0.00 100.00 CASCADE 0 4 3 0 0 7 0.00 57.14 42.86 0.00 0.00 100.00 SP 0 1 9 0 0 10 0.00 10.00 90.00 0.00 0.00 100.00 RAPIDS 0 0 0 1 0 1 0.00 0:00 0.00 100.00 0.00 100.00 RP 0 0 0 2 4 6 0.00 0.00 0.00 33.33 66.67 100.00 Total 1 6 12 3 4 26 3.85 23.08 46.15 11 .54 15.38 100.00 Error Count Estimates for chtype BEDROCK CASCADE SP RAPIDS RP Total Rate 0.5000 0.4286 0.1000 0.0000 0.3333 0.2724 Priors 0.2000 0.2000 0.2000 0.2000 0.2000 The poor discrimination achieved between boulder-cascade and step-pool reaches should not surprise. I f in fact, these two channel types are perfectly distinguishable at the channel unit scale, they do become difficult to separate at the channel-reach scale during ground surveys. Frequently, step-pool dominated reaches are intermixed with boulder-cascade units, and vice versa. In fact, boulder-cascades may simply be boulder-choked step-pool systems. In light of this evidence, step-pool and cascade channel types were then merged into one class, and identical analytical procedures were conducted on the same study reaches. The analysis yielded the identical best discriminant model, which includes slope, shear stress and relative roughness. Jackknife validated E R , equal to 0.118 (89% success rate, see Table 5.10), improved significantly from the five-category model. When the Capilano dataset was validated against Elliott Creek, similarly to what was seen before, the best model assumed a two-variable structure (i.e. slope and relative roughness), and total E R drops to 0.223. 140 Overall, 78% success rate is a rather satisfactory result, especially when compared to 25% from random allocation (Table 5.11). Misclassification still occurs, especially with respect to bedrock-controlled channel reaches (cf., F igure 5.12). Table 5.10. Jackknife-validated membership classification results: 3 variables (S, T, D95M), 4 classes Number of Observations and Percent Classified into chtype From chtype BEDROCK CASC & SP RAPIDS RP Total BEDROCK 7 2 0 0 9 77.78 22,22 0.00 0.00 100.00 CASC & SP 4 53 3 0 60 6.67 88.33 5.00 0.00 100.00 RAPIDS 0 1 13 1 15 0.00 6.67 86.67 6.67 100.00 RP 0 0 0 14 14 0.00 0.00 0.00 100.00 100.00 Total 11 56 16 15 98 11 .22 57.14 16.33 15.31 100.00 Error Count Estimates for chtype BEDROCK CASC & SP RAPIDS RP Total Rate 0.2222 0.1167 0.1333 0.0000 0.1181 Priors 0.2500 0.2500 0.2500 0.2500 It is important to highlight that Elliott Creek is not an optimal validation dataset. This is because some categories, such as rapids (n = 1) and bedrock channels (n = 2), are poorly represented. It follows that the occurrence of a single misclassification w i l l result in a shift from 100% to 0% success rate (rapids) or from 100% to 50% success rate (bedrock). B y definition, the jackknife cross-validation procedure is undeniably more resilient to single membership misclassifications; for this reason it is generally preferred to group dataset splitting. Stepwise Discriminant Analysis ( S D A ) was employed as a possible alternative to P C A for variable reduction. However, the S D A final model did not include slope gradient and relative roughness within the reduced set of variables (Table 5.12). This resulted in a significantly lower jackknife success rate (ER = 0.405) when only shear stress was included in the model. Similarly, after validation conducted in Elliott Creek, total E R peaks to 0.406 and to 0.363 respectively for five and four (cascade and step-pool are merged) channel type categories 141 (tables with detailed classification results are not reported). In conclusion, P C A was more efficient than S D A for variable reduction. Table 5.11. Cross-validated membership classification results: 2 variables (S, D9s/d), 4 classes. Training dataset: Capilano River sub-basins; validation dataset: Elliott Creek Number of Observations and Percent Classified into chtype From chtype BEDROCK CASC & SP RAPIDS RP Total BEDROCK 1 1 0 0 2 50.00 50.00 0.00 0.00 100.00 CASC & SP 1 16 0 0 17 5.88 94.12 0.00 0.00 100.00 RAPIDS 0 0 1 0 1 / 0 00 0.00 100.00 0.00 100.00 RP 0 . 0 2 4 6 0 00 0.00 33.33 66.67 100.00 Total 2 17 3 4 26 7 69 65.38 11 .54 15.38 100.00 Error Count Estimates for chtype BEDROCK CASC & SP RAPIDS RP Total Rate 0.5000 0.0588 . 0.0000 0.3333 0.2230 Priors 0.2500 0.2500 0.2500 0.2500 Table 5.12. Stepwise selection summary Number Partial Wilks' Pr < Step In Entered Removed R-Square F Value Pr > F Lambda Lambda 1 1 lnshstress 0.7842 74.50 <.0001 0.21579479 <.0001 2 2 lnGmega_D 0.5112 21.18 <.0001 6.10547444 <.0001 3 3 lncontr_area 0.2366 6.20 0.0002 0.08051966 <.0001 4 4 lnavg_depth 0.1182 2.65 0.0395 0.07100518 <.0001 Number Average Squared Step In Entered Removed Canonical Correlation Pr > ASCC 1 1 lnshstress 0.19605130 <.0001 2 2 lnGmega_D 0.26009286 <.0001 3 3 lncontr_area 0.30768255 <.0001 4 4 lnavg_depth 0.31521211 <.0001 5.8 Discussion This study identifies the existence o f a direct scale linkage between glacial macro-forms and channel reach morphology (Figures 5.4 through 5.7). The glacial macro-forms impose channel gradient and degree o f colluvialr-alluvial coupling, which in turn determine reach 142 channel morphology (see chapter 3). Accordingly, channels that originate from cirque walls exhibit bedrock, chaotic, and boulder-cascade morphology which then switches to rapid and riffle-pool typologies in decoupled hanging valleys. In turn, hanging valleys reset the entire downstream channel-type sequence; in other words, the number o f hanging valleys along a longitudinal profile determines the number of colluvial-alluvial transitions. The consequence is a downstream morphological sequence that progresses with boulder-cascades and step-pools on confined colluvial channels flowing through valley steps (relict glacial macro-forms connecting hanging valleys to main troughs), and terminates with rapid and riffle-pool channel types along fully developed relict glacial troughs (distal fluvial domain). A s a result, the full sequence o f channel types proposed by Montgomery and Buffington [1997] is replicated n+1 times (« = number of hanging valleys in a longitudinal profile). Wi th respect to sediment transport regime as inferred from channel types [Schumm, 1985; Church, 1992; Montgomery and Buffington, 1997], it follows that transport capacity decreases down the headmost morphological series, then resetting at supply-limited conditions at the inception of the valley step in boulder-cascade reaches. In this view, similar to the role of check dams, hanging valleys act as energy dissipaters, sediment filters that block the coarse-grained sediment cascade, and likely prevent, or limit, anadromous species from accessing potentially suitable spawning and rearing habitats. B y analogy, one expects hanging valleys to affect and disrupt the river continuum [Vanhote et al., 1980], according to which river systems are characterized by a gradational continuum o f physical conditions that control aquatic community composition from small headwater streams to large flood plain rivers. In the context of formerly glaciated mountain drainage basins, the disturbance-cascade approach embedded in the concept o f geomorphic process domains [Montgomery, 1999] appears to be more flexible and appropriate to explain the spatial heterogeneity o f aquatic ecosystems. Although there are typically two identical full sequences o f channel-reach typologies (as one hanging valley appears to be the norm), their relative position within the channel network appears to matter, as this imparts specific hydrologic and sediment supply regimes. Accordingly, two sub-categories within each channel typology may be identified; a headmost one, with an ephemeral/seasonal hydrologic regime, and distal counterpart which begins immediately downstream of the hanging valley, where water flow is perennial. Sub-143 categories are apparent in respect to bedrock-dominated, boulder-cascade, and riffle-pool morphologies. Specifically, headmost reaches o f the bedrock and boulder-cascade types cover most part o f steep channels flowing down cirque and valley walls. They are within the source colluvial domain, and as such are periodically scoured by debris flows. The other sub-category sits at the apices o f valley steps and is within the sink colluvial domain and receives coarse-grain sized colluvial loads from tributary junctions. Headmost (source) channel types have highest slope, lowest bankfull width and coarse-grain fraction, but exhibit bankfull depth and relative roughness comparable to those o f downstream (sink) analogues. A s for riffle-pool morphologies, even though headmost and distal reaches are subjected to the same geomorphic processes (i.e., fluvial), they display different cross-sectional and bed-material characteristics; specifically, distal reaches are characterized by lower slope, higher bankfull width and bankfull depth, coarser D95, hence by higher relative roughness. It seems that, i f on one hand local slope is the product o f glacial and paraglacial activities, the magnitude and the temporal distribution o f runoff events, which become systematically larger and more frequent in the downstream direction, explain the occurrence of deeper channels, coarser particle sizes (Atf), and higher relative roughness in distal reaches. In other words, hydrological effects appear to be superimposed on glacial morphometric effects. Unexpectedly, calculated stream power indices (unit and total) and their corresponding ratios with the coarse-grain sediment fraction did not help isolating any single channel type. This finding testifies to the limitations associated with the use of Manning-based parameters in stream channels dominated or even rarely affected by geomorphic processes other than fluvial transport. O n the contrary, despite the numerous influences on channel form, drainage area and slope - the first derivative of topography - appear to act as primary controls on channel-reach morphology in the study drainage basins. In fact, gross discrimination between channel types is achieved by the slope-area and slope-relative roughness representations, as well as by shear stress expressed as a function o f contributing area. These outcomes agree with previous studies conducted in unglaciated mountain streams [e.g., Montgomery and Buffington, 1997] and therefore indicate that landscape glacial history does not confound the separation between channel types. Interestingly, the Quaternary legacy appears to affect the first-order physical conditions (approximated in the slope-area space) that characterize different morphologies; in fact, the glaciated slope range of each morphological category 144 (Figure 5.9) sits at notably higher values in comparison with the corresponding unglaciated analogues [i.e., Buffington, 1995; Montgomery et al., 1995; Montgomery and Buffington, 1997]. Even though based on data analyzed at the channel unit scale, in a study conducted in formerly glaciated headwater streams, Halwas and Church [2002] also noted exceptionally high slope ranges; reasons for such high values were attributed to channel geometry, hence potential shear stress. Examination of channel cross-sectional variables and bed material properties across process domains and channel types indicates that the contributing area required to attain a given bankfull depth, bankfull width, and D95 is much smaller in steep topographies (i.e., step-pools, boulder-cascades), where fluvial sediment transport is coupled by debris flow activity and other mass wasting processes, than in riffle-pool and rapids reaches, where fluvial transport acts alone. The case of D95 is particularly instructive; in fact, despite the potential confounding associated with contemporary remobilization of large boulders stored in glacial/paraglacial valley-floor deposits [Church and Slaymaker, 1989; Heller et al, 2001], process-dependent controls on the spatial distribution of the coarse-grain fraction are apparent. Multivariate discriminant analysis confirms the trends observed in bi-dimensional plots. Accordingly, best channel-reach discrimination is achieved by combining slope, relative roughness, and shear stress when all five morphological categories are considered; shear stress becomes redundant (note that shear stress contains slope and bankfull depth; T = pgdS) when boulder-cascades and step-pools are grouped into one class (two-variable four-category model). Success rates are relatively high, respectively 76% and 89% in the five- and four-category models. In comparison, a study by Wohl and Merritt [2005], which examined exclusively three fluvially-dominated channel typologies (i.e., step-pools, rapids, and riffle-pools) in both unglaciated and glaciated drainage basins, achieved 69% discriminatory efficiency. Reasons for the greater success rate in the present study may be related to the characteristic stepped topography o f the landscape of coastal British Columbia. Steep valley walls and steps, juxtaposed to flat and wide hanging valleys and troughs likely promote greater differentiation between channel morphologies. In fact, Wohl and Merritt did not stratify their dataset into glaciated and unglaciated subsets; this might have been a significant source of variability and might explain the lower ( 145 discriminatory power accomplished by their model. Like ly for the same reasons, the model by Wohl and Merritt includes substantially different variables such as Dg4, and bankfull width (other than slope). If on one hand slope constitutes a common denominator between the present study and that conducted by Wohl and Merritt, on the other, bankfull width would not seem to be a good indicator of channel-reach morphology in coastal British Columbia, owing to the existence o f multiple channel-type sequences located at significantly different drainage areas (hence characteristic hydrological scales). Should these results be confirmed in other streams o f coastal British Columbia, an automated classification o f channel-reach morphology, which one would pursue v ia acquisition o f remotely-sensed data (e.g., D E M s and air ortho-photos), appears to be a challenging task in the Pacific and Insular Ranges of the Coast Mountains. Certainly, slope gradient (the most important predictor) can be conveniently extracted from D E M s - provided that DEM-based slopes are satisfactory approximations of channel-reach true values - and used for prediction. However, data like relative roughness and, eventually, shear stress (which also requires knowledge of bankfull depth) need be collected on the ground, hence defeating the purpose o f a remotely-based prediction. Alternatively, the same objective might be pursued by limiting channel classification to headmost (immediately upstream of valley steps) or distal (downstream of hanging valleys) portions o f the channel network, a partition that can be easily achieved via A P I . In that case, bankfull width (measurable with good confidence on air ortho-photos [i.e., Campbell, 2005]), in addition to channel slope, might become a significant variable for predicting channel typology. Clearly, in order to find out whether this is a realistic option, new multivariate statistical analyses w i l l have to be performed on both data subsets. 146 CHAPTER 6 Downstream Hydraulic Geometry in Glaciated Mountain Streams and Implications for Channel Width Prediction 6.1 Introduction The concept of hydraulic geometry of natural channels is thought to express the mutual adjustment o f cross-sectional variables to imposed water discharges (among other things) [Leopold and Maddock, 1953]. Specifically, water surface width (w), mean depth (d), and mean velocity (v) scale to discharge (Q) according to single power-law relations of the form: These relations may be considered at-a-station through time, or along the network o f a stream channel. Among these two, only the latter, commonly termed downstream hydraulic geometry (DHG) , is a legitimate scaling relation, and as such w i l l be the focus o f this chapter. Large numbers of studies conducted worldwide have shown the existence of relations 6.1, 6.2, and 6.3 [e.g., Ferguson, 1986; Knighton, 1998; Wohl, 2000] and have explored potential trends related to bio-geo-climatic controls. However, functional explanation for such relations is still unclear; in particular, as many as 20 approaches, based on 9 theories (i.e., regime, power function, tractive force, similarity, hydrodynamic, thermodynamic entropy, energy-entropy, minimum extremal, and maximum extremal) have been proposed in the last 50 years [Singh, 2003]. w = aQb d = cQf v = kQm (6.1) (6.2) (6.3) 147 Substantial empirical work indicates that cross-sectional variables in alluvial channels and man-made canals exhibit systematic downstream adjustments to universal scaling relations with water discharge. Specifically, channel width, channel depth, and water velocity tend to scale (with error bars) respectively to the power o f 0.5, 0.33, and 0.1 [e.g., Church, 1992; Knighton, 1998]. 6.1.1 Downstream Hydraulic Geometry in Mountain Streams In mountain streams, owing to the existence o f potentially perturbing factors, such as those brought about by interactions between colluvial and fluvial geomorphic process domains, past episodes of climate change, and tectonic activity, D H G relations are less understood. Accordingly, different studies have yielded contradictory results: in some cases standard alluvial D H G relations have been reported [e.g., Day, 1969; Osterkamp and Hedman, 1977; Montgomery and Gran, 2001; Molnar and Ramirez, 2002; Wohl, 2004a; Wohl and Wilcox, 2005]; in others significant deviations are apparent [e.g., Ponton, 1972; Phillips and Harlin, 1984; Montgomery and Bolton, 2003; Wohl et al, 2004] (cf., Figure 6.1). Figure 6.1. Plots of channel width vs. drainage area showing the lack o f systematic hydraulic geometry relationship for drainage areas below 1 and 10 k m 2 in: (a) Deton Creek (Oregon); and (b) Pojaque River (New Mexico) [from Montgomery and Bolton, 2003]. Pojaque River data are from Miller [1958]. Wohl [2004b], in the quest for limits to D H G relations, examined cross-sectional datasets from ten mountain streams3 (eight of which were formerly subjected to various degree of glaciation). These streams were said to have a "wel l -developed" D H G when water discharge could explain at least half of the total variance (R 2 ^ 0.5) of two of the three cross-sectional variables, certainly a questionable criterion for statistical 10.0D i.00 r •a; § O 100 Cranage area (km?) discrimination. Wohl tested a set o f parameters expressing dimensional ratios of driving force Defined as channels with an average downstream gradient ;> 0.002 m/m. 148 to substrate resistance; among these, QJDs4 yielded a coherent separation between the so called "well-developed" D H G relations and the rest. The threshold for discrimination was estimated to be approximately 10,000 kg/s 3 . In her study, Wohl does not consider eventual departures o f the empirical exponents (i.e., b,f, and m) from widely-accepted alluvial values (i.e., 0.5, 0.33, and 0.1); she justifies her choice by citing Park's [1977] compilation of hydraulic geometry studies, according to which scaling exponents would exhibit a high degree of variability. In truth, I think that limited progress can be made in understanding D H G relations and predicting cross-sectional variates [e.g., Whipple, 2004; Finnegan et al, 2005], without first accepting largely documented D H G exponents [e.g., Church, 1992; Knighton, 1998], at least for well-studied typologies such as pristine, large rivers flowing through steady-state topographies. In fact, I suppose all studies listed above share one common limitation; they have considered D H G as one single power-law relation able to fit the entire longitudinal profile o f a given stream, no matter what. Apparently, a quantification o f the within-long profile heterogeneity is missing; in order to better understand D H G controls and dependences and eventually reconcile contrasting results this aspect cannot be overlooked. To my knowledge, Church [1980] and Brummer and Montgomery [2003] have conducted the only studies that move in that methodological direction, and provides context for topographic and process-driven heterogeneity. In the latter work, four case studies are reported from Washington State, where network-wide patterns of bankfull width are examined in conjunction with other parameters thought to influence D H G relations, such as median bed material grain size (D50), and stream power indices. Their results indicate that geomorphic process domains control downstream systematic variations of D50 and stream power, but not channel width. Specifically, Dso and stream power increase monotonically along debris-flow dominated channels (colluvial domain), attaining maximum values in proximity of debris flow fans, then decreasing (reversal in area-Dso and area-power trends) further downstream where fluvial transport prevails. Bankfull width increases systematically downstream, regardless of transitions in process dominance. Last but not least, Brummer and Montgomery [2003], discussing issues related to field data collection, highlight the question of spatially aggregated data sets (i.e., collected in a number o f branches of a given drainage basin), and 149 find these yielding less systematic scaling dependences compared to relations derived from single longitudinal profiles. Undeniably, part of the complex behaviour displayed by D H G relations in the literature, can be ascribed to (1) inconsistent protocols for field data collection, for example different surveyors may establish different indicators for bankfull width and depth; (2) relations derived from an aggregated set o f reaches belonging to a number o f tributaries, as opposed to the main stem long profile, and/or (3) from a discontinuous series of reaches along a single long profile, so that critical channel segments characterized by peculiar D H G deviations (e.g., colluvial-alluvial transition zones, lithologic contacts, bedrock knick-points) are not included; and (4) by mixing different regime types (e.g., sand and gravel). If on one hand the first problem may be difficult to rectify, the other two can be addressed by conducting continuous ground surveys (with no interruptions) along the principal axis o f stream channels under examination. This type of approach holds important implications for prediction in geomorphology and problems of landscape evolution. For example, the consideration o f spatial heterogeneity in unglaciated, tectonically active settings would aid clarifying to what extent D H G relations may be used as diagnostics to differentiate steady-state from transient topographic conditions [Snyder et al, 2003; Duvall et al, 2004]. In the case of glaciated mountain systems - the focus of this dissertation - the incorporation of spatial heterogeneity into the analysis w i l l allow documenting (or ruling out) systematic dependences o f D H G relations from relict glacial features, contemporary geomorphic process domains (chapter 3), colluvial inputs (chapter 4), and channel types (chapter 5). Indeed, many studies have examined D H G relations in drainage basins that were affected by partial [e.g., Brummer and Montgomery, 2003; Wohl, 2004b; Wohl et al, 2004; Wohl and Wilcox, 2005] or complete [e.g., Day, 1969; Ponton, 1972; Cenderelli, 1998] degree o f glaciation; but while the impact of glacially-inherited topography is usually mentioned as one potential cause o f D H G anomalies, according to my knowledge, no study has ever examined this question in causal and quantitative terms. Reasons for this are (i) GIS and/or detailed digital topography were not available [e.g., Day, 1969; Ponton, 1972]; (ii) glacial imprints were limited to a portion of the study basin [e.g., Ibbitt, 1997; Molnar and Ramirez, 2002; Brummer and Montgomery, 2003]; (iii) glaciated and unglaciated settings have not been opportunely stratified [Wohl, 2004b]; and (iv) optimality in energy expenditure was 150 considered to overwhelm any other confounding factor [e.g., Rodriguez-Iturbe et al, 1992; Molnar and Ramirez, 1998a]. A n exception in the work by Ibbitt [1997] and Molnar and Ramirez [2002] (this last based on Ibbitt's data) illustrates how basin and channel heterogeneity can play a critical role in influencing D H G and the spatial distribution of energy expenditure in two river systems of N e w Zealand. However, since the density o f field measurements was low, as channel variates were taken "upstream o f every confluence shown on the 1:50,000 maps and at 0.5 k m intervals where the distance between two confluences exceeded 1 km", a detailed consideration o f the impacts brought about by geomorphic process domains and/or glacial macro-forms (where present) was missing in this case too. 6.1.2 Prediction of Bankful l Channel Width Characteristic slope-area scaling dependences define distinct geomorphic process domains, which in turn are associated with specific rates o f local erosion (section 1.1 and chapter 3). In channelled topography, the energy available for incision, hence to detach and transport material is approximated by total stream power (Q). Specifically, estimation of river power per unit bed area (co), also termed specific or unit stream power, is directly dependent -besides local slope (S) and contributing area ((A) proxy for water discharge (Q)) - on channel width (ro = Q/w = pgQS/w). A s a consequence, the ability to predict channel width has important implications for understanding landscape evolution and building relevant models. In the last decade, researchers in long-term landscape evolution have dedicated particular attention to what controls channel width in bedrock settings [e.g., Seidl and Dietrich, 1992; Tinkler and Wohl, 1998; Montgomery and Gran, 2001; Snyder et al, 2003; Duvall et al, 2004; Whipple, 2004; Finnegan et al, 2005; Stark, 2006]. Even though the definition of bedrock channel is rather vague in the literature, this channel type has been privileged because o f its greatly simplified conditions in comparison to alluvial counterparts. For example, the effects of sedimentation, channel bed-forms, and bed armouring, which necessarily would complicate the overall scenario to be reproduced, can be neglected. In this simplified context, Finnegan et al. [2005] have elaborated an expression (based on the Manning [1891] equation (5.1), and mass conservation principles) for modelling channel width (w) o f bedrock channels in tectonically transient, unglaciated settings: w = [a (a + 2)2/3f8Q3/8S3/16n3/8 (6.4) 151 where channel cross-section is rectangular; width-to-depth ratio (a=w/d) is considered to be constant; and the Manning's coefficient (n) is also set constant. Note that, according to Finnegan et al. [2005] width-to-depth ratio is relatively constant in natural channels for a given channel bed material (i.e., bedrock; cf., Figure 6.2); in fact, without such a condition bankfull width would appear in both sides o f equation 6.4. Width (m) Figure 6.2. Width versus depth for different dorninant channel substrates (from Finnegan et al. [2005]. Gravel data are from Yellowstone River [Leopold and Maddock, 1953]. Although the authors do not report any statistical comparison between predictive models, undeniably in unglaciated complex terrain (i.e., Yarlung Tsangpo River (Tibet), and Northern Coastal California) equation (6.4) provides a far better graphical approximation of satellite-measured bankfull widths, than the discharge-dependent, power-law relation (equation (6.1)). This outcome is of critical importance with respect to local rates of channel incision, as equation (6.4) yields specific stream power (i.e., erosivity) values as much as 40% higher than otherwise predicted by equation (6.1). In the physisographic setting o f this dissertation, owing to the superimposition o f currently active geomorphic process domains on relict glacial topography, every study basin exhibits a channel long profile with complex segmented structure (see section 5.4) that resembles those of tectonically transient terrain [e.g., Schoenbohm et al, 2004; Whipple, 2004; Finnegan et al, 2005]. W i l l such departures from the equilibrium concave-up profile impart significant deviations to the simple discharge-based power-law dependences [Leopold and Maddock, 1953]? A n d by extension, to what degree can equation (6.4) reasonably predict bankfull width in glaciated, topographically complex, mountain rivers? 152 6.2 Objectives In consideration o f the prominent influence that glacial macro-forms have on the organization of geomorphic process domains (see chapter 3), and reckoning that process-based causal linkages between glaciated topography and D H G variability (hence prediction) are virtually unknown, three main objectives w i l l be pursued in this chapter. These include examining how the spatial organization o f glacial macro-forms and process domains affects D H G relations, and testing the Q/D95 threshold proposed by Wohl [2004b] in the continental glaciated setting o f coastal British Columbia. Last, the question o f bankfull width prediction w i l l be tackled; a series of models w i l l be contrasted and critically evaluated (section 6.5.6). 6.3 Study Areas Study sites are four tributaries of the Capilano River and one tributary of the Tsitika River. They are all located in formerly glaciated mountain terrain o f coastal British Columbia, an ideal setting for conducting detailed analysis on complex topographic variability and examining the existence of potential causal linkages between relict glacial macro-forms and reach-based D H G relations. See section 5.2 for detailed description. 6.4 Data Collection and Analysis The specifics for the collection of channel variates (i.e., w, d, and D95) and the calculations at the reach scale o f corresponding indices of available stream energy (i.e., r, Q , and 00) and resistance (i.e., QJD95 and (0/D95), have been already described in section 5.3. D H G relations are constructed at the reach scale so that relevant findings can be compared to prior studies, and can be evaluated in conjunction with insights previously gained in terms of process domains (chapter 3) and channel-reach morphology (chapter 5). Since the main goal of this section is to compare (as opposed to predict) D H G relations to unglaciated alluvial analogues, relations are determined via functional analysis rather than by applying simple regression procedures [Mark and Church, 1977]. Addressing this last objective, the question of bankfull width prediction entailed applying equation (6.4) to the study basins under a number of conditions and specifications. First, bankfull discharge (Q) was approximated by contributing area (A). Second, the assumption o f rectangular cross-section was retained, so the hydraulic radius R in the Manning equation was equal to (dw)/(2d+w). Third, the assumption o f constant a within channels with consistent substrate needed be tested. This was achieved, considering that different channel 153 types (i.e., bedrock, boulder-cascades, step-pools, rapids, and riffle-pools) have specific dominant substrates, by examining width-to-depth ratios (a) across channel morphologies. Last, given the wide range of channel types included in the study basins, Manning's coefficient (n) was considered variable between channel reaches. 1.6 ct m Q 1.4 1.2 1 0.8 0.6 0.4 -I 0.2 0 a (ca) = 18 + . , ' ' « ( S P ) = 25 a (br, rd) = 38 a (rp) = 53 • bedrock A cascade O rapids X riffle-pool + step-pool 10 20 30 40 50 Width (m) Figure 6.3. Width-to-depth ratio across channel types. The corresponding R squared values are: 0.91 (riffle-pools), 0.30 (rapids), 0.74 (step-pools), 0.78 (boulder-cascades), and 0.60 (bedrock). Data points are from the Capilano River channel, and from East Cap, Elliott, Hesketh, and Lembke Creeks. Specifically, coefficients computed in two different ways were compared, one obtained through visual evaluation against measured standards [Hicks and Mason, 1991]; the other obtained by applying the basic Keulegan [1938] flow resistance equation as modified by Thompson and Campbell [1979], expresses n as a function of field-measured D95. The choice is supported by a comparative study conducted by Church et al. [1990], according to which Thompson and Campbell's equation was found to fit empirical data, covering a wider range of flow conditions than other equations. Thompson and Campbell's equation has the form: 1/f2 = (1- 0. lk/R) 2.03 log (12.2R/k) (6.5) where / i s the Darcy-Weisbach number (f= 8a), k is a roughness length scale dependent on grain diameter (i.e., k = 2 D95), R is the hydraulic radius [R = (dw)/(2d+w)], and a is the constant o f proportionality according to the Chezy equation [fv = gRS/a)1/2]. Finally, by entering the field-measured data in equation (6.5) and by rearranging equation (5.1) as: n = (Rl/3a/g) 1/2 (6.6) 154 the coefficient n can then be incorporated into equation (6.4) and compared against its visually-estimated analogue. This method, as opposed to the one based on visual comparison, has the advantage of being more objective, as no room is left for personal judgment. Interestingly, width-to-depth ratio (a) in the study basins (Figure 6.3) appears to somewhat mimic the pattern highlighted by Finnegan et al. [2005], with a increasing systematically as gravel-bed material offers less resistance to entrainment. In this idealized continuum, however, bedrock channels do not occupy the expected position on the graph (they plot together with rapids). This outcome, in conjunction with the relatively low R squared values (see caption in Figure 6.3) and the high scatter on the graph itself, indicate that associating a constant a to each channel type would imply accumulating large errors in equation (6.4). For this reason, it appears more appropriate to model channel width by assigning reach-specific, field-based a values. Equation 6.4 is a hydraulics equation with the assumption of a fixed a, not a theory for channel width per se. For this reason a specific assumption needs to be made, that is, channel width is simply adjusted to convey the flow specified as characterized by the Manning's expression. This is not a very mechanistic notion, therefore one should expect that spatial variability in bank strength and sediment supply (since the study channels are not bedrock channels) w i l l strongly affect measured bankfull-width values. 6.5 Results Results are outlined in the same order adopted in chapter 3, that is, by beginning with streams of simplest structure (transverse transects; i.e., HeskethlOO Creek), and continuing with streams o f more complex configuration (longitudinal transects; East Cap Creek, Elliott Creek, Hesketh Creek, and Lembke Creek). Discharge-dependent variables, for which reach-based downstream scaling relations are examined, include bankfull width, bankfull depth, D 9 5 , and stream power. However, before considering such relations, in order to explore how well scaling relations based on reach averages approximate those constructed from all data points, the case of HeskethlOO is examined. 6.5.1 Transverse Transect: Ground Measurements Versus Reach Averages The aim o f this section is to test whether or not reach-based scaling relations are a faithful approximation o f those constructed from the actual ground measurements. The test is 155 performed on HeskethlOO Creek, which represents a typical low-order stream in a formerly glaciated setting. Specifically, it is composed of two fundamental landscape building blocks (i) a colluvial domain (C; a debris-flow dominated channel eroding an oversteepened valley wall), which extends from the headwaters down to the terminus of a paraglacial fan (hatched area in Figure 6.4), and (ii) a fluvial domain (F), which occupies the valley floor o f a relict glacial trough. A s w i l l become clear in the remainder of this chapter, such landscape units are arranged in multiple and different combinations throughout the more complex longitudinal transects (see sections 6.5.2-4). The reach-based area-width relation in HeskethlOO mirrors the spatial organization of the geomorphic process domains described above and as such is composed o f two segments (Figure 6.4). The channel exhibits downstream widening (b = 0.610±0.103) along the colluvial portion (C), reaching a maximum (~10 m) at the terminus of the paraglacial fan. Lower in the basin, the scaling relation inverts (b = -5.913±5.587) and significant channel narrowing is observed (Table 6.1). The fluvial and colluvial relations are significant, as they explain a larger portion of variance (R 2 = 0.939 for C ; R 2 = 0.683 for F) than the combined Table 6.1. Hydraulic geometry relations in HeskethlOO Cr.: field data points vs. reach averages Exponent Intercept Process Domain Method Equat ion' CI (95%) S E E CI (95%) S E E p Reach W = 25.6AU B 1 U 0.939 [0.508-0.713] 0:045 [19.532-33.6] 0.054 12 F D P w = 21.83A0 5 2 3 0.894 [0.457-0.589] 0.031 [18.13-26.29] 0.039 33 TJ p Reach w = 0.017A5 9 1 3 0.683 [-11.5- -0.324] 1.660 [0-4.212] 0.86 5 r F D P w = 0.002A"7985 0.695 [-12.29- -3.68] 1.519 [0-0.155] 0.781 9 combin. Reach w = 12.023A0 5 4 5 0.458 [0.219-0.871] 0.104 [6.97-20.753] 0.111 17 F D P w = 13.95A 0 4 9 1 0.588 [0.358-0.624] 0.050 [10.56-18.42] 0.06 42 p Reach d = 0.758A"-*' 0.242 [-0.165-0.819] 0.094 [0.509-1.127] 0.067 7 F D P d = 0.491 A 0 8 2 3 0.208 [-0.06-1.706] 0.189 [0.414-0.583] 0.035 17 Q. p Reach d = 0.107A'1 4 6 2 0.845 [-2.33- -0.595] 0.289 [0.041-0.278] 0.149 4 CD Q r F D P d = 0.047A"2106 0.909 [-2.65- -1.554] 0.224 [0.025-0.089] 0.115 9 combin. Reach d = 0.51A0 3 4 2 0.025 [-1.844-1.195] 0.106 [0.357-0.727] 0.068 11 F D P d = 0.525A"0303 0.012 [-1.42-0.817] 0.061 [0.424-0.644] 0.044 26 p Reach D = 1.217AU2UU 0.591 [0.126-0.434] 0.054 [0.878-1.687] 0.065 13 F D P D = 0.086A 0 2 8 3 0.504 [0.167-0.399] 0.040 [0.935-1.587] 0.056 33 D95 p Reach D = 0.015A3 2 5 6 0.918 [-4.602--1.91] 0.461 [0-0.069] 0.238 4 D95 r F D P D = 0.015A3 4 5 2 0.828 [-4.637- -2.27] 0.471 [0.004-0.054] 0.249 9 combin. Reach F D P D D = 0.83A 0 2 8 0 = 0.9A 0 2 6 4 0.138 0.208 [-0.111-0.671] [0.09-0.438] 0.067 0.039 [0.582-1.183] [0.714-1.11] 0.072 0.047 17 42 a. Relations are functional, rather than least squares regressions [Mark and Church, 1977]. 156 10 a. o CO a) valley wall (colluvium/bedrock) parag lac ia l fan (colluvium) O + + • • + • t I + Slope • Width • Width (reach) 0.1 0.001 10 trough floor (alluvium) 100 10 TJ 5 0.1 0.01 0.1 Area (km ) ta Q 0.1 b) valley wall (colluvium/bedrock) paraglac ia l fan (colluvium) • • A trough floor (alluvium) 8 o • • D95 O D95 (reach) a Depth A Depth (reach) T Q. d> Q 0.1 0.001 0.01 0.1 1 Area (km2) Figure 6.4. Scaling relations in Hesketh 100 Creek, based on all field data points (solid symbols) and reach averages (open symbols), of contributing area with a) bankfull channel width, and b) bankfull channel depth and D95. Relevant power-law relations are reported in Table 6.1. Local slope gradient is shown for reference to geomorphic process domains. C and F refer to colluvial and fluvial domains (see chapter 3 for more details). ^ = tributary junction: fluvial (solid) and colluvial (dashed); ^ = active debris flow fan. Hatched area defines the extent o f the paraglacial fan. 157 relation does (R 2 = 0.458). Area-width relations constructed using all field data points (hereafter termed as FDP) reproduce closely those based on reach averages, both in terms o f exponents (b = 0.523±0.660 in C ; b = -7.985±4.305 in F) and shape (location of inflection/reversal points in Figures 6.4a and 6.4b). Interestingly, the exponent of the F D P -based colluvial relation is not significantly different from the standard 0.5 value; the reach-based exponent is significantly higher (even though only slightly), at the 95% level o f significance. The combined reach-based area-depth relation o f HeskethlOO Creek indicates that a single power-law relation yields a poorer fitting (R 2 = 0.025 in Table 6.1) than i f separated into domain-wise partitions (R 2 = 0.242 in C; R 2 = 0.845 in F). In fact, the relation displays high scatter in the colluvial domain (C in Figure 6.4b) where, incidentally, establishing bankfiill depth in the field represents a real challenge. Downstream, bankfull depth remains virtually constant across the paraglacial fan, then decreasing remarkably along the fluvial reaches o f the trough floor (F in Figure 6.4b; / = -1.462±0.868). Similar to what was observed for bankfull width, FDP-based area-depth relations are in line with reach-based downstream patterns (Figures 6.4a and 6.4b). In terms of aiea-D^ scaling, HeskethlOO reaches show colluvial downstream coarsening (j = 0.280 in C ; R 2 = 0.591) and high fluvial downstream fining (j = -3.256 in F ; R 2 = 0.918). In line with the behaviour of the other channel variates, the overall (combined) reach-based area-Dp5 relation exhibits inferior fitting (R 2 = 0.138) compared to domain-specific relations. FDP-based relations are virtually identical to those based on reach averages just described (Figure 6.4b and Table 6.1). In order to be considered not statistically different (i.e., a = 0.05), the real and the reach-based power-law scaling relations require that the respective confidence intervals (i.e., 95%) exhibit some degree o f overlapping, both in terms of exponent and intercept. In summary, such conditions are perfectly met in Hesketh-100 Creek (Table 6.1) where each reach-based scaling relation is statistically equal to the one based on all field data points. Ultimately, this outcome supports using reach averages for inferring downstream hydraulic geometry relations. 158 6.5.2 Longitudinal Transects: Channel Width With the exception of East Cap Creek, all combined area-width relations of the study basins exhibit an exponent not significantly different ( a = 0.05) from the conventional value. R values range between 0.715 and 0.795 and b are consistently smaller than 0.5 (see Table 6.2). Nevertheless, major deviations within each study basin are apparent, and deserve discussion in more depth. In fact, process-specific segmentations are evident in all case studies; overall, a total o f eleven segments (out of 19) exhibit exponents significantly different from 0.5 (Table 6.2). However, owing to the limited number of reaches within some process domains confidence intervals are remarkably large, so statistical discrimination from "standard" exponents becomes problematic. For this reason, in each study basin the "standard" relation is imposed through the headmost reach and cumulative downstream departure patterns are evaluated graphically in light o f variations in local slope, and in water/sediment supply by noting the location of fluvial (non torrented) and colluvial (torrented) tributaries. In Hesketh Creek (Figure 6.5a) three distinct segments may be identified. Proceeding in the downstream direction, bankfull width increases according to unglaciated fluvial standards (b = 0.566±0.368) at the headwaters (CI and HF1), then it stays nearly constant along the cirque wall , in the debris-flow affected channel (b = 0.089±0.367; C2). Hence, bankfull width first resets at smaller values (from 7.87 m in the run-out zone of C 2 , to 4.53 m at the inception o f HF2), then increasing dramatically along the fluvially dominated reaches of the hanging valley and continuing to show the same pattern down the valley step (b ~ 1.591±0.3; HF2+C3). The fitting yielded by H F 2 and C3 together (R 2 = 0.913, Table 6.2) is superior to those of the segments considered separately, as well as to the combination of the hanging fluvial reaches (R 2 = 0.59; HF1+HF2). To siimmarize, two segments (i.e., C 2 , and HF2-C3) , out of three, display an exponent that is significantly different from 0.5, at a = 0.05. Interestingly, a discontinuous field survey carried out only on C1/HF1 and on the distal-most reaches of Hesketh Creek (F) would have approximately yielded a 0.5 exponent, leaving area-width deviations undetected. When imposing the 0.5 power-law relation through the headmost reach, departure occurs along C2 (i.e., width is nearly constant), where the channel is confined, gradient decreases quickly, and lateral colluvial sediment supply is high (note the colluvial tributary in Figure 6.5a); further downstream, along the hanging valley (HF2) and 159 the valley step (C3) the scaling appears to compensate for the upstream departures and abnormal channel widening occurs. In Elliott Creek (Figure 6.5b), the bankfull width-area relation exhibits a lesser degree of segmentation. Accordingly, except for C I (R 2 = 0.896), the combined relation displays superior fitting (R 2 = 0.795) than those associated with the single process domains (Table 6.2). Interestingly, zones HF1 and H F 2 together (fluvial domain) seem to yield better fitting than when taken separately. In summary, the exponents of C I and HF1+HF2 are significantly smaller than b = 0.5 ( a = 0.05) and do not differ from each other. In general terms, it is apparent that H F 2 lies below and C2 and C3 lie above the general trend line. Therefore, even Table 6.2. Bankfull channel width as a function of contributing area across process domains c Process domain Exponent Intercept to CD CD Equation a R 2 CI (95%) S E E CI (95%) S E E n H100 C F combined w w w = 2 5 . 6 A U B 1 U = 0.017A" 5 9 1 3 = 12.02A 0 5 4 5 + rs ~ ~ .0.566 0.939 0.683 0.458 [0.508 -0.713] [-11.5--0.324] [0.219-0.871] 0.045 1.660 0.104 [19.532-33.6] [0-4.212] [6.97-20.753] 0.054 0.860 0.111 12 5 17 CD I C2 HF2 C3 HF1+HF2 HF2+C3 combined w = 7.37A w = 3.049A1 w = 1.413A w = 4.799A' w = 1.553A w = 6.823A' 0.089 0.838 1.707 0.245 1.591 0.453 0.164 0.674 0.882 0.590 0.913 0.763 [-0.279 -0.456] [-0.506 -2.183] [1.232-2.182] [-0.055 -0.544] [1.291 -1.879] [0.335 -0.571] 0.039 0.256 0.194 0.072 0.129 0.049 [6.808-7.98] [1.117-8.337] [0.748-2.673] [0.577-0.786] [1.076-2.244] [5.834-7.98] 0.011 0.102 0.120 0.033 0.073 0.032 5 4 10 5 14 22 C1 w = 2 .906A" 2 4 4 0.896 [0.114-0.375] 0.039 [2.368-3.566] 0.028 5 HF1 w = 4 .575A° 0 0 0 -0.225 [-0.002 -0.002] 0.234 [3.263-6.413] 0.034 4 C2 w = 6 . 6 7 4 A 0 7 1 0 -0.111 [-2.205 -3.624] 0.305 [2.498-17.83] 0.134 5 O HF2 w = 4.221A 1 2 6 0 -0.022 [-4.345 -6.866] 0.193 [0.982-18.15] 0.147 4 Qj C3 w = 2.853A 1 8 6 4 0.366 [-0.237 -3.865] 0.525 [-1.19-1.037] 0.483 10 HF2+C3 w = 1 .109A 1 2 5 6 0.622 [0.608-1.91] 0.233 [-0.41-0.497] 0.206 13 HF1+HF2 w = 4 . 3 2 A 0 2 0 0 0.684 [0.064 -0.337] 0.046 [3.746^1.982] 0.025 8 combined w = 4 . 0 9 3 A 0 4 2 9 0.795 [0.339-0.5191 0.039 [3.589-4.667] 0.028 27 C1 w = 1 4 . 9 8 A 0 4 0 4 0.936 [0.145 -0.663] 0.058 [5.409-41.49] 0.103 4 CD HF w = 2 .941A" 0 2 2 4 0.819 [-0.466 -0.027] 0.052 [2.515-3.44] 0.016 4 C2a w = 7 .09A- ° 1 9 5 -0.161 [-1.413-1.024] 0.190 [5.631-8.938] 0.039 7 E C2b w = 3.762A0 8 3 6 0.950 [0.635 -1.036] 0.076 [2.925-4.839] 0.043 7 CD _ l C2c w = 82 .05A" 0 5 3 1 0.810 [-0.71--0.349] 0.073 [55.181-122] 0.077 12 HF+C2a-b w = 5.223A 0 6 2 2 0.846 [0.475 -0.768] 0.063 [4.602-5.916] 0.025 17 combined w = 8 . 1 1 4 A 0 4 1 5 0.715 [0.319-0.511] 0.040 [6.815-9.66] 0.037 33 C1+HF+B w = 5 . 7 8 6 A 0 2 0 b = 15.46A" 1 3 2 1 = 3.224A 0 6 4 2 0.668 [0.059 -0.35] 0.046 [-0.174-0.07] 0.036 7 CD O to C2 w 0.941 [-2.15--0.507] 0.184 [0.001-0.139] 0.044 4 F w 0.918 [0.536 -0.747] 0.047 [-0.38-0.222] 0.043 17 CD LU C1-HF-B-C2 w = 6.397A0 2 4 2 0.773 [0.143-0.341] 0.038 [-0.124-0.07] 0.024 11 combined w = 6.18A 0 3 4 9 0.746 [0.267-0.4311 0.035 [-0.135-0.07] 0.028 28 a. Relations are functional, rather than least squares regressions. 160 though no domain effect is statistically detected, differences may be appreciated by graphical examination. In Elliott Creek, departure from the imposed alluvial scaling (0.5 line) occurs right at the headwaters (CI). This behaviour is likely a consequence of the glacially-inherited topography; specifically, the headwall of the relict cirque is partially open (Figure 5.1b), so the slope of this first-order stream is relatively low (S < 0.3) in comparison to the other study basins, and downstream widening is lower than along other cirque walls. Further downstream, the relation proceeds by steps where slope gradient is remarkably low (HF1 and HF2), and lateral sediment supply is high (C2, four colluvial tributaries), hinting at the existence of distinct fluvial and colluvial regimes and at feed back controls exerted by channel gradient and sediment supply on bankfull width. Along the valley step (C3), and similar to what was observed in Hesketh Creek, the scaling seems to compensate for upstream departures by showing high downstream widening. At first glance, the width-area scaling of Lembke-Sisters Creek (Figure 6.5c) may be broken down into three segments (i.e., CI, HF-C2a-b, and C2c). Conventional downstream widening is observed in the colluvial head-most reaches (CI), thence channel width drops from 4.38 m (end of CI) to 3.62 m (downstream of the paraglacial fan, Figure 6.5c), then widening further downstream with an exponent equal to 0.622±0.147. Down from the confluence with Sisters Creek, width scaling agrees with that of Sisters' headmost reaches, and so exhibits remarkable downstream narrowing (b = -0.53110.179; C2c). Closer examination of the hanging fluvial reaches (HF) shows slight downstream channel narrowing (b = -0.224±0.242), similar to what was seen in Hesketh 100. Overall, process domains do not impart distinct downstream trends (narrowing or widening), which instead appear to be controlled by relict glacial macro-forms: hanging valley in zone HF, and the legacy of a relict trough confluence in zone C2c. In Lembke Creek, departure from the 0.5 trend occurs in the hanging valley; comparable to the appearance in Elliott Creek, the width-area scaling relation proceeds by steps in transport limited reaches: (i) in gentle, decoupled reaches (HF) where transport is limited by slope gradient; and (ii) in steep, sediment choked colluvial channels (C2a and C2c; see colluvial tributaries), where transport of colluvial material is limited by flow competence. In agreement with the interpretation that low slope gradient and high lateral colluvial sediment supply may prevent channel downstream widening, where channel / 161 100 a) £ 10 • t fluvial tributary A i colluvial tributary i V alluvial fan • Width • Slope C1 • • • 1 • HF1 0.1 £ » a o vi 0.01 0.001 0.01 0.1 Area (km2) 10 0.001 Area (km') Figure 6.5. Bankfull channel width as a function o f contributing area for: (a) Hesketh Creek, and (b) Elliott Creek. Values are reach averages. Relevant power-law relations are reported in Table 6.2. Codes refer to process domains defined in chapter 3. Channel slope is reported for reference. 162 0.001 0.01 0.1 , 1 Area (km') 100 d) 10 •o 0.1 t alluvial fan i i fluvial tributary 4 i e C1 HF B 0.01 0.1 1 Area (km2) 10 B 100 100 Figure 6.5. (Continues from previous page). Bankfull channel width as a function o f contributing area for: (c) Lembke Creek, and (d) East Cap Creek. Values are reach averages. Relevant power-law relations are reported in Table 6.2. Codes refer to process domains defined in chapter 3. Channel slope is reported for reference. 163 slope is consistently high and sediment supply is reduced (C2b), high downstream widening is observed. In the area-width plot of East Cap Creek (Figure 6.5d) two main segments may be distinguished (i.e., C 1 - H F - B - C 2 , and F). Respectively, b equals 0.205±0.145 in the headmost portion (for drainage areas smaller than 2 km 2 ) and 0.642±0.106 along the fluvial reaches of the relict glacial trough (F). However, careful examination shows downstream channel narrowing (b = -1.321±0.829) in C2 (debris-flow run-out zone) at the approximate scale of glacial trough initiation. C2 may be seen as a transition zone between a bedrock-controlled regime (B) and a fluvial regime (F). Similar to what is observed in all other study basins, channel width resets to lower values (from 6.64 m to 4.67 m) at the beginning o f the fluvial domain. In terms o f area-width scaling exponents, all segments deviate significantly ( a = 0.05) from widely accepted standard values and such deviations are apparently induced by the inherited glacial topography. The predominantly fluvial nature of East Cap Creek (no colluvial tributaries in Figure 6.5d) appears to support earlier observations made in terms o f slope-colluvial supply interaction; accordingly, in the absence of low-slope or high-supply reaches the pattern of the width-area relation does not proceed by steps. Owing to the scarce number of data points, interpreting zones C I and HF1 is impossible. Downstream of these zones, deviations from the imposed 0.5 power-law trend are certainly reduced in comparison with Hesketh and Lembke Creeks. 6.5.3 Longitudinal Transects: Channel Depth According to studies mainly conducted in large alluvial rivers, bankfull depth typically increases with drainage area to a lesser degree (f= 0.33) than bankfull width. In the present study basins, which clearly don't have strictly alluvial character, two of the combined area-depth relations (i.e., Hesketh Creek and Lembke Creek, Table 6.3) exhibit an exponent (/) that is not significantly different from the expected conventional value at the 95% confidence level; conversely, Elliott and EastCap Creeks exhibit significantly lower (than 0.33) downstream channel deepening (Table 6.3). A l l combined relations have rather high proportions of unexplained variance (i.e., 0.48 < R 2 < 0.56), while in Hesketh and Lembke Creeks single segments appears to have far superior fitting than the combined relation, therefore indicating that such area-depth segmentations are statistically significant. 164 In Hesketh Creek, departures from the imposed 0.33 line mimic those observed in terms o f channel width; accordingly, major departure occurs in C2 and "attraction" to the 0.33 line is observed along the valley step (C3). A s a result, the relation (Figure 6.6a) may be subdivided into three segments (i.e., C1+HF1, C 2 , HF2+C3). Bankfull depth scales with drainage area along its headmost colluvial reaches and the incipient hanging valley with an exponent f-0.249±0.050. Significant downstream channel narrowing occurs along the debris-flow dominated reaches of C2 (f= -0.168±0.0450), and channel depth attains a minimum in the main hanging valley (HF2), then increasing substantially along the valley step if = 1.239+0.194; C3). In the distal most fluvial reach bankfull depth resets at drastically smaller values (from 1.2 m in C3 to 0.6 m in F ; Figure 6.6a). Table 6.3. Bankfull channel depth as a function of contributing area across process domains Basin Process Equation a R 2 • Exponent Intercept n domain CI (95%) S E E CI (95%) S E E HesklOO C d = 0.491 A U B " 0.208 [-0.06-1.706] 0.189 [0.414-0.583] 0.035 12 F d = 0 . 0 4 7 A 2 1 0 6 0.909 [-2.65-1.554] 0.224 [0.025-0.089] 0.115 5 combined d = 0.525A" 0 3 0 3 0.012 [-1.42-0.817] 0.061 [0.424-0.644] 0.044 17 Hesketh C1-HF1 d = 0 . 5 6 4 A U 7 4 y 0.999 [0.198-0.299] 0.004 [0.487-0.652] 0.005 3 C2 d = 0 .602A"° 1 6 8 0.989 [-0.21-0.123] 0.010 [0.585-0.62] 0.003 4 HF2-C3 d = 0 . 1 8 6 A 1 2 3 9 0.879 [0.891-1.433] 0.124 [0.134-0.26] 0.067 14 combined d = 0.575A 0 3 1 8 0.560 [0.140-0.336] 0.047 [0.495-0.667] 0.031 22 Elliott combined d = 0.386A 0 J 4 1 / 0.484 [0.125-0.309] 0.031 [0.347-0.429] 0.022 27 Lembke C1 d = 1 .186A U J * 4 0.998 [0.233-0.295] 0.007 [1.045-1.346] 0.013 4 HF-C2 d = 0.351A 0 4 9 3 0.930 [0.432-0.555] 0.028 [0.319-0.387] 0.020 23 combined d = 0 . 5 4 2 A 0 2 4 9 0.485 [0.143-0.355] 0.036 [0.462-0.6371 0.034 27 EastCap combined d = 0.523A U - 1 U S 0.552 [0.115-0.275] 0.029 [0.478-0.573] 0.019 23 a. Relations are functional, rather than least squares regressions. The depth-area relation of Elliott Creek exhibits a rather uniform pattern (Figure 6.6b). However, two major deviations stand out from the general trend: (i) an exceptionally deep channel reach in C2 , and (ii) markedly shallow reaches in H F 2 . The former is the result of an abrupt transition in local channel morphology at the inception o f the valley step from gentle riffle-pools and rapids to steep boulder-cascades (cf., Figures 6.7a and 6.7b). The latter is the expression o f shallow, fully decoupled, fluvial reaches, dominated by riffle-pool morphology in the primary hanging valley of Elliott Creek (e.g., Figure 5.2b). A s observed for channel width, the morphometry of the relict cirque, whose headwall is partially open, imparts the nearly constant bankfull depth in C I . 165 10 a) .c 1 2 0.1 1 fluvial tributary • depth O D 9 5 i colluvial tributary paraglacial fan O O C1 O HF1 O O o 4 o 4 C 2 4-1 HF2 C 3 1.0 IO CT) Q 4- 0.1 0.01 0.01 0.1 10 Area (km ) Area (km2) Figure 6.6. Bankfull channel depth and D 9 5 as a function of contributing area for: (a) Hesketh Creek, and (b) Elliott Creek. Values are reach averages. Relevant power-law relations for channel depth and coarse grain-size fraction are reported respectively in Table 6.3 and 6.4. Codes refer to process domains defined in chapter 3. 166 10 c) 5 1 a a 0.1 ^ fluvial tributary • colluvial tributary paraglacial fan O O O Y Q C1 •6 o d o Q .0 o • depth O D 9 5 HF ii 11 111 C2a C2b 1 1 1 1 >jvi 1 1 1 I C2c 10 S 0.1 0.01 0.001 0.01 0.1 1 Area (km2) 10 100 10 d) f 1 2 0.1 4 t alluvial fan fluvial tributary O C1 • depth O D 9 5 O o o t HF B O C2 4 -1 10 io s 0.1 0.01 0.01 0.1 10 Area (km ) Figure 6.6. (continues from previous page). Bankfull channel depth and D95 as a function of contributing area for: (c) Lembke Creek, and (d) East Cap Creek. Values are reach averages. Relevant power-law relations for channel depth and coarse grain-size fraction are reported respectively in Table 6.3 and 6.4. Codes refer to process domains defined in chapter 3. 167 In Lembke-Sisters Creek two principal, main trends showing downstream channel deepening are observed (Figure 6.6c). One encloses the colluvial reaches of the cirque wall (CI in Table 6.3); the other encompasses the hanging valley, the valley step, and Lembke-Sisters valley trunk (HF-C2 in Table 6.3). A s previously noted for channel width, careful examination of Figure 6.6c reveals that the scaling relation proceeds by steps in H F and C2a, implying that the respective fluvial and colluvial regimes are also effective on bankfull depth. Finally, the area-depth relation in East Cap Creek (Figure 6.6d) may be approximated by a simple power-law relation (f = 0.195+0.080) which, however, explains only about half o f the total variability (R 2 = 0.552). A high degree of scatter is present in the debris-flow run-out zone (C2) and along the entrenched, distal reaches of East Cap relict glacial trough (F). Figure 6.7. Elliott Creek: a) rapids morphology in the headmost hanging valley (zone HF1); and (b) boulder-cascade morphology along the secondary valley step (zone C2). Boulder-cascade reaches are located immediately downstream o f rapid channel types. 168 6.5.4 Longitudinal Transects: Coarse Grain-Size Fraction The scaling relations between the coarse grain-size fraction (D95) and drainage area match closely those described for barikfull depth (Figure 6.6a-d). Accordingly, all combined relations, even though characterized by low R values, display downstream coarsening (Table 6.4) with an exponent (/) ranging between 0.192 and 0.453. In fact, in all study basins, when reaches are separated into process-specific area-Do^ scaling relations, either the colluvial or the fluvial relation yields superior fitting relative to the combined option. Table 6.4. D95 as a function o f contributing area across process domains Basin Process Equation a R 2 Exponent Intercept n domain CI (95%) SEE CI (95%) SEE HesklOO C D = 0.086AUi:'" 0.504 [0.167-0.399] 0.04 [0.935-1.587] 0.056 12 F D = 0.015A3 4 5 2 0.828 [-4.637-2.266] 0.471 [0.004-0.054] 0.249 5 combined D = 0.9A0 2 6 4 0.208 [0.09-0.438] 0.039 [0.714-1.11] 0.047 17 Hesketh C1-C2-C3 D = 0.99A u * " 0.806 [0.163-0.298] 0.028 [0.894-1.096] 0.020 17 HF1-HF2 D = 0.362A"0354 0.364 [-1-0.259] 0.141 [0.247-0.532] 0.060 5 combined D = 0.714A0 4 2 4 0.112 [-0.132-0.981] 0.089 [0.538-0.947] 0.059 22 Elliott C1-C2-C3 D = 0.557AU3UU 0.413 [0.117-0.484] 0.056 [0.452-0.687] 0.043 19 HF1-HF2 D = 0.451A"0 6 9 1 0.367 [-1.597-0.215] 0.224 [0.225-0.903] 0.123 8 combined D = 0.467A 0 4 5 3 0.075 [-0.201-1.107] 0.087 [0.348-0.627] 0.062 27 Lembke C1-C2 D = 0.839A U / U 4 0.800 [0.159-0.249] 0.019 [0.765-0.921] 0.019 24 combined D = 0.705A 0 3 0 3 0.512 [0.183-0.422] 0.042 [0.587-0.847] 0.039 28 EastCap C1-HF D = 1.41 O A 0 * ' 0.917 [-0.422-0.936] 0.051 [0.263-7.565] 0.057 3 B D = 0.6A- 0 6 7 7 0.998 [-0.746-0.607] 0.016 [0.57-0.631] 0.005 4 F D = 0.433A 0 6 6 2 0.684 [0.345-0.979] 0.118 [0.286-0.653] 0.080 12 combined D = 0.886A 0 1 9 2 0.151 [-0.015-0.399] 0.039 [0.784-1] 0.026 23 a. Relations are functional, rather than least squares regressions. Downstream fining is observed in (i) the distal fluvial domain (F), with j = -3.452 in HeskethlOO; and (ii) the hanging fluvial domain (HF), with j = -0.354 in Hesketh Creek and j = -0.691 in Elliott Creek (note large confidence intervals in Table 6.4). Conversely, a more statistically significant downstream coarsening occurs across colluvial reaches, with j = 0.283 in HeskethlOO (C),y = 0.231 in Hesketh Creek (C1-C2-C3), . / = 0.300 in Elliott Creek ( C l -C2-C3) , j = 0.204 in Lembke Creek (C1-C2), and j = 0.257 in East Cap Creek ( C l - H F ) (Table 6.4). These exponents are in accordance with values reported by Brummer and Montgomery [2003] for area-Dsn relations in unglaciated and weakly glaciated (due to alpine, warm-based glaciers) mountain drainage basins of Washington State. According to these results, it appears that Dg5, owing to less onerous data requirements (i.e., the measurement o f the five largest stones), may be a valid replacement for D50 when the purpose is to assess basin-wide trends o f grain size in mountain environments. 169 Notwithstanding such commonalities, it should be noted that distal fluvial reaches in East Cap Creek (F) display significant downstream coarsening and therefore are the "exception" to what is observed in the other study basins, and to results obtained from prior work conducted in unglaciated settings [Brummer and Montgomery, 2003]. A t the same time, the distal fluvial domain (F) in HeskethlOO behaves in a hanging fluvial fashion (downstream fining). This discrepancy can be explained by the existence o f glacially-derived topographic anisotropics that impose the characteristic arrangements of process domains. Since HeskethlOO does not contain a hanging valley, its distal fluvial reaches are associated with contributing areas otherwise proper o f hanging valleys ( A F » A H F ) ; for the same reason, debris flow inputs are not blocked further upstream but impact directly the distal fluvial domain in HeskethlOO. 6.5.5 Longitudinal Transects: Stream Power To begin with, it should be noted that the stream power influence applies to fluvial reworking of sediment-covered channels only, and not to incision into bedrock; otherwise stream power is meaningless in debris-flow scoured channels. The calculated values of field-based unit and total stream power (see section 6.4), do not appear to change systematically with contributing area (Figure 6.8 and Appendix C) . This outcome represents an element o f surprise with respect to previous field studies [e.g., Knighton, 1999; Brummer and Montgomery, 2003; Wohl and Wilcox, 2005] and conceptual models [e.g., Schumm, 1977; Church, 1992], according to which stream power increases monotonically in the erosional (colluvial) part o f the basin, then declining systematically along depositional (fluvial) reaches. Owing to the definition of total power itself (Q. = co w), the variation o f total stream power with drainage area parallels that exhibited by unit power, which obviously plots at lower values. For this reason, in this section I w i l l comment on unit stream power only, total power being reported for completeness in Appendix C . In Hesketh Creek, stream power plots around 1,000 Wm" at the headwaters (CI and HF1 in Figure 6.8a); it reaches a maximum (-6,000 Wm" 2) at the inception of the debris-flow dominated channel (C2), along which it decreases monotonically. A clear area-power reversal is observed in the main hanging valley floor (HF2), where stream power attains an absolute minimum (-200 W m " ) and then increases systematically along the valley step (C2). Finally, co decreases markedly along the distal reaches ( A > 5km 2 ) of the relict trough (F). 170 In Elliott Creek (Figure 6.8b), stream power variability is contained between 100 and 1,000 W m ' 2 . Specifically, co exhibits three maximum values in colluvial channels: at its headmost 10000 a) E I $ | 1000 o Q. CO 100 • • Unit power • Slope C1 • HF1 • • C 2 1 q t i i PD i i i i i i i i 1 j HF2 C 3 0.1 E i 0> Q. O CO 0.01 0.001 0.01 0.1 10 Area (km ) 10000 0.01 0.1 , 1 10 Area (km2) Figure 6.8. Unit stream power as a function o f drainage area for: (a) Hesketh Creek, and (b) Elliott Creek. Values are reach averages. Codes refer to process domains defined in chapter 3. Slope is reported for reference. 171 10000 c) 1000 i 1 100 4 • • Unit power • Slope C1 10 0.001 e HF • • d C2a C2b C2c 0.01 0.1 Area (km ) 10 10000 d) E 1000 -t o Q. £ 100 co 10 • C1 • • • • HF B CO • • C 2 ^ 3 3 ° C M • 4- 1 10 E 1. a> Q. O m 0.1 0.01 100 +1 10 E i , o a o <n 0.1 0.01 0.01 0.1 1 10 Area (km2) Figure 6.8. (continues from previous page) Unit stream power as a function o f drainage area for: (c) Lembke-Sisters Creek, and (d) East Cap Creek. Values are reach averages. Codes refer to geomorphic process domains defined in chapter 3. 4* = beginning of alluvial fan crossing (see text). Slope is reported for reference. reaches (CI) , at the apex of the secondary valley step (C2), and along the primary valley step (C3). Min ima l stream power is attained along the main hanging valley floor (HF2). 172 In Lembke-Sisters Creek (Figure 6.8c), stream power is highest (-5,000 Wm" 2) along its headmost, debris-flow scoured reaches (CI) , lowest in correspondence with the hanging fluvial reaches (HF1), and plots approximately between 300 and 1,000 Wm" 2 along sink colluvial reaches (C2) that occupy the valley step and the relict trough. O f the four basins considered, East Cap Creek displays the most scattered scaling (Figure 6.8d). In particular, while patterns in zones C I , H F , B , and C2 virtually mirror those observed in Hesketh and Lembke Creeks, at first glance the saw-tooth scaling trend along the fluvial reaches of the trough (F in Figure 6.8d) is somewhat unexpected. In fact, such behaviour is highly dependent on (and mirrors) the area-slope scaling shown. Specifically, steep (S > 0.1) and entrenched, step-pool and boulder-cascade reaches that are chronically 2 2 affected by bank-erosion, generate a high-power channel stretch (3km <A< 4 k m ) . Downstream sits a flat, fully decoupled, depositional area (with islands, riffle-pool and rapids morphology), in which stream power decreases monotonically down to a reversal point (A -6 k m ). Remarkably, the reversal occurs at the crossing o f the large alluvial fan associated with the tributary East Cap 110 (Figure 3.1), along which East Cap Creek reacquires an entrenched, step-pool nature. In addition, ice-flow confluence effect at this location likely resulted in augmented glacial excavation [MacGregor et al, 2000], and still today produces locally higher channel slopes. The combination of these two contingencies explains the systematic increase of stream power for areas greater than about 6 k m 2 (Figure 6.8d). 6.5.6 Prediction of Bankfull Channel Width This section aims to explore existing models for the prediction of bankfull widths in formerly glaciated, mountain streams that are not exclusively bedrock controlled. First, estimates derived by the two methods for evaluating the Manning coefficient are compared. Accordingly, in Table 6.5 are reported the root mean squared error ( R M S E ) values for departure from field-measured bankfull widths (true values). In combined cases the visual method generally yields lowest R M S E , Elliott Creek being the only exception. In the latter case study, the Thompson-Campbell method is only slightly superior to the visually-based procedure; interestingly, both methods yield error terms considerably smaller than those recorded in the other study basins (i.e., tributaries of the Capilano River). When only fluvial reaches are considered, the error term is generally reduced by half and more (except in Elliott Creek), and R M S E values across the basins are approximately contained within 2 meters. 173 Overall, the two methods yield virtually identical error terms in purely alluvial environments. Because the visual method performed better than Thompson-Campbell's, only the error associated with the former procedure, is reported for graphical evaluation in Figure 6.9. In addition, reach-averaged slopes are included to ease the identification of potential systematic errors related to specific geomorphic process domains or relict glacial macro-forms. Table 6.5 Root Mean Squared Error o f bankfull width R M S E (predicted - field measured) a Roughness Manning visual Thompson/Campbell Domain Combined Fluvial Combined Fluvial East Cap 2.27 1.93 3.56 2.10 •§ Elliott 1.56 1.56 1.39 1.59 m Hesketh 4.53 1.64 5.43 1.95' Lembke 3.68 0.92 5.58 0.67 a. Values are expressed in meters. In Hesketh Creek (Figure 6.9a), bankfull widths are systematically under-predicted, error being as large as 9 m. A s expected from R M S E outcomes (Table 6.5), the error term is minimal along the hanging fluvial domain (HF) and increases consistently downstream of the hanging valley, to reach remarkably high values at the mouth (F). Interestingly, the typical resetting of channel width observed at the inception of hanging valleys is predicted only by the visual method, suggesting that five stones (i.e., D95) might be too small a sample size for estimating total resistance to flow. In Elliott Creek (Figure 6.9b), the error term plots approximately inside the [-lm; +3m] envelope. Field values are slightly underestimated in the headmost reaches (CI and HF1), with the trend reversing along the only portion o f Elliott Creek that is periodically scoured by debris flows (C2), so that increasingly higher bankfull width over-prediction is recorded downstream o f the primary hanging valley (HF2). Given these trends, the behaviour of the error function appears to be somewhat related to slope variations. The error function in Lembke-Sisters Creek (Figure 6.9c) in places mirrors that observed in Hesketh Creek. Accordingly, bankfull width is consistently under-predicted throughout the basin (up to a maximum of about 9 meters where Sisters Creek joins Lembke Creek). It is modelled reasonably well along the hanging valley (HF) and the source colluvial part o f the valley step (C2a), then becomes increasingly under-predicted down the sink colluvial portion of the channel (C2b). Further downstream, along the debris-flow coupled trough (C2c), pre-174 25 20 15 ? 1 0 i 1 Hes i 1 keth Creek V C2 HF2 C3 J 0 ^ F C1-HF1 -5 4 14 12 10 8 ? 6 S 4 -Field - Manning -Thompson/Campbell - Error (Manning - field)( Slope 4- 0.1 £ g o 0.01 1000 1500 2000 2500 Distance (m) 3000 3500 4000 4500 ! Elliott Cr< i I >ek *_ vy 11 "^e \\r—r \ f •/ \ f / \ Mr V »\ / • / —B— Field • Manning Thompson/Campbell Error (Manning - Field) —(—Slope — C1 HF1 C2 HF2 C3 E I. <u a o to 0.01 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Distance (m) Figure 6.9. Comparison o f measured bankfull width and channel width modelled using two variants of equation (6.4) in: (a) Hesketh Creek, and (b) Elliott Creek. In the first variant the Manning coefficient was derived by visual comparison against known standards; in the other, the coefficient was obtained by applying the Thompson-Campbell [1979] variation o f the Keulegan [1938] equation. Local channel slope and the error associated with the visual estimation method are also reported. 1 7 5 30 25 20 15 £ 10 i 5 -10 C1 HF Lembke Creek C2a C2b C2c -B— Field - • - Manning —Thompson/Campbel l Error (Manning - field) -I—Slope 0.1 E I <u a. o co 0.01 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Distance (m) 25 -a-Field - •— Manning ^—Thompson/Campbell Error (Manning - field) — I — Slope (m/m) 0.01 500 1000 1500 2000 2500 Distance (m) 3000 3500 4000 Figure 6.9. (continues from previous page) Comparison o f measured bankfull width and channel width modelled using two variants o f equation (6.4) in: (c) Lembke Creek, and (b) East Cap Creek. In the first variant the Manning coefficient was derived by visual comparison against known standards; in the other, the coefficient was obtained by applying the Thompson-Campbell [1979] variation o f the Keulegan [1938] equation. Local channel slope and the error associated w i t h the visual estimation method are also reported. 176 dieted channels are approximately 5 meters narrower than is measured on the ground. In East Cap Creek (Figure 6.9d) the error term plots within the [-5m; +3m] interval. Similar to the appearance in Elliott Creek, bankfull widths are under-predicted in the headmost zone, downstream the error sign reverses, and as one approaches the distal-most reaches in zone F increasing tendency to over-prediction is observed. In line with outcomes in Elliott Creek, and in agreement with R M S E values, discrepancies between observed and predicted values are more contained than in Hesketh and Lembke-Sisters Creeks. 6.6 Discussion Downstream Hydraulic Geometry The spatial organization o f geomorphic process domains imposed by relict glacial macro-forms (chapter 3) exerts a strong control on the downstream hydraulic geometry. This statement is strongly supported in the system with the simplest structure (i.e., Hesketh 100), where the scaling relations of bankfull width, bankfull depth, and D95 (in addition to local channel slope) with contributing area differ considerably between geomorphic process domains. Specifically, scaling exponents are positive in the colluvial, oversteepened portion, and switch to negative values in riverine, decoupled reaches. Reversal points, which correspond to maxima in channel variates, occur within the relict paraglacial fan. D H G relations and area-Atf scaling become far more complex when colluvial and alluvial landscape building blocks are arranged in different combinations (with repetitions) along the axes of formerly active ice flows. In these settings, all variates (i.e., width, depth, and D95) tend to increase down source colluvial channels, then resetting to remarkably lower values at the inception o f hanging valleys (i.e., Elliott (HF2), Hesketh (HF2), and Lembke (HF)). This behaviour, in terms o f width and depth, is significant only at primary hanging valleys (not at headmost, short, secondary ones), where contributing area exceeds approximately 1 k m and incoming colluvial slope is greater than 0.1. In comparison, D95 appears to be relatively more sensitive to changes in process dominance than bankfull width and depth; accordingly, the downstream coarsening of the coarse-grain fraction that occurs along colluvial channels is abruptly interrupted whenever a hanging valley (either primary or secondary) is encroached. Within hanging valley floors, the behaviour of channel width appears to be inconsistent; downstream channel narrowing and widening are both observed in different basins. On the contrary, bankfull depth and D95 stay nearly constant. A long intermediate valley steps - those 177 connecting primary and secondary hanging valleys - sit source colluvial channels, which are the most active geomorphic features o f the landscape. They receive large amounts o f material from debris flows and rock avalanches (channel bed and banks are typically made o f angular, clast-supported material), and are periodically scoured by debris flows. A t these locations, such a spatial arrangement of processes produces channels with quasi-constant width, depth, and D95 (e.g., C2a in Lembke Creek, and C2 in Hesketh Creek). Lower in the basin, along primary valley steps - those connecting primary hanging Valleys with troughs - sink colluvial channels with low colluvial load exhibit high downstream widening, deepening and significant bed material coarsening. Lastly, along relict glacial troughs two different situations are observed depending on the strength o f geomorphic coupling. In decoupled conditions (i.e., zone F in East Cap Creek), remarkable downstream widening, significant coarsening, and nearly constant depths are observed. In coupled conditions (i.e., zone C2c in Lembke-Sisters Creek), bankfull width decreases downstream, or remains almost constant, as opposed to bankfull depth and D95 that increase systematically with drainage area. In different ways, both instances are exceptions, as they do not conform to scaling trends previously described; however they can be explained by the history o f the landscape. The case of downstream coarsening in distal fluvial reaches of East Cap Creek (A > 3 km 2 ) appears to contradict what is observed in hanging fluvial reaches, as well as results from prior studies conducted in unglaciated settings in which downstream fining occurs [i.e., Brummer and Montgomery, 2003]. This may be explained by the long history o f glacial erosion in coastal British Columbia [e.g., Church and Slaymaker, 1989; Heller et al, 2001]. Accordingly, fluvial reaches located in the valley floor o f East Cap Creek are entrenched in glacially derived deposits, and are chronically supplied with large boulders (from morainal t i l l or outwash deposits) v ia near-bank erosion processes. Summarizing, significant downstream coarsening of average D95 is observed across colluvial reaches, interrupted in decoupled hanging valleys where the coarser grain-size fraction resets to markedly lower values and downstream fining occurs. In fluvial environments that are actively reworking glacially-derived deposits, coarse material is episodically supplied to the channel and downstream coarsening is observed. The second exception, represented by the systematic channel narrowing that occurs along the Lembke-Sisters valley trunk, can be interpreted as supplementary evidence of the ongoing 178 transient conditions following the last glacial maximum. Apparently, during the last ice age, the ice flow associated with Sisters Creek was dominant over that o f Lembke Creek - a hypothesis supported by the pronounced valley step (absent in Sisters Creek) located in Lembke Creek (see MacGregor et al. [2000] for justification of valley step formation downstream of trough confluences). Nowadays, even though Lembke Creek at the confluence has a larger contributing area than Sisters Creek, the configuration o f relict glacial macro-forms (hence process domains) still favours the propagation of water and sediment inputs from upper Sisters Creek over those from Lembke Creek (here the hanging valley blocks large part of the colluvial load from upstream), hence explaining why the area-width relation in the Lembke-Sisters valley trunk accords with the former. In summary, the result o f Quaternary glaciations in each study basin translates into a multi-segmented pattern of bankfull width, depth, and D95, when expressed as functions o f contributing area. Segmentations are statistically significant, as single segments typically explain a greater proportion of variance compared to a simple, comprehensive power-law relation. Deviations from the general power-law trend appear to be directly proportional to the corresponding departure of the long profile from an idealized, equilibrium concave-up prototype. Accordingly, degree of segmentation in East Cap and Elliott Creeks is lower than in Hesketh and Lembke Creeks (cf., long-profiles in chapter 5). Interestingly enough, one should remember that the generalized pattern o f D H G segmentation could be detected only thanks to the way data were collected and analysed. Uninterrupted field surveys were conducted along the main axis of drainage basins, and then each long profile was considered separately; as opposed to being combined with all the others (see section 6.1.1). This outcome, which applies to al l the variables examined in the present study, is apparent when one compares the combined plots shown in chapter 5 (Figures 5.13a-c) with the corresponding basin-specific analogues (Figures 6.4-8). For example, a discontinuous field survey conducted only on C1/HF1 and the distal-most reaches o f Hesketh Creek (F) would have yielded a single power-law relation, leaving area-width deviations undetected. In the spirit o f Mackin [1964] one then wonders whether or not any other study, in which regional relations combine several long profiles, may hide similar basin-specific trends [e.g., Snyder et al, 2003; Wohl and Wilcox, 2005]. 179 In relation to alluvial scaling exponents, combined basin-wide relations of bankfull width and depth display exponents that are not significantly different from 0.5 and 0.33. Examination o f within long-profile variability reveals that major departures from simple power-law relations occur in systematic fashion. In terms o f bankfull width (Figure 4.10a), downstream widening is directly proportional to the glacially-inherited channel slope. This relation is particularly clear in fluvial reaches (cf , H F and C2b in Lembke Creek) and in colluvial reaches with no colluvial tributaries (cf, C I in Elliott Creek with other C I segments). Departures occur at debris flow run-out zones, in aggrading reaches where fluvial transport cannot keep pace with the colluvial sediment load from upstream. In conjunction, the presence of sedimentary linkages (paraglacial fans) promotes drainage loss to the subsurface at the gully-hanging valley (C /HF zones) and gully-glacial trough (C/F zones) transitions. A s a result, a sharp reduction in channel width is observed in the scaling relation (discontinuity), and strong channel narrowing is observed (zone C2 in East Cap Creek, and zone F in HeskethlOO Creek). Even though to a lesser extent, lateral debris flow sediment inputs at tributary junctions appear to have analogous effect on area-width scaling relations. Specifically, in reaches where slope is high (S ^ 0.1) lateral colluvial sediment inputs (colluvial tributaries) appear to impart a negative feedback, so channel width remains nearly constant (zones C2a and C2c in Lembke Creek and C2 in Hesketh Creek). In accordance with the conceptual framework enunciated above, exceptional downstream widening (b » 0.5) occurs in steep channels along primary valley steps that are subjected to low colluvial sediment load (no colluvial tributaries; zones C2b of Lembke Creek, C3 of Hesketh Creek, and C3 in Elliott Creek). In this context, distal-most fluvial reaches in East Cap trough, where high channel widening occurs, may be thought of as situated in an exceptionally long valley step. In summary, deviations from widely accepted values are common, and such deviations appear to be modulated by interactions between the inherited glacial topography and the rates of colluvial sediment delivery to streams. Surprisingly, the effect o f flow increase downstream of fluvial (non torrented) tributaries is completely masked. These outcomes, and the fact that channel width-area scaling changes across domains (contrary to findings by Brummer and Montgomery [2003]) reinforce the statement that active process domains are still out o f balance with (not adjusted to) the current prevailing environmental conditions. 180 0.001 0.01 10 b) a & 0.1 0.1 1 , Area (km ) 10 100 cirque wall (or valley wall) hanging valley valley step glacial trough 0.01 ; colluvial ; regime fluvial j regime | A A A i „--! - - - ! I I I I I I I 0.1 E § as o. o CO 0.01 0.001 10 100 Area (km2) Figure 6.10. Schematic representation of (a) area-width and (b) area-depth scaling relations with specific reference to channel slope (grey line) and colluvial load variability (dashed arrows). Solid arrows indicate paraglacial fans. Note that for valley steps and glacial troughs both the high-sediment load (three dashed arrows) and low-sediment load situations are reported. Black dashed lines indicate the range of variability around the downstream trends. Two regimes are inferred, a fluvial regime in hanging valleys (riffle-pool, pebble-dominated reaches), and an imposed colluvial regime along strongly coupled valley steps and relict glacial troughs. 181 Overall, cumulative departures from the 0.5 line imposed through headmost channel reaches yield systematically smaller bankfull widths in distal reaches. In area-depth plots (Figure 6.10b), deviations are similar to those identified in terms of bankfull width. However, owing to the greater resistance exerted by the channel bed (as opposed to the channel banks), the degree of power-law segmentation is notably lower and glacially-induced effects are in places weaker or completely absent. For example, Elliott and East Cap Creeks can be approximated by a single power-law relation, and no confluence effect in Lembke-Sisters Creek is detected. Interestingly, al l segments in the other two study basins are significantly different from 0.33. Specifically, headmost colluvial channels (CI in Hesketh and Lembke Creek) exhibit lower downstream deepening; and hanging fluvial reaches share identical scaling relations with sink colluvial channels, displaying downstream deepening higher than expected. Similar to the appearance o f bankfull width, distal reaches of the study basins exhibit lower channel depth in comparison with the prediction given by the 0.33 line. Stream Power and the Ci/Dgs Ratio Specific and total stream power values appear to be highly dependent on channel slope. Since local channel slope is largely the product of subglacial erosion and paraglacial deposition, indices of stream power mirror the spatial organization o f relict glacial features. It follows that area-power scaling relations behave differently than described in prior studies [e.g., Schumm, 1977; Brummer and Montgomery, 2003; Wohl and Wilcox, 2005]. In particular, stream power does not increase monotonically within the degrading colluvial part of the system, nor declines systematically in the aggrading fluvial portion. Instead, characteristic fluctuations are observed, with minima recorded in hanging valleys and maxima located along source colluvial channels and in distal-most reaches; the former features acting as shock (i.e., debris-flow) absorbers. Even though one expects these patterns to approximate reasonably well the actual hydro-geomorphic picture, major uncertainties lie behind the calculation of stream power in mountain drainage basins. Specifically, one should bear in mind that the estimation of stream power, based on the Manning's equation, in principle was empirically developed for purely alluvial reaches in large riverine environments. B y contrast, debris-flow erosion dominates (or affects) great part of the drainage network under examination; as a result, values of 182 bankfull width and depth that enter in the stream power expression, are not the mere product o f fluvial activity. For this reason, I believe stream power values in colluvial channels should be considered systematically overestimated. Notwithstanding these limitations, which are common to any study seeking to evaluate stream power in mountain streams, one of the four study basins (i.e., East Cap Creek; see Tables 6.6 and 6.7 in conjunction with Figure 6.11) contradicts the D H G discriminant proxy Table 6.6. Exponents of D H G relations for the study basins Stream R square (DHG exponent) channel A vs. width A vs. depth A vs. velocity East C a p a Elliott Heske th a L e m b k e a 0.746 (0.349) 0.795 (0.429) 0.763 (0.453) 0.715(0.415) 0.552 (0.195) 0.484(0.217) 0.560 (0.318) 0.485 (0.249) 0.427 (-0.335) 0.091 (0.062) 0.001 (-0.018) 0.505 (-0.111) a. R square for 2 out of 3 variates is greater than 0.5. Table 6.7. Dimensional ratios of driving force (Q) to substrate resistance (D95) Stream D95 (m) a(W) Q/D95 (W/m or kg/s'3) n channel Mean Median Mean Median Mean Median East C a p a 0.97 0.94 5,452 2,601 6,146 3,081 24 Elliott 0.63 0.75 3,768 2,083 5,229 4,050 26 Hesketh a 0.89 0.90 15,808 8,813 17,159 12,147 22 L e m b k e a 0.93 0.88 8,328 7,137 10,147 6,142 27 a. According to Wohl [2004b] the stream should exhibit mean Q / D 9 5 > 10,000 kg/s 3 . 8 r — Mean I—I2SV75* X . 101-90% * Ouflers Bsc Cap Bliott Hesketh Lerrfcke Figure 6.11. Ratio of Q/D95 plotted for the study basins. Dashed line marks the threshold identified by Wohl [2004b]. 30000 20000 10000 S000 8000 7000 6000 5000 4000 3000 2000 1000 900 300 183 proposed by Wohl [2004b]. That is, drainage basins that have a mean OJD95 > 10,000 kg/s 3 should exhibit well-developed D H G relations 4. Rather, this threshold separates basins that have a strongly stepped long-profile (i.e., Hesketh and Lembke Creeks) from those with a structure adhering more closely to an equilibrium concave-up prototype. The test outcome gets remarkably worse when median values are considered (which would be more appropriate to consider, given that Q/D95 distributions within each basin are systematically skewed towards low magnitude values). Accordingly, this measure plots below the 10,000 kg/s 3 threshold for Lembke Creek, and sits further below for East Cap Creek. Prediction of Bankfull Width Application o f the Manning-based equation proposed by Finnegan et al. [2005] for bedrock channels - opportunely modified to fit the channel substrate variability of the study basins -partly succeeds in reproducing measured bankfull widths; for example, the reset occurring at the inception of hanging valleys is correctly predicted. In general, o f the two variants tested, the one estimating the resistance coefficient by visual comparison accomplished better prediction (lower error) than that incorporating information on D95 [Thompson and Campbell, 1979], an indication that five largest stones are probably too few for representing the true D95 in poorly-sorted sediments and that Thompson-CampbelVs equation does not reflect total resistance in these channels. Both models perform best in hanging fluvial settings (as opposed to colluvial and distal alluvial stretches), where the discrepancy between measured and predicted channel width drops at least by 50%. For the most part, this outcome is a consequence o f (i) the empirical derivation o f the Manning coefficient, originally derived in purely alluvial settings; and (ii) the approximation of mean annual flood with contributing area. In this context, an overwhelming tendency to tinder-predict measured bankfull width in the study basins is apparent, and in some cases this could be argued to be the effect o f debris-flow activity. Once again, the glacial legacy appears to be the first-order control on bankfull channel size; specifically, those long profiles that deviate more strongly from an equilibrium concave-up prototype show higher R M S error. 4 Recall: Wohl states that a drainage basins exhibits well-developed DHG relations when R 2 for two (out of three) variates is greater than 0.5. 184 Inspection of the error function (i.e., predicted width minus measured width) reveals an inverse relation with local channel slope. In channel stretches where local slope decreases convergence between the error function and slope is observed; on the contrary, where slope increases the two curves tend to diverge. A s a result, valley steps (i.e., sink colluvial channels with limited colluvial load), where exceptionally high downstream widening is observed, seem to be the most problematic loci along the glaciated profile. According to Finnegan et al. [2005], in bedrock channels their model predicts that "anomalously steep reaches w i l l have higher water velocities - provided that changes in channel-bed roughness do not offset those in slope - and, in order to conserve water flux, smaller cross-sections" (p. 231). Given the pace at which downstream channel widening occurs, this appears to be the case in the present study basins, where high-roughness reaches characterize the morphology of channels flowing along valley steps (i.e., boulder-cascades and step-pools; see chapter 5). 185 CHAPTER 7 Conclusions This study demonstrates that the initial working hypothesis of glacially-induced transient scaling relations should be accepted. Specifically, pervasive departures from unglaciated scaling relations have been detected, and direct causal linkages across the spatial scales examined have been shown. Glacial macro-forms (coarse scale level), by imposing local channel gradient and degree of colluvial-alluvial coupling, drive the active processes that dominate mass transport at the local level, such as the channel reach scale (see Figures 3.8a and 3.8b in conjunction with Table 3.2). Specifically, the spatial distribution of process domains reflects colluvial activity as expressed by net mass gain or loss (Tables 4.16 and 4.17) and landslide-driven annual sediment yield (Figure 4.25), and controls downstream patterns o f channel-reach morphology (Figures 5.4-6), hydraulic geometry (Figures 6.4-6 and 6.10), coarse grain-size fraction (Figure 6.8), and stream power (Figure 6.9). In terms of geomorphic process domains, the results portray a more complex picture than that described for unglaciated catchments [e.g., Montgomery and Foufoula-Georgiou, 1993; Stock and Dietrich, 2003]. This study, by considering the inherited effects o f glacial geomorphic processes extends previous results and characterizes process domains and topographic signatures in glaciated mountain environments. Quaternary climate changes in glaciated British Columbia have left a landscape where process-specific topographic signatures rarely match the domains o f currently active geomorphic process. 186 Transverse and longitudinal slope-area transects indicate widespread process-form disequilibrium resulting from the superimposition o f ongoing Earth surface processes on a glacial palimpsest, so that glacial topographic signatures override those produced by contemporary geomorphic processes. Particularly relevant is the finding that longitudinal profiles of channels periodically scoured by debris flows (which are defined as source colluvial domains) remain largely controlled by the inherited glacial topography (Figure 3.2). Along the direction of formerly active ice flows, relict glacial cirques and hanging valleys enclose typical hanging fluvial domains and characterize the morphological structure of the landscape (Figure 3.3). Like ly , these w i l l persist as first-order landforms throughout this interglacial period. Although topographic signatures are imposed by glacial macro-forms the concept of process domains appears to apply. However, an important deviation from the unglaciated model [Montgomery and Foufoula-Georgiou, 1993; Sklar and Dietrich, 1998] is observed: the transition between colluvial and alluvial channels, which occurs at a constant slope o f about 0.2 for small drainage areas, starts declining systematically for contributing areas larger than about 1 km . This trend is explained by the glacially-imposed degree of coupling (sink colluvial channels), which is controlled by the morphometric characteristics of glacial troughs and adjoining valley walls. Therefore, the spatial distribution o f process domains on a slope-area plot may be to some degree similar in landscapes with different history (i.e., glaciated vs. unglaciated) but where the topography plots within these process domains varies between landscape types (cf , Figures 2.2 and 3.8b). Similarly, the long history o f glacial erosion affects contemporary landslide activity in many respects. First, the nature and distribution of Quaternary-derived surficial deposits confounds primary lithologic effects; as a result, topographies underlain by less resistant geology are not typically associated with higher rates o f landslide erosion. Second, the outcome that open-slope landslides delivering material to unchanneled topography are dominant source-to-sink pathways, which is typical of colluvial drainage networks at early stages of development, reinforces the notion of transient environmental conditions following generalized glacial aggradation. Third, the fundamental control that, in tectonically active settings, is exerted by glacial erosion on relief production and orogen height [e.g., Whipple et al, 1999; Brocklehurst and Whipple, 2002; Oskin and Burbank, 2005], seems also to impose the 187 characteristic hillslope length throughout the basins studied in coastal British Columbia. In fact, glacially-derived hillslope geometry appears to control the shape o f L M F relations: the kink observed in the L M F scaling at about 4,000 m 3 originally detected in the Capilano River [Brardinoni and Church, 2004], is also observed in inventories conducted in the Tsitika and Eve River basins, which share identical relief with the former. In addition, the detailed stratifications of L M F by landslide and terrain attributes have allowed detecting for the first time characteristic landslide length scales dependent on (i) movement style (e.g., slide, avalanche, and flow); (ii) type o f material mobilized (i.e., bedrock and debris); and (iii) land use (i.e., forest clearing). A s a conclusion, landscape bio-morphometric controls do override the theoretical self-organized criticality o f L M F relations. Fourth, slope-area analysis on landslide initiation and deposition (end of transportation) points reveals that bedrock landslides dominate the landscape on mountain summits and ridges above the treeline; these processes appear to deliver mass to source colluvial channels (gullies), in which debris is temporarily stored until remobilization occurs via full-scale debris flows. In old-growth forest, during the seventy years examined, colluvial activity across process domains (seen as sediment reservoirs) has generated net volume accumulation in unchannelled valleys, sink colluvial and fluvially-dominated channels; in contrast, planar slopes and gullies have been degrading the Quaternary excess sediment load. In this context, logging operations have accentuated aggradation in gullies and in unchannelled topographies. Finally, for drainage areas comprised between 5 and 50 k m , the contemporary, specific fluvial sediment yield (suspended) of British Columbia exceeds the specific landslide yield estimated in the Tsitika-Eve region. This outcome suggests that at this spatial scale contemporary sediment dynamics may be out of equilibrium and degradation may occur. In order to develop a landslide-yield relation for British Columbia, which then can be directly evaluated in the context of the regional fluvial yield, the compilation of more landslide inventories is needed. In terms of channel-reach morphology, hanging valleys are probably the most characteristic features that testify to the glacially-inherited effects. In fact, hanging valleys enclose purely alluvial reaches that separate strongly-coupled colluvial reaches located both up- and down-stream. In so doing, they reset the idealized downstream continuum of channel types as proposed by Montgomery and Buffington [1997] (see Figure 2.3). Typically, two full bedform sequences are observed: a headmost series, characterized by an ephemeral/seasonal 188 hydrologic regime and by the episodic occurrence of debris flows along its axis; and a distal series, in which water runoff is perennial and colluvial sediment inputs ( i f any) are chiefly lateral. The channel type variability in the study basins is predicted reasonably well v ia Principal Component Analysis ( P C A ) followed by cross-validated Multivariate Discriminant Analysis ( M D A ) . Accordingly, a discriminatory model based on average channel slope, and relative roughness is able to predict the channel morphology in 89% of the reaches stratified into bedrock-controlled, cascade/step-pool, rapid, and riffle-pool typologies. Process transitions that occur at hanging valleys also reset downstream scaling dependencies of channel width, and depth. In relation to alluvial scaling exponents, combined basin-wide relations o f bankfull width and depth display values that are not significantly different from 0.5 and 0.33. Examination of within-long profile variability reveals that major deviations from simple power-law trends occur systematically. In terms o f bankfull width (Figure 4.10a), downstream widening is directly proportional to the glacially-inherited channel slope. Departures occur at debris flow run-out zones, in aggrading reaches where fluvial transport cannot transmit the colluvial load from upstream, and where paraglacial fans at colluvial-fluvial transitions promote drainage loss to the subsurface. It follows that sharp discontinuities (reductions) in channel width are observed at these locations. Even though to a lesser extent, lateral debris flow sediment inputs at tributary junctions appear to have a similar effect on area-width scaling relations. In particular, where channel slope is greater than 0.1 lateral colluvial inputs impart a negative feedback, and channel width does not change substantially downstream. In terms of bankfull depth (Figure 4.10b), deviations are similar to those identified for bankfull width. However, owing to the greater resistance exerted by the channel bed (as opposed to the channel banks), the degree o f scaling segmentation is substantially reduced and glacially-inherited effects are in places weaker or completely erased. Summarizing, deviations from accepted alluvial scaling exponents are common (multi-segmented power-law relations), and such deviations appear to be controlled by interactions between the inherited glacial topography - including the presence o f sedimentary linkages such as paraglacial fans - and the rates of colluvial sediment delivery to streams. Surprisingly, the effect o f flow increase downstream of fluvial tributaries is completely confounded. These outcomes, and the fact that channel width-area scaling changes across 189 domains (contrary to findings documented by Brummer and Montgomery [2003]) reinforce the statement that active process domains are still out o f balance with the current prevailing environmental conditions. Between basins, deviations from alluvial simple power-law trends are directly dependent on the ruggedness of the channel longitudinal profile as imposed by past glacial carving. That is, the more a channel long profile is transient (deviates from the idealized concave-up prototype); the greater is the degree of segmentation displayed by the corresponding downstream scaling relations. In comparison with imposed 0.5 and 0.33 alluvial trends cross-sections of the glaciated study channels are typically narrower and shallower than expected. H o w well can such multi-segmented scaling relations be predicted? In the case o f channel width, the testing of two Manning-based expressions indicates that, when total roughness is estimated via visual comparison against measured values [Hicks and Mason, 1991] (as opposed to being a function of D95 [Thompson and Campbell, 1979]), the R M S error is systematically reduced. B y means o f this expression, complex channel-width trends that were measured in the field are described reasonably well , especially in fluvially-dominated reaches. On the contrary, channel width is consistently underestimated in colluvial environments, valley steps being the most problematic locations of all . Notwithstanding the ability to detect and predict systematic departures and consistent patterns of scaling segmentation, the complexity of the factors involved in downstream hydraulic geometry leaves an underlying sense of geomorphological indeterminacy [Leopold and Langbein, 1964]; future work in the study basins w i l l aim to parameterize colluvial sediment load, so that multivariate analysis o f covariance ( M A N C Q V A ) can be performed, and interactions between slope gradient, sediment feed, and hydrologic scaling may be investigated quantitatively. In agreement with the notion of a disequilibrium landscape and in contrast with prior studies [Schumm, 1977; Knighton, 1999; Brummer and Montgomery, 2003; Wohl and Wilcox, 2005], field-based indices of stream power indicate no systematic variation with drainage area (Figure 6.8); rather, high dependence on the glacially-inherited channel slope is observed. In particular, the area-power relation exhibits distinct fluctuations, with minimum values recorded in hanging valley floors and maxima attained along source colluvial channels and in distal-most reaches; the former features acting as colluvial shock absorbers and substantial 190 sediment traps. Similarly, downstream trends of Dc, 5 exhibit regular oscillations; downstream coarsening, which typically occurs in colluvial channels, is systematically interrupted at hanging valleys, where downstream fining is observed. From a watershed management perspective, assessing the ability to identify process domains from GIS-extracted slope-area plots is critical for predicting patterns o f natural and anthropogenic disturbances, as well as in-stream habitat conditions. The 25 m D E M currently available for glaciated coastal British Columbia does not ensure an automated discrimination of process domains (cf , Figures 3.4a and 3.4b) and signatures (Figure 3.3d) that can be detected in the field. Similarly, in light of the results obtained in the study basins (section 5.7) a remotely-based prediction o f channel types appears to be not directly applicable to glaciated mountain basins. However, after opportune preliminary partition of drainage basins into headmost and distal sub-systems, discriminant models based on channel slope and bankfull width may allow accomplishing such a goal. In summary, direct scale linkages are detected between glacial macro-forms, landslide activity, geomorphic process domains, channel-reach morphology, and downstream hydraulic geometry. The stepped topography o f glaciated landscapes appears to be an ideal natural laboratory to study how channel geometry and morphology respond to a wide range of imposed slope gradients and sediment supply. From the standpoint o f long-term evolution, in addition to local channel slope, it is proposed that variates such as landslide-driven annual sediment yield and bankfull channel width, be represented as functions of contributing area and used as remotely-based indicators of transient environmental conditions. In this context, this thesis, by combining the analysis o f relict glacial topography with the spatial arrangement of geomorphic process domains, landslide-driven sediment dynamics, channel-reach morphology, downstream hydraulic geometry, coarse grain-size sediment fraction and stream power, has successfully identified an integrated set o f metrics for quantifying the degree o f departure from equilibrium conditions (transience) in a given landscape. After about 14 ka since the last ice retreat occurred locally, the landscape examined has not recovered significantly from past glaciations and is out o f balance with prevailing conditions. Given how little modification of the glacial signature has occurred in the 14 ka since deglaciation, and the typical duration o f interglacial periods (10-50 ka [e.g., Berger and Loutre, 2002]), glacial signatures w i l l l ikely persist until the onset of the next glacial period. 191 References Ahnert, F. (1998), Introduction to Geomorphology, Arnold, London, 352 pp. Anderson, R.S. , P. Molnar, and M . A . Kessler (2006), Features of glacial valley profiles simply explained, J. Geophys. Res., Ill, F01004, doi: 10.1029/2005JF000344. Atmospheric Environment Service (1995), Climate normal data for stations, Alert Bay and Chatham Point, Government of Canada. Bak, P., C . Tang, and K . Weisenfeld (1987), Self-organised criticality: an explanation of 1/f noise, Physical Review Letters, 59, 381-384. Bak, P., C. Tang, and K . Weisenfeld (1988), Self-organised criticality, Physical Review A, 38, 364-374. Be l l , F . G . (1981), Engineering Properties of Soils and Rocks, Butterworths, Sevenoaks, U K . Benda, L . , and J. Cundy, (1990), Predicting deposition of debris flows in mountain channels, Canadian Geotechnical Journal, 27, 409-417. Benda, L . , and T. Dunne (1997), Stochastic forcing o f sediment supply to the channel network from landsliding and debris flow, Water Resour. Res., 33, 2849-2863. Benda, L . , D . Mi l le r , T. Dunne, J. Agee, and G . Reeves (1998), Dynamic landscape systems, in River Ecology and Management: Lessons from the Pacific Coastal Ecoregion, edited by R. Naiman, R. and R. Bi lby , 261-288 pp., Springer-Verlag, Reiskirchen, Germany. Benda, L . , M . A . Hassan, M . Church, and C . L . M a y (2005), Geomorphology o f steepland headwaters, the transition from hillslopes to channels, JAWRA, 41, 835-851. Beschta, R . L . , T. Bl inn , G . E . Grant, F J . Swanson, and G . G . Ice (1987), Erosion and Sedimentation in the Pacific Rim, Publication 165, 510 pp, International Association for Hydrological Science, Oxfordshire, U K . Berger, A . , and M . F . Loutre (2002), A n exceptionally long interglacial ahead?, Science, 297, 1287-1288. Bisson, P .A . , J .L. Nielsen, R . A . Palmason, and L . E . Grove (1981), A system of naming habitat types in small streams, with examples o f habitat utilization by salmonids during low stream flow, in Acquisition and Utilization of Aquatic Habitat Inventory 192 Information, edited by N . B . Armentrout, pp. 291-298, American Fisheries Society, Western Divis ion, Portland, O R . Bovis , M . J . , and B . R . Dagg (1992), Debris flow triggering by impulsive loading: mechanical modelling and case studies, Canadian GeotechnicalJournal, 29, 345-352. Bovis , M . J . , and M . Jakob (1999), The role of debris supply conditions in predicting debris flow activity, Earth Surface Processes and Landforms, 24, 1039-1054. Bovis , M . J , T . H . Mil lard , and M . E . Oden (1998), Gul ly processes in coastal British Columbia: the role o f woody debris, in Carnation Creek and Queen Charlotte Islands Fish/Forestry Interaction Workshop: applying 20 years of coastal research to management solutions, edited by D . L . Hogan, P.J. Tschaplinski and S. Chatwin, Land Management Handbook 41, 49-75 pp., British Columbia Ministry o f Forests, Research Branch, Victoria, Canada. Brardinoni, F . (2001), Identification of natural and logging-related landslides in the Capilano River basin (Coastal British Columbia): A comparison between remotely sensed survey and ground survey, M . S c . Thesis, University of British Columbia, Vancouver, British Columbia, 127 pp. Brardinoni, F. , and M . Church (2004), Representing the landslide magnitude-frequency relation: Capilano River Basin, British Columbia, Earth Surf Processes Landforms, 29, 115-124. Brardinoni, F , M . A . Hassan, and O. Slaymaker (2003a), Complex mass wasting response o f drainage basins to forest management in coastal British Columbia, Geomorphology, 49, 109-124. Brardinoni, F. , O. Slaymaker, and M . A . Hassan (2003b), Landslide inventory in a rugged forested watershed: a comparison between remotely sensed and field survey data, Geomorphology, 54, Yi'9-196. Braun, J. , D . Zwartz, and J. Tomkin (1999), A new surface processes model combining glacial and fluvial erosion, Annals of Glaciology, 282-290. Brayshaw, D . D . (1997), Factors affecting post-logging debris flow initiation in steep forested gullies of the southwestern Canadian Cordillera, Fraser Valley Region, M . S c . Thesis, The University of British Columbia, Vancouver, 190 pp. 193 British Columbia Ministry of Forests (1995), Mapping and Assessing Terrain Stability Guidebook, 34 pp. Brocklehurst, S. and K . Whipple (2002), Glacial erosion and relief production in the Eastern Sierra Nevada, California, Geomorphology, 42, 1-24. Brummer, C.J . , and D.R. Montgomery (2003), Downstream coarsening in headwater channels, Water Resour. Res., 39, 1294, 10.1029/2003WR001981 Brunsden, D . (1993), Barriers to geomorphological change, in Landscape Sensitivity, edited by D . S . G . Thomas and R.J . Al l i son , 7-12 pp., John Wiley & Sons, N e w York. Brunsden, D . , and J .B. Thornes (1979), Landscape sensitivity and change, Trans. Inst. Brit. Geogr.,4, 463-484. Buffington, J . M . (1995), Effects of hydraulic roughness and sediment supply on surface textures of gravel-bedded rivers, M . S c . Thesis, University o f Washington, Seattle, 184 pp. B u l l , W . B . (1975), Allometric change of landforms. Geol. Soc. Am. Bull., 86, 1489-1498. Burbank, D . W . (2002), Rates of erosion and their implications for exhumation, Mineral. Mag, 66,25-52. Caine, N . , and F.J . Swanson (1989), Geomorphic coupling of hillslope and channel systems in two small mountain basins, Zeitschrift fur Geomorphologie N.F., 33, 189-203. Campbell, D . A . (2005), Watershed responses to timber harvesting disturbance, M . S c . Thesis, The University of British Columbia, Vancouver, B C , 123 pp. Campbell D , and M . Church (2003), Reconnaissance sediment budgets for Lynn Valley, British Columbia: Holocene and contemporary time scales, Canadian Journal of Earth Science, 40, 701-713. Canovaro, F. , E . Paris, and L . Solari (2004), Influence o f macro-roughness arrangement on flow regime, in River Flow 2004, edited by Greco, Caravetta, and Delia Morte, 287-293 pp., Taylor and Francis, London, U K . Cenderelli, D . A . (1998), Glacial-lake outburst floods in the Mount Everest region of Nepal: F low processes, flow hydraulics, and geomorphic effects, Ph.D. thesis, Colorado State University, Fort Collins, Colorado, 247 pp. Chorley, R . J , and B . A . Kennedy (1971), Physical Geography: a systems approach, Prentice-Hal l , London, U K . 194 Church, M . (1980), On the equations of hydraulic geometry, Department of Geography, University o f British Columbia, Vancouver, Canada. Church, M . (1992), Channel morphology and typology, in The Rivers handbook, edited by P. Carlow and G . E . Petts, 126-143 pp., Blackwell Scientific Publications, Oxford, U K . Church, M . (1998), The landscape of the Pacific Northwest, in Carnation Creek and Queen Charlotte Islands Fish/Forestry Workshop: Applying 20 Years of Coastal Research to Management Solutions, edited by D . L . Hogan, P.J. Tschaplinski, and S. Chatwin, Land Management Handbook, vol . 41, 13-22 pp., British Columbia Ministry o f Forests, Victoria. Church, M . (2002), Fluvial sediment transfer in cold regions, in Landscapes of transition, edited by K . Hewitt et al., 93-117 pp., Amsterdam, Kluwer. Church, M . , and D . M . Mark (1980), On size and scale in geomorphology, Progress in Physical Geography, 4, 342-390. Church, M . , and J . M . Ryder (1972), Paraglacial sedimentation: a consideration o f fluvial processes conditioned by glaciation, Geol. Soc. Am. Bull, 83, 3059-3072. Church, M . , and O. Slaymaker (1989), Disequilibrium o f Holocene sediment yield in glaciated British Columbia, Nature, 337, 452-454. Church, M . , R. Kellerhals, and T.J. Day (1989), Regional clastic sedimentyield in British Columbia, Canadian Journal of Earth Sciences, 26, 31-45. Church, M . , J. Wolcott, and J. Maizels (1990), Palaeovelocity: A parsimonious proposal, Earth Surface Processes and Landforms, 15, 475-480. Church, M . , D.Ham, M . Hassan, and O. Slaymaker (1999), Fluvial clastic sediment yield in Canada: scaled analysis, Canadian Journal of Earth Sciences, 36, 1267-1280. Coates, D .R. (1969), Hydraulic geometry in a glaciated region, Transactions, American Geophysical Union, 50, 149 pp. Crozier, M . J . , E . E . Vaughan, and J . M . Tippett (1990), Relative instability o f colluvium-filled bedrock depressions, Earth Surface Processes and Landforms, 15, 329-339. Dadson, S. (2000), Episodic Processes in Fluvial Landscape Evolution, M . S c . thesis, The University o f British Columbia, Vancouver, B . C . , 165 pp. Day, T.J. (1969), The channel geometry of mountain streams, M A thesis, The University o f British Columbia, Vancouver, B . C . , 59 pp. 195 Densmore, A . L . , R .S . Anderson, B . G . MacAdoo, and M . A . E l l i s (1997), Hillslope evolution by bedrock landslides, Science, 275, 369-372. Dietrich, W . E . , and T. Dunne (1978), Sediment budget for a small catchment in mountainous terrain, Zeitschriftfur Geomorphologie, N.F. Suppl.-Bd. 29,191-206. Dietrich, W . E . , and T. Dunne (1993), The channel head, in Channel Network Hydrology, edited by K . Beven and M . J. Kirkby, pp. 175-219, J. Wiley and Sons, London, U K . D'Odorico, P., S. Fagherazzi, and R. Rigon (2005), Potential for landsliding: Dependence on hyetograph characteristics, J. Geophys. Res., 110, F01007, doi: 10.1029/2004 JF000127. Dunne, T. (1991), Stochastic aspects o f the relations between climate, hydrology and landform evolution, Trans. Japanese Geomorph. Union, 12,1-24. Dunne, T. (1998), Critical data requirements for prediction of erosion and sedimentation in mountain drainage basins, Journal of the American Water Resources Association, 34, 795-808. Duval l , A . , E . Kirby , and D . Burbank (2004), Tectonic and lithologic controls on bedrock channel profiles and processes in coastal California, J. Geophys. Res., 109, F03002, doi: 10.1029/2003JF000086. Eaton, B . , M . Church, and D . Ham (2002), Scaling and regionalization o f flood flows in British Columbia, Canada, Hydrological Processes, 16, 3245-3263. Evans, I.E. (2005), Local aspect asymmetry o f mountain glaciation: A global survey of consistency of favoured directions for glacier numbers and altitudes, Geomorphology, 73, 166-184. Fannin, R.J . , and T. P. Rollerson (1993), Debris flows: some physical characteristics and behavior, Can. GeotechJ., 30, 71-81. Ferguson, R. I. (1986), Hydraulics and hydraulic geometry, Progress in Physical Geography, 10,1-31. Finnegan, N . J . , G . Roe, D .R . Montgomery, and B . Hallet (2005), Controls on the channel width of rivers: Implications for modeling fluvial incision o f bedrock, Geology, 33, 229-232. Garbrecht, J., and L . W . Martz (1997), The assignment of drainage direction over flat surfaces in raster digital elevation models, J. Hydrol, 193, 204.-213. 196 Grant, G .E . , F.J . Swanson, and M . G . Wolman (1990), Pattern and origin of stepped-bed morphology, in high gradient streams, Western Cascades, Oregon, Geol. Soc. Am. Bull, 102, 340-352. Greater Vancouver Regional District (1999), C D Annex to G V R D Analysis Report Watershed Management Plan #5. February 1999. Griffiths, G . A . (1989), Form resistance in gravel channels with mobile beds, Journal of Hydraulic Engineering, 775,340-355. Guthrie, R . H . , and S.G. Evans (2004), Analysis of landslide frequencies and characteristics in a natural system, coastal British Columbia, Earth Surface Processes and Landforms, 29, 1321-1339. Guthrie, R . H . , and E . V a n der Flier-Keller (1998), The contribution of geology, to debris slides on Vancouver Island, B . C . Proceedings o f the 8 t h Congress o f the International Association for Engineering Geology and the Environment, Vancouver, Canada, V o l . , 3, pp. 1993-1999, Balkema, Rotterdam. Guzzetti F. , B . D . Malamud, D . L . Turcotte, and P. Reichenbach (2002), Power-law correlations o f landslide areas in central Italy, Earth and Planetary Science Letters, 195, 169-183. Guzzetti, F. , P. Reichenbach, M . Cardinali, F. Ga l l i , and F. Ardizzone (2005), Probabilistic landslide hazard assessment at the basin scale, Geomorphology, 72, 272-299. Hack, J.T. (1957), Studies o f longitudinal stream profiles in Virginia and Maryland: U .S . Geological Survey Professional Paper 294-B. 45-97. Hack, J.T., and J .C. Goodlett (1960), Geomorphology and forest ecology of a mountain region in the Central Appalachians, Professional Paper 347, U . S . Geological Survey. Hallet, B . (1989), A theoretical model for glacial abrasion, J. Glaciol, 23, 39-50. Halwas, K . L . , and M . Church (2002), Channel units in small, high gradient streams on Vancouver Island, British Columbia, Geomorphology, 43, 243-256. Harbor, J . M . (1992), Numerical modeling of the development of U-shaped valleys by glacial erosion, Geol. Soc. Am. Bull, 104,1364-1375. Hassan M A , M . Church, T. Lisle , F. Brardinoni, L . Benda, and G . Grant (2005), Sediment transport and channel morphology of small, forested streams, Journal of the American Water Resources Association, 41, 835-851. 197 Heller, P .L . , P .E . Beland, N . F . Humphrey, S .K. Konrad, R . M . Lynds, M . E . M c M i l l a n , K . E . Valentine, Y . A . Widman, and D.J . Furbish (2001), Paradox of downstream fining and weathering-rind formation in the lower Hoh River, Olympic Peninsula, Washington, Geology, 29, 971-974. Hicks, D . M . , and P .D. Mason (1991), Roughness Characteristics of New Zealand Rivers, Water Resources Survey, Wellington. Hogan, D . L . , P.J. Tschaplinski, and S. Chatwin (1998), Carnation Creek and Queen Charlotte Islands Fish/Forestry Workshop: Applying 20 Years of Coastal Research to Management Solutions, Land Management Handbook, vol . 41, 275 pp., British Columbia Ministry of Forests, Victoria. Holland, S.S. (1964), Landforms of British Columbia: A Physiographic Outline, Bulletin 48, British Columbia Mines and Petroleum Resources, Victoria, B . C . , Canada, 138 pp. Hooke, R . L . (1991), Positive feedbacks associated with erosion of glacial cirques and overdeepenings, Geol. Soc. Am^ Bull, 103, 1104-1108. Horton, R . E . (1945), Erosional development of streams and their drainage basins: hydrophysical approach to quantitative morphology, Geol. Soc. Am. Bull, 56, 275-370. Hovius, N , C P . Stark, and P. A . A l l en (1997), Sediment flux from a mountain belt derived by landslide mapping, Geology, 25, 231-234. Howes, D . E . (1981), Terrain inventory and geological hazards, northern Vancouver Island, British Columbia Ministry of Environment, Assessment and Planning Division, Bulletin 5, Victoria. Hungr, O., G . C Morgan, and R. Kellerhals (1984), Quantitative analysis of debris torrent hazards for design of remedial measures, Can. Geotech. J., 21, 663-677. Hungr, O., S.G. Evans, and J. Hazzard (1999), Magnitude and frequency o f rock falls and rock slides along the main transportation corridors of southwestern British Columbia, Canadian Geotechnical Journal, 36, 224-238. Hungr, O., S.G. Evans, M . J . Bovis , and J .N. Hutchinson (2001), A review o f the classification of landslides of the flow type, Environmental and Engineering Geoscience, 7, 221-238. 198 Ibbitt, R .P . (1997), Evaluation of optimal channel network and river basin heterogeneity concepts using measured flows and channel properties, Journal of Hydrology, 196, 119-138. Ijjasz-Vasquez, E.J . , and R . L . Bras (1995), Scaling regimes o f local slope versus contributing area in digital elevation models, Geomorphology, 2, 299-311. Istanbulluoglu, E . , and R . L . Bras (2005), Vegetation-modulated landscape evolution: Effects of vegetation on landscape evolution processes, drainage density, and topography, J. Geophys. Res., 110: F02012, doi:10.1029/2004JF000249. Jackli, H . (1957), Gegemvarts Geologie des Bundnerischen Rheingebietes, Beitrage zur Geologie der Schweiz, Geotech. Series, vol . 36, 135 pp., Kummerl i and Frey, Bern, Switzerland. Jackson, D . A . (1993), Stopping Rules in Principal Component Analysis: a Comparison of Heuristical and Statistical Approaches, Ecology, 74, 2204-2214. Jakob, M . (2000), The impacts o f logging on landslide activity at Clayoquot Sound, British Columbia, Catena, 38, 279-300. Jakob, M . , M . Bovis , and M . Oden (2005), The significance of channel recharge rates for estimating debris-flow magnitude and frequency, Earth Surface Processes and Landforms, 30, 755-766. Johnson, A . C . , D . N . Swanston, and K . E . McGee (2000), Landslide initiation, runout, and deposition within clearcuts and old-growth forests of Alaska, Journal of the American Water Resources Association, 36, 17-30. Keulegan, G . H . (1938), Laws o f turbulent flow in open channels, United Clatec National Bureau of Standards, Journal of Research, 21, 727-741 Kirby , E . , and K . Whipple (2001), Quantifying differential rock-uplift rates via stream profile analysis, Geology, 29, 415-418. Knighton, D . A . (1998), Fluvial Forms and Processes: A New Perspective, Arnold, London, 383 pp. Knighton, D . A . (1999), Downstream variation in stream power, Geomorphology, 29, 293-306. Korup, O. (2005), Geomorphic imprint o f landslides on alpine river systems, southwest N e w Zealand, Earth Surface Processes and Landforms, 30, 783-800. 199 Kovanen, D.J . , and D.J . Easterbrook (2002), Timing and extent of Allerod and Younger Dryas age (ca. 12 500-10 0 0 0 1 4 C yr B.P.) oscillations o f the Cordilleran ice sheet in the Fraser Lowland, western North America, Quaternary Research, 57, 208-224. Krajina, V . J . (1969), Ecology of Western North America, 2(1), 1-147, Department of Botany, University o f British Columbia, Vancouver, Canada. Leopold, L . B . , and W . B . Langbein (1964), Association and indeterminacy in geomorphology, in The Fabric of Geology, edited by C . C . Albritton, 184-192 pp., Addison-Wesley Publishing Co. , Reading, Massachusetts. Leopold, L . B . , and T. Maddock (1953), The hydraulic geometry o f stream channels and some physiographic implications, U.S.G.S. Professional Paper 252, 57 pp. L u , FL, C.J . Moran, and M . Sivapalan (2005), A theoretical exploration of catchment-scale sediment delivery, Water Resour. Res., 41, W09415, doi: 10.1029/2005WR004018 MacGregor, K . R . , R .S . Anderson, S.P. Anderson, and E . D . Waddington (2000), Numerical simulations of glacial-valley longitudinal profile evolution, Geology, 28, 1031-1034. Mackin , J .H . (1964), Rational and empirical methods of investigation in geology, in The Fabric of Geology, edited by C . C . Albritton, 135-163 pp., Addison-Wesley Publishing Co. , Reading, Massachusetts. Malamud, B . D . , D . L . Turcotte, F. Guzzetti, and P. Reichenbach (2004), Landslide inventories and their statistical properties, Earth Surface Processes and Landforms, 29,687-711. Manning, R. (1891), On the flow of water in open channels and pipes, Institute of Civil Engineers of Ireland Transactions, 20, 161-207. Mark, D . M . , and M . Church (1977), On the misuse of regression in Earth science, Mathematical Geology, 9, 63-75. Martin, Y . , K . Rood, J .W. Schwab, and M . " Church (2002), Sediment transfer by shallow landsliding in the Queen Charlotte Islands, British Columbia, Canadian Journal of Earth Science, 39, 189-205. Marutani, T., G.J . Brierley, N . A . Trustrum, and M . Page (2001), Source-to-Sink Sedimentary Cascades in Pacific Rim Geo-Systems, Matsumoto Sabo Work Office, Ministry of Land, Infrastructure and Transport, Nagano, Japan. 184 pp. 200 Maynard, D . (1991), Tsitika river watershed: Sediment source inventory, Unpublished Report for British Columbia Ministry of Forests, Research Branch, Victoria, 18 pp. Maynard D . and Associates Ltd. , and Golder Associates Ltd. (2004), Tsitika River and Eve River Historic Landslide Inventory, Report prepared for Weyerhaeuser Company Ltd. Coastal Group, Nanaimo Woodlands, Nanaimo, B . C . McGarigal , K . , S. Cushman, and S. Stafford (2000), Multivariate statistics for wildlife and ecology research, Springer-Verlag, N e w York. Meidinger, D . , and J. Pojar, (1991), Ecosystems of British Columbia, British Columbia Ministry of Forests, http://www.for.gov.bc.ca/hfd/pubs/Docs/Srs/SRseries.htm Mil la rd , T . H . , (1993), Sediment in forested and logged gullies, coastal British Columbia. Unpublished M . S . Thesis, Dept. o f Geography, Univ . o f British Columbia, Vancouver, Canada, 202 pp. Mil la rd , T. (1999), Debris flow initiation in coastal British Columbia gullies, B . C . Ministry o f Forests, Nanaimo, B . C . Technical Report, TR-002/1999. Mil la rd , T., T.P. Rollerson, and P. Thomson (2002), Post-logging landslide rates in the Cascade Mountains, southwestern British Columbia, Technical Report, TR-023/2002, B . C . Ministry of Forests, Nanaimo, British Columbia. Mi l le r , J.P. (1958), High mountain streams: Effects of geology on channel characteristics and bed material, Memoir 4, State Bureau of Mines and Mineral Resources, N e w Mexico Institute o f Min ing and Technology, Socorro, N e w Mexico , 53 pp. Molnar, P, and J .A. Ramirez (1998b), A n analysis of energy expenditure in Goodwin Creek, Water Resour. Res., 34, 1819-1829. Molnar, P, and J .A. Ramirez (2002), On downstream hydraulic geometry and optimal energy expenditure: Case studies of the Ashley and Taieri Rivers, Journal of Hydrology, 259, 105-115. Monger, J . W . H . (1989), Geology, Hope British Columbia, 41-1989, sheetl, Geol . Surv. o f Can., Dept. o f Energy, Mines and Res., Ottawa, Ont.. Montgomery, D .R. (1994), Road surface drainage, channel initiation, and slope instability, Water Resour. Res., 30, 1925-1932. Montgomery, D .R. (1999), Process domains and the river continuum, J. Am. Water Resour. Ass., 35, 397-410. 201 Montgomery, D .R. (2001a), Geomorphology, river ecology, and ecosystem management, in Geomorphic Processes and Riverine Habitat, edited by J. Dorava, D . Montgomery, B . Palcsak, and F. Fitzpatrick, Water Science and Application Volume 4, 247-253 pp., American Geophysical Union, Washington, D . C . Montgomery, D .R. (2001b), Slope distributions, threshold hillslopes, and steady-state topography, Am. J. Sci., 301,432-454. Montgomery, D .R. (2002), Val ley formation by fluvial and glacial erosion, Geology, 30, 1047-1050. Montgomery, D . R., and S . M . Bolton (2003), Hydrogeomorphic variability and river restoration, in Strategies for Restoring River Ecosystems: Sources of Variability and Uncertainty in Natural and Managed Systems, edited by R . C . Wissmar and P . A . Bisson, pp. 39-80, American Fisheries Society, Bethesda, Maryland. Montgomery, D.R. , and J. M . Buffington (1997), Channel-reach morphology in mountain drainage basins, Geol. Soc. Am. Bull., 109, 596-611. Montgomery, D . R., and J . M . Buffington, (1998), Channel processes, classification, and response potential, in River Ecology and Management, edited by R. J. Naiman and R. E . Bi lby , 13-42 pp., Springer-Verlag Inc., N e w York. Montgomery, D.R. , and W . E . Dietrich (1988), Where do channels begin? Nature, 336, 232-234. Montgomery, D.R. , and W . E . Dietrich (1989), Source areas, drainage density, and channel initiation, Water Resour. Res., 25,1907-1918. Montgomery, D.R. , and W . E . Dietrich (1992), Channel initiation and the problem of landscape scale, Science, 255, 826-830. Montgomery, D.R. , and W . E . Dietrich (1994a), Landscape dissection and drainage area-slope thresholds, in Theory in Geomorphology, edited by M . J . Kirkby, 221-246 pp., John Wiley, N e w York. Montgomery, D.R. , and W . E . Dietrich (1994b), A physically based model for the topographic control on shallow landsliding, Water Resour. Res., 30, 1153-1171. Montgomery, D.R. , and E . Foufoula-Georgiou (1993), Channel network source representation using digital elevation models, Water Resour. Res., 29, 3925-3934. 202 Montgomery. D.R. , and K . B . Gran (2001), Downstream variations in the width of bedrock channels, Water Resour. Res., 37, 1841 -1846. Montgomery, D.R. , J . M . Buffington, R . D . Smith, K . M . Schmidt, and G . Pess (1995), Pool spacing in forest channels, Water Resour. Res., 31,1097-1105. Montgomery, D.R. , T . B . Abbe, N . P . Peterson, J . M . Buffington, K . M . Schmidt, and J .D. Stock (1996), Distribution of bedrock and alluvial channels in forested mountain drainage basins, Nature, 381, 587-589. Montgomery, D.R. , T . M . Massong, and S.C.S. Hawley (2003), Debris flows, log jams and the formation of pools and alluvial channel reaches in the Oregon Coast Range, Geol. Soc. Am. Bull., 115, 78-88. Muhs, D.R. , R . M . Thorson, J.J. Clague, W . H . Mathews, P.F. MacDowel l , and H . M . Kelsey (1987), Pacific Coast and Mountain Systems, in Geomorphic Systems of North America, Centennial Special, vol . 2, edited by W . L . Graf, pp. 517-581, G S A , Boulder, C O . Muller , J .E., K . E . Nothcote, and D . Carlisle (1974), Geology and mineral deposits o f Alert Bay - Cape Scott map Area, Vancouver Island, British Columbia, Paper 74-8,11 pp., Geol . Surv. o f Can.., Ottawa, Ont. Nakamura, F. , F.J . Swanson, and S . M . Wondzell (2000), Disturbance regimes and riparian systems - a disturbance-cascade perspective, Hydrological Processes, 14, 2849-2860. Noever D A . (1993), Himalayan sandpiles, Phys. Rev., E47, 724-725. O'Callaghan, J.F., and D . M . Mark (1984), The extraction of drainage networks from digital elevation data, Computer Vision, Graphics and Image Processing, 28, 328-344. Oden, M . E . (1994), Debris recharge rates in torrented gullies in the Queen Charlotte Islands. M . S c . Thesis, University o f British Columbia, Vancouver, Canada, 100 pp. Oskin M . , and D . Burbank (2005), Alpine landscape evolution dominated by cirque retreat, Geology, 33, 933-936. Osterkamp, W.R. , and Hedman E .R. (1977), Variation of width and discharge for high-gradient stream channels, Water Resour. Res., 13, 256-258. Pack, R. T., D . G . Tarboton, and C . N . Goodwin, (1998), The S I N M A P Approach to Terrain Stability Mapping, 8 pp., 8th Congress of the International Association of Engineering Geology, Vancouver, British Columbia, Canada. 203 Park, C . C . (1977), World-wide variations in hydraulic geometry exponents of stream channels: A n analysis and some observations, Journal of Hydrology, 33, 133-146. Phillips, P.J., and J . M . Harlin (1984), Spatial dependency of hydraulic geometry in a subalpine stream, Journal of Hydrology, 71, 277-283. Prestegaard, K . L . (1983), Bar resistance in gravel bed streams at bankfull stage, Water Resour., Res., 19, 472-476. Ponton, J.R. (1972), Hydraulic geometry in the Green and Birkenhead basins, British Columbia, in Mountain Geomorphology: Geomorphological Processes in the Canadian Cordillera, edited by O . H . Slaymaker, and H.J . McPherson, pp. 151-160, Tantalus Research, Vancouver, Canada. Reid, L . M . , and T. Dunne (1996), Rapid Evaluation of Sediment Budgets, GeoEcology Paperback, 164 pp., Catena Verlag, Reiskirchen, Germany. Reneau, S.L., and W . E . Dietrich (1987), The importance of hollows in debris How studies; examples from Mar in County, California, G.S.A., Reviews in Engineering Geology, 7, 165-180. Reneau, S.L., and W . E . Dietrich (1991), Erosion rates in the southern Oregon Coast Range: evidence for an equilibrium between hillslope erosion and sediment yield, Earth Surface Processes and Landforms, 16, 307-322. Roberts, R . G . , and M . Church (1986), The sediment budget in severely disturbed watersheds, Queen Charlotte Ranges, British Columbia, Canadian Journal of Forest Research, 16, 1092-1106. Robison, E . G . , K . M i l l s , J. Paul, L . Dent, and A . Skiaugset (1999), Storm Impacts and Landslides of 1996: Final Report. Forest Practices Technical Report N o . 4. Oregon Department o f Forestry, 145 pp. Roddick, J .A . (1965), Vancouver North, Coquitlam and Pitt Lake Map Areas, British Columbia. Memoir vol . 335, Geological Survey o f Canada, Ottawa, Ontario. Rodriguez-Iturbe, I., A . Rinaldo, R.Rigon, R . L . Bras, A . Marani, and E . J . Ijjasz-Vasquez (1992), Energy dissipation, runoff production, and the three-dimensional structure o f river basins, Water Resour. Res., 28,1095-1103. 204 Rollerson, T. (1992), Relationships between landscape attributes and landslide frequencies after logging: Skidegate Plateau, Queen Charlotte Islands, Land Management Report N o . 76., 13 pp., B . C . Ministry of Forests, Victoria, British Columbia. Rollerson, T.P., C . Jones, K . Trainor, and B . Thomson (1998), Linking post-logging landslides to terrain variables: Coast Mountains, British Columbia - preliminary analyses, Proceedings of the 8th Congress of the Int. Assoc. for Eng. Geol. and the Environment, Vancouver, vol . 3, 1973-1979 pp., Balkema, Rotterdam, The Netherlands. Rollerson, T., T. Mi l la rd , C . Jones, K . Trainor, and B . Thomson (2001), Predicting Post-Logging Landslide Activi ty Using Terrain Attributes: Coast Mountains, British Columbia. Forest Service British Columbia, Technical Report O i l , Nanaimo, 20 pp. Rollerson, T.P., T. Mi l la rd , and B . Thomson (2002), Using terrain attributes to predict post-logging landslide likelihood on southwestern Vancouver Island, Forest Research Technical Report TR-015. Research Section, Vancouver Forest Region, B . C . Ministry of Forests, Nanaimo, British Columbia. 15 pp. Rood, K . M . , (1984), A n aerial photograph inventory of the frequency and yield o f mass wasting on the Queen Charlotte Islands, British Columbia, Land Management Report, vol . 34. B . C . Ministry of Forests, Victoria, British Columbia, 55 pp. Rood, K . M . (1990), Site characteristics and landsliding in forested and clearcut terrain, Queen Charlotte Islands, British Columbia, Land Management Report, N o . 64, B . C . Ministry of Forests, Victoria, British Columbia 46 pp. Rosgen, D . L . (1985), A stream classification system, in Riparian Ecosystems and Their Management, First North American Riparian Conference, Rocky Mountain Forest and Range Experiment Station, RM-120 , pp. 91-95. Rosgen, D . L . (1994), A classification of natural rivers, Catena, 22,169-199. Ryder, J . M . (1971), Some aspects o f the morphometry o f paraglacial alluvial fans in south-central British Columbia, Can. J. Earth Sci., 8, 1252-1264. Ryder, J . M . (1981), Geomorphology o f the southern part o f the Coast Mountains of British Columbia, Z.fur Geomorph., N.F. Suppl., 37, 120-147. 205 Schaefer D . G . , and S .N. Nikleva, (1973), Mean precipitation and snowfall maps for a mountainous area o f potential urban development, in Proceedings of the Forty-first Annual Western Show Conference in Denver, CO. Schmidt, K . M . , J.J. Roering, J .D. Stock, W . E . Dietrich, D .R . Montgomery, and T. Schaub (2001), Root cohesion variability and shallow landslide susceptibility in the Oregon Coast Range, Canadian Geotechnical Journal, 38, 995-1024. Schoenbohm, L . M . , K . X . Whipple, B . C . Burchfiel, and L . Chen (2004), Geomorphic constraints on surface uplift, exhumation, and plateau growth in the Red River region, Yunnan Province, China, Geol. Soc. Am. Bull., 116, 895-909. Schumm, S.A. (1973), Geomorphic thresholds and complex response o f drainage systems, in Fluvial geomorphology, edited by M . E . Morisawa, Proceedings volume of the 4th Binghamton Symposium, 299-310 pp., State University of N e w York at Binghamton. Schumm, S.A. (1977), The Fluvial System, John Wiley and Sons, N e w York, 338 pp. Schumm, S.A. (1985), Patterns of alluvial rivers, Annual Reviews of Earth and Planetary Sciences, 13, 5-27. Seidl, M . , and W . E . Dietrich (1992), The problem of channel incision into bedrock, in Functional Geomorphology, Catena Suppl, vo l .23, edited by K - H . Schmidt, and J. de Ploey, pp. 101-124, Cremlingen, Germany. Sidle, R . C . , A . J . Pearce, and C . L . O 'Loughl in (1985), Hillslope stability and land use, Water Resources Monograph Series N o . 11, A G U , Washington, D . C , 140 pp. Singh, V . P . (2003), On the theories of hydraulic geometry, International Journal of Sediment Research, 18, 196-218. Sklar, L . , and W . E . Dietrich (1998), River longitudinal profiles and bedrock incision models: Stream power and the influence o f sediment supply, in Rivers Over Rock: Fluvial Processes in Bedrock Channels, Geophys. Monogr. Ser., vol.107, edited by K . J . Tinkler and E . E . Wohl , pp. 237-260, A G U , Washington, D . C . Slaymaker, O. (1987), Sediment and solute yields in British Columbia and Yukon: their geomorphic significance re-examined, in International Geomorphology, edited by V . Gardiner, Part I, 925-945 pp., John Wiley and sons, Chichester, U . K . Slaymaker, O., and H.J . McPherson (1977), A n overview o f geomorphic processes in the Canadian Cordillera, Zeit. Geomorph, 21, 169-186. 206 Smith, R . B . , P.R. Commandeur, and M . W . Ryan (1983), Natural revegetation, soil development, and forest growth in the Queen Charlotte Islands, Progress Report, Working Paper N o 7/83, B C Ministry of Forests and Ministry of Environment, Victoria, British Columbia, 44 pp. Smith, R . B . , P.R. Commandeur, and M . W . Ryan (1986), Soils, vegetation, and forest growth on landslides and surrounding logged and old-growth areas on the Queen Charlotte Islands, B C Ministry o f Forests, Land Management Report, N o . 41, 95 pp. Snyder, N . , K . X . Whipple, G . Tucker, and D . Merritts (2000), Landscape response to tectonic forcing: analysis of stream morphology and hydrology in the Mendocino triple junction region, northern California, Geol Soc. Am. Bull, 112, 1250-1263. Snyder, N . P . , K . X . Whipple, G . E . Tucker, and D.J . Merritts (2003), Channel response to tectonic forcing: field analysis o f stream morphology and hydrology in the Mendocino triple junction region, northern California, Geomorphology, 53, 97-127. Stark, C P . (2006), A self-regulating model of bedrock river channel geometry, Geophysical Research Letters, 33, L04402, doi: 10.1029/2005GL023193. Stark, C P . , and N . Hovius (2001), The characterization o f landslide size distributions. Geophys. Res. Lett., 28, 1091-1094. Sterling, S . M . (1997) The influence of bedrock type on magnitude, frequency and spatial distribution of debris torrents on northern Vancouver Island, M . S c . thesis, The University o f British Columbia, 117 pp. Sterling, S., and O. Slaymaker (in press), Lithology control of debris torrent occurrence, Geomorphology. Stock, J., and W . E . Dietrich (2003), Val ley incision by debris flows: evidence of a topographic signature, Water Resour. Res., 39, 11-25. Strahler, A . N . (1956), The nature of induced erosion and aggradation. In Thomas, W . L . (editor), Man 's Role in Changing the Face o f the Earth. The University o f Chicago Press, Illinois, 621-638. Sullivan, K . (1986), Hydraulics and fish habitat in relation to channel morphology. Ph.D. thesis, The John Hopkins University, Baltimore, M D . 207 Swanson, F.J . , R .J . Janda, T. Dunne, and D . N . Swanston (1982), Sediment budgets and routing in forested drainage basins, U S D A Forest Service, Pacific Northwest Forest and Range Experiment Station, General Technical Report, PNW-141,165 pp. Swanston, D . N . (1989), A preliminary analysis o f landslide response to timber management in southeast Alaska: an extended abstract, in Proceedings of Watershed '89, Juneau, March 21-23 1989, edited by E . B . Alexander, U S D A Forest Service, Alaska Region, Juneau, 117-120 pp. Swanston, D . N . , and F.J . Swanson (1976), Timber harvesting, mass erosion, and steepland forest geomorphology in the Pacific Northwest, in Geomorphology and Engineering, edited by D.R. Coates, 199-221 pp., Dowden, Hutchinson & Ross, Inc. Stroudsburg, Pennsylvania. Swanston, D . N . , and D . A . Marion (1991), Landslide response to timber harvest in southeast Alaska, Proceedings of the Fifth Federal Interagency Sedimentation Conference, edited by S-S. Fan and Y . - H . Kuo , volume 2,10.49-10.56 pp., Las Vegas, Nevada. Tabachnick, B . G . , and L . S . Fidell (2001), Using Multivariate Statistics, A l l y n and Bacon, Boston, 966 pp. Tarboton, D . G . (1997), A new method for the determination of flow directions and contributing areas in grid digital elevation models, Water Resour. Res., 33, 309-319. Thompson, S . M . , and P . L . Campbell (1979), Hydraulics of a large channel paved with boulders, Journal of Hydraulic Research, 17, 341-354. Thornes, J. B . (1970), The hydraulic geometry o f stream channels in the Xingu-Araguaia headwaters, Geographical Journal, 136, 376-382. Tinkler, K . , and E . Wohl (1998), Rivers Over Rock, American Geophysical Union Geophysical Monograph 107, 323 pp., A G U , Washington, D . C . Tomkin, J .H. , and J. Braun (2002), The influence of alpine glaciation on the relief of tectonically active mountain belts, Am. J. Sci., 302,169-190. Tsukamoto, Y . (1973), Study on the growth of stream channel (I). Relationship between stream channel growth and landslides occurring during heavy storm, Journal of the Japanese Erosion Control Society, 25, 4-13 (in Japanese). Tucker, G .E . , and R . L . Bras (1998), Hillslope processes, drainage density, and landscape morphology, Water Resour. Res., 34, 2751-2764. 208 Tucker, G .E . , and R. Slingerland (1997), Drainage basin response to climate change, Water Resources Research, 33, 2031-2047. VanDine, D .F . (1985), Debris flows and debris torrents in the southern Canadian Cordillera, Can. Geotech. J., 22, 44-68. VanDine, D.F . , and S.G. Evans (1992), Large landslides on Vancouver Island, British Columbia, Proceedings of the First Canadian Symposium on Geotechnique and Natural Hazards, Vancouver, pp. 193-201, BiTech Publishers Ltd. , Vancouver, Canada. Vannote, R . L . , G . W . Minshal l , K . W . Cummins, J.R. Sedell, and C . E . Cushing (1980), The river continuum concept, Can. J. Fish. Aquat. Sci., 37, 130-137. Varnes, D .J . (1978), Slope movement types and processes, in Landslides: Analysis and Control, Special Report 173, 11-33 pp., Transport. Res. Board, National Academy o f Science, Natl . , Res. Counc , Washington, D . C . Veneziano, D . , and V . Iacobellis (1999), Self-similarity and multifractality o f topographic surfaces at basin and subbasin scales, J. Geophys. Res., 104, 12,797-12,812. Wall ing, D . E . (1983), The sediment delivery problem, Journal of Hydrology, 65, 209-237. Whipple, K . X . (2001), Fluvial landscape response time: how plausible is steady-state denudation?, Am. J. Sci., 301, 313-325. Whipple, K . X . (2004), Bedrock rivers and the geomorphology of active orogens, Annual Reviews of Earth and Planetary Sciences, 32,151 -185. Whipple, K . X , E . Kirby, and S.E. Brocklehurst (1999)^ Geomorphic limits to climate-induced increase in topographic relief, Nature, 401, 39-43. Whipple, K . X . , and G . E . Tucker (1999), Dynamics of the stream-power river incision model: implications for height limits o f mountain ranges, landscape response timescales, and research needs, J . Geophys. Res., 104, 17661-74. White, R. (2002), Geomorphic Process Domains in a Mountain Basin. M . S c . thesis, The University of British Columbia, Vancouver, B . C . , 121 pp. Wil l iams, G.P. (1978), Bank-full discharge o f rivers, Water Resour. Res., 14,1141-1153 Will iams, P.J. (1982), The Surface of the Earth: An Introduction to Geotechnical Science, Longman, London, U K . 209 Wohl , E . (2000), Mountain Rivers, American Geophysical Union Water Resources Monograph 14, 320 pp. Wohl , E . (2004a), Limits of downstream hydraulic geometry, Geology, 32, 897-900. Wohl , E . (2004b), Downstream hydraulic geometry along a tropical mountain river, in The Rio Chagres, Panama - A Multidisciplinary Profile of a Tropical Watershed, edited by R.Harmon, 169-188 pp., Kluver, Dordrecht, Germany. Wohl , E . , and D . Merritt (2005), Prediction of mountain stream morphology, Water Resour. Res., 41, W08419, doi: 10.1029/2004WR003779. Wohl , E . , and A . Wi lcox (2005), Channel geometry of mountain streams in N e w Zealand, Journal of Hydrology, 300, 252-266. Wohl , E . , J .N . Kuzma, and N . E . Brown (2004), Reach-scale channel geometry o f a mountain river, Earth Surface Processes and Landforms, 29, 969-981. Wolinsky M . A . , and L . F . Pratson (2005), Constraints on landscape evolution from slope histograms, Geology, 33, 477-480 W u , W. , and R . C . Sidle (1995), A distributed slope stability model for steep forested basins. Water Resour. Res., 31, 2097-2110. Zimmerman, A . , and M . Church (2001), Channel morphology, gradient profiles and bed stresses during flood in a step-pool channel, Geomorphology, 40, 311-327. 210 Appendix A Sediment Sources A.1 Landslide Terminus and Rounout Zones Classification used in the original inventory by Roller son and Maynard [2004]: • Connected gully channel (eg): landslide stops in a gully channel that appears to have a direct connection to either a main stem river channel or to a tributary; • Gully channel (gc): landslide appears to stop in a gully channel but there is no clear connection or lack o f connection to a river channel or a tributary. For example there may be a fan at the base of the gully but it is not clear i f a stream crosses the fan to the valley-floor stream; • Gully channel fan (gef): landside stops in bottom of gully channel and on the fan; • Concave headwater drainage, or hollow (ch): landslide stops in a headwater basin; • Connected tributary (ct): landslide stops in a tributary stream that is connected to a river; • Unconnected tributary (ni): landslide stops in a tributary stream that is connected to another tributary (not connected to a permanent stream); • Connected tributary/floodplain (ctfl): landslide stops on a floodplain adjacent to the tributary channel; • Fan (f): landslide appears to stop on a fan surface and may or may not be linked by a stream channel to a valley-floor stream; • Fan/connected tributary (fct): landslide stops in part on fan and in part in the channel o f a connected tributary. In places, it is not possible to determine with certainty that the landslide reached the stream or that there was post-event downstream transport of sediment and debris to the valley-floor stream; • Fan and main channel (fine): the landslide appears to stop both on a fan surface and in the channel o f a valley-floor river channel; • Floodplain, glaciofluvial terrace or valley flat (fit): the landslide appears to stop on a floodplain, glaciofluvial terrace or valley flat; • Lake (Ik): landslide stops in a lake; • Upper slope (us): the landslide appears to stop on an upper slope; • Mid slope (ms) the landslide appears to stop on a mid slope; • Toe slope (ts): the landslide appears to stop on a lower or toe slope; • Toe slope/main channel (tsmc): the landslide appears to stop both on an toe slope and in a main stream/river channel; • Main channel (mc): landslide stops in the main channel of a valley-floor stream or river; • Road (xd): landslide stops on a road. 211 Table A1. Volume of material mobilized (m3) categorized by initiation site, landslide type, and land use Land use / T , Landslide type (m3) Initiation da dadf df ds dsda dsdf DSIs rfds rfrs rfrsdf rs rsda rsdadf rsdf rsds rsdsdf rsra u ch 19640 0 6 0 235 6 19405 0 6 0 0 ~0 6 0 6 0 0 6 0 eg 195 0 0 0 195 0 0 0 0 0 0 0 0 0 0 0 0 0 0 es 38135 0 0 0 20293 11996 3425 0 0 0 0 0 0 0 0 0 0 0 2421 Nf gc 34666 0 0 0 0 0 27392 0 0 0 0 0 0 0 3515 0 3759 0 0 gh 389622 0 0 0 856 0 267000 8009 0 3762 939 0 0 0 25716 1659 81680 0 0 g S 268568 0 0 0 13249 0 225136 0 0 0 0 0 0 0 2234 0 23435 4453 61 OS 1558322 307990 162841 1500 10521 398562 361878 0 2799 13105 163 10295 126674 24824 4210 44511 88448 0 0 ch 0 0 0 0 0 6 6 1) 0 0 0 (j 0 0 0 0 0 0 0 eg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 es 6180 0 0 0 4496 593 1091 0 0 0 0 0 0 0 0 0 0 0 0 R d g c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 gh 1573 0 0 0 0 0 1573 0 0 0 0 0 0 0 0 0 0 0 0 g s 4542 0 0 0 4329 0 213 0 0 0 0 0 0 0 0 0 0 0 0 OS 100060 3105 5273 600 7198 46115 37769 0 0 0 0 0 0 0 0 0 0 0 0 Ch o o o o o o o o o ; o o o o o o o o o o eg 9242 0 0 0 1954 0 7288 0 0 0 0 0 0 0 0 0 0 0 0 es 21388 0 0 544 15335 0 3265 0 0 0 0 0 0 0 0 0 0 0 2244 Cc g C 1353 0 0 0 0 0 1353 0 0 0 0 0 0 0 0 0 0 0 0 gh 8712 0 0 0 0 0 8712 0 0 0 0 0 0 0 0 0 0 0 0 g S 29122 0 0 0 20722 0 8400 0 0 0 0 0 0 0 0 0 0 0 0 os 110401 3377 - 0 1971 9441 48502 47110 0 0 0 0 0 0 0 0 0 0 0 0 ro to Table A2. Volume of material mobilized (m3) in natural terrain, categorized by terminus and landslide type NATURAL Landslide type (ma) Terminus Total da dadf df ds dsda dsdf DSIs rfds rfrs rfrsdf rs rsda rsdadf rsdf rsds rsdsdf rsra u CO 111452 0 0 0 0 0 38312 8009 0 3762 0 0 8809 0 19020 3151 30388 0 0 Ct 136268 0 29998 0 11786 47541 42045 0 0 0 0 0 0 0 0 0 4172 0 726 Ctfl 75946 0 0 0 0 75946 0 0 0 0 0 0 0 0 0 0 0 0 0 es 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f 101997 0 17629 0 0 0 47255 0 0 0 0 0 3810 24824 0 0 8479 0 0 fct 123491 0 13673 0 0 25191 73654 0 0 0 0 0 0 0 0 0 10973 0 0 fit 82563 0 0 0 0 51459 15685 0 0 0 0 0 15419 0 0 0 0 0 0 fmc 104414 0 58261 0 0 46152 0 0 0 0 0 0 0 0 0 0 0 0 0 frd 6254 0 0 0 0 0 6254 0 0 0 0 0 0 0 0 0 0 0 0 gc 502364 3755 473 0 14299 0 373779 0 0 0 163 6257 16705 0 8497 10866 63056 4453 61 gcct 4874 0 0 0 0 0 4874 0 0 0 0 0 0 0 0 0 0 0 0 gcf 105348 0 0 0 0 3678 89810 0 0 0 0 0 0 0 3948 0 7912 . 0 0 gs 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ik 304236 304236 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Is 29115 0 0 0 0 20629 8486 0 0 0 0 0 0 0 0 0 0 0 0 mc 86421 0 0 0 8368 47676 28682 0 0 0 0 0 0 0 0 0 0 0 1695 ms 243435 0 38306 1500 6934 27408 57372 0 2799 11897 0 4038 28860 0 2818 29012 32490 0 0 rd 4449 0 0 0 916 0 3533 0 0 0 0 0 0 0 0 0 0 0 0 rdms 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 rdts 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ts 264378 , 0 0 0 235 63013 105064 0 0 o- 0 0 53071 0 1391 1753 39851 0 0 tsf 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 tsmc 1238 0 0 0 0 0 1238 0 0 0 0 0 0 0 0 0 0 0 0 us 8069 0 0 0 2671 1865 0 0 0 1207 939 0 0 0 0 1387 0 0 0 ut 138 0 0 0 138 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total 2309147 307990 162841 1500 45349 410558 904236 8009 2799 16867 1103 10295 126674 24824 35675 46170 197322 4453 2482 to Table A3. Volume of material mobilized (m3) in clearcut terrain, categorized by terminus and landslide type CLEARCUT Landslide type (m3) Terminus Total da dadf df ds dsda dsdf DSIS rfds rfrs rfrsdf rs rsda rsdadf rsdf rsds rsdsdf rsra u CO 417 0 0 0 0 0 417 0 0 0 0 0 0 0 0 0 0 0 0 ct 9996 0 0 0 3322 1953 4514 0 0 0 0 0 0 0 0 0 0 0 207 ctfl 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 es 667 0 0 0 667 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f 6957 0 0 0 0 0 6957 0 0 0 0 0 0 0 0 0 0 0 0 fct 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 fit 8108 0 0 544 3286 0 3897 0 0 0 0 0 0 0 0 0 0 0 381 fmc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 frd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 gc 26855 0 0 0 15786 0 11069 0 0 0 0 0 0 0 0 0 0 0 0 gcct 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 gcf 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 gs 6207 0 0 0 5373 0 834 0 0 0 0 0 0 0 0 0 0 0 0 Ik 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 mc 3063 0 0 0 1407 0 0 0 0 0 0 0 0 0 0 0 0 0 1656 ms 33002 3377 0 0 11769 2350 15506 0 0 0 0 0 0 0 0 0 0 0 0 rd 7503 0 0 0 0 0 7503 0 0 0 0 0 0 0 0 0 0 0 0 rdms 7507 0 0 339 1597 3394 2177 0 0 0 0 0 0 0 0 0 0 0 0 rdts 21382 0 0 0 0 9050 12332 0 0 0 0 0 0 0 0 0 0 0 0 ts 47331 0 0 1632 4242 31355 10102 0 0 0 0 0 0 0 0 0 0 0 0 tsf 819 0 0 0 0 0 819 0 0 0 0 0 0 0 0 0 0 0 0 tsmc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 us 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ut 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total 180218 3377 0 2515 47452 48502 76128 0 0 0 0 0 0 0 0 0 0 0 2244 Table A4. Volume of material mobilized (m3) at road-related locations, categorized by terminus and landslide type R O A D - R E L A T E D Landslide type (m3) Terminus total da dadf df ds dsda dsdf DSIs rfds rfrs rfrsdf rs rsda rsdadf rsdf rsds rsdsdf rsra u CO 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ct 32322 0 0 0 2412 9530 20380 0 0 0 0 0 0 0 0 0 0 0 0 ctfl 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 es 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 fct 3761 0 3761 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 fit 1924 0 0 0 1924 0 0 0 0 0 0 0 0 0 0 0 0 0 0 fmc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 frd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 gc 7005 0 0 0 4329 0 2676 0 0 0 0 0 0 0 0 0 0 0 0 gcct 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 gcf 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 gs 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ik 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 mc 593 0 0 0 0 593 0 0 0 0 0 0 0 0 0 0 0 0 0 ms 30237 0 0 600 1613 20127 7897 0 0 0 0 0 0 0 0 0 0 0 0 rd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 rdms 4762 0 0 0 4762 0 0 0 0 0 0 0 0 0 0 0 0 0 0 rdts 2481 0 0 0 0 0 2481 0 0 0 0 0 0 0 0 0 0 0 0 ts 25182 b 1512 0 0 16458 7212 0 0 0 0 0 0 0 0 0 0 0 0 tsf 3105 3105 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 tsmc 0 ' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 us 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ut 983 0 0 0 983 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total 112354 3105 5273 600 16023 46708 40645 0 0 0 0 0 0 0 0 0 0 0 0 A.2 Landslide Geometry Previous studies have hypothesized that landslide area (or volume), and so landslide magnitude-frequency relations, may be controlled to a significant extent by hillslope geometry [e.g., Hovius et al, 1997; Guzzetti et al, 2002; Brardinoni and Church, 2004]. I f one approximates the shape of landslide tracks to a rectangle, then digitized landslide area may be expressed as the product o f landslide length and width. Since landslide width tends to change considerably along the track of a given landslide, particularly in the case of debris avalanches, during GIS data preparation only landslide lengths were measured; average landslide width was calculated from the landslide area-length ratio. In consequence o f this, higher uncertainty is associated with landslide width as opposed to landslide length, which ultimately was chosen as equivalent landslide length scale. Hillslope length, which in the simplest possible configuration is the ridge-to-valley floor length, represents the maximum size that a landslide can attain by exploiting all available potential energy for a given relative relief, assuming the valley floor is sufficiently flat (or narrow) to prevent further landslide advancement. Ultimately, landslide length depends on where along the hillslope the conditions for initiation and deposition are met. Probability o f initiation, expressed as factor of safety, is concerned with the location where effective shear stress is able to overcome resistance resulting from intrinsic interactions between local variables such as slope gradient, substrate cohesion, friction, depth, hydraulic conductivity, vegetation cohesion, and abrupt discontinuities of one o f the above [e.g., Sidle et al, 1985]. Landslide deposition depends on effective friction, hence on the rheology of the moving material, degree of local confinement, and slope gradient. To improve current knowledge on the question of landslide length and hillslope length it was decided to examine how landslide geometry varies with its size. Specifically, the goal was to determine the empirical proportional relation between landslide length and landslide area, and evaluate how this relation is affected by landslide type, and terrain attributes. The approach is clearly statistical (study of landslide distributions) rather than mechanistic, and is intended to.help detecting landslide threshold length scales (see section 4.4.7). In geomorphology the use of empirical proportional relations is common [e.g., Hack, 1957; Bull, 1975; Church and Mark, 1980]. In this context, prior studies have showed that landslide 216 length ( L s ) and area ( A s ) [e.g., Korup, 2005] and landslide width ( W s ) and area [e.g., Hovius et al, 1997] are related by power-law expressions o f the form: Ws = cAsd (A.1) Ls = aAsb (A.2) where a, b, c, and d are constants (Table A.5) . In fact, i f Ws = As/Ls, then ac = 1.0 and b+d = 1.0, so that c = 1/a, and d = 1-b. Due to the limited control in the present dataset on landslide width, equation A . 1 w i l l not be considered here. In equation (A.2), an exponent b equal to 0.5 indicates isometry (or self similarity), that is, landslide shape does not change with size; b smaller or greater than 0.5 indicates negative or positive allometry respectively. In the former case, as landslides become larger their shape becomes more compact; in the latter case, larger slides are relatively more elongated. Table A . 5 . Landslide geometry by lithology Landslide Geometry Relations ° Lithology Land use Intercept (a) Exponent (b) n R 2 Coeff. CI (95%) Coeff. CI (95%) Extrusive Natural 0.424 [0.332 - 0.542] 0.814 [0.778 - 0.850] 422 0.824 Logged a 0.381 [0.280-0.517] 0.840 [0.790 - 0.890] 203 0.847 Intrusive Natural 0.481 [0.324 - 0.714] 0.846 [0.786 - 0.906] 89 0.899 Logged 8 1.631 [0.772 - 3.445] 0.638 [0.481 - 0.797] 36 0.665 Combined Natural 0.439 [0.356 - 0.543] 0.800 [0.769 - 0.830] 511 0.838 Clearcut 0.390 [0.282 - 0.538] 0.848 [0.792 - 0.903] 189 0.829 Road 0.675 [0.343-1.326] 0.758 [0.654 - 0.861] 50 0.819 L o g g e d a 0.449 [0.341 - 0.592] 0.817 [0.771 - 0.863] 239 0.838 Combined 0.491 [0.418-0.576] 0.785 [0.761 - 0.809] 750 0.847 a. Clearcut and Road; b. Relations are functional rather than based on least squares. When considering all landslides of the inventory, landslide length is positively allometric with respect to landslide area (Table A.5) . Specifically, the exponent of the relation is significantly greater than 0.7 at the 0.05 level o f significance. The value is rather different from that reported for two other landslide inventories conducted in south-western N e w Zealand [Korup, 2005], which exhibited 0.46 (n = 333) and 0.48 (n = 445). The comparison is not very helpful, since these inventories considered landslides with area larger than 10,000 m , including initiation, transportation and deposition zone. B y contrast, in Tsitika-Eve, landslide area ranges between 100 and 100,000 m 2 , not considering deposition area. 217 The allometry is positive for all land-use types (Figure A . l a ) . When the inventory is partitioned into sub-samples according to land-use type and lithology (Table A . 5 and Figure A . l c - d ) , all lithology-land use combinations exhibit an exponent that is significantly higher than 0.5. However, the isometric hypothesis cannot be dismissed for landslides occurring in logged terrain underlain by intrusive lithology (b = 0.638 ± 0.157, n = 36). In particular, the exponent for intrusive-logged landslides is significantly lower than for intrusive-natural landslides. The landslide length-area relation with respect to initiation position is analysed only for natural terrain (Figure A . l b ) . In fact, the lithologic control detected in logged terrain (i.e., extrusive-related slides are larger than intrusive ones) requires that the six initiation categories be split accordingly; however, since some categories (Table A.6) have already a limited number of observations, further splitting would weaken statistical inference even more. For all position types that have a reasonable number o f observations (i.e., n > 30), b is significantly greater than 0.5, at the 0.05 statistical level. While the intercept is not significantly different among position types, gully-sidewall and -headwall relations exhibit statistically higher exponent (psw = 0.833 and bmr= 0.825) than open-slope analogues (b = 0.681). In agreement with prior observations (section 4.4.2), sidewall, headwall, and open slope landslides describe in the length-area space a continuum for increasing event sizes (Figure A . l b ) . Finally, the exponent for escarpment-related failures matches the whole range covered by the open-slope, headwall, and sidewall categories. Table A . 6 . Natural landslide geometry by position at initiation Landslide Geometry Relations a Land use Position Intercept (a) Exponent (b) 2 Coeff. CI (95%) Coeff. CI (95%) Natural Headwat. basin 0.157 [0.005 • - 4.655] 0.980 [0.491 -1.469] 6 0.857 Escarpment 0.485 [0.193-• 1.219] 0.781 [0.613 - 0.948] 35 0.724 Gully channel 0.356 [0.018--6.985] 0.905 [0.483 -1.327] 9 0.755 Gully headwall 0.780 [0.395 --1.542] 0.825 [0.741 - 0.929] 109 0.698 Gully sidewall 0.326 [0.232 -- 0.458] 0.833 [0.778 -- 0.887] 173 0.840 Open slope 0.056 [0.793 --1.628] 0.681 [0.633 -- 0.730] 179 0.813 a. Relations are functional rather than based on least squares. Figure A . l . (Next pages) Landslide length-area plots categorized according to a) land-use type, b) initiation position, c) lithology in logged terrain, d) lithology in natural terrain, e) landslide type in natural terrain, f) landslide type in logged terrain, g-h) selected landslide types in natural terrain. Solid line indicates isometry (b = 0.5). 218 61Z Landslide Length (m) ~—' Landslide Length (m) Landslide Length (m) -i± _^ Landslide Length (m) ozz Landslide types have been grouped into five classes (i) debris avalanche-related movements (da, dadf, dsda, rsda), (ii) rock movements (rf, rs), (iii) slide movements involving rock and debris (ds, rsds), (iv) slide-to-flow movements involving rock and debris (dsdf, rsdf), and (v) complex movements (rsdsdf) (Table A . 7 and Figure A . l e -h ) . In natural terrain, rock slides and rock falls (rf-rs) are virtually self-similar (b = 0.603 ± 0.159); all other typologies are positively allometric. The exponent o f the length-area relation for rf-rs is significantly smaller than for dsdf-rsdf (b - 0.858 ± 0.046); as stated above, higher water content and degree o f confinement appear to explain the more elongated nature o f flow movements. Table A . 7 . Landslide geometry by landslide type Landslide Geometry Relations 0 Land use LS type Intercept (a) Exponent(b) n R 2 Coeff. CI (95%) Coeff. CI (95%) Natural da-related b 0.832 [0.387-1.787] 0.704 [0.613-0.796] 52 0.826 rf-rs 1.649 [0.531 -5.123] 0.603 [0.444 - 0.763] 12 0.865 dsdf-rsdf 0.368 [0.270-0.501] 0.858 [0.812-0.905] 321 0.805 ds-rsds 0.357 [0.221 - 0.576] 0.791 [0.712-0.871] 76 0.842 rsdsdf 0.357 [0.389-1.536] 0.717 [0.625 - 0.809] 43 0.855 Logged a ds 0.756 [0.477-1.199] 0.761 [0.669 - 0.853] 113 0.708 dsda 0.857 [0.326 - 2.256] 0.740 [0.596 - 0.884] 34 0.767 dsdf 0.434 [0.288 - 0.653] 0.828 [0.765 - 0.892] 80 0.897 a. Clearcut and Road b. Includes: da, dadf, dsda, rsda c. Relations are functional rather than based on least squares. In logged terrain, the exponent for debris slides (b = 0.761) is smaller (but not significantly) than for slide-flow events (b = 0.828); as a result the two relations start diverging beyond •y 2000 m (80-90 m length scale, Figure A . I f ) . In other words, beyond this threshold, debris slide-flows tend to assume a more elongated shape than debris slides of comparable size. L ike ly debris slide-flows become relatively more elongated than debris slides when the former encroach headwater channels. In this view, the 80-90 m distance may be seen as the threshold length scale that landslides have to travel before reaching low-order streams. Applying this thinking, the corresponding threshold length appears to be about 200 m in natural terrain (Figure A . l h ) . The slope of the length-area relation for debris slide-avalanches (dsda) is intermediate (b = 0.740) and it is not significantly different from the other two typologies. 221 A.3 Landslide Area as a Function of Elevation Figure A . 2 . Landslide area as a 1 8 1 0 function of elevation in natural terrain: (a) at initiation point; and 1610 (b) at deposition point. 1410 •g- 1210 c o '« 1010 'E 15 c 810 o 1 5 Qj 610 410 210 10 1610 10 o • 3 •5 o a 1410 1210 1010 4 8 810 4 c o 1 1 LU 610 410 210 10 a) Natural o debris • bedrock 100 1000 10000 100000 1000000 b) Natural o debris • bedrock 10 10000 100000 1000000 Landslide Area (m ) 222 Appendix B Multivariate Statistical Analysis: Testing the Assumptions B l . Normal i ty Tests Variable: lnlength (lnlength) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 5.01789256 0.63502421 -0.4194093 2506.68189 12.6551974 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 491.753471 0.40325575 1.40266052 39.1158075 0.06414713 Basic S t a t i s t i c a l Measures Location Mean 5.017893 Median 5.023881 Mode 5.010635 Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling Variability Std Deviation Variance Range Interquartile Range Tests for Normality --Statistic---0.63502 0.40326 3.80295 0.90756 W 0.962888 D 0.063515 W-Sq 0.07241 A-Sq 0.612348 p Value Pr < W 0.0073 Pr > D >0.1500 Pr > W-Sq >0.2500 Pr > A-Sq 0.1099 Stem 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 Variable: lnlength (lnlength) Leaf # 19 2 2457 4 11691779 8 2889 4 3688897 7 013568002246 12 111122241124566689 18 23588 5 111255581468 12 24447790025 11 25582247888 11 8 1 1 1 8 1 Boxplot + + I I 8 + + .... + + Multiply Stem.Leaf by 10**-1 Variable: lnlength (lnlength) Normal Probability Plot 6.3+ ++* **** * * * * * **++ *** +* * * ***** * *+ **** ***** ** * **+ * ++++ *++ +*+ +++ 2.5+* + + + + + + + + + + + -2 -1 0 +1 +2 The UNIVARIATE Procedure Variable: lncontr_area (lncontr_area) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 0.83295745 1 .61754796 -0.9705703 321.79093 194.193348 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 81.62983 2.6164614 2.85487001 253.796755 0.16339702 Basic S t a t i s t i c a l Measures Location Mean 0.832957 Median 1.105939 Mode Variability Std Deviation 1.61755 Variance 2.61646 Range 10.15203 Interquartile Range 1.62175 Test Tests for Normality --Statistic--- p Value-Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises. Anderson-Darling W 0.910482 D 0.125638 W-Sq 0.40255 A-Sq 2.583715 Pr < W <0.0001 Pr > D <0.0100 Pr > W-Sq <0.0050 Pr > A-Sq <0.0050 Stem Leaf # Boxplot 5 22 2 0 4 4 3 3 2 66788 5 I 2 0111223344 10 I 1 555666666678889999999 21 + + 1 000112222234444 15 * * 0 5556666667778999 16 I + I 0 00122344 8 + + -0 432210 6 I -0 87766 5 I -1 430 3 I -1 88 2 I -2 -2 -3 11 2 0 -3 9 1 0 -4 1 1 0 -4 -5 0 1 * + + + +. Variable: lncontr_area (lncontr_area) 5.25+ Normal Probability Plot I • . +++ I +++ I +++ I +++ | +++ ***** | ++•**** •j .75+ * * * * * * * * | *****+ j ****•++ j ****++ | ***++ j ***+ I **+ 1 .75+ I +++ I +++ I++ * * 5.25+ + + : — + + + + + + + + + - 2 - 1 0 +1 +2 Variable: lnw_avg_slope (lnw_avg_slope) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 -2.3739585 0.87409183 -0.4384198 626.40809 -36.820013 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean Basic S t a t i s t i c a l Measures Location Mean -2.37396 Median -2.26590 Mode Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling Variability Std Deviation Variance Range Interquartile Range Tests for Normality --Statistic---98 -232.64793 0.76403653 1.98296056 74.1115438 0.08829661 0.87409 0.76404 5.39135 0.84815 W 0.958651 D 0.111136 W-Sq 0.241878 A-Sq 1.338031 p Value Pr < W 0.0036 Pr > D <0.0100 Pr > W-Sq <0.0050 Pr > A-Sq O.0050 Stem Leaf # Boxplot -0 41 2 0 -0 765 3 0 -1 44200 5 | -1 999999998886655 15 + + -2 4443333322222222111111110000000 31 *..+..* -2 99988888877666666555555 23 + + -3 22221111 8 | -3 8775555 7 j -4 20 2 0 -4 -5 0 . 1 0 -5 5 1 * 4 + + + + + . 226 Variable: lnw_avg_slope (lnw_avg_slope) Normal Probability Plot -0.25+ *+++* * * ** *++ ++***+ +****** ********* ******* ****+ ****** +++++* + * -5.75+* + + + + + + + + + + + -2 -1 0 +1 +2 Variable: lnavg_width (lnavg_width) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 2.05780119 0.64791554 0.17684902 455.705555 31.4858181 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 201.664517 0.41979455 0.53686943 40.720071 0.06544935 Basic S t a t i s t i c a l Measures Location Variability Mean 2.057801 Std Deviation 0.64792 Median 1.998057 Variance 0.41979 Mode 1.515127 Range 3.56407 Interquartile Range 0.66222 NOTE: The mode displayed i s the smallest of 3 modes with a count of 2. Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling Tests for Normality - - S t a t i s t i c — W 0.988142 D 0.075688 W-Sq 0.099038 A-Sq 0.513096 -p Value-Pr < W 0.5336 Pr > D >0.1500 Pr > W-Sq 0.1171 Pr > A-Sq 0.1982 Stem Leaf # Boxplot 38 0 1 0 36 6 1 0 34 32 33 2 | 30 25049 5 | 28 0428 4 | 26 155934 6 | 24 25666 5 | 22 22233346122789 14 ' + + 20 14567223689 11 *__+__* 18 00225678990144455699 20 I I 16 344234499 9 + + 14 891224 6 I 12 06378 5 I 10 6224 4 I 8 06 2 I 6 95 2 0 4 2 4 1 0 + + + + Multiply Stem,Leaf by 10**-1 Variable: lnavg_width (lnavg_width) Normal Probability Plot 3.9+ * + +++ **+ * *** * * + *** 4.* * ***** 2 _-\+ **** ****** * * **+ *** *** *** 4.* * + * + * | + + + 0.3+* + + + _ _ _ _ + + + + + + + -2 - 1 0 +1 +2 Variable: lnavg_depth (lnavg_depth) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 -0.5623617 0.42245917 0.15201061 48.3043282 -75.122322 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 -55.111448 0.17847175 -0.2975396 17.3117602 0.04267482 Basic S t a t i s t i c a l Measures Location Mean -0.56236 Median -0.57982 Mode -0.73397 Test Variability Std Deviation 0.42246 Variance 0.17847 Range 1.87546 Interquartile Range 0.49248 Tests for Normality - - S t a t i s t i c — p Value Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling W 0.982106 D 0.055245 W-Sq 0.065364 A-Sq 0.486723 Pr < W 0.2040 Pr > D >0.1500 Pr > W-Sq >0.2500 Pr > A-Sq 0.2274 Stem Leaf # Boxplot 3 1 1 | 2 22558 5 | 1 0388 4 | 0 249 3 | -0 654 3 | -1 1 1 | -2 96650 5 | -3 999644331 9 + + -4 998862222 9 I I -5 8866433111 10 -6 999977555300 12 I I -7 86333331 8 I I -8 7442200 7 + + -9 9774422 7 | -10 8852 4 -11 7444 4 | -12 70 2 | -13 11 2 | -14 7 1 | -15 6 1 0 + + + + Multiply Stem.Leaf by 10**-1 Variable: lnavg_depth (lnavg_depth) 0.35+ Normal Probability Plot ++ * * * * + * * +++ **++ +*** *** * * * * *** *** * * * +*+ -1.55+*++ + + + + . -2 -1 . + + . 0 - - + -+1 . + + . +2 Variable: avg_d95 (avg_d95) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 0.87714286 0.41301007 0.09407979 91.9452 47.0858388 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 85.96 0.17057732 -0.6721939 16.546 0.04172032 Basic S t a t i s t i c a l Measures Location Mean 0.877143 Median 0.875000 Mode 0.750000 Variability Std Deviation 0.41301 Variance 0.17058 Range 1.74000 Interquartile Range 0.65000 Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling Tests for Normality - - S t a t i s t i c — W 0.977198 D 0.064901 W-Sq 0.07656 A-Sq 0.559718 -p Value-Pr < W 0.0862 Pr > D >0.1500 Pr > W-Sq 0.2326 Pr > A-Sq 0.1478 Stem Leaf # Boxplot 18 9 1 | 17 9 1 | 16 1 1 | 15 0036 4 | 14 3366 4 | 13 1224777 7 | 12 0117889 7 + + 11 002559 6 I I 10 15566 5 I I 9 001134589 9 I I 8 0022244578899 13 7 033455556889 12 I I 6 I I 5 25799 5 + + , 4 3444789 7 I 3 1123466 7 I 2 13567 5 I 1 5667 4 I + + + + Multiply Stem.Leaf by 10**-1 Va riable: avg_d95 (avg_d95) Normal Probability Plot 1.85+ ++* | +*+ I + * i * * * * I ***+ I ***+ I ***+ I **+ | +*+ I *** I **** I * * * * I + + | ++** i +**** I * * * * I **** 0.15+* * *+ + + + + + + + + + + + -2 -1 0 +1 +2 231 Variable: lnshstress (lnshstress) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 6.25378873 0.9500535 -0.6929616 3920.31996 15.1916468 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 612.871296 0.90260165 0.30517734 87.5523598 0.0959699 Basic S t a t i s t i c a l Measures Location Variability Mean 6.253789 Std Deviation . 0.95005 Median 6.470484 Variance 0.90260 Mode . Range 4.68325 Interquartile Range 1.03161 Test Tests for Normality - - S t a t i s t i c — p Value-Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson -Darling W 0.952558 D 0.117175 W-Sq 0.369406 A-Sq 1.926794 Pr < W 0.0014 Pr > D <0.0100 Pr > W-Sq <0.0050 Pr > A-Sq <0.0050 Variable: lnshstress (lnshstress) Stem Leaf Boxplot 82 1 1 | 80 | 78 256 3 | 76 45 2 | 74 60 2 | 72 222 3 | 70 29925 5 | 68 12345793568 11 + + 66 1112344567223579 16 I I 64 12246833579 11 * * 62 0178358 7 I + I 60 0015580357 10 I I 58 014 3 + + 56 53 2 | 54 845 3 | 52 572 3 j 50 47077 5 | 48 | 46 0689 4 | 44 1 1 | 42 6898 4 | 40 38 5 1 0 36 34 2 1 0 + + + + Multiply Stem.Leaf by 10**-1 232 Variable: lnshstress (lnshstress) Normal Probability Plot 8.3+ 5.9+ ++ +** * +** +** ++*** ***** ***** ***++ * ++ +*** ++ *** ++ * ++ 3.5+* - - + --1 - - + -+1 - - + -+2 Variable: lnwoodcount (lnwoodcount) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 87 2.53939679 1 .10149743 -0.3469903 665.366145 43.3763418 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 87 220.927521 1.21329659 0.28320461 104.343507 0.11809292 Basic S t a t i s t i c a l Measures Location Mean 2.539397 Median 2.639057 Mode 1.945910 Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Ande rson-Darling Variability Std Deviation Variance Range Interquartile Range Tests for Normality --Statistic---1.10150 1.21330 5.09375 1 .34993 -p Value-W 0.973641 D 0.08773 W-Sq 0.090343 A-Sq 0.647571 Pr < W 0.0725 Pr > D 0.0958 Pr > W-Sq 0.1508 Pr > A-Sq 0.0908 Missing Values Percent Of Missing Missing Value Count A l l Obs Obs 11 11.22 100.00 Variable: lnwoodcount (lnwoodcount) Stem Leaf # Boxplot 50 9 1 48 8 1 46 9 1 44 42 40 4463 4 38 15 2 36 14148 5 34 070668 6 32 200 3 + + 30 00049 5 | | 28 3333999944 10 j | 26 4441777 7 * * 24 0888666 7 I + I 22 00000 5 | | 20 88888 5 | | 18 555555 6 + + 16 99999 5 14 12 999 3 10 0000 4 8 6 99 2 4 2 0 00000 5 + + + + Multiply Stem.Leaf by 10**-1 Variable: lnwoodcount (lnwoodcount) Normal Probability Plot 5.1+ +* *+ *+ ++ + * * * * *** *** +* **** **+ * *+ *** ** ***+ ***+ ++ +** *** ++ ++** ++ ++ 0.1+ *++* * ** + + + + + + + + + + -2 -1 0 +1 +2 r 235 Variable: lnunipower (lnunipower) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 6.22688066 1.10472067 -0.1907276 3918.23574 17.741157 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 610.234305 1.22040777 0.67561048 118.379553 0.11159364 Basic S t a t i s t i c a l Measures Location Variability Mean 6.226881 Std Deviation 1.10472 Median 6.251714 Variance 1.22041 Mode . Range 6.06043 Interquartile Range 1.04709 Tests for Normality Test --Statistic--- p Value Shapiro-Wilk W Kolmogorov-Smirnov D Cramer-von Mises W-Sq Anderson-Darling A-Sq 0.980974 Pr < W 0.1677 0.086779 Pr > D 0.0693 0.127081 Pr > W-Sq 0.0480 0.679861 Pr > A-Sq 0.0776 Stem Leaf # Boxplot 8 567 3 0 8 000234 6 0 7 569 3 I 7 001122334 9 I 6 555556666677777899 18 + + 6 000011111112222223333444444 27 * _ _ -i * 5 555577777888 12 + + 5 0123344 7 I 4 56677889 8 I 4 233 3 I 3 6 1 0 3 2 6 1 0 + + + + + Variable: lnunipower (lnunipower) Normal Probability Plot 8.75+ *+++* j ****+ j ****+. | +**** | ****** j ******** 5.75+ ****+ | +***+ | * * * * * | 4 . * * * * I +++* 1 + 2.75+* + + + + + + + + + + + -2 -1 0 +1 +2 Variable: lntotpower (lntotpower) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 8.28468185 1.2773511 -0.4863239 6884.59114 15.4182275 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 811.898822 1.63162583 0.31016986 158.267706 0.12903195 Basic S t a t i s t i c a l Measures Location Variability Mean 8.284682 Std Deviation 1.27735 Median 8.438442 Variance 1.63163 Mode . Range 6.87022 Interquartile Range 1.71996 Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Ande rson-Darling Tests for Normality --Statistic-- -W 0.9806 D 0.068266 W-Sq 0.062188 A-Sq 0.394457 p Value-Pr < W 0.1571 Pr > D >0.1500 Pr > W-Sq >0.2500 Pr > A-Sq >0.2500 Variable: lntotpower (lntotpower) Stem Leaf # Boxplot 10 578 3 I 10 1133 4 I 9 556666777999 12 I 9 0001111222233344 16 + + 8 55555666778999 14 I I 8 0000000122334 13 *__+_-* 7 556666677899 12 + + 7 00111234 8 I 6 5566777899 10 I 6 13 2 I 5 688 3 I 5 4 4 3 9 + + +... 1 - + 0 Variable: lntotpower (lntotpower) Normal Probability Plot 10.75+ +++* | * * j ***** | ***** | * * * * + | * * * * * | * * * * * 7.25+ +*** j ***** | ** * * j *+** | ++++ i i 3.75+* + + + + + + + + + + _ -2 -1 0 +1 +2 Variable: sqrtD_d (sqrtD_d) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 1 .17312767 0.21621612 0.07082128 139.405089 18.4307406 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 114.966512 0.04674941 0.71973243 4.53469272 0.02184113 Basic S t a t i s t i c a l Measures Location Mean 1.173128 Median 1.174329 Mode 1.095445 Variability Std Deviation 0.21622 Variance 0.04675 Range 1.19821 Interquartile Range 0.25493 NOTE: The mode displayed i s the smallest of 5 modes with a count of 2. Test Tests for Normality --Statistic--- -p Value-Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling W 0.980275 D 0.077658 W-Sq 0.10224 A-Sq 0.676811 Pr < W 0.1484 Pr > D >0.1500 Pr > W-Sq 0.1048 Pr > A-Sq 0.0789 Variable: sqrtD_d (sqrtD_d) Stem Leaf # Boxplot 18 0 1 0 17 17 1 1 0 16 59 2 | 16 15 | 15 | 14 67 2 | 14 00011333 8 | 13 568889 6 | 13 0122334 7 + + 12 55567 5 I I 12 0001123444 10 I I 11 66666777888999 14 11 0002222223 10 I I 10 667788999 9 + + 10 02333444 8 | 9 79 2 [ 9 2 1 | 8 55699 5 | 8 0 1 | 7 589 3 | 7 14 2 | 6 6 0 1 0 + + + + Multiply Stem.Leaf by 10**-1 239 Variable: sqrtD_d (sqrtD_d) Normal Probability Plot 1.825+ 1 .225+ * +++ ++ ++ +++** +**** ***** *** +** **** ***** *** **** ****+ * *+ +* +** +++* +**** *+* +++ 0.625+* + + + + + + + + + + + -2 -1 0 +1 +2 Variable: sqrtw_d (sqrtwd) N Mean Std Deviation Skewness Uncorrected SS Coeff Variation Moments 98 Sum Weights 3.77421888 Sum Observations 0.74250988 Variance 1.01152947 Kurtosis 1449.46149 19.6732067 Corrected SS Std Error Mean 98 369.87345 0.55132092 2.25267177 53.4781294 0.07500482 Basic S t a t i s t i c a l Measures Location Mean 3.774219 Median 3.699681 Mode Variability Std Deviation 0.74251 Variance 0.55132 Range 4.32947 Interquartile Range 0.87568 Test Tests for Normality --Statistic--- p Value-Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Ande rson-Darling W 0.939497 D 0.062558 W-Sq 0.162189 A-Sq 1.180958 Pr < W 0.0002 Pr > D 0.0582 Pr > W-Sq 0.0175 Pr > A-Sq <0.0050 Variable: sqrtw_d (sqrtw_d) Stem Leaf # 64 2 1 62 6 1 60 • 58 2 1 56 54 5 1 52 50 8 1 48 12 2 46 81 2 44 1127079 7 42 00146868 8 40 34457959 8 38 0346888013 10 36 12445891266689 14 34 0344566914668889 16 32 680112 6 30 238883 6 28 01577901 8 26 02355 5 24 22 20 9 1 Boxplot 0 0 + + + + Multiply Stem.Leaf by 10* >-1 Variable: sqrtw_d (sqrtw_d) Normal Probability Plot 6.5+ 4.3+ ++* +**** +**** +*** +*** ***** ***** *** *** * * * * * *****.{. +++ +++ 2.1+* ++ + + + -2 + + + + + + + . 1 0 + 1 + 2 Variable: lnmean_vel (lnmean_vel) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 -0.0269081 0.43243299 0.4293679 18.2097903 -1607.0753 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 -2.6369911 0.18699829 0.3196923 18.138834 0.04368233 Location Basic S t a t i s t i c a l Measures 'Variability Mean Median Mode -0.02691 -0.07484 Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson -Darling Std Deviation Variance Range Interquartile Range Tests for Normality - - S t a t i s t i c — 0.43243 0.18700 2:08609 0.54979 W 0.975694 D 0.107756 W-Sq 0.130497 A-Sq 0.771568 p Value Pr < W 0.0660 Pr > D O.0100 Pr > W-Sq 0.0441 Pr > A-Sq 0.0447 \ Stem Leaf # Boxplot 10 89 2 0 9 028 3 | 8 05 2 | 7 | 6 | 5 023 3 | 4 46679 5 | 3 1233444 7 | 2 003567 6 + + 1 022457 6 I I 0 078 3 I I -0 98766654332210 14 -1 9996644422200 13 I I -2 776544331 9 I I -3 9855432210 10 + + -4 99830 5 | -5 6 1 | -6 421 3 | -7 82 2 | -8 731 3 | -9 9 1 | + + + + Multiply Stem.Leaf by 10**-1 242 Variable: lnmean_vel (lnmean_vel) Normal Probability Plot 1.05+ I 0.85+ I 0.65+ I 0.45+ I 0.25+ I 0.05+ I -0.15+ I -0.35+ I -0.55+ ** ++ *** +++ ++ *** *** ** +*** ++** ***** **** * * * * **** **++ *++ -0.75+ | *+* -0.95+* ++ + + --2 . . + + . . -1 . + + . . +1 . . + — +2 N Mean Std Deviation Skewness Uncorrected SS Coeff Variation Variable: InomegaD (lnomega_D) Moments 98 Sum Weights 98 6.50541626 Sum Observations 637.530793 1.08398258 Variance 1.17501824 0.01046832- KurtOSis 1.61314268 4261.37996 Corrected SS 113.976769 16.6627705 Std Error Mean 0.10949878 Basic S t a t i s t i c a l Measures Location Variability Mean 6.505416 Std Deviation 1.08398 Median 6.433653 Variance 1.17502 Mode . Range 6.60684 Interquartile Range 1.03559 Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling Tests for Normality --Statistic-- -W 0.960979 D 0.063029 W-Sq 0.237522 A-Sq 1.448763 p Value Pr < W 0.0053 Pr > D 0.0563 Pr > W-Sq <0.0050 Pr > A-Sq <0.0050 Stem Leaf # Boxplot 9 6 1 0 9 03 2 0 8 5578 4 0 8 4 1 | 7 567 3 | 7 0001112223333344 16 + + 6 555566677778889999999 21 I + I 6 0000111122223333333344444444 28 * * 5 55777777889 11 | 5 0034 4 | 4 599 3 j 4 003 3 0 3 3 0 1 0 2 Variable: lnomega_D (lnomega_D) Normal Probability Plot 9.75+ * | * ++ | * * * * + + + + | **+++ | ++*** | +******* j .(.****** Q 25+ ******** | ******++ | * * * + + | 4 * * * * | ++++** |++ * I 2.75+* + + + + + + + + + + + -2 -1 0 +1 +2 Variable: lnGmega_D (lnGmega_D) Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 98 8.56321745 1.03480343 -0.2553484 7290.08129 12.084283 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 98 839.19531 1.07081814 0.20731608 103.869359 0.10453093 Basic S t a t i s t i c a l Measures Location Variability Mean 8.563217 Std Deviation 1.03480 Median 8.656048 Variance 1.07082 Mode . Range 5.44569 Interquartile Range 1.22513 Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson - Darling Tests for Normality --Statistic-- -W 0.989303 D Oi050441 W-Sq 0.041615 A-Sq 0.251519 p Value Pr < W 0.6227 Pr > D >0.1500 Pr > W-Sq >0.2500 Pr > A-Sq >0.2500 Stem Leaf # Boxplot 10 77 2 I 10 00122444 8 I 9 6677889 7 I 9 000001111222223444 18 + + 8 566677778888999999 18 *-_+__* 8 000001111122233333444 21 + + 7 5677778999 10 I 7 012334 6 I 6 678999 6 I 6 4 1 I 5 5 3 1 0 + + + + -Variable: lnGmega_D (lnGmega_D) Normal Probability Plot 10.75+ ++*++ * ****** ***** ******* ****** ****+ +***** ****** +++*+ i+ 5.25+* + + + + + + + + + + + -2 -1 0 +1 +2 B 2 . Bartlett's Test of Homogeneity of Within Covariance Matrices The DISCRIM Procedure Test of Homogeneity of Within Covariance Matrices Notation: K = Number of Groups P = Number of Variables N = Total Number of Observations - Number of Groups N(i) = Number of Observations in the i'th Group - 1 _ N(i)/2 || |Within SS Matrix(i)| V = N/2 |Pooled SS Matrix| | 1 1 | 2P + 3P - 1 RHO = 1.0 - j SUM - | |_ N(i) N J 6(P+1)(K-1) DF = .5(K-1)P(P+1) Under the null hypothesis: -2 RHO In PN/2 N V _ PN(i)/2 II N(i) is distributed approximately as Chi-Square(DF). Chi-Square 370.636444 DF Pr > ChiSq 264 <.0001 Since the Chi-Square value i s significant at the 0.05 level, the with covariance matrices w i l l be used in the discriminant function. Reference: Morrison, D.F. (1976) Multivariate S t a t i s t i c a l Methods p252. Appendix C Total Stream Power 100000 110000 E 1 Q. E 1000 (0 £ CO 100 a) o • Unit power O Total power C1 O HF1 O O O O C 2 : o: o o : O i : O ?<9 j ? i ab •: 1 HF2 C 3 ! F 0.01 0.1 Area (km2) 10 100000 10000 T3 c CO 1000 4 E i 1 §. 100 E a £ 10 4 : b) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r I i " : 1 1 1 1 j 0 ° o is - : 8 o • • : f 1 ; / : C1 j HF1 | C2 HF2 ; C 3 0.01 0.1 10 Area (km ) Figure C I . Unit and total stream power as functions of drainage area for: (a) Hesketh Creek, and (b) Elliott Creek. Values are reach averages. Codes refer to process domains defined in chapter 3. 247 100000 g" 10000 T3 c co E r 1000 ! a. E s * 100 10 c) o c? o • Unit power O Total power C1 O 93 o % o • H F O o p C2a C2b C2c 0.001 0.01 0.1 , 1 Area (km') 10 100 100000 10000 T3 c co 1000 -t E I I o. E co •b 100 10 d) o C1 o o o o cf H F B O C2 0 D ° O o o # o • o • • • % • • • t 0.01 0.1 Area (km ) 10 Figure C I . (Continues from previous page) Unit and total stream power as functions o f drainage area for: (c) Lembke-Sisters Creek, and (d) East Cap Creek. Values are reach averages. Arrow marks the beginning of alluvial fan crossing (see text). Codes refer to geomorphic process domains defined in chapter 3. 248 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.