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Geomorphic process domains in a mountain basin White, Russell 2002

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GEOMORPHIC PROCESS DOMAINS IN A MOUNTAIN BASIN by RUSSELL WHITE B.Sc, The University of British Columbia, 1998 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Geography) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A September 2002 © Russell White, 2002. In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date DE-6 (2/88) Abstract This study seeks to identify geomorphic process domains in a mountain basin by examining the manner in which channel widths and channel gradients change with increasing drainage basin scale. A conceptual model was proposed which identified hillslope, colluvial and alluvial process domains. These domains were thought to be governed by processes of mass wasting, deposition of hillslope materials and fluvial processes and purely fluvial processes, respectively. Channel widths and gradients were measured in 62 reaches. Drainage areas were determined cartographically, except for basins smaller than approximately 0.01 km 2, which were mapped in the field. Results show that process domains can be delineated on the basis of spatial scale as power law exponents were significantly different between the hillslope and colluvial process domains. The alluvial process domain was not detected. Three distinct groups were identified at the hillslope scale. At the smallest scale channels are unincised and have not experienced mass wasting. At larger scale channels are incised and reflect the magnitude/frequency regime of mass wasting events. No significant difference was detected between the slope co-efficients of the three hillslope classes. However, offsets were significantly different, reflecting changes in sediment transport regime. Two geomorphic thresholds were identified by this study; the constants of channel maintenance for unincised and incised channels, with values of 0.01 and 0.06 km respectively. The value of the constant of channel maintenance is therefore a function of the process by which the channel is maintained. n Table of Contents Abstract i i Table of Contents i i i List of Tables vii List of Figures viii Acknowledgements ix Chapter One: Introduction 1 1.1 Conceptual Overview 1 1.2 Approaches to Scaling 3 1.2.1 Allometric Analysis 4 1.2.2 Dimensional Analysis 6 1.3 Scaling Behaviour in Fluvial Landscapes 6 1.3.1 Scaling Behaviour of River Channels 6 1.3.1.1 Hydraulic Geometry 7 1.3.1.2 Hydromorphic Relations 10 1.3.1.3 Morphology of Channel Margins 14 1.3.2 Scaling Behaviour of Hillslopes 17 1.4 Process Domains 18 1.4.1 Definition 18 1.4.2 Conceptual Model of Process Domains 19 1.4.2.1 The Hillslope Domain 20 1.4.2.2 The Colluvial Domain 21 1.4.2.3 The Alluvial Domain 22 1.4.2.4 Deviations 23 1.4.2.5 Scaling Behaviour in Process Domains 24 1.5 Dimensional Analysis of Hillslope Channels 25 1.5.1 Governing Processes 25 1.5.2 Pi Theorem 26 ii i c 1.6 Hypotheses... 28 Chapter Two: Methodology 30 2.1 Study Area. . . . ! . . . . . . . . . . . . . . . . 30 2.1.1 Climate and Vegetation 30 2.1.2 Geomorphology 31 2.1.3 Land Use History 34 2.1.3.1 Anthropogenic Disturbance 34 2.1.3.2 Natural Disturbance 34 2.2 Sampling Strategy : 35 2.2.1 Introduction 35 2.2.2 Variables for Measurement 35 2.2.2.1 Scale Index 35 2.2.2.2 System Attributes 36 2.2.3 Data Collection Methods 37 2.2.3.1 Basin Drainage Area 37 2.2.3.2 Channel Gradient 39 2.2.3.3 Channel Width 39 2.2.3.4 Additional Observations 39 2.2.4 Sampling Strategy 40 2.2.4.1 Landscape Sampling 40 2.2.4.2 Site Sampling 41 2.3 Pilot Study 42 2.3.1 Hypothesis/Objectives 42 2.3.2 Methods 42 2.3.3 Results 43 2.3.4 Analysis 44 2.3.5 Conclusion 46 2.4 Reach Delineation 48 iv Chapter Three: Results 49 3.1 Introduction 49 3.1.1 Basin Description 49 3.1.1.1 Sisters Creek 49 3.1.1.2 Hesketh Creek : 50 3.1.1.3 Healmond Creek 50 3.1.1.4 Miscellaneous Basins 50 3.1.2 Observed Sources of Variability 51 3.1.2.1 Hillslope Scale 51 3.1.2.2 Colluvial Scale 52 3.1.2.3 Alluvial Scale 53 3.2 Results of Stream Surveys 53 3.2.1 Survey Results by Stream Link 53 3.2.2 Survey Results by Reach 58 3.2.2.1 Reach Classification..... 58 3.2.2.2 Survey Results for Channel Reaches 59 3.2.2.3 Scaling Behaviour of Channel Widths 65 3.2.2.4 Scaling Behaviour of Channel Gradients at Reach Level 68 Chapter Four: Analyses 69 4.0 Overview of Analyses 69 4.1 Scaling Behaviour of Channel Widths 70 4.1.1 Hillslope Process Domain 70 4.1.1.1 Comparison of slope exponents within the hillslope process domain 70 4.1.1.2 Comparison of intercepts 72 4.1.2 Colluvial and Alluvial Process Domains 75 4.1.2.1 Identifying reach classes.. 75 4.1.2.2 Final scaling relations 77 4.1.2.3 Comparisons between process domains 79 4.1.2.4 Depositional scaling 80 v 4.2 Scaling Behaviour of Channel Gradients 82 4.2.1 Overview of Analyses 82 4.2.2 Analysis of Residuals 82 4.3 Summary of Analyses 83 Chapter Five: Discussion 84 5.0 Introduction 84 5.1 Scaling Behaviour of Channel Widths 84 5.1.1 Process Variability within the Hillslope Domain 87 5.2 Scaling Behaviour of Channel Gradients 91 5.2.1 Introduction 91 5.2.2 Comparison with Regional Studies 96 5.2.3 Summary 98 Chapter Six: Conclusions 101 6.0 Summary of Findings 101 6.1 Process Domains 102 6.2 Theoretical Predictions 102 6.3 Geomorphic Thresholds 104 6.4 Further Work . 104 7.0 References 105 Appendix A: Surveys of Channel Width and Channel Gradient 113 vi List of Tables Table 1. Variables controlling channel morphology in channels dominated by mass Wasting 26 Table 2. Results of stream surveys of channel links 55 Table 3. Results of stream surveys; channel reaches 60 Table 4. Comparison of power law relations for pooled data between reaches and links 65 Table 5. Results of regression analysis for reach data 67 Table 6. Analysis of covariance to test differences in ^ -values of reach classes in the hillslope process domain .. 71 Table 7. One way A N O V A to test the difference between means of the channel reach sub groups 72 Table 8. T-test assuming equal variance to identify which of the groups differ significantly in terms of mean channel width where H 0 : u l = u2 ........... 73 Table 9. Calculation of common scaling exponent using Analysis of Covariance.... 73 Table 10. Final scaling relations 79 Table 11. Terms for calculation of the F statistic to compare the slopes between process domains. 79 Table 12. Scaling relations of regional studies 98 vii List of Figures Figure 1. Generic representation of isometry, allometry and compound allometry... 5 Figure 2. Compound model of process domains 20 Figure 3. Map of the Capilano valley showing the major creeks and sub basins studied..... 33 Figure 4. Width variability at 1-meter intervals in Rapid Creek 44 Figure 5. Relation between mean channel width and measurement interval 45 Figure 6. Mean channel width of randomly selected populations of varying sample size 47 Figure 7. Overall scaling behaviour of channel widths in stream links 56 Figure 8. Overall scaling behaviour of channel gradient in stream links 57 Figure 9. Scaling behaviour of channel widths from homogeneous reaches 63 Figure 10. Scaling behaviour of channel gradients from homogeneous reaches 64 Figure 11. Scaling behaviour of channel gradients, alluvial and colluvial scales 77 Figure 12. Scaling behaviour of aggrading reaches. 81 Figure 13. Distribution of gradient-area residuals 83 Figure 14. Final scaling relations for channel width 86 Figure 15a. Gradient-area scaling, Capilano Valley; Figure 15b. Process domains after Montgomery and Foufoula-Geourgio, 1993; Figure 15c. Process domains after Montgomery, 2001..... 95 Figure 16. Comparison with Day (1969), data collected from Southern Coast Mountains and Hogan et al. (1997) data from Queen Charlotte Islands... 97 Figure 17. Comparison of channel width-area scaling between Day (1969), Hogan et al. (1997) and the Capilano Valley 100 Figure 18. Process domains in headwater streams 103 viii Acknowledgements I wish to thank Olav Slaymaker for his endless patience and all the support he gave me during this project. He shared his knowledge and experience with me, yet allowed me the freedom to careen down my own blind alleys. Mike Church also made a significant contribution to this thesis. The insight he provided at crucial stages was invaluable. Dan Hogan and Dan Moore assisted me with issues of sampling and field procedure. Elaine Cho and Sandy Lapsky helped me to negotiate bureaucracy with humour and encouragement. I wish to thank Dan Goltzmann, not only for all the effort he put into the field work, but also for his good humour in the face of bad weather and difficult terrain, his supply of good tunes in the face of Lions Gate Bridge traffic and his ear for the music of a conversation. Amongst my peers my thanks go to Kristie Trainor, Dave Oldmeadow, Simon Dadson, Francesco Brardinoni and Laura Rempel for their wisdom and tomfoolery. My office-mates Brian Menounous, Andres Soux and Darren Ham also provided support and distraction. Annika, Sam and Lina I thank for their love and support. ix Chapter One: Introduction 1.1 Conceptual Overview The precept that the landscape behaves as a process-response system, namely that a geomorphic process will elicit a coherent response, has been popular in physical geography since the 1960s (Schumm and Lichty, 1965; Chorley and Kennedy, 1971). Under this view of landscape function a geomorphic process elicits a response by rearrangement or alteration of landscape attributes. However, the complexity of the landscape belies the simplicity of the process-response model. Complexity results from the interaction of an array of geomorphic processes acting on a heterogeneous landscape, which already bears the imprint of previous events, at a variety of spatial and temporal scales. Examination of the extent to which the form of stream channels is controlled by geomorphic processes must contend with the complexity of the system. It is conceivable that control exerted by individual or by assemblages of associated processes can not be isolated from the complexity. Study of system behaviour over a range of scales, hereafter referred to as scaling behaviour, is a technique that can be used to assess the validity of the process-response model. It is a method of examining system function without studying the individual processes in isolation. It is especially applicable when complexity and the lack of a deterministic framework limit the insight to be gained from single site studies (Church and Mark, 1980). Often investigation into scaling behaviour focuses on the uniformity of behaviour over a wide range of scales and from this observation a universal principle is inferred. For example, Rodriguez-Iturbe and Rinaldo (1997) studied the fractal behaviour of river networks and argued for scale invariance in the landscape. Montgomery and Dietrich 1 (1989) pointed out that the scale invariance of river networks does not aid understanding of landscape evolution since the formative processes are not scale invariant. Kennedy (1977) proposed that understanding of linkages between process and form can only be gained in the context of specific temporal and spatial scales. De Boer (1992) further argued that geomorphic systems have a nested hierarchical structure, such that processes are linked to a specific spatial scale. If geomorphic systems can be described by the process-response model and i f geomorphic processes operate at specific spatial scales, as well as impart an unambiguous signal to the landscape, then the scaling behaviour of a geomorphic system will not be scale invariant. It should be noted that limitation of scale invariant behaviour can also be due to physical limits of the system. For example, Beauvais and Montgomery (1996) observed uniform scaling behaviour between the limits of the channel width and the maximum meander wavelength when investigating the fractal behaviour of river plan morphology. River morphology results from a complex interaction of sediment supply and calibre, flood regime, landscape gradients and settings, bank vegetation and anthropomorphic factors. Powerful statements regarding the uniformity of the scaling behaviour of alluvial rivers have been made by Leopold and Maddock (1953). Yet, a cursory investigation of river morphology reveals a profound difference between the morphology of a steep mountain stream and that of a large alluvial river. Whether these differences result from the operation of geomorphic processes at discrete spatial scales can be investigated by a study of the scaling behaviour of rivers. This study will focus on the behaviour of river systems at the non-alluvial-alluvial transition. By definition the material forming the channel margin of an alluvial river has previously been eroded and deposited by the river itself. Unless there is a change in the governing conditions, such as a climatic change that reduces the magnitude of peak flows, there is every reason to assume that the river will be able to transport these materials in the future. The erosion and deposition of channel margin materials permits morphological adjustment to balance the fluxes of sediment and water transported by the river. In headwater streams, where gradients are steeper and channels are coupled to hillslopes, materials are introduced to the channels by hillslope processes that can radically alter channel morphology. These materials are non-alluvial and, in large part, are beyond the mobilising forces of even rare floods. Whereas alluvial rivers are adjusted to regular fluvial processes headwater channels are adjusted to episodic events more akin to hillslope processes. This study will attempt to identify the scale at which the transition from a hillslope to a fluvial process domain occurs. Furthermore, the nature of the scaling behaviour within each process domain will be examined. 1.2 Approaches to Scaling The term scaling is used to describe several distinct ideas. It can describe the process by which forces and physical properties are matched between an experimental model and the real world, such as by the use of the Froude scaling in the design of flume experiments. Also the term scaling has been used describe the transfer of information between scales, such as the estimation of catchment rainfall from a point source of data (Bloschl, 1996). This study uses the term "scaling" to describe the behaviour of geomorphic systems as system size changes. Considering variations in river channel morphology over a range of scales amounts to seeking a correlation between the magnitude of a governing variable and a response variable. Drainage area may be used as a surrogate for a governing variable such as peak flow or mass movement events as these types of forcing functions are difficult to quantify. An attribute of the system such as channel width or bank full capacity can 3 be used as the response variable. The scaling behaviour is then described by the mathematical relation between the variables. For this relation to inform the behaviour of the system it should relate to the underlying mechanics (Church and Mark, 1980). 1.2.1 Allometric Analysis Allometric analysis is an established technique in biology. It studies changes in geometry with increasing organism size (Gould, 1966). Application of the principles to geomorphology is described by Church and Mark (1980). Most geomorphic processes occur at rates which preclude studies of dynamic allometry, i.e. observations of the growth of individual landforms. Instead, static allometry, the study of a population of landforms of different sizes, is employed. Static allometry thus relies on the substitution of space for time (the ergodic hypothesis). Allometric relations are described by power laws: y = a x b where x is an index of system scale, y is an attribute of the system, a is a constant and the exponent b represents the scale rated variation in the ratio of x and y. Two specific conditions are defined; allometry and isometry. Figure 1 illustrates generic allometric and isometric relations as well as compound allometry which will be discussed later. If x and y have the same units the state of isometry exists when b = 1. Under this condition there is no change in the relative proportions of JC and y with increasing scale: therefore the system remains self-similar. When b * 1 the relation is allometric, implying a scale-related distortion of geometry. When b > 1 the allometry is positive and y, the system attribute, grows more rapidly than the system as a whole. Conversely, negative allometry implies that b < 1 and that the system attribute grows less rapidly than the system as a whole. 4 •0— isometry •H— negative allometry - - A- - • positive allometry — -X — compound allometry 1 10 100 Spatial scale Figure 1. Generic representation of isometry, allometry and compound allometry, the units of the x and y axes are dimensional ly equivalent. The isometric condition implies that a uniform assemblage of processes governs the behaviour of the system under study. Allometric behaviour implies that the ratio of the x and y variables changes with scale. This may be due to the dominance of differing processes at specific scales, or it may be due to emergent behaviour resulting from the action of the same processes. For example, in Bull's (1964) analyses of the areas of alluvial fans and their contributing drainage areas an area is scaled with an area hence b = 1 for isometry. Bull (1964) found b = 0.9, which implies negative allometry, thus, alluvial fans grow less quickly than their contributing areas. Hooke (1968) interpreted this result as an indication that larger drainage basins have a greater tendency to store sediment at channel margins. Sediment storage is not a new process in this context but -+-» 3 o -a —i 5 an emergent characteristic of the process of sediment transport acting over increasingly large scales. If a shift between the dominance of differing geomorphic processes occurs as scale increases, or if there is a transfer to a new assemblage of processes at some threshold spatial scale a compound allometric relation could be found. Such a relation, showing a distinct change in the value of the b exponent is illustrated in figure 1. 1.2.2 Dimensional Analysis Dimensional analysis is a technique which allows relations describing the fundamental behaviour of a system to be written in the absence of a deterministic theory (Stull, 1988). If the behaviour of a physical system can be described by dimensional qualities then these can be arranged in dimensibnless form and still describe the behavior of the system (Lacey,1995). The approach is to write the factors thought to govern system behaviour in terms of their fundamental parameters. These factors are then arranged into dimensionless groups, the number of groups needed to describe the system being determined from the Buckingham 17 theorem (Buckingham, 1914). The success of the approach depends on the inclusion of all the governing factors. The specific functional form of the relation then requires empirical testing. For example Kellerhals (1969) found from dimensional analysis that channel width varies in proportion to Q° 4 . 1.3 Scaling Behaviour in Fluvial Landscapes 1.3.1 Scaling Behaviour of River Channels Fluvial studies which consider the relation between a governing factor, which varies systematically with scale, and a response variable may reveal whether geomorphic process domains are detectable. Research in this vein includes studies of hydraulic 6 geometry, hydromorphic relations as well as investigations of how channel morphology varies through drainage networks. Furthermore, fluvial erosion and mass wasting are major forces of landscape development. Therefore, evidence of compound scaling behaviour may be sought in studies of topography and hillslope morphology 1.3.1.1 Hydraulic Geometry The concept of hydraulic geometry (Leopold and Maddock, 1953) constitutes a major statement on the scaling behaviour of rivers. Leopold and Maddock (1953) presented power law relations for specific river cross sections subject to differing flows, termed at-a-station hydraulic geometry, and for differing river cross sections subject to flows of the same recurrence interval, termed downstream hydraulic geometry. The relations take the form: w - a Q b d = cQ f v = k Q m where w is width, d is depth, v is velocity. Continuity demands that the sum of the exponents and the product of the coefficients equal unity, i.e.; Q = wdv therefore b +f+ m = 1 and ack = 1 The relations of hydraulic geometry are empirical scale relations (Church and Mark, 1980). An isometric condition cannot be defined as the variables are not dimensionally balanced under any reasonable definition of the constants. Nevertheless, the approach is akin to static allometric analysis in the sense that the scaling factor, discharge, is 7 proportional to drainage area. Therefore, the analysis describes how river dimensions behave with increasing system size. The essential findings of Leopold and Maddock (1953) from downstream hydraulic geometry were that rivers increase in size in a systematic fashion and that width grows faster than depth, while velocity increases only slightly. Numerous studies of hydraulic geometry have been conducted. Ferguson (1986) provides a thorough review of the topic. While local variations in the exponents have been observed the average values have been found to be b = 0.5,/= 0.4 and m = 0.1 (Knighton, 1974). When reviewing the literature on hydraulic geometry in search of evidence for a shift in scale behaviour three problems arise. Firstly, the majority of studies focus on larger alluvial rivers. Only rarely are rivers coupled to hillslope processes represented, i.e. rivers which receive sediments eroded from adjacent hillslopes rather than those eroded upstream by fluvial processes. The magnitude of the formative flow in the smaller unmonitored basins is extrapolated linearly from the relation between basin area and discharge in the larger basins. This is the indirect method used by Miller (1958) and Brush (1961). Both Smith (1992) and Bloschl (1996) note that this relation is not linear, consequently the apparent scale behaviour of small basins may be biased. Secondly, studies of downstream hydraulic geometry rest on the selection of a flow thought to influence channel morphology, such as mean annual flow or bank full flow. As drainage networks cumulate runoff from the landscape there is a positive relation between drainage basin area and discharge. A flow of a given recurrence, therefore, will have a different magnitude depending on its relative position in the drainage network. Furthermore, the magnitude-frequency distribution of flows changes as drainage basins become smaller. Smaller basins experience high magnitude flows less frequently than larger basins, but the magnitude of these floods is greater relative to the mean flow (Wolman and Miller, 1960). The flows that have the greatest influence on channel morphology may be considerably less frequent than on alluvial rivers 8 (Baker, 1977), since small headward channels generally contain coarse materials that adopt structures which are stable under all but the most extreme flows (Church et al. 1998). Consequently, selection of a flood of constant recurrence interval throughout the drainage network may not adequately represent forcing in smaller basins Thirdly, the variation in the techniques used makes comparison between studies difficult (Park, 1977). The definition of bank full width, the ease with which it can be identified in different climates and at different locations in the basin, the curve fitting techniques used and the recurrence interval of the formative discharge used can all affect the representation of channel geometry. While comparisons between studies are difficult to make, there is evidence within studies of downstream hydraulic geometry of shifts in scaling behaviour. Coates (1969) working on the Appalachian Plateau found the b, f and m exponents for channels in basins with an average drainage area of 26 square miles were similar to global results. However, the width and depth of channels draining basins with a mean area of 6 square miles grew at a lesser rate with increasing discharge. The increased flow was accommodated by increases in velocity. Coates attributes the difference in scaling behaviour to the size of the basins (although the two groups came from separate watersheds) but made no comment as to the processes behind such behaviour. Based on Coates' description of the area it is reasonable to assume that the smaller streams would contain non-alluvial materials and be coupled to hillslope processes. Consequently, the shift in behaviour may represent a shift from fluvial to hillslope processes governing channel morphology. Thorne (1971) also found a shift in the exponents of downstream hydraulic geometry in his study of channels in north eastern Brazil. Thorne used two regression lines and identified the break between the two populations by a process of iteration until the combined sum of squares of the two populations was minimized. He identified a break in the scaling behaviour at a discharge of 5.02 cusecs, with no reference to the basin area, nor to the slope of the channels. Thorne (1971) reports similar results to Coates, 9 namely that widths and depths increased at a lesser rate in small channels and that increases in discharge are accommodated by greater velocity. He ruled out the influence of coarse bed materials as the cause of the behaviour and concluded that the behaviour of small, low order streams reflected adjustment to long term erosion of upland areas as well as seasonal variations in peak flows. Ponton (1972) conducted his in a similar environment circa 100 km north of this study. His results, therefore, are of particular interest. While Ponton did not consider separate populations based on basin drainage area he noted that channel widths grew at considerably higher rate, b = 0.69. He attributed this result to the fact that the smaller channels were constrained by bed rock and non-alluvial materials. These channels were narrower, in comparison to their discharge, than larger unconstrained channels. Therefore, the overall slope of the relation between discharge and width is increased. A drawback of the downstream hydraulic geometry approach is the data requirements. Stream flow data are rarely available for channels in environments where mass wasting may be the dominant geomorphic process 1.3.1.2 Hydromorphic Relations The equations of downstream hydraulic geometry utilize discharge as the scaling variable, though often the magnitude of the discharge is estimated through its correlation with drainage basin area. Hydromorphic relations correlate aspects of basin morphology, often area, with attributes of the geomorphic system, in this case channel parameters. These are allometric relations where an isometric condition can be identified (Church and Mark, 1984). 10 Day (1969) studied the allometric relation between drainage area and channel width in coastal and interior basins of British Columbia. Using dimensional analysis he showed that a river system could be defined by the formative discharge, QD , the slope, S, and a channel dimension for which Day proposed the bankfull width, Wo- Since discharge is proportional to drainage area and appropriate discharge data were unavailable drainage area, A, was used as the scaling factor. Thus WD=f(A,S) A main focus of Day's study was the comparison of allometric relations in moist coastal and dry interior climates. In both cases Day found relations that were approximately isometric; Wc= 3.7 A053 WI = 1.3A053 Where WQ is the width of coastal stream channels and Wj is the width of interior channels. The isometry permits the comparison of the coefficients, since these are to a degree dependent on the exponents. For a given drainage area streams on the coast will be larger than in the interior although they both grow at the same rate with increasing drainage area. The coastal regions received between 2240 mm and 4450 mm of precipitation per year while annual precipitation in the interior is only 200 mm p.a. This result suggests that discharge controls the size of stream channels but not their scaling behaviour. In spite of the dimensional analysis, Day demonstrated the channel slope was not significant in determining channel width in either coastal or interior basins. This was attributed to the fact slopes were imposed by recent geomorphic history. Ponton (1972) reached a similar conclusion from a study of downstream hydraulic geometry located circa 50km North of Day's coastal streams. 11 A further explanation of the independence of width from slope may be that the sample of streams in Day's study did not represent the range of channel gradients encountered in mountainous terrain. Most of the streams fell in the gradient range 0.2 - 0.07. The steepest channel gradient was 0.35. This likely represents the lower range of channel slopes where rapid mass wasting will initiate or enter the channel from adjacent slopes. Consequently, width may be independent of slope within a range of gradients which best characterizes channels of 2 n d or 3 r d order, occupying valley bottoms rather than hillslopes. Day's regular, isometric result either contradicts the notion that there is a shift in governing processes at small scale or suggests that channel widths and channel gradients are not appropriate indicators of such behaviour. Park (1978) studied the allometry of rivers in southwestern U . K Unfortunately, his publication does not provide information regarding the nature of the river environments he sampled beyond their scale behaviour. For this reason his data are difficult to interpret in the light of the governing processes. However, his consideration of scale behaviour at local, regional and global scales is of interest. Park (1978) compares bankfull channel capacity to drainage area, using b y = ax where y is channel capacity (m2) and x is drainage basin area (km2). Since the variables are dimensionally balanced isometry exists when b=\. Examining the behaviour of channels in terms of the channel capacity, i.e. the cross-sectional area of the channel at bank-full flow, tends to guide interpretations towards consideration of flood hydrology and the response of the channel form to fluxes of water rather than sediment. 12 Over a scale range of 0.1 - 47 km 2, Park (1978) found that b values were not constant, which is an indication of compound allometry. Furthermore, the b values were strongly and inversely correlated with channel slope. Therefore, in steeper channels the channel capacity grows more slowly in relation to drainage area than in gentler channels. This result is similar to that of Coates (1969), Thorne (1971) and Ponton (1972). However, their results found slower rates of growth for both width and depth where Park attributes the lower b values to changes in depth rather than width. Examination of the distribution of b values with scale suggests a shift in scaling towards larger b values at larger scale, but data from basins at intermediate scale would be required to substantiate this observation. Park (1978) concluded that high channel slopes influenced channel capacity via the effects of slope on channel velocity and on the rapidity of hillslope hydrological response. It is conceivable that the observed scaling behaviour is due to hillslope processes dominating channel morphology at small scale. These processes deposit non-alluvial materials in the channel which constrain its growth rate. Based on a regional data set from Devon, U.K. Park (1978) found that b values were correlated with various basin parameters. The strongest correlations were with annual rainfall, various flood quantiles and measures of basin relief. Hence the channel capacity is responding primarily to hydrological forcing since even basin relief, through enhancement of precipitation and lack of storage opportunity, will affect flood magnitude. To extend his range of scales Park (1978) introduced data from the literature. Given the difficulty of comparing studies containing such subjective measures as bankfull width and the lack of a uniform methodology, the results should be viewed critically. Nevertheless, Park's suggestion that at large scales rivers tend towards a steady state isometric condition is interesting in the context of process domains. Since the data come from different regional settings the conformity of behaviour implies that at some scale the system is not bounded by local conditions. 13 , ' Klein (1981) predicted a change in scaling behavior of rivers at basin areas of 250 km 2 based on observed variation in the peakedness index (ratio of mean to peak flow). He predicted that other inflection points would exist in response to scale based variations in runoff generating mechanisms. Carragher et al (1993) sought to test the predictions of Klein (1981) by collecting data from small headwater streams. They find a positive, compound relation between drainage area and bankfull channel width. The data seem to reflect the influence of the size of bed materials on channel widths. Interpretation is complicated by the fact that the progression of bed materials, from sand in the headwaters through cobbles to rock downstream, is the inverse of the classic pattern. Carragher et al (1983) claim that inflection points at 0.07 km 2 and 0.7 km 2 are due to a shift in hydrologic regime and changes in bed material size respectively. Although the inflection point at 0.07 km 2 coincides with a discontinuity in bed materials from sand to cobble they argue that the coarser bed materials should result in more positive allometry. Since the allometry becomes negative the scale shift must be due to factors other than bed materials (Carragher et al, 1983). The second inflexion occurs at the shift to boulder and bedrock channels. The apparent increase in the rate of channel widening is counterintuitive; normally bedrock and large clasts would constrain the channel but alternative hypotheses are not possible in the absence of any detailed information on the river environment. While this study fails to provide convincing explanations of the observed behaviour, the observation itself is valuable since very few studies focus on deviations from monotonic scaling behaviour 1.3.1.3 Morphology of Channel Margins Channel morphology results from the interaction of the channel gradient, the supply and calibre of the sediment and the hydrologic forcing. In short, channel morphology 14 is an expression of the interaction of the governing processes and therefore may be a strong indicator of changes in these processes. Channel morphology can be considered by examining the arrangement of the materials that constitute the outer boundary of the channel, i.e. the bed and banks. This involves the classification of morphologies into channel units or dominant morphologies within homogeneous reaches (Bisson et al., 1982; Sullivan, 1986; Montgomery and Buffington, 1997). While an experienced geomorphologist can identify channel morphological units with reliability, the literature is confounded by differences between the classifications and the scales of study. The common finding in this field is that channel morphology is a function of gradient. For example, Grant et al (1990) showed that channel morphological units (pools, riffles, rapids, cascades and steps) occupy slope ranges which, with the exception of cascades and steps, display very little overlap. Montgomery and Buffington (1997) classified channel morphologies into alluvial, bedrock and colluvial groups.. They define alluvial channels as those flowing over a contiguous layer of valley fill material. These channels can exhibit a large range of morphologies and valley configurations, depending on the channel gradient and position with in the drainage network. Bedrock channels are those lacking a contiguous covering of valley fill materials, while colluvial channels are the small, steep channels at the upper extremities of the drainage network. Montgomery and Buffington (1997), referring to the work of Dietrich and Dunne (1978), Benda (1990), and Seidl and Dietrich (1992), characterize colluvial channels as displaying weak or ephemeral sediment transport. Sediment storage times are on the order of hundreds of years and sediment transport is accomplished by catastrophic mass movement events. The colluvial channels are therefore defined by the dominance of hillslope over fluvial processes. Since there is a shift in the governing processes we may expect a shift in the scaling behaviour. 15 Montgomery and Buffington (1997) examined the relation between drainage area and channel gradient and found a negative compound relation. Beyond an inflection point at 0.5 km 2 the slope of the relation became steeper. The inflection point corresponded to the shift from colluvial to alluvial channels. The bedrock channels occurred at all scales in the study and their scaling behaviour appears more consistent with that of the colluvial channels. They interpreted this result as indicative of long term differences in sediment transport regime between the two groups. In colluvial channels sediment transport is the result of rapid mass wasting and in alluvial channels it is the result of fluvial erosion. In terms of this study, the shift in the scaling behaviour corresponds to a shift in geomorphic process domain; from the domain of mass wasting to the domain of fluvial processes. The shift between colluvial and alluvial channels may reflect the influence of hillslope gradients rather than changes in basin drainage area. In colluvial channels the imposed hillslope gradient approaches the angle of repose for coarse unconsolidated material, 35%. There is little opportunity for the channel to adjust its gradient through deposition as sediment storage is limited and between episodes of rapid mass movement the calibre of materials that can be entrained is insufficient to alter the channel morphology (Baker 1977; Church, 2000). Conversely, in alluvial channels material is finer while bankfull stresses remain approximately constant (Montgomery and Buffington, 1997). Therefore materials are more readily transported, resulting in more frequent rearrangement of the channel boundary and, consequently, the channel gradient. Furthermore, unconfined valleys associated with larger drainage basins permit lateral migration and further adjustments to gradient. Although channel morphology is associated with distinctive process domains this seems to be primarily a response to changes in channel gradient. It is therefore 16 preferable to measure the determining factor, gradient, especially considering the difficulties in quantifying morphological classification. 1.3.2 Scaling Behaviour of Hillslopes In a critical examination of the methodology for extracting channel networks from digital elevation models (DEMs) Montgomery and Foufoula-Georgiou (1993) found a compound relation between slope and drainage area. They observed inflection points at very small drainage areas, 10"4 km 2, and at drainage areas of 10"1 - 10"2 km 2 , where slope gradients were approximately 0.2-0.3. They suggested that the small-scale inflection represents the shift from hillslopes to channelised valleys, and that the inflection at larger scale represents the shift from channels containing alluvial veneers over bedrock to low gradient channels within alluvial valleys. The inflection point at 10"4 km 2 represents the second power of the constant of channel maintenance. This is the spatial scale at which sufficient flow can be concentrated to erode material and sustain an identifiable channel Seidl and Dietrich (1992) noted a similar shift between the dominance of erosion by debris flows and fluvial processes at a slope of 0.2 on the basis of ratios between channel slope and contributing area at tributary junctions. The compound allometric relation found by Montgomery and Foufoula-Georgiou (1993) suggests that the scaling behaviour of hillslopes may be an appropriate indicator of, at least, the transition between the mass wasting and fluvial process domains. From a review of the literature we can see evidence for the existence of process domains in deviations from classic hydraulic geometry relations at small scale, in compound relations between basin area and both channel dimensions and hillslope 17 gradient as well as in the systematic distribution of channel morphologies over a range of channel gradients. 1.4 Process Domains 1.4.1 Definition A process domain will be defined as a scale delimited landscape unit within which the landscape attributes bear the signal of a particular process or assemblage of processes There are numerous river classification systems based upon morphological features (Leopold and Wolman, 1957; Schumm, 1963; Rosgen, 1994). These classifications tend to focus on alluvial rivers. In principle morphology is an expression of the interaction of the controlling factors; sediment calibre and supply regime, flow regime, channel gradient and vegetation. Rivers displaying similar morphologies will likely display similar behaviour and have similar responses to perturbation. When considering headwater channels the changes in morphology are correlated with changes in channel and valley gradients as well as degrees of confinement, all of which vary systematically with scale. Consequently a classification system such as that of Rosgen (1994) may inherently distinguish process domains without addressing them explicitly. Whiting and Bradley (1993) developed a classification system for forested, headwater streams. They sought to utilise discontinuities in governing variables to delimit process domains. Their classification scheme rests upon three criteria. Each criterion reflects the mechanics underlying the physical processes in three distinct process domains hereafter referred to as the hillslope, colluvial and alluvial domains. 18 The hillslope domain is characterised by the ratio of channel gradients to adjacent hillslope gradients (or calculations of stability if the information is available). This reflects the control that slope exerts over the initiation and deposition of mass movements. The colluvial domain is characterised by the ratio of channel width to valley width. This criterion reflects the degree to which the channel is buffered from hillslope processes and thereby the likelihood of the channel being impacted by non-alluvial materials. The alluvial domain is characterised by Shield's Criterion, which describes the propensity for bed materials to become mobilized by the flow, reflecting the dominance of fluvial processes in sediment transport. Whiting and Bradley (1993) focus on the classification of individual streams based on these three criteria, rather than on the delimitation of process domains. They use system scale indirectly via the ratio of channel width to valley width. This ratio, as well as that of hillslope to channel gradients and channel depth to sediment calibre, varies systematically with system scale, albeit in a coarse sense. Consequently, the process domains they identify may provide a context within which to examine scaling behaviour 1.4.2 Conceptual Model of Process Domains Figure 2 shows a conceptual model of process domains in a mountainous region. This model is based on conditions in the Coast Mountains of British Columbia and reflects the process domains of Whiting and Bradley (1993). It should apply to all mountainous regions but may break down in low gradient landscapes. The essential precept of the model is that the conditions that govern geomorphic processes vary systematically with scale. Strahler's (1952) channel ordering system provides a framework to view landscapes. Stream channels, and hence their source areas, are arranged in a nested hierarchal 19 structure. Drainage areas decline with decreasing basin order (Schumm, 1956). Furthermore, channel and hillslope gradients increase as drainage areas decrease. Figure 2. Conceptual model of process domains 1.4.2.1 The Hillslope Domain Drainage basins of the hillslope domain are characterised by steep slopes on which initiation of rapid mass movement occurs through either open slope failure, gully sidewall or gully headwall failure (Dietrich and Dunne, 1978 ). There are few storage opportunities at the base of slopes, therefore, hillslopes are strongly coupled to channels (Church, 1983). Rapid mass movements quickly become channelised and may mix with water to become debris flows. These events scour the hillslope channels 20 and deliver large quantities of unsorted clastic and organic material to their lower reaches or, more likely, to higher order colluvial channels (Church, 1983). Channel sediments are coarse and individual clasts act as both roughness and morphological elements. Channel morphology is typically scoured chutes or boulder cascades (Montgomery and Buffington, 1997) that persist through all but the most extreme flows, which may in fact be debris torrents rather than hydrologic flows (Slaymaker, 1988). Channels are often deeply incised and constrained by hillslope materials, bedrock or, on lower reaches, by coarse depositional levees. The hydrologic regime is characterised by small mean flows, due to the small drainage area, and infrequent high flows due to the low probability of cells of intense precipitation coinciding spatially with the small drainage area. There is little opportunity for soil moisture storage due to thin soils and steep hydraulic gradients, consequently the hydrologic response to precipitation is essentially a hillslope response (Dunne, 1980). 1.4.2.2 The.Colluvial Domain Beyond the limit of hillslope length increases in basin area result in gentler gradients (Montgomery and Foufoula-Georgiou, 1997). While this may appear as a smooth function when examining data from numerous basins actual drainage basins reveal an abrupt transition from hillslopes to valleys (Dietrich and Montgomery, 1998) The colluvial domain is the recipient of material entrained in the hillslope domain (Benda, 1990). Rapid mass movements events deposit in response to reductions in gradient (Benda and Cundy, 1990) and confinement. This accumulation of material is evident as in-channel sediment wedges (Roberts, 1986), debris fans and cones (Benda, 1990) and as colluvial valley fill. Upon delivery the material is unsorted and may contain large amounts of coarse woody debris as well as clastic material. The coarse 21 woody debris becomes an important structural component of the channel (e.g. Keller and Tally, 1979; Hogan, 1986; Nakamura and Swanson, 1993 ). The accumulation of material isolates the channel from the hillslope. A "floodplain" of colluvial origin develops. The channel thus becomes decoupled from the hillslope (Church, 1983). Inputs of material arrive via the channel network rather than via the hillslope (Benda, 1990). The channel is now connected to the hillslope, rather than coupled, although the hillslope processes still exert control over channel morphology via the non-alluvial materials (Grant and Swanson, 1995). Material within the range of forces that can be mustered by the discharge and gradient of the channel will be successively removed by fluvial action, leaving coarse lag deposits (Benda, 1990). These lag deposits seed the development of stable sediment configurations, such as step pools, which inhibit sediment transport (Church, pers.comm). The hydrologic regime is less flashy as partial source areas and cumulation of flow from spatially disparate areas results in higher mean flow and more frequent floods. The floodplain acts as a water storage reservoir so hydrologic response to precipitation input tends to be slower under dry antecedent conditions, but swift responses under saturated antecedent conditions are possible due to saturated overland flow on the floodplain. 1.4.2.3 The Alluvial Domain In the alluvial domain fluvial processes are completely dominant. Channels are now decoupled and disconnected from upstream inputs of, at least, the coarsest materials. In general, mean clast size of bed materials declines progressively downstream due to sorting and abrasion (Sternberg, 1875). Relatively frequent floods are now capable of entraining the bed materials and the channel adopts riffle-pool or plane bed 22 morphologies depending on gradient and sediment calibre. Grant and Swanson (1995) found that morphological change in alluvial valleys was regular and progressive Morphological features of the channel, such as bars, consist of assemblages of multiple particles and both width and depth are equivalent to tens or hundreds of mean sized bed particles (Church, 1992). The floodplain is broad and flat and is maintained by deposition of fine materials during overbank flow. The channel is now unconstrained and can adjust its gradient by meandering. 1.4.2.4 Deviations The notion that grain size declines progressively throughout the drainage network (Sternberg, 1875) does not apply to headwater streams as colluvial inputs disrupt the pattern ( Miller, 1958; Church and Rice, 1996). Therefore, the presence of colluvial material may preclude scaling behaviour associated with the alluvial process domain. Distinctive alluvial scaling may only occur in fully alluvial channels. Coarse woody debris, hereafter CWD, was not considered explicitly in the description of the process domains. Yet, there is a body of work regarding the influence of CWD on channel morphology. Morphological effects include the creation of sediment storage sites (Heede, 1981), increases in depth variability (Keller and Tally, 1979) and width variability (Robinson and Beschta, 1990) and modulation of sediment transport (Hogan, 1986). Nakamura and Swanson (1993) note that the influence of CWD on channel morphology is most pervasive at what here is described as the colluvial scale. This is because the size of the tree boles is commensurate with that of the channel such that individual pieces, as well as accumulations of CWD, may become significant morphological elements. At the hillslope and alluvial scales they argue that the CWD is too large and too small, respectively, to influence channel morphology. 23 Furthermore, the majority of CWD transport occurs during mass movement events. Consequently the zone of deposition, the colluvial process domain, is most affected. The development of debris jams by debris flows is a natural occurrence found in undisturbed regions. Hogan (1986 ) describes the effects of an individual CWD jam on channel morphology. It is apparent that channel widths can be affected, at least temporarily. In an undisturbed landscape the distribution of ages amongst debris jams, would reflect the stochastic nature of sediment inputs (Benda and Dunne, 1997). Logging has been noted to increase the rate of landsliding (Rood, 1984; 1990) and thereby alter the age distribution of debris jams. Therefore, in an area recently impacted by logging the scale behaviour of the channel widths may reflect temporary perturbation (Hogan et.al, 1997). The land use history should be considered when interpreting the scaling behaviour. 1.4.2.5 Scaling Behaviour in Process Domains Ideally, hypotheses for the magnitude of scaling exponents, i.e. b values in power law relations, would rest upon deterministic relations. Since these are untenable, formal analyses which reflect the underlying mechanics will suffice. For alluvial channels the bulk of empirical evidence from downstream hydraulic geometry suggests that widths are proportional to the 0.5 power of formative discharge. A formal analysis by Church (1980) which employed empirical equations of sediment transport and flow resistance for closure also supports this value. However, the relation between drainage area and formative discharge is complex (Smith, 1992; Bloschl and Sivaplan, 1995) so we cannot assume that a value of 0.5 is appropriate in hydromorphic equations. Church and Mark (1980) predict negative allometry between basin area and channel width for large areas as runoff generation from partial source areas and storage effects modulate the magnitude of peak flows. 24 Kellerhals (1969) described the factors controlling a channel where the boundary materials were immobile at all but extreme flows, slope was imposed and sediment transport was limited to sediment calibres below the size of the boundary grains. This is akin to the colluvial channels described here. Using dimensional analysis he found that channel width was proportional to the 0.4 power of formative discharge. The modulation of peak flows previously described does not take effect at the scale of colluvial channels, therefore the formative discharge is proportional to area (Church and Mark, 1980) and we would expect 6-values of 0.4 in the colluvial process domain. No dimensional analysis pertaining to channels controlled by mass wasting has been reported. Therefore, a quantitative hypothesis is developed as part of this study. 1.5 Dimensional Analysis of Hillslope Channels 1.5.1 Governing Processes Since 6-values for hillslope channels are not available in the literature the values will be determined through field measurement. It is expected that process control in hillslope channels differs from those controlling colluvial or alluvial channels. Therefore it is necessary to ensure that the correct variables are measured. Dimensional analysis provides a framework to investigate system function and identify the critical variables. Table 1 lists the variables thought to control channel morphology when mass wasting is the dominant geomorphic process. Sediment discharge, Q s , is used instead of discharge as it is assumed that flows of sediment control these channels rather than flows of water. Channel gradient, S, and gravitational acceleration, g, provide the driving force which acts upon the material and water densities, p s and p respectively. Material length, L m , and material resistance per unit area, R, reflect the fact that these channels are eroding hillslope, rather main alluvial materials. The material resistance represents the strength of the hillslope materials and the material .25 length reflects the spacing of planes of weakness. In effect, the material length refers to joint spacing in bedrock as well as the size of root wads from mature trees or the size of the largest clasts in till deposits. Table 1. Variables controlling channel morphology in channels dominated by mass wasting Symbol Variable Fundamental dimensions Qs Sediment discharge L 3 T - 1 s Channel gradient dimensionless g Gravitational acceleration L T "2 p Density of the flow M L "3 Ps Density of materials M L "3 Lm Material length L R Material resistance per unit area M L" 1 T"2 w Channel width L 1.5.2 Pi Theorem Pi theorem (Buckingham, 1914) states that (N-n) dimensionless groups are sufficient to describe a system where N is the number of variables and n is the number of fundamental dimensions. In this case five dimensionless groups will be sufficient. Selecting Lm, ps and g as the repeating variables, in the method described by Middleton and Wilcock (1994), gives the following Yl groups; ( f = s, P R W V ^ ' T ~~ ' r'5/2 1/2 ' j m J 26 Relating the Pi groups to the underlying mechanics 111 describes the energy grade, II2 is a ratio of densities which accounts for the variation in constituents of mass movement events, II3 is a ratio of forces, FL; is a form of the Froude number and IT5 is a scaled dimension. For this study Ik and II3 will be ignored on the basis that their influence on scaling behaviour can be considered constant within the study area. FIi will be measured as gradient is a governing variable. II4 and II5 contain two of the variables of interest, namely sediment discharge, Qs, and width, w. We consider there to be a functional relation between these two groups. Based on other scale relations we shall assume that the relation can be described by a power law, thus; The sporadic nature of sediment discharge precludes its measurement. However, in small, steep headward basins Qs xcA, where A is basin drainage area and c is a constant reflecting sediment production (Church and Mark, 1980) which gives; If we suppose that/is a simple proportional relation then; 2 7 f w = cA r 3 / 2 1/2 J We can define a constant, v, to represent the influence of material length, gravitational acceleration and sediment production thus; w = vA and V - 12 Of gravitational acceleration, g, material length, Lm and c, the sediment production only c is likely to vary systematically within the study area. Therefore, the investigation of hillslope channels will quantify c and b through a power law relation y = axb where y is the channel width, a is the constant v, JC is the drainage area and b is the slope of the relation. 1.6 Hypotheses Hoi Geomorphic processes do not operate at specific spatial scales. Therefore, the scale behaviour of landscape attributes will not change with scale. 28 Ho2 The power law relations between basin area and'channel width and basin area and channel gradient will not display compound allometry. Consequently, there will be no significant difference between their b values The b-values will be determined empirically. Surveys of channel widths will be conducted in a sample of channels which cover a range of scales and represent the three geomorphic process domains proposed in the conceptual model. Based on results from previous studies b-values for the scaling of channel widths will likely approach 0.4 in the colluvial process domain and 0.5 in the alluvial process domain. 29 Chapter Two: Methodology 2.1 Study Area The study was conducted in the Capilano Watershed between June and October of 1999. The Capilano Valley is located in the Pacific Ranges of the Southern Coast Mountains. It lies approximately ten kilometres north west of downtown Vancouver. The valley has been dammed to create a reservoir for water supply purposes. The site was selected for a number of reasons. Since the watershed is managed for drinking water quality, it has been the subject of numerous investigations. As a result, there is a large body of knowledge available for consultation. For example, an extensive ecologic inventory was undertaken which addressed both ecosystems and physical environments (Acres Int., 1997). The area is easily accessible and the access within the valley is relatively good. Most major tributary valleys contain roads although these seldom attain any altitude. Finally, the area provides an example of a typical British Columbia Coast Mountain environment, which formed the template for the conceptual model 2.1.1 Climate and vegetation The climate of the area is characterised by a mild wet winter and a dry summer (Oke and Hay, 1994). During winter months, regular low pressure systems approaching from the Pacific produce large amounts of precipitation. Mean annual precipitation is strongly influenced by orographic enhancement. Schaefer and Nikleva (1973) estimate annual precipitation at 5000 mm at The Lions, the highest point in the Capilano watershed at 1646 m above sea level. Snow packs are normal at high elevation, although periods of thaw are common throughout the winter. During the summer high pressure is commonplace and the low pressure systems that do occur are less intense, 30 resulting in less precipitation and a summer deficit in the water balance (Oke and Hay, 1994). The hydrologic regime of the area is summarized by Acres et al. (1997) based on analyses of stream flow records collected by both B.C Hydro and Water Survey of Canada. The annual hydrograph is characterised by both seasonal and synoptic forcing. Snowmelt results in the highest monthly inflow to the reservoir in May or June, while instantaneous peak flows usually occur during October or November. Fall floods are the result of frontal storms but annual instantaneous peak flows can also result from summer convective storms or rain-on-snow events. Three biogeoclimatic zones are encountered in the Capilano valley; Coastal Western Hemlock , Mountain Hemlock and Alpine Tundra. These zones are distributed by altitude from Coastal Western Hemlock in the valley bottoms through Mountain Hemlock on valley sidewalls up to Alpine Tundra on summit areas. There is only limited Alpine Tundra in the Capilano watershed; Coastal Western Hemlock and Mountain Hemlock are the dominant forms (Acres Int., 1997) 2.1.2 Geomorphology The bedrock geology of the study area is dominated by igneous intrusive rock types; granodiorite, quartz diorite, diorite and lesser amounts of more mafic rock types such as gabbro and migmatite (Roddick, 1965). These rocks have high strength and broad joint spacing that permits the maintenance of the steep slopes characteristic of the area (Acres Int., 1997). While the present landscape derives from a late Tertiary, low relief erosion surface (Acres Int., 1997), it's current function and morphology are largely determined by the modification that occurred through tectonic uplift and Pleistocene glaciations. Numerous glaciations occurred the last of which being the Fraser Glaciation, which 31 ended approximately 13 000 years ago (Lian and Hickin, 1993). Their legacy is a landscape dominated by glacial features; deeply scoured u-shaped valleys with steep slopes, hanging valleys and cirques. Terrain mapping of the Capilano drainage basin (GVRD, 1997) indicates that glacial materials dominate the landscape. The distribution of surficial materials can be broadly considered in three zones. On steep slopes at high elevation, little surficial material is present aside from pockets of colluvium and till. Less steep slopes, which tend to be found at lower elevation, are mantled with till and colluvium, which has been derived from erosion of till and bedrock outcrops. Glacio-fluvial sediments are found along relict drainage lines. Valley bottoms contain alluvium and colluvium, and glacio-lacustrine terraces can be found in the southern part of the valley to an altitude of circa 250 m a.s.l. Much of the drainage network is thought to predate glaciation. The major valleys were already eroded in response to uplift of the Coast Mountains (Mathews, 1989) and were only modified by glaciation. The pattern of the drainage network is as follows; first order streams, as seen on 1:20 000 maps, tend to be linear, regularly spaced gullies. These drain steep valley side walls of tributary valleys. They are ephemeral, prone to mass wasting and often incised into bedrock or glacial drift. They tend to flow approximately at right angles to the tributary valley stream. The tributary valleys tend to be of second to fourth Horton-Strahler order. The headwater is a cirque where tributaries join at more acute angles than further downstream. These streams flow in valley fill materials of colluvial/alluvial origin. The main valley is joined both by tributary valleys and by steep low order streams draining the steep valley sidewalls. Both overbank deposits and colluvial inputs maintain an alluvial plain. 32 Figure 3. Map of the Capilano Valley showing major creeks and sub-basins studied 33 2.1.3 Land Use History 2.1.3.1 Anthropogenic Disturbance The Capilano Watershed, see figure 3, has provided a water supply to the city of Vancouver since 1886 (City of Vancouver, 2002). Current management practice does not permit commercial logging operations. However, froml918 to 1931 the Capilano Timber Company conducted railway logging operations. Also between 1964 and 1992 the G V R D conducted logging under a tree farm license. Logging is thought to have an effect on the frequency, and perhaps magnitude, of rapid mass movement events (Slaymaker, 2000) Consequently, the morphology and behaviour of any channel prone to these events may reflect recent land use history. Early logging practice was more invasive and less concerned with environmental impacts. Sluicing was used to extract logs from steep terrain. This technique involves the use of stream channels as conduits for felled timber. To prevent the timber becoming trapped in the channel, potential obstacles were removed. This entailed removing natural features of the channel, such as logjams and steps, which evolved in response to the fluxes of water and debris. A flood wave was created to float the logs downstream by damming the channel in the headwaters. When sufficient cut timber had accumulated in the dry channel the dam was breached. The impacts on channel morphology or patterns of recovery from this type of disturbance are undocumented (Hogan, pers. comm.. 1999) 2.1.3.2 Natural Disturbance Natural disturbances include landslides, fires, beetle infestations, blowdowns, climate change, earthquakes and glaciation. Such events occur at a range of temporal and spatial scales. The resultant landscape is complex due to the varying states of 34 recovery that can co-exist. For example, the flux of fine material due to the erosion of glacio lacustrine deposits via mass wasting is a form of recovery from the Fraser glaciation, while at the same time the frequency of the mass wasting events which mobilize the material may be heightened in response to climate change. 2.2 Sampling Strategy 2.2.1 Introduction To investigate the scaling behaviour of river systems the following issues must be addressed. A n attribute of the system must be selected which can be identified and measured over a range of scales. This attribute must be sensitive to variations in system behaviour, yet not exhibit such large variability at constant scale that scale related behaviour is obscured. A n index of system size must be selected. A sampling scheme must be developed to select sites for measurement as well as to determine the frequency and location of measurements at each site. The objective of this study is to illuminate system behaviour at landscape level, not to focus on individual sites. Therefore, in the trade off between site-specific detail and the spatial extent of the data, the latter is given precedence. 2.2.2 Variables for Measurement 2.2.2.1 Scale Index Basin drainage area was selected as a suitable scale index. It is the most fundamental expression of system size when the river system is perceived to include the source area of water and sediment. Furthermore, it can be measured from topographic maps down to the spatial scale at which stream channels are defined. 35 2.2.2.2 System Attributes Channel gradient and channel width were selected as the landscape attributes for measurement. Channel gradient was chosen as it addresses both the force behind flow and the relative stability of bed and bank materials. The selection of channel width was guided by Day's (1969) assertion that a single physical dimension is sufficient to characterize the channel. Width was selected over depth as it can be defined by a single measurement, whereas depth requires an average of numerous measurements particularly in small channels, where the size of boundary materials can approach channel depth. Channel width can be measured at a number of reference points indicated by morphology or vegetation, for example, at the height of channel bars or at the limit of terrestrial vegetation. Each of these widths represents flow regimes of differing magnitudes and return periods (Williams, 1978). For this study, the channel width was measured at the maximum dimensions of the channel in order to reflect the impact of formative events. The width at this point is referred to hereafter as bankfull width Bankfull width can be defined by a number of criteria. Leopold (1994) cites changes in vegetation, topography and sediment as possible indicators. Vegetation indicators can include changes from bare ground to trees or changes from lignified to herbaceous vegetation. Topographical changes can include break of slope from alluvial plain to channel bank or a break of slope from a steep slope to a steeper bank. Sedimentary indicators consist of changes in sediment calibre. The lower limit of fine material can delineate the maximum dimension of the channel. Through morphologic features and patterns of vegetation, stream channels have a memory for past events. It is the impression made by these individual events, or the 36 cumulative results of several events, that are interpreted as the maximum dimensions of the channel. The frequency of channel forming events changes throughout the drainage network (Pickup and Warner, 1976; Williams 1978). Bankfull flows have been associated with return periods of 1 to 2 years (Knighton, 1998) on alluvial rivers. In headward streams the channel forming flow may be a mass movement event with a considerably longer recurrence interval. In a systematic survey of U.S.G.S. gauging stations it was shown that the recurrence interval of bankfull flow can be on the order of twenty to thirty years (Slaymaker and Emmett, 1963). A survey of channel widths at a range of positions in a drainage network will result in a snapshot effect. The dimensions of the channel will be determined in part by the time since the last disturbance. This effect of disturbance history may be largest in the small, steep channels impacted by large infrequent events, as the potential variability is greatest here. It is apparent that identification of bank full width is to some degree subjective and requires experience. 2.2.3 Data Collection Methods 2.2.3.1 Basin Drainage Area The basin drainage area projected onto a horizontal plane was measured in a GIS environment using ArcView. A digital elevation model (DEM) was constructed from TRIM digital terrain data at 25 metre resolution. Drainage basins were delineated as polygons using the D E M and contours as a guide. The drainage area of each basin was calculated by ArcView from the number of pixels within each polygon. 37 The drainage network depicted on a TRIM map at 1:20 000 scale is a model. In reality, numerous streams do not appear on the maps. In steep terrain, first order streams on the map are generally second order streams in the field. Consequently, some of the streams surveyed were not present on the TRIM map. The location of these unmarked streams and the extent of their drainage basins was found using aerial photographs, the altitude of the outlet, morphology of the land surface and distance from a known point, such as a stream confluence or a road. The basin area was measured in the same manner as with mapped streams. As basin size decreases, the scale of variation in the land surface approaches the pixel resolution. Consequently, there is insufficient detail to assess the drainage field and thereby delimit the drainage basin. In these cases, a field mapping technique was used. Ideally, methodology should be consistent across all scales. However, in the absence of very detailed maps, digital or otherwise, this methodological break is unavoidable if we wish to examine small scale phenomena. The field mapping technique employed a compass, a clinometer and a tape measure. The first step is to identify the limits of the drainage basin based on breaks in topography. This proved a difficult task. Several attempts were abandoned. On planar hillslopes, when the line of sight is obscured by vegetation, a topographic survey would be required to determine the drainage divide between small basins. This would not guarantee that the drainage pattern followed the identified breaks in micro-topography. Indeed, observations of stream segments occurring and disappearing on planar hillslopes, particularly where surficial materials are colluvial, with no apparent organization suggest the influence of subsurface heterogeneity is important. Field mapping was limited to areas where the perimeter of the drainage basin could be clearly defined by topographic breaks. Traverses were hiked across the hillslope to identify and flag the basin perimeter. The identified perimeter was then recorded in segments of circa 20m as a distance, a slope angle and an azimuth angle. This 38 information was then plotted, correcting distances for slope angle. The area of the basin was then digitized Assessing the error of the field mapping is difficult. There is neither absolute truth with which to compare, nor a large enough sample to employ statistical analyses. Since the method was applied judiciously, the error is estimated as 10%. 2.2.3.2 Channel Gradient In steep channels, a hand held clinometer was used to measure channel gradient. Where possible, levels were measured over distances of several channel widths. Frequently, vegetation or the large steps reduced this distance. Care was taken to measure the gradient over more than one morphologic channel unit when the channel profile was stepped. Gradient was measured between two people either with their feet at the waters edge, or at the deepest point of the channel. In large, low gradient channels the differences in gradient cannot be resolved with hand held clinometer, so a surveyor's level was used. 2.2.3.3 Channel Width Channel width was measured using a fibreglass tape to a resolution of ±0.1 m. In large channels, the width exceeded the length that can be accurately measure by tape. Since a surveyor's level was used for measurement of channel gradient, tacheometry was used in conjunction with the tape to measure channel width. 2.2.3.4 Additional Observations Observations of channel morphology (e.g. chute, cascade, step-pool, riffle pool) and channel setting (e.g. incision, degree of coupling) were recorded. The D50 and D90 39 were estimated and any changes noted. The locations of tributaries were recorded as a distance along the channel and an altitude above seal level. 2.2.4 Sampling Strategy 2.2.4.1 Landscape Sampling The landscape sampling strategy selects streams for study amongst the array of possible streams within the study area. The issues to consider are representation of a range of scales as well as replication within each "scale class". Due to the hierarchical structure of drainage networks, replication of the largest stream within the study area is not possible without using data from an adjacent drainage basin and thereby introducing additional variability. The sampling scheme must also permit the investigation of factors that could confound the results. For this study the effects of physical basin characteristics, such as steepness, aspect, relief and drainage density, were considered important as were both the natural and anthropogenic land use history. While in general basins could be identified which would facilitate the assessment of the confounding factors, issues of access and safety heavily influenced basin selection. The terrain of the study area is rugged and becomes progressively more so with altitude. Vegetation is dense, particularly at low altitude. Consequently, travel through the forest is very difficult and road access, at least to the outlet of a study basin, is crucial in order to maximize the amount of data that could be collected in the time available. The previous winter's snowfall had been exceptional, resulting in extensive snow deposits at high altitude as late as July. The heavy snow pack caused frequent avalanching. Many gullies, particularly those occupying bedrock canyons at high 40 altitude, contained avalanche deposits, which prevented measurement. These deposits, aided by shading, persisted for the entire season. A further factor which influenced basin selection was safety. Close to ridge lines, many gullies become so steep that mountaineering equipment would be required to work with safety. In addition, there is much unstable colluvium that frequently becomes dislodged and moves down slope. As a result of snow deposits and safety concerns steep, unstable, rock controlled gullies close to ridge lines are not represented in this study. Their lower reaches, which are impacted by high mass wasting frequencies, have been surveyed. 2.2.4.2 Site Sampling Once streams have been selected for study, the within stream sampling schema must be decided. Here, the objective is to collect sufficient information to make robust estimates of mean channel width and gradient. Inevitably, there is a trade off between the amount of data collected at each site and the number of sites sampled. This study seeks to compare the behaviour of the system over a range of scales. To maximize the range of scales, the representation at each scale class, and the power of the experiment we desire a large number of data points. Since each data point represents a site, i.e. a stream channel or reach, a question that informs the sampling strategy is what is the minimum sampling effort that can be expended at each site, to adequately quantify mean conditions found there? There is little information regarding the variability of small stream channels available in the literature to guide such a decision. On large rivers, examination of topographic maps and aerial photographs permits an assessment of channel variability and the definition of homogeneous reaches. This is not possible in the study of small channels. While the path of first order streams is delineated on 1:20 000 aerial photographs and 41 TRIM maps it is impossible to assess channel gradients, channel habit or tributary inputs. Consequently, reach delineation must be accomplished post facto based on field survey. The unit of study will be the stream link, based on the Horton-Strahler ordering schema, as stream links can be approximated from maps and aerial photographs. It is well established that maps do not show the lowest order streams; therefore, these are identified through field survey. The lack of information to guide decisions regarding the sampling schema led to the design of a pilot study. 2.3 Pilot Study 2.3.1 Hypothesis/Objectives The objective is to assess the variability of channel width in order to design an appropriate sampling scheme. Channel width was selected as the variable for measurement rather than channel gradient, since channel gradient is a forcing function rather than a response variable. The null hypothesis shall be that frequency of measurement has no influence on the error of the mean. Ho: The mean channel width is not affected by the spatial frequency of measurement. H/. The mean channel width is affected by the spatial frequency of measurement 2.3.2 Methods Rapid Creek, with an area of 1.2 k m 2 , was selected for this study as it was considered a good example of a channel draining a steep headwater. Morphological features, such 42 as depositional levees and lobes of coarse material, suggest that this channel is prone to mass wasting events. The field methodology entailed making measurements at very high frequency. Subsequent analysis compared the effect of using successively thinned samples. The measurement increment of 1 m was selected to represent the size of coarse channel forming clasts. This length scale was thought to represent the lower limit of detectable variability in the fashion of Dietrich and Montgomery (1991). The flux of material and energy is directed down slope in stream channels. Change is progressive and organized; conditions at any point in the channel are correlated with conditions upstream. For this reason, an ordered sampling scheme, that takes measurements at a fixed interval, as opposed to a random sampling scheme, is used to estimate mean channel widths. An ordered schema also permits the sub-division of the data into homogeneous reaches. Channel widths were measured with a taut fibreglass tape to 0.1m resolution. A tape was stretched along the thalweg to identify measurement locations. Channel gradients were measured using a clinometer. When the channel profile was stepped, gradients were measured in excess of one channel unit upstream and downstream of the width measurement. On uniform channel profiles the gradient spanned 20 m of the channel. The survey was conducted for a distance of 420 m. After this point, the channel became incised and strongly coupled to adjacent hillslopes. This coupled reach was surveyed for the study in general, but not at the 1 metre frequency of the pilot study. 2.3.3 Results Figure 4 illustrates the changes in width over the surveyed reach. The channel width displays an irregular cyclical pattern. Variability exists at several length scales. There 43 are several areas of pronounced channel widening, most notably that from circa 168 to 210 m. These areas correspond to lobes of coarse material deposited by debris flows. Variability also exists at the 3-5 m length scale, which likely corresponds to channel unit morphology, root wads or large clasts. No correlation was found between channel width and channel gradient. 2.3.4 Analysis 25 n 0 J . © T OO ' CN V © © OO CN VO © rf- OO (N VO O c s ^ r r - . O N f N ' i - v o o s ' — ' • ' S - v o o o i — i m v o ' o o Distance along channel (m) Figure 4. Width variability at 1-meter intervals in Rapid Creek The stream link is the unit of data collection. Stream links are of finite length. Therefore, the number of measurements taken per link will determine the spacing between measurements. The length of exterior links, however, can be ambiguous both in the field and on maps. 44 Horton's (1945) link length ratio shows that link length is positively correlated with stream order; longer links are larger channels. Thus, the spacing of the measurements will be consistent in channels of different sizes when the spacing is measured in terms of intrinsic stream scale i.e. i f the spacing is measured in channel widths. Measurement Interval (m) S3 > Figure 5. Relation between mean channel width and measurement interval. Note the small increments on the y-axes For the purposes of the pilot study the objective is to decide the number of measurements per link that are required to characterize the variability. The mean channel width can be defined based on progressively larger measurement intervals. Figure 5 displays the relation between the mean channel width and the measurement interval. Increasing the measurement interval appears to have little effect on the mean channel width, while the variance declines at greater measurement intervals. An 45 important point to consider here is the influence of sample size, which declines from 417 at 1 m intervals to 11 at intervals of 40 m. The number of samples collected and the measurement interval are interdependent. To isolate the effects of measurement interval, random sampling with replacement was used to select subsets of measurements of different sample size. Sub populations were created with sample sizes of 10, 15, 20, 25, 30, 35, 40, 45, 50 and 55 measurements. Each sub population consisted of thirty replications. Figure 6 illustrates the results of the analysis. The sub-population mean is the mean of all the sample means. For the purposes of this analysis the sample of widths taken at 1 meter intervals is considered equivalent to the population mean, and is labeled accordingly in figure 6. The 95% confidence interval for the sub-population means diminishes with increased sample size, from 0.64 m at 10 measurements per link to 0.37 m at 55 measurements per link. This implies that mean channel width can be estimated with greater precision when a larger number of measurements is collected, although the increment of precision above a sampling size of 30 is minimal. The deviation of the sub-population means around the population mean describes the accuracy of the sampling schema. Increasing the sample size effects no significant increase in the accuracy of the estimate. 2.3.5 Conclusion This analysis suggests that small sample sizes, on the order of 10 - 20 measurements provide reasonable estimates of mean channel width. This represents a measurement interval of 2 to 4 channel widths in Rapid Creek. A sampling frequency of 30 measurements per link was selected. This provided sufficient measurements to estimate mean channel width once links were stratified into homogeneous reaches. 46 o VO O O O O <X><33*»«X»<XX> > <XXX>0C3*XX> 0»0 oo o <xaii *'<yxx> os> O 03^ <X><M3KS>C(X> I I I I O 0O«X3»lKJCXX> <X> O003«>«<X><»O«> t * , I o o<K»<amPcox> o o OO 0D>O> >^€C^ 0C8>X> o o o«> oxfcaw o«*> oocs> o in o o in © CN o o o o c o i c o « > o c o o> o in cn in CN CN i n r-i in in OV (Hi) mpiAV T3UimUO WB3]ft 2.4 Reach Delineation Homogeneous reaches were delineated after field survey. Factors used to identify these reaches were the degree of coupling, degree of incision, changes in channel morphology, changes in sediment calibre, changes in channel gradient based on field observations or cumulative departures from the mean, and the occurrence of tributaries. Since the homogeneous reaches could not be identified from topographic maps or digital elevation data the boundaries between reaches were identified by distance along the channel, distance from any identifiable point, such as a tributary or road, and altitude above sea level. There is undoubtedly some error involved in this process which is difficult to quantify. The forest cover precluded the use of GPS positioning which would have reduced the uncertainty. 48 Chapter Three: Results 3.1 Introduction 3.1.1 Basin Description Figure 3 illustrates the main basins selected for study within the Capilano valley: Sisters Creek, Healmond Creek and Hesketh Creek. Within these basins several streams were sampled in a nested design. Streams were studied from other basins to complement those covered by the nested study design. 3.1.1.1 Sisters Creek Sisters Creek basin lies on the western side of the valley. The headwaters form the leeward side of the ridge that receives the brunt of oncoming frontal systems from the Strait of Georgia. Orographic enhancement is considerable, as the land rises to a height of 1500 m in approximately 2.5 km, and annual precipitation is estimated at 5000 mm (Schaefer and Nikleva, 1973). Sisters Creek is one of the largest tributary valleys and is less elongate than most. Levels of geomorphic activity are high in this area as indicated by the high drainage density (Brardinoni, 2001). There are numerous sediment sources due to extensive steep till covered slopes and some unstable rock slopes. There is evidence of avalanche activity and recent mass movement events. The valley bottom and lower side slopes were logged in the early part of the century. More recent forest harvesting occurred in Lempke Creek in the 1970s. Sisters Creek basin contains both hillslope and colluvial channels. Sisters Creek itself is a colluvial channel that receives a large sediment load evidenced by extensive sediment 49 wedges downstream of low order tributary inputs. A nested design was employed in this basin. 3.1.1.2 Hesketh Creek Hesketh Creek is a tributary basin on the west side of Capilano valley. Unlike Sisters Creek it does not drain the lee side of the ridge and may therefore receive less precipitation. A nested design was used. None of the surveyed streams displayed evidence of recent mass wasting events. The third order stream Hesketh 2B displayed considerable variability due to bedrock control. Large bedrock outcrops resulted in steps of up 30 m in height. Such features are more commonly found in small streams at a higher position in the basin. While the lower areas of Hesketh Creek basin have been logged, first and second order streams run through old growth forest that has been fire disturbed. It was observed that in small 1 s t and 2 n d order streams coarse woody debris formed a structural element in the channel, acting as a channel bank. 3.1.1.3 Healmond Creek Healmond Creek lies on the east side of the Capilano valley and is a large cirque. There are numerous avalanche tracks and evidence of recent mass movement events. A nested design was employed. The low order stream surveyed drained the north side of the valley. Close to the ridgeline the hillslope morphology is distinctly convex. 3.1.1.4 Miscellaneous Basins In order to fully represent the range of geomorphic settings, as well as to provide controls and replication at various scales, links were selected from other basins (East Cap Creek, 50 Hanover Creek and Rapid Creek). In these cases there was no nesting hence individual links were surveyed. 3.1.2 Observed Sources of Variability At long temporal scales, channel width is expected to scale with a governing factor. However, at shorter time scales i.e. at the time of an individual measurement the channel width is governed by the most recent significant forcing. Channel width can be regarded as a balance between forces which expand the channel, such as floods or debris flows, and forces which reduce the width, such as revegetation and soil creep. While channel widening occurs more or less instantaneously, reductions in channel width mitigated by revegetation or creep occur much more slowly. A similar scenario with respect to alluvial fans is described by Church and Mark (1980). Since the behaviour of individual channels reflects recent events a sample of channels at a specific scale may be required to identify scaling in response to the governing factor. 3.1.2.1 Hillslope Scale At the hillslope scale, a source of variability was observed that had not been predicted in the model of process domains. In general, hillslope channels are impacted by mass wasting. They are steep, contain coarse bouldery material and are incised into surficial materials or bedrock. At upper elevations, channels were observed which were neither incised nor did they contain coarse material and were considerably narrower than the incised channels. These channels were small, ephemeral and eroded into the upper soil horizons. Channel beds were formed by roots, fine organic material (twigs) or clastic material. The clastic material appeared to have been mined from in situ deposits, rather than transported by the stream. 51 In several cases, the transition from an unincised channel to an incised channel was clearly marked by the head scarp of a previous landslide. In the incised channel factors which induce channel widening are landslide initiation sites in banks, deposition of coarse material and avulsions. The latter two cases occur in lower reaches as gradients decline. Some avulsions seem to occur in response to large trees or clasts with widths on the order or meters. Bedrock canyons were observed most frequently close to ridge lines where slope profiles are concave. This type of channel is poorly represented as they were often clogged with avalanche deposits that did not melt during the summer of 1999. Gradients are generally imposed at the hillslope scale. Gradient can be locally influenced by sediment accumulations behind large clasts or pieces of coarse woody debris, bedrock steps. On lower slopes aggradation modifies gradients over distances of several channel widths. 3.1.2.2 Colluvial Scale Variability in the width of colluvial channels, beyond that due to variations between local morphological features such as pools and riffles (Montgomery et al., 1995), is strongly influenced by the delivery of coarse sediment from low order tributaries. Channel widening results from deposition of coarse material in the channel, as well as from debris flows moving down the channel. The leading edge of depositional lobes is often marked by a logjam which contributes to widening (Hogan, 1989). Also individual large clasts which may have been transported by debris flows or arrived via rock fall from surrounding cliffs can impact width by promoting the development of steps which trap sediment and modify gradients, or by redirecting flow towards the bank resulting in erosion. Levees deposited by debris flows can constrain the channel i f the size of the materials renders them immobile to subsequent events. 52 At the colluvial scale, bedrock control of channel gradient is less frequent than at the hillslope scale, but occurs nonetheless. Accumulations of sediment at tributary mouths and behind debris jams are the major sources of variability aside from any imposed gradient. 3.1.2.3 Alluvial Scale At the alluvial scale width variability stems from tributary sediment inputs and from changes in sediment calibre. With a single exception the alluvial channels are gravel bedded. While gravel is alluvial material in these channels large non-alluvial clasts are still present and may influence width. The Capilano above East Cap is predominantly gravel bedded but contains a reach with a sand bed. Here the morphology changes to a single threaded channel with a smaller width to depth ratio. 3.2 Results of Stream Surveys 3.2.1 Survey Results by Stream Link Table 2 displays the summary data from the stream links surveyed. The links are grouped into their respective watersheds. Both morphological position and the method by which the drainage area was determined are also indicated. Figures 7 and 8 illustrate the scaling behaviour of channel widths and channel gradients respectively. The overall scaling behaviour of channel widths, figure 7, conforms reasonably to a power law model, with no obvious scale specific departures from the model. At a scale of 0.001 k m 2 to 0.02 km 2 a group of points corresponding to unincised streams lies beneath the trend , while the incised streams lie above it. This may confirm field observations that unincised streams at the upper extremities of the drainage network constitute a distinct 53 class of stream. In addition channels the colluvial that have experienced recent mass wasting plot considerably above the trend. The scaling behaviour of channel gradients, figure 8, exhibits distinct compound allometry with an inflexion at 0.1 km 2 . Again outliers are noted; three data points from the Viberg basin with basin areas between 0.001 and 0.02 k m 2 display a positive relation at a lower level than the rest of the data,. Also, the gradient of the main river, Capilano above East Cap with a basin area of 87 km 2 , has a distinctly lower channel gradient than other channels in the study. To assess the impact of land use, comparisons would be made between links in disturbed and undisturbed basins with other factors held equal over a range of scales. The pattern of disturbance however did not permit these comparisons. Consequently, the results reflect the behaviour of a disturbed system 54 Table 2. Results of stream surveys of channel links Watershed n • Mean Basin Mean , „ . „ . . Channel Drainage Channel .. , » /i 2\ • j . u / \ Gradient Area (km2) width (m) / 0 . . Morphological position Area determination Healmond Creek Watershed Viberg 2A Viberg ID Viberg IA Viberg IB Viberg 1C Healmond Hesketh Creek Watershed Hesketh Main Hesketh 3B Hesketh H2B Hesketh H2A Hesketh H2D Hesketh HI A Hesketh H1B Sisters Creek Watershed Sisters above Strachan Sisters above Lempke Sluice Creek Lempke Creek Lempke Headwater Strachan Creek Brothers Creek Miscellaneous Hollyburn Creek Hollyburn 2A Capilano above East Cap Rapid Creek Hanover Creek 0.051 3.83 61.8 Hillslope Cartographic 0.0029 0.90 74.2 Hillslope Field mapping 0.0143 0.90 35.5 Hillslope Field mapping 0.0019 0.72 20.3 Hillslope Field mapping 0.0065 0.95 30.6 Hillslope Field mapping 6.054 16.41 12.3 Trunk valley Cartographic 5.359 21.03 10.9 trunk valley Cartographic 0.343 7.83 36.6 Hillslope Cartographic 0.124 4.32 62.2 Hillslope Cartographic 0.051 4.64 64.3 Hillslope Cartographic 0.0008 1.09 70.2 Hillslope Cartographic 0.0001 0.45 65.3 Hillslope Field mapping 0.0002 0.32 65.8 Hillslope Field mapping 19.434 28.35 7.4 Trunk valley Cartographic 5.394 35.39 16.8 Trunk valley Cartographic 0.175 15.41 42.5 Hillslope Cartographic 4.05 10.04 11.7 trunk valley Cartographic 0.0071 3.45 56.3 Hillslope Field mapping 4.637 13.50 15.1 Trunk valley Cartographic 0.189 13.91 49.9 valley side slope Cartographic 1.276 8.20 13.2 Hillslope Cartographic 0.223 4.96 36.5 Hillslope Cartographic 86.923 32.25 0.2 Main valley Cartographic 1.192 11.21 27.7 Hillslope (adj. to main valley) Cartographic 6.548 10.95 10.4 Trunk valley Cartographic 55 3.2.2 Survey Results by Reach 3.2.2.1 Reach Classification At the hillslope scale reaches were classified initially as incised or unincised. However, the incised streams displayed considerable variability and consequently were further classified as transport, deposition, recent event and rock controlled. Reaches classified as "incised transport" are characterised by a lack of clastic material or obvious sediment wedges. There is evidence of mass wasting, at the very least through the degree of incision but little material has been deposited. These reaches were generally found in mid-slope positions. Reaches classified as "incised deposition" are aggrading reaches characterised by accumulations of clastic material resulting in step-pool or boulder-cascade morphologies. Depositional levees were also observed. These reaches occur generally on lower slopes. At upper elevations channels are sometimes confined by bedrock walls. These reaches were isolated to see if the confinement affects the scaling behaviour. Likewise, several reaches had experienced large mass wasting events recently. These channels were noticeably larger than other channels draining similar sized basins and contained steep rocky areas in their drainage basins. These reaches were therefore isolated to test whether the frequency/magnitude of events had any influence on scaling behaviour. At the colluvial scale reaches were classified as either deposition or transport. Here the distinction rests on the input of coarse sediment from low order hillslope channels. Reduction in channel gradient when hillslope channels reach valley bottom colluvial channels triggers deposition resulting in channel widening. Reaches not clearly aggrading from tributary input were classified as transport, although normal processes of transport and deposition occur here as well. 5 8 At the alluvial scale no distinctions were made between reaches. Only one reach was identified as being free from non-alluvial material, Capilano River - lower. This reach exhibited a distinctly different morphology, a narrow single thread channel with steep, relatively fine grained banks. 3.2.2.2 Survey Results for Channel Reaches Table 3 displays the summary data for the reaches. Charts of changes in channel width and channel gradient with distance along the channel are displayed in Appendix A . 59 Table 3. Results of stream surveys; channel reaches Stream Reach n Area Outlet (km2) Mean channel width (m) Mean channel gradient Unincised Hesketh IA 11 0.0001 0.45 0.65 Hesketh IB 11 0.0002 0.32 0.66 Hesketh ID 15 0.0034 1.01 0.86 Hesketh 2D 13 0.001 1.09 0.70 Hesketh 2B - upper 2 0.071 1.70 0.75 Viberg IA 13 0.0143 0.90 0.36 Viberg IB 19 0.0019 0.74 0.19 Viberg IC 53 0.0065 0.95 0.30 Viberg ID 6 0.0029 0.86 0.73 Viberg 2A- upper 16 0.061 2.99 0.81 Lempke 1A - upper 7 0.0047 1.24 0.61 Hollyburn IA 23 0.141 2.70 0.45 Incised - transport Hesketh IC 15 0.0034 1.96 0.78 Hesketh 2A - upper 4 0.021 3.15 0.62 Hesketh 2A - lower 18 0.051 4.76 0.62 Hesketh 2B - mid 3 0.083 4.90 0.65 Viberg 2A - lower 21 0.116 4.16 0.51 Viberg 2A - mid 7 0.077 4.53 0.53 Lempke 1A - lower 7 0.007 3.29 0.52 Lempke - upper 14 3.026 8.89 0.13 Strachan - lower 7 4.637 12.90 0.17 Hollyburn main - upper 45 1.175 7.82 0.19 Hollyburn 2A - lower 51 0.223 5.25 0.32 Hollyburn 2A - upper 69 0.215 5.00 0.37 60 Table 3 continued Stream Reach n Area Outlet (km2) Mean Channel Width (m) Mean channel gradient Incised - deposition Lempke - mid 14 3.434 9.40 0.08 Sluice - lower 6 0.175 6.57 0.54 Hollyburn main - mid 88 1.228 9.70 0.09 Rapid - mid 396 1.183 11.10 0.28 Hollyburn main - lower 12 1.276 6.50 0.07 Incised - recent Brothers - mid 6 0.183 14.00 0.44 Sluice - upper 8 0.162 14.44 0.35 Brothers - R-control 3 0.037 12.23 0.73 Sisters above Lempke - lower 4 5.394 26.78 0.18 Sisters above Lempke - upper 8 5.057 39.70 0.16 Brothers - upper 10 0.129 16.66 0.55 Incised - rock control Hesketh 2B - lower 9 0.124 4.71 0.58 Hesketh 3B - lower 9 0.343 8.61 0.38 Hesketh 3B - upper 8 0.284 7.53 0.45 Rapid - upper 23 1.116 11.72 0.26 Strachan - upper 13 4.626 14.48 0.15 61 Table 3 continued Stream Reach n Area Outlet (km2) Mean Channel Width (m) Mean channel gradient Colluvial transport Hesketh Main - upper mid . 7 5.232 15.71 0.16 Healmond - mid 9 6.008 16.26 0.12 Healmond - upper 10 5.381 17.09 0.16 Sisters - 3 5 16.825 24.98 0.07 Sisters - 4 5 15.712 24.10 0.07 Sisters - 5 5 13.913 31.66 0.08 Hanover - upper 4 4.630 6.63 0.12 Lempke - lower 7 4.054 13.60 0.16 Colluvial - deposition Hesketh Main - mid 7 5.350 26.67 0.07 Hesketh Main - upper 5 5.013 24.58 0.16 Sisters -1 6 19.439 20.98 0.08 Sisters - 2 5 18.066 41.52 0.06 Hanover - lower 7 6.548 10.26 0.15 Hanover - mid 8 5.955 13.71 0.06 Hesketh Main - lower 4 5.359 16.03 0.03 Healmond - lower 6 6.054 15.52 0.05 Alluvial East Cap lower 5 43.074 25.46 0.05 East Cap mid 4 40.956 42.55 0.06 East Cap upper 4 40.383 26.63 0.05 Capilano River - lower 10 86.923 36.43 0.01 Capilano River- mid 11 81.010 27.07 0.01 Capilano River - upper 5 84.598 35.30 0.01 62 c ve o <u cx CO C3 u J3 i -rec TD TD U CD CO 05 'a ' o a c •4 • V O in O N O o tJ o to I "3 O X c _o £ 3 cn O Q. <o TD TD U co c e o o a o TD U co c > 3 • co O O . <u I CJ I + oo cd C '3 o d o o o o o o o d (in) W!AV I 3 U U t 3 l D U B 3 N CO <u O OS a o w c u 60 O E o 43 C u 43 o o u 3 O '1 43 u X! 60 . C "« o C/5 OV u t> 3 60 CO VO • m X 4 O-o o (o/0) ;usipBjS jaumuQ tresj/^ 3.2.2.3 Scaling Behaviour of Channel Widths Figure 9 displays the scaling behaviour of channel widths in stream reaches. Comparison with figure 7 reveals a similar pattern. There is no obvious compound relation and, when considering all the groups combined, agreement with the power law model is good. Table 4 displays the similarities in the coefficients, exponents and degree of variance explained between the link and reach data. Table 4. Comparison of power law relations for pooled data between reaches and links 9 a B R 2 Link 9.648 0.350 0.888 Reach 9.559 0.335 0.852 The patterns observed in the link data are also present in the reach data. The unincised and recent event groups plot below and above the overall trend, respectively. It appears that there is little differentiation amongst the incised - transport, incised - deposition and incised - recent event groups. Also, their scaling behaviour is similar to that of the overall trend. The colluvial reaches cover only two orders of magnitude in basin area compared to five for the hillslope reaches. There is no obvious difference between the depositional and transport reaches nor is there any discernible pattern in their variation around the central tendency. 65 Table 5 displays the scaling relation for each class of reach. A log transformation was used on both x and y variables. The data were fitted to a linear model hence; y = b x + a where y is the logarithm of channel width, JC is the logarithm of drainage area, a is the logarithm of the intercept and b is the slope exponent. Simple linear regression was performed. Calculation of the anti-logs provides the power law relation: y = anti-log (a) xb At this stage the bias incurred when back calculating values for a and b was not corrected. Comparisons were made using the log transformed data until final relations were identified. Since the objective of this study is to ascertain the value of co-efficients relating physical parameters, rather than to predict one of the variables based upon measurement of the other, the use of simple linear regression is inappropriate. Mark and Church (1977) describe functional analysis, the appropriate curve fitting technique when attempting to establish physical relations. Functional analysis requires quantification of the error in both x and y variables. In this study, unique measurements of basin area were obtained precluding quantification of the error in the independent variable. The deviation between coefficients obtained by linear regression and functional analysis is inversely proportional to the magnitude of the R value. Given the lack of information regarding the error in the x-variable and the tolerably high correlations found in preliminary investigations, simple linear regression was used as a surrogate for functional analysis 66 At the hillslope scale all scaling relations are significant at the 0.05 level except that of the Incised - deposition class. Amalgamation of the depositional reaches with the parent group, referred to as incised resultant in table 5, leads to a weaker relation but one that is significant at a = 0.05 nonetheless. Neither the colluvial - deposition nor the alluvial scaling relation are significant at a = 0.05. Pooling all the colluvial channels produced a significant relation. The alluvial class suffers from a small sample size and small range of basin areas, as well as the lack of true alluvial character. A n amalgamation of colluvial and alluvial reaches is discussed in Chapter Four. Table 5. Results of regression analysis for reach data. The a-values are calculated without correction. * indicates relations not significant at a =0.05 a b n F R 2 S.E Unincised 4.118 0.256 12 42.151 0.808 0.128 Incised - transport 7.745 0.217 12 138.915 0.933 0.059 Incised - deposition 8.432 0.124 5 1.309* 0.304 0.102 Incised - recent event 22.720 0.206 6 29.540 0.881 0.076 Incised - rock control 10.311 0.292 5 28.267 0.904 0.067 Incised - resultant 8.657 0.235 24 137.618 0.862 0.081 Colluvial - transport 4.012 0.699 7 8.928 0.641 0.144 Colluvial - deposition 9.026 0.375 8 1.762* 0.227 0.181 Colluvial - all 6.306 0.520 15 8.373 0.392 0.161 Alluvial 23.048 0.078 6 0.084* 0.021 0.101 67 3.2.2.4 Scaling Behaviour of Channel Gradients at Reach Level Figure 10 illustrates the scaling behaviour of channel gradient when homogeneous reaches are considered. The pattern displayed is similar to figure 8. An obvious inflection point exists at a scale of circa 0.1 km 2. The small scale links did not display sufficient variability to warrant subdivision. Therefore, the patterns are identical to figure 8 up to a scale of 0.2 km 2. It is notable that the depositional reaches from both the hillslope and colluvial process domains plot below the trend. 68 Chapter Four: Analyses 4.0 Overview of Analyses The analyses test the hypotheses put forward in section 1.6. They seek to establish whether scaling behaviour is consistent over the range of spatial scales covered by the field study. Spatial scales are delimited using the empirical model of process domains as a template. Comparisons of scaling behaviour between process domains as well as within process domains are made based upon the statistically significant groups identified by reach classification. The hillslope process domain yielded four significant scaling relations for reach classes unincised, incised - resultant, incised - rock control and incised - recent event. The incised resultant class is hereafter referred to as Incised. While these four relations may be significant it is necessary to establish whether there is any significant difference between these relations, or i f a single relation can be defined. This is a precursor to comparing scaling behaviour between process domains. Scaling relations in the colluvial and alluvial process domains are less well defined than those of the hillslope process domain. Here, the behaviour of the reach classes must be examined in order to define a meaningful scaling relation so that comparisons between process domains can be made. Channel width is used as the primary variable to investigate scaling behaviour. Channel gradients are used to evaluate the validity of the process domain concept as well as assist in the interpretation of the scaling behaviour observed in the channel width data. 69 4.1 Scaling Behaviour of Channel Widths 4.1.1 Hillslope Process Domain 4.1.1.1 Comparison of slope exponents within the hillslope process domain It appears that the four reach classes from the hillslope process domain exhibit similar scaling behaviour in terms of their slopes, although intercepts vary. Analysis of Covariance can be used to test statistically i f there is any difference in the slope of the four relations (Zar, 1984). The hypotheses to test are given by; H0 . b unincised & incised & incised-rock control & incised - recent HA • b unincised ^ & incised ^ & incised-rock control ^ & incised - recent Zar (1984) describes the method for computing an F-value to test the hypotheses as follows; common pooled F = k-l Spooled pooled Where SS refers to the residual sum of squares, k refers to the number of individual regression equations and df refers to the residual degrees of freedom. The pooled regression residual sum of squares is derived by the summation of the residual sum of 70 squares of the k regressions. The common residual sum of squares is derived by summing the L x 2 Yy2 and Jjcy values from each individual regression. See Zar (1984) for a full description of the equations. Table 6 . Analysis of covariance to test differences in 6-values of reach classes in the hillslope process domain. Zy1 SSres dfres Unincised 10.5432 2.6951 0.8524 0.1634 10 Incised 14.0576 3.0844 0.7548 0.0781 15 Incised recent event 4.0721 0.8386 0.1961 0.0234 4 Incised - rock control 1.4894 0.4352 0.1407 0.0135 3 Pooled regression 0.2784 32 Common Regression 30.1623 7.0533 1.9439 0.2945 35 Thus: 0.2945-0.2784 F - 042784 = ° - 6 1 9 7 32 Since F 0.05 (3,32)« 2.922, Ho is not rejected. Thus, there is no significant difference in the slopes of the scaling relations between the reach classes at the hillslope scale. The mean width of all channels grows at the same rate with respect to increasing drainage area. The slope of the four relations can be represented using the common value of b - 0.238. The scaling relations in the hillslope process domain plot as a series of parallel lines with varying intercepts, see figure 10 and table 5. The values of the intercept increase from unincised reaches, through transport and rock controlled reaches up to reaches recently 71 scoured by mass wasting. This pattern may reflect underlying behaviour typical of each reach class 4.1.1.2 Comparison of intercepts It has been demonstrated that there is no significant difference in the slopes of the scaling relations between the reach classes unincised, incised, incised - rock control and incised - recent event. Therefore, the differences between the intercept of the relation can be examined by comparing the mean of the y values, mean channel width, between each group. Analysis of Variance (ANOVA) will be used to test the hypotheses: H0 • M unincised M incised M incised-rock control M incised - recent HA • . M unincised^ M incised ^ M incised-rock control ^ M incised - recent Table 7. One way ANOVA to test the difference between means of the channel reach sub groups. Groups n Unincised 12 Incised 17 Incised - recent event 6 Incised - rock control 5 Source of Variation SS df MS F Between Groups 7.786857 3 2.595619 48.06847 Within Groups 1.943941 36 0.053998 Total 9.730798 39 Since F 0.05 (3,36)« 2.8387 H0 is rejected. The mean channel widths do vary significantly. This implies that at least one of the intercepts is significantly different from the others, t-tests assuming equal variance will be used to establish between which groups the difference or differences lie. The null and alternate hypotheses remain as stated for the A N O V A in table 7 72 Table 8. T-test assuming equal variance to identify which of the groups differ significantly in terms of mean channel width where H<, : \i] = (0.2 Unincised Incised Incised - recent event t-statistic ^critical t-statistic ^critical t-statistic •^critical Incised -8.1072 2.0518 Incised - recent event -9.8219 2.1199 -5.0606 2.0796 Incised - rock control -6.7648 2.1315 -1.6787 2.0860 2.8228 2.2622 H0is rejected when \t\ > t(i.a/2) with («; + «?-2) degrees of freedom at a = 0.05. Comparison of the t- statistic values and the critical t values in table 8 shows that Ha is rejected in all cases but one: the comparison between incised and incised - rock controlled reaches. In this case H0 cannot be rejected hence there is no significant difference between the mean channel widths of these groups. The incised - rock control reaches are a sub group of incised channels. Since there is no significant difference in the scaling behaviour of these two groups, with respect either to the exponent or intercept of the power relation, they are amalgamated. The common scaling exponent must now be recalculated based on the three reach classes using analysis of covariance as per section 4.1.1.1. Table 9. Calculation of common scaling exponent using Analysis of Covariance. IJC 2 SSres dfre, b Unincised 10.5432 2.6951 0.8524 0.1634 10 0.2556 Incised 16.1416 3.7936 1.0217 0.1301 20 0.2350 Incised - recent event 4.0721 0.8386 0.1961 0.0234 4 0.2059 Common regression 30.7569 7.3273 2.0701 0.3245 36 0.2382 73 Three distinct groups emerge in the hillslope process domain: unincised channels, incised channels and incised channels impacted by recent events. Table 4.1.4 illustrates the recalculated slopes as well as the common regression. Since there is no significant difference between the slope of the scaling relations the common value, b = 0.2382 can be used to describe scaling behaviour in the hillslope process domain and make comparisons with other domains. Although the intercepts of the three reach classes differ it is desirable to calculate the intercept of the common hillslope scaling relation to facilitate graphical and statistical comparison with other domains . The common intercept is calculated as; where k is the number of regressions, n is the number of samples in each regression, X and Y are mean values of drainage basin area and channel width respectively thus; a common = 0.594 - (0.238 x -1.179) = 0.8746 therefore the common hillslope scaling relation, ignoring backtransfer bias is given by; ^common y = 7.492 x 0.238 74 4.1.2 Colluvial and Alluvial Process Domains Channel reaches surveyed within the colluvial and alluvial process domains cover a smaller range of spatial scales and are fewer in number than within the hillslope process domain. That fewer channels were surveyed at the larger scales is in keeping with the frequency of different sized channels suggested by Horton's bifurcation ratio (1945). That the channels cover a narrow range of spatial scale is in part due to the gross morphology of the area and it part to the upper size limit imposed by the drainage area of the main trunk valley. It is apparent from figure 9 that there is considerable scatter around the global trend at the colluvial scale. Nevertheless, the spread is smaller than that found at the hillslope scale i f all the hillslope classes are considered as one group. The alluvial process domain described in Chapter one is poorly represented in the study. Only two links are considered alluvial on the basis of their position in the hierarchy of the hillslope valley system: Capilano River and East Cap Creek. Amongst these two channels only one reach was considered purely alluvial. A l l other reaches are best described as being semi alluvial: while the bulk of the bed material is alluvial, colluvial clasts are still present in the bed and contribute to the structure and morphology of the channel. On this basis the colluvial and alluvial reaches are amalgamated to a single class. 4.1.2.1 Identifying reach classes Table 5 displays the power law relations for the reach classes. The power laws describing colluvial deposition and alluvial classes were not significant at the a = 0.05 level. P-values for b were 0.233 and 0.786 respectively. At the hillslope scale the depositional reach class was also insignificant. Recalculation of the relation for the incised channels to include the depositional reaches resulted in a 75 reduction in the amount of variance explained by the scaling relation from 0.933 to 0.897. Following the same procedure at the colluvial scale results, however, in a larger drop in the portion of the variance accounted for by the relation; from 0.641 to 0.392. Though the amalgamated relation is still significant at a = 0.05, the weakness of the relation will undermine any statement made regarding the magnitude of scaling exponents as well as add uncertainty to comparisons of scaling behaviour between process domains. The scaling of the channel gradients within the colluvial deposition class indicates that several reaches depart from the overall trend depicted in figure 11. Three of theses reaches, Hesketh Main - lower, Hesketh Main - mid and Healmond lower, are located where the colluvial channel crosses the alluvial plain of the main trunk stream, the Capilano River. These reaches form a separate population from the rest of the class and perhaps could have been investigated as another class of channel if they had been sufficiently represented. Their width is influenced by reduction in gradient and by reduction in confinement, as generally colluvial channels are constrained to some degree by valley walls or colluvial deposits from low order streams. Hesketh Main - mid is influenced by inputs of sediment from a tributary channel which drains an area of chronic sediment production; a steep bedrock area with abundant colluvial material. The tributary channel has deposited an extensive sheet of coarse material. The alluvial reaches of the Capilano River, labeled 5 in figure 11, also depart from the gradient scaling trend. Capilano mid is a distinct reach with a sand bed, a narrow single thread channel and relatively cohesive banks, while Capilano upper and lower are more typical gravel bed reaches. The upper reach is aggrading due to large inputs of coarse sediment from Hesketh Creek. 76 100 -a t-i • Unincised A Incised-transport • Incised - deposition + Incised -recent event — Incised — rock control x Colluvial transport o Colluvial deposition • All Alluvial 5 • 0. 1 0.1 1 10 100 Drainage Area (km2) Figure 11. Scaling behaviour of channel gradients at the alluvial and colluvial scales. Reaches identified by number: 1 = Hesketh Main - lower, 2 = Healmond - lower, 3 = Hanover - mid, 4 = Hesketh Main - mid and 5 = all Capilano river reaches To preserve a homogenous population at the colluvial scale reaches labeled 1 to 5 in figure 11 shall be removed. The remaining alluvial reaches from East Cap Creek are amalgamated with the colluvial transport class because they do not display distinct alluvial morphology, the influence of colluvial material being visible, and because three reaches is insufficient for useful statistical analysis 4.1.2.2 Final scaling relations A l l data were log transformed to improve the homogeneity of variances. Simple linear regressions were performed on the log transformed data. Thus far all relations have been quoted in log terms. While the exponent, b, remains unchanged the coefficient, a, must be back calculated to provide scaling relations in the form: 77 Simple back calculation, taking the antilog of a, imparts a bias to the data (Smillie and Koch, 1984). The simple back fitted relation will estimate the median response of the dependent variable, rather than the mean response (Miller, 1984). The linear model for regression analysis includes an error term, e, giving; log y = log a + log x b + e Back transformation gives y = ax b10 6 Smillie and Koch (1984) propose a method for estimating 10G which is used to back calculate all final scaling relations; E(10 6 )=10 z 2 where cry = the variance of y and R is the coefficient of determination for the regression. Table 10 displays the final scaling relations. 78 Table 10 Final scaling relations Reach Class n R 2 Standard Error log a s2y z corrected a b Unincised 12 0.808 0.128 0.615 0.077 0.007 4.189 0.256 Incised •22 0.873 0.081 1.356 0.039 0.002 22.851 0.235 Incised - recent event 6 0.881 0.076 0.931 0.049 0.003 8.591 0.206 Colluvial 13 0.583 0.154 0.770 0.052 0.011 6.037 0.487 Common hillslope relation 40 0.789 0.232 0.875 0.247 0.026 7.963 0.283 4.1.2.3 Comparisons between process domains Comparison of the scaling behaviour of channel widths between process domains is accomplished by the same method as the comparison within the hillslope process domain. Since the hillslope process domain is characterised by three relations the common relation is used. The hypotheses to test become; H0 • b hillslope common ~ b colluvial HA • b hillslope common ^ b colluvial Table 11 Terms for calculation of the F statistic to compare the slopes between process domains. Reach class I JC 2 I j 2 SSTes dfres Common hillslope regression 30.7569 7.3273 2.0701 0.3245 36 Colluvial regression 1.5348 0.7472 0.6244 0.2606 11 Pooled regression 0.5852 49 Common regression 32.2917 8.0744 2.6945 0.6755 50 79 0.6755-0.5852 F = = 7 5647 0.5852 49 Since Fo.os (2,49)« 3.2 HQ is rejected. In other words there is a significant difference between the slopes of the scaling relations between the hillslope and colluvial process domains. 4.1.2.4 Depositional scaling The observation that depositional reaches plotted as a distinct group in figure 11 raised the question of whether there was any consistency in their area-width scaling. To this end the aggrading reaches from the hillslope, colluvial process and proposed alluvial domains were amalgamated. Simple linear regression on the log transformed data reveals a statistically significant relation at a =0.05, which is illustrated in figure 12. The magnitude of the exponent is similar to the values of the hillslope process domain, which range from 0.206 to 0.256, and distinctly different from the colluvial process domain at 0.487. While the relation is statistically significant, aside from the cluster of points at drainage areas of approximately 5 km 2, the sparseness of the data undermines any conclusion that may be drawn. Nevertheless, the data suggest that deposition acts as a scale invariant process over the three orders of magnitude of spatial scale observed here. 80 100 0.1 1 10 100 Basin Area (km2) Figure 12 Scaling behaviour of aggrading reaches 81 4.2 Scaling Behaviour of Channel Gradients 4.2.1 Overview of Analyses Channel gradient, or the gradient imposed by hillslopes or valleys, is one of the forcing functions behind channel morphology. By comparison, channel width can be seen as a response variable. Consequently, the scaling behaviour of channel gradients can be used to inform the behaviour observed in the investigation of channel widths. For example, the scaling behaviour of the channel gradients assisted in the identification of the reach classes within the colluvial process domain. It is apparent that the channel gradient scaling exhibits compound allometry, see figure 10. The scale at which the inflection occurs will be used to test the validity of the empirical model of process domains, as well as to interpret the character of the geomorphic processes at work 4.2.2 Analysis of Residuals In order to identify the drainage basin area at which the inflexion occurs a linear function was fitted to the log transformed gradient data. The depositional reaches excluded from the colluvial reach class were also excluded here. Figure 13 displays the pattern of the residuals around the function log y = log 1.331 -0.240 log x. The inflexion point indicated on the graph was determined by eye. The inflexion point occurs at log -1.25, or 0.06 km 2. The interpretation of the compound allometry and the reasons behind the shift in scaling are discussed in Chapter Five. In terms of the empirical model the inflexion point is straddled by the transition between the dominance of incised and unincised reaches with both groups represented on either side of the inflexion, see figure 10. 82 Figure 13. Distribution of gradient-area residuals around the function logy = log 1.331 - 0.240 logx 4.3 Summary of Analyses 1. Slopes were compared within the hillslope process domain. No difference was found and a common slope was defined. 2. Intercepts were compared within the hillslope process domain. Three significantly different domains were identified 3. Gradient-area scaling identified outliers which when removed from the analysis strengthened relations in the colluvial process domain 4. Slopes were compared between the hillslope and colluvial process domains. Scaling behaviour was found to be specific to each process domain. 83 Chapter Five: Discussion 5.0 Introduction The fundamental finding of this study is that process domains can be delineated on the basis of system scale. The evidence for this conclusion is provided by the behaviour of the exponent and coefficient of power law scaling relations between drainage basin area and channel widths and gradients. The conceptual model put forward in Chapter One focused on the shift from the dominance of mass wasting processes in small channels draining steep valley side walls, to the dominance of deposition and fluvial transport at the colluvial and alluvial scales. The distinction between the colluvial and alluvial process domains lay in the degree of decoupling from hillslope processes. Alluvial channels are decoupled to the point that channel morphology is unconstrained by immobile clasts, whereas colluvial channels are impacted by the deposition of mass wasting materials which are beyond the competence of all but extreme flows or further mass wasting events. The postulated alluvial process domain was not detected in this study. However, the classification of channel reaches in accordance with the conceptual model demonstrated scaling behaviour which is significantly different between the hillslope and colluvial process domains as well as being different from conventionally accepted alluvial scaling. 5.1 Scaling Behaviour of Channel Widths The scaling of channel widths can be examined by considering both the exponent, b, and the coefficient, a, in the relation^ = axb, where y is channel width and x is drainage basin area. 84 Considering first the pooled hillslope relation; we can see from figure 20 that the scaling behaviour of channel widths exhibits compound allometry. There is a shift in 6-values from 0.28 to 0.49 between the hillslope and colluvial process domains, see table 10. The conceptual model postulated a break in scaling behaviour at this scale. The break marked the transition between mass wasting dominated channels and channels dominated by fluvial processes, modified by inputs of coarse material. The negative allometry exhibited by hillslope channels likely reflects the controlling influence of steep gradients as well as strength of boundary materials The value of b - 0.49 is larger than the theoretical value of b = 0.4 for colluvial channels (Kellerhals,1969). Relations for the colluvial domain were less clearly defined than those for hillslope channels. In part this may be due to the smaller sample size and the smaller range of spatial scales covered. It is also apparent that there is considerable variability at this scale part of which is introduced by the deposition of hillslope materials. Reduction in confinement and in the influence of gradient also means that there is greater latitude for variability. The disparity in the values may be attributed to the fact that Kellerhals assumed an immobile channel boundary in his dimensional analysis. The larger channels, such as East Cap Creek, are semi-alluvial, therefore a significant portion of the bed material is of a calibre that is within the competence of relatively frequent flows. The number of immobile clasts is small. While the theoretical b-values for colluvial channels do not agree precisely with the values obtained in this study, the change in scaling behaviour between hillslope and colluvial domains suggests that there is indeed a shift in the dominant geomorphic process. Channels in the hillslope domain above the areal threshold of channel maintenance for incised channels are governed by mass wasting while channels in the colluvial process domain are governed by fluvial processes 85 O O r-l •—1 © 2 o (ui) inpiAv puuBq3 ireaj^ 5.1.1 Process Variability within the Hillslope Domain While the common hillslope regression was used to compare scaling between domains, Chapter four established evidence that there is distinct variability in scaling behaviour within the hillslope process domain. Figure 14 illustrates the scaling behaviour of the channel classes that emerged as statistically distinct at the hillslope scale. Namely, unincised channels, incised channel and incised channels recently impacted by mass wasting. These three groups display no significant difference in their b values, but significantly different a values. The groups plot as three parallel lines with visibly coherent spread and distinct offsets. Neither the unincised or the incised recent event classes were predicted by the conceptual model, but emerged from field observation and analysis of the data. The characteristics of these three channel classes were described in section 3.2.2.1, but can be summarized here as follows. Unincised channels were found at the upper extremes of the channel network, although they were not always present. They are very small channels that are ephemeral and often become discontinuous. Their incision is limited to organic or weathered soil horizons and the channel bed often consists of roots. The surrounding hillslopes are planar hence there is no apparent coupling between hillslope and channel. Incised channels are commonly referred to as gullies in the region of the study. They maintain v-notch or u-shaped profiles and are incised into either surficial materials (till or colluvium) or into bedrock. Surrounding hillslopes often converge on the channel resulting in a coupled channel, particularly at mid-slope. Channel materials are bouldery and channel banks are often immobile due to bedrock or large clasts. The incised recent event class is a sub group of incised channels which displayed evidence of recent or chronic sediment transport. 87 On several occasions the transition between unincised and incised channels within a stream link is marked by a clearly defined head scarp. Below the headscarp the channel is incised as a result of mass wasting whereas above the headscarp fluvial processes dominate and mass wasting has not occurred, or occurred so long ago that channel recovery has been complete. The intercept a in the power lawj; = axb can be interpreted as a regional factor encompassing variations in materials or as a climatic factor Day (1969). The regional extent of this study precludes significant variations in either climate or materials. Since the morphology of the three reach classes reflect the influence of sediment transport the variation in a can be interpreted as a bulk transfer parameter. Recall that dimensional analysis identified the intercept of the scaling relation as representing the influence of gravitational acceleration, material length and sediment production. Of these factors sediment production likely increases progressively between the unincised, incised and incised recent event reach classes. Thus the three values of a reflect the mass fluxes of material. The incremental change in a between the incised and unincised channels can be attributed to the onset of mass wasting, if we assume that failures are triggered by high pore water pressure (Dunne, 1980; Montgomery and Dietrich, 1989). Unincised channels experience no mass wasting. Here, the small drainage area cannot concentrate sufficient water in the soil profile to raise pore pressures to the threshold of instability. However, as drainage area increases the volume of water that can converge in the soil profile also increases to the point where the threshold of instability is exceeded and failure occurs resulting in an incised channel. Figure 14 shows that the transition from unincised to incised channels does not occur at a discrete spatial scale. Rather, there is a transition between the two types suggesting other factors, such as soil hydraulic properties, subsurface flow paths or gradient are important. 88 Considering the minimum drainage area for the unincised and incised channels, <A>unincised and <A>incised respectively, we can see that these values represent geomorphic thresholds that mark the transition between landforms. The transition between unchanneled hillslopes and channeled hillslopes is marked by <A>unjncised, while the transition between unincised and incised channel is marked by <A>jnCised-These thresholds are analogous to the constant of channel maintenance, C (Horton, 1945). Thus, C = < A > 0 - 5 Cunincised = 0.0001 0 5 km 2= 0.01 km Cincised = 0.0034 0 5 k m 2 = 0.058 km A finding of this study is that the constant of channel maintenance is specific to the process by which the channel is maintained. Horton (1945) considered the process of channelization to result from erosion by overland flow under the control of infiltration capacity. This study has conducted no measurements to refute that idea. However, at the extremes of the channel network unincised channels often were observed as discontinuous segments. These segments had the appearance of continuous subsurface conduits that were revealed by the collapse and/or entrainment of overlying material. Furthermore, no evidence of overland flow, in the form of rills or disturbance of the surface organic layer, was found upslope of unincised channels. This suggests that sub-surface flow concentration is a more accurate model for the initiation of unincised channels. The incised recent event group is a subclass of incised channels. In the field these channels were distinguished by their size as well as evidence of recent mass wasting, such as the removal of vegetation and recent deposits of coarse clastic material. The upper extremities of these channels were inaccessible. Many were still clogged with 89 avalanche deposits, in some active ravel involving large clasts was taking place and some were simply too steep to survey without roping in. As a result the threshold C incised-recent event cannot be computed or compared with the thresholds for unincised and incised channels. Using the available evidence, aerial photographs, topographic maps and terrain classification (GVRD, 1997), it is apparent that the drainage basins of the recent event channels are characterised by the presence of steep bedrock exposures acting as sources of colluvium. From studies of similar channels in the region (Hungr and Morgan, 1984; Bovis and Jakob, 1999) we can postulate that, while pore pressures or freeze-thaw processes in rock crevices may play a role in triggering mass movements, the magnitude and frequency of events is controlled by the rate of supply. While the character of the channels observed in the field may reflect recent events, the morphology of these channels is likely a result of a higher failure frequency and/or a potential for large events due to an abundant supply of coarse clastic material. It has been stated that a shift in the exponent of the scaling relation, b, should be interpreted as a shift in the dominant geomorphic process. At the hillslope scale an important shift in the process governing channel morphology was detected in the coefficient, a, rather than the exponent. A possible explanation for the consistency of b throughout the process domain may be the dominance of the downslope force in response to the steep gradients. Gradients at the hillslope scale range from 15 to 75%. The magnitude of any force directed towards the channel bank, that could accomplish modification of channel width, is small compared to the downslope force exerted by gravity on any particle in motion. This argument prompts us to examine the scaling of channel gradients In summary, the scaling of channel widths in the hillslope process domain has lead to modification of the proposed conceptual model. While the hillslope and colluvial domains exhibit distinct scaling behaviour reflective of the shift from hillslope to fluvial processes, an additional process domain exists upstream of mass wasting dominated 90 hillslope domains, namely, a zone of fluvially governed channels with little or no coupling to adjacent hillslopes. These results can be compared with other studies of process domains, notably Montgomery and Foufoula-Georgiou (1993) and Montgomery (2001), and with studies that have collected data from proximal regions without specific focus on process domains. First, however, the behaviour of channel gradients must be considered. 5.2 Scaling behaviour of channel gradients 5.2.1 Introduction The scaling behaviour of channel gradients, figure 15a displays striking compound allometry. From analysis of the residuals we saw that the inflection point occurs at a drainage area of 0.06 km 2. This shift in scaling behaviour occurs during the transition from unincised to incised channels. Therefore, at the inflection point there is a shift in geomorphic process domain. At spatial scales less than 0.06 km 2 channels are controlled by fluvial processes, while at greater scales mass wasting processes dominate. The gradients of the steepest channels approximate 35°, which is the angle of repose for unconsolidated material. At scales greater 0.6 km 2 there is a negative relation between area and gradient. From figure 15a it is evident that there is no change in area-gradient scaling at the transition from the hillslope to the colluvial process domain, at circa 5 km. The continuous gradient-area relation may reflect the dominance of imposed gradients throughout the hillslope and colluvial process domains. The colluvial class of reaches was modified by the exclusion of several aggrading reaches which plotted beneath the general area-gradient trend. Similarly, a group of depositional 91 reaches from the hillslope scale also plotted beneath the general trend. The amalgamation of the depositional reaches from both process domains resulted in a single significant scaling relation between basin area and channel width. While the distribution of the data precludes any conclusions, an interesting issue is raised. Namely, is the process of deposition scale-invariant? The alluvial channels also diverge from the trend of area-gradient scaling (see figure 8). The gradient of the Capilano River reaches plot approximately an order of magnitude beneath the general trend. A similar pattern is observed by Montgomery (2001) in data from two separate regions. Although alluvial channels were not sufficiently well represented in this study to characterize their scaling behaviour, the anomalous result is of interest. The step change in the gradient scaling of alluvial channels may reflect a change in control. At the scale of alluvial channels the channel gradient may be adjusted to fluxes of water and sediment rather than controlled by landscape-imposed gradients. Had more data been collected from alluvial channels the boundary between colluvial and alluvial process domains may have been defined by this discontinuity in the gradient scaling relation. Figures 15b and 15c illustrate the results of two other studies of process domains; Montgomery and Foufoula-Georgiou's (1993) and Montgomery's (2001). Comparison with the results of this study, figure 15 a, reveal a similar pattern. In all three studies there is an inflection point at small scale. Beyond the inflection point the area-gradient relation is negative in all cases. At drainage areas below the scale of the inflection point the relation is positive in figure 15b and 15c but is zero in figure 15a. The most striking difference between the results is the spatial scale at which the inflexion point occurs. The inflection point is interpreted as representing the onset of channels maintained by mass wasting in all three studies, and is interpreted here as being equivalent to the second power of the constant of channel maintenance for mass wasting dominated channels. The spatial scale at which the inflection occurs is between two and three orders of magnitude larger in the Capilano Valley. While the difference in the study methods may explain 92 some of the disparity, the results of Montgomery and Foufoula-Georgiou (1993) are supported by field observations. A more likely explanation is differences in landscape history and the strength of surficial materials and bedrock. Montgomery and Foufoula-Georgiou's (1993) results represent an amalgamation of data sets from Oregon, California and New York State, while Montgomery (2001) uses data from the Oregon Coast Range and the Olympic Mountains. Figure 15c illustrates the results from the Oregon Coast Range which are equivalent to those from the Olympic Mountains. Climate, bedrock geology and hydrology vary between these regions. The less resistant the environment, the faster the growth of the drainage network. Therefore, over a given period of time, the more extensive the network would become, all other things being equal. The more extensive the drainage network the smaller the constant of channel maintenance. In a moister climate the same effect can be achieved since more work can be accomplished by erosion. Part of the difference the between the scale of the inflections may be due to regional physiographic differences. However, there is a smaller difference in the value of the constant of channel maintenance between Montgomery and Foufoula-Georgiou (1993) and Montgomery (2001) than there is between these two studies and value found in the Capilano valley. Since there are physiographic differences between the regions studied by Montgomery and Foufoula-Georgiou (1993) and Montgomery (2001) other factors might explain the large discrepancy with the Capilano results. The southern Coast Mountains were glacially overridden in the Fraser glaciation (Lian and Hickin, 1993) and have had only 10 000 years to develop the current drainage network. A l l other regions, with the exception of the Schoharie Creek data set (Montgomery and Foufoula-Georgiou, 1993), lie beyond the limit of the most recent glaciation. As a consequence, processes of erosion have acted over longer time spans resulting in a more highly dissected landscape and an inflection point at smaller scale than in recently perturbed landscapes. 93 This argument suggests that while the pattern of gradient scaling behaviour remains consistent between landscapes the length scales of geomorphic thresholds depend on local factors. At smaller scales than the inflection point only the Capilano results suggest the presence of unincised channels. The resolution of the other studies, the lack of field measurements and the focus on hillslope gradients precludes the detection of features at this small scale. In both figures 15b and 15c the area-gradient relation is positive at small scale while figure 15a displays a zero relation with some outliers. The differences in gradient-area relations below the threshold of channel maintenance for channels maintained by mass wasting reflect slope morphology. Since gradient increases with distance from the ridgeline, the upper slopes must be convex. A similar pattern is observed amongst the reaches from the most headward sections of Viberg Creek. Here the summit area is distinctly convex as a result of glacial erosion. These reaches show a positive area-gradient relation in figure 15a. While the terminology used to describe the process domains differs, as does the scales of the transitions, there is basic agreement between this study and those of Montgomery and Foufoula-Georgiou (1993) and Montgomery (2001). The hillslope domains in figures 15b and 15c likely correspond to the unincised channels observed in the Capilano Valley. The inflection point is universally interpreted as representing the onset of a process domain where hillslope/channel processes are dominated by mass wasting. A l l three studies agree that at some scale the dominance of mass wasting is superceded by the dominance of fluvial processes. The scale at which this occurs and the transition types between mass wasting and fluvial vary. Montgomery (2001) shows a compound relation and ascribes processes to the delineated domains based on Montgomery and Buffington (1997). The observation that alluvial channels plot as a separate group is also made by Montgomery (2001) in both the Olympic Mountains and the Oregon Coast Range, although no hypothesis is offered to account for this behaviour. 94 15a o.i c •5 43 3 o.oi^ c u 0.001 O O O unincised channels 't"»"t<irm'- 1 < ' • ' i w i w ' i t - n n m r"«"r B incised channels H H »"» IMUH » ^ Unincised O Incised - recent event A Incised * Colluvial colluvial channels 0.00001 0.0001 0.001 0.01 0.1 1 Drainage Area (km2) 10 100 1000 10000 15c a o •3 SB C L o hillslopes valleyheads colluvial o.oi 4 o.ooi. 0.00001 0.0001 0.001 ' 0.1 1 Drainage Area (km2) Figure 15a. Gradient-area scaling Capilano Valley. Figure 15b. Process domains after Montgomery and Foufoula-Geourgio, 1993. Data from three non-glaciated areas. Figure 15c. Process domains after Montgomery, 2001. Data are from Oregon Coast Range. 95 5.2.2 Comparison with regional studies Figure 16 illustrates the area-gradient relations of Day (1969) from the southern Coast Mountains and Hogan et al. (1997) from the Queen Charlotte Islands in comparison with the results of this study. While Day (1969) and Hogan et al. (1997) do not address process domains their results can extend the generality of this study. Field methods differ between the studies. Both Day (1969) and Hogan et al. (1997) used a surveyor's level exclusively to measure channel gradients while clinometers were used in all but the largest channels of the Capilano Valley. It also worth noting that interpretations of channel dimensions are not without operator bias. Hogan et al, (1997) employed methods outlined in B.C Ministry of Forests (1996) which also guided the methods used in this study. The inflection marking the threshold of channels controlled by mass wasting is not seen in either of the regional studies as they did not cover small enough channels. Hogan et al. (1997) find a negative relation in all channels that runs approximately parallel to the Capilano relation. For a given drainage area channel gradients are less steep in the Queen Charlotte Islands. This may reflect the weaker bedrock geology which cannot sustain such steep slopes or the fact that this area remained ice-free during the Fraser Glaciation. Day's (1969) coastal results are from a wider area than that covered in this study. Nonetheless, part of his study area is very similar to conditions in the Capilano Valley. The lack of relation between area and gradient led him to conclude that channel gradients are independent of channel processes and are imposed by landscape history. The larger channels in this data set plot in the range of the Capilano channels. The data sets diverge at drainage areas of circa 5 km 2. Channels at smaller scales exhibit lesser gradients in Day's study. Examination of photographs from the paper and topographic maps 96 1.00 c 0.10 2 •3 « f-C (50 13 c c g 0.01 0.00 x x J $ £ * • Capilano X Day (1969) O Hogan etal. (1997) O A i ' ' in 1—i i 111111 0.0001 0.001 0.01 0.1 1 Basin Area (km2) 10 100 1000 Figure 16. Comparison with Day (1969), data collected from Southern Coast Mountains and Hogan et al. (1997) data from Queen Charlotte Islands. indicate that the channels selected by Day are not typical of those draining the valley side walls of glacially scoured valleys. This suggests that the conceptual model applies specifically to mountainous topography and is perhaps not directly transferable to other landscapes. While the small scale is not represented in either Day (1969) or Hogan et al (1997), we can see from figure 17 and table 12 that the exponent in Day's study is similar to the colluvial relation of the Capilano Valley while the coefficient is considerably lower. The data of Hogan et al (1997) exhibit a relation that approximates an amalgamated relation for all the Capilano channels. 97 Table 12. Scaling relations of regional studies Source a b R 2 Hogan etal. (1997) 9.27 0.33 0.519 Day (1969) 3.6 0.52 0.973 Since Day's data are collected from a similar region the differences likely stem from the nature of the channels selected and the methodology employed. Day (1969) did not select his reaches with reference to dominant processes. His smallest channel, Brockton Creek, may not have experienced mass wasting. Such a stream may have been classified as unincised in this study but the lack of other small channels precludes exploration of other groupings. 5.2.3 Summary In the hillslope process domain the scaling behaviour of channel widths is characterised by order. The expression of channel morphology in response to controlling factors conforms to three distinct types. At the colluvial scale patterns are less orderly. Recall that, prior to the removal of aggrading reaches that were outliers in gradient-area space, width relations were not significant at a = 0.05. On steep slopes, the range of responses (forms) is constrained by physical confinement (as a result of incision) and the dominance of the downslope force vector. Removal of these constraints at the onset of the colluvial scale, where steep hillslope channels meet valley bottoms, results in greater variability. 98 The scaling behaviour of channel widths also displays order. Relations are distinct and distinctly different between unincised and incised channels. Aside from the variability introduced by aggrading reaches the scaling behaviour is consistent from the onset of incised channels throughout the colluvial domain. This consistency across three orders of magnitude and two process domains suggests that gradients are imposed upon the stream. It appears that there is a discontinuity in the gradient scaling at what was thought to be the onset of the alluvial process domain. This pattern has been observed by Montgomery (2001) though not commented upon. This discontinuity may indicate the point at which channel gradients are adjusted to flows of water and sediment and gradients are no longer imposed. To detect the alluvial process domain, drainage area must be sufficiently large that the main trunk stream is buffered from hillslope inputs both from tributaries and adjacent hillslopes. 99 Chapter Six: Conclusions 6.0 Summary of findings 1. The hillslope process domain yielded three distinct channel classes not predicted by the conceptual model; unincised channels , incised channels and incised channels recently impacted by mass wasting events. 2. The scaling behaviour of the three groups at the hillslope scale was compared. No difference was found between b values, so a common slope was calculated with b = 0.28. 3. Significant differences were found between a-values; 4.1, 8.7 and 22.7 for unincised, incised and incised recent event respectively. This progressive increase reflects increases in sediment transport. 4. Constants of channel maintenance were found to be specific to the process governing channel evolution. For unincised channels CUnincised = 0.01 km and for incised Qncised ~ 0.06 km. 5. In the colluvial process domain the scaling relations for channel were weak due to considerable variability and small sample size. Gradient-area scaling was used to identify depositional reaches as outliers resulting in a significant relation between area and channel width. 6. For colluvial channels b = 0.49 which does not agree closely with the value b = 0.4 obtained by Kellerhals (1969) from dimensional analysis. 7. The b values from the hillslope and colluvial process domains were compared and found to be significantly different. The scaling behaviour of channel widths exhibits compound allometry. 8. Patterns of both channel width and channel gradient scaling were recognized in other studies, albeit modified by local conditions. 101 6.1 Process domains This study has shown that process domains in mountainous areas can be delineated using scale as a defining parameter. Evidence for this is found in the compound allometry exhibited by relations between drainage area and both channel width and channel gradient. The conceptual model of process domains correctly predicted the shift from the dominance of mass wasting on hillslopes to the dominance of fluvial processes with modification by hillslope inputs in small valleys. The alluvial process domain was not detected in this study. A process domain not predicted by the conceptual model was detected in the smallest headward streams. Here channels are maintained by fluvial processes rather than mass wasting. The small drainage area does not accumulate sufficient run off to generate high soil pore pressure and thereby initiate failure. Other studies of process domains that measured hillslope gradients from digital elevation data did not detect this zone, perhaps because, at present, the observational scale provided by digital elevation data is not commensurate with the scale of the channels 6.2 Theoretical predictions The factors thought to control the morphology of channels maintained by mass wasting were analysed by dimensional analysis. Field measurement identified a common scaling exponent of b = 0.28. The negative allometry may reflect constraints on channel width imposed by immobile boundaries. A theoretical value for colluvial channels developed by Kellerhals (1969), b = 0.4, was compared to the value determined from field measurements, b = 0.49. Here, the agreement was less convincing. The disparity may be due to the fact that Kellerhals' 102 analysis assumed an immobile channel boundary. In this study, a significant portion of boundary materials in the larger channels are within the competence of relatively frequent floods. Figure 18. Process domains in headwater streams Figure 18 illustrates the arrangement of the process domains determined by this study. Area 1 is the domain of unincised channels upslope of the constant of channel maintenance for incised channels. Area 2 is the source area for channels subjected to recent or frequent events. The scaling behaviour for this domain has not been defined. At "A" incised channels are found while at "B" oversized incised channels are found. Area 3 represents the colluvial process domain. 103 6.3 Geomorphic thresholds This study has defined two geomorphic thresholds which mark the transition between landforms. The square root of the threshold drainage area at which unincised channels are initiated represents the constant of channel maintenance for this channel type. Likewise, a threshold is defined for the maintenance of channels by mass wasting. The fact that the magnitude of the constant of channel maintenance depends on the process by which the channel is maintained is a unique finding of this study. The constant of channel maintenance for mass wasting channels can be compared to studies from other regions. If methodological discrepancies between studies can be ignored it appears that the value of the constant is smaller in landscapes that have not undergone recent glaciation. 6.4 Further work This topic would benefit from a thorough theoretical analysis of conditions in colluvial streams. In general the colluvial scale received insufficient sampling effort which could be rectified by further study. Focus on this type of stream might also address the question of the scale invariance of aggrading reaches. A similar, field based study in another physiographic region with a different geomorphic history might serve to establish whether the unincised channels are unique to conditions in this study area. Some of the error involved in mapping small basins could be avoided if a region with no forest cover were selected and GPS positioning used to map basins and geolocate the channel surveys. 104 7.0 References Acres International. 1997. 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Zar, J.H. 1984. Biostatistical analysis. 2nd ed. Prentice Hall, New Jersey 112 Appendix A: Surveys of channel width and channel gradient The following graphs illustrate the results of the stream surveys. Reach subdivisions are identified within each link. Each data point represents a measurement of width or gradient at a discrete distance along the channel. 0.9 -i 0.8 -0.7 -0.6 -¥ 0.5 0.4 0.3 0.2 -0.1 o -Hesketh I A • • « — 4 6 8 Distance (m) 10 1 0.8 0.6 u 0.4 5 3 0.2 0 12 Width (m) — • — Slope 0.6 o.5 ^ 0.4 •S 0.3 0.2 0.1 0 E, -a Hesketh IB 4 6 8 Distance (m) 10 1 0.8 0.6 0.4 0.2 0 D. O 12 Width (m) • Slope 14 -12 -10 f—s l l £ 8 -•S -4 -2 -0 Hesketh I C 20 40 60 Distance (m) 80 T 1 0.8 0.6 u a _o 0.4 M 0.2 0 100 Width (m) — • — Slope 113 8 7 6 4 ? 5 5 3 2 1 0 Hesketh 2 A Upper and Lower ©G5 . 0 1 0.8 0.6 0.4 0.2 0 - - - - - - Width Lower(m) — A — - Width upper (m) — • — - Slope Lower - - Q - - • Slope upper (nVm) 100 200 300 400 Distance (m) 114 Hesketh 2B Upper, Mid and Lower 100 200 300 Distance (m) 400 1 0.8 0.6 <u o. o 0.4 K + 0.2 0 500 Width lower (m) -A—Width mid (m) - * — Width upper (m)| - • — Slope Lower - -O—Slope mid — • - — Slope upper Hesketh Main Lower, Mid, Upper-mid and Upper 35 30 ^ 25 ^ 20 I 15 10 5 H 0 ®OGGGQ 0 200 DistaTTct (m) 600 1 0.8 0.6 0 a. o 0.4 5 5 - f 0.2 0 800 Width lower -Width mid — * — Width upper-mid —B—Width upper — • — Slope lower - -O—Slope mid — • — Slope uppermid — 0 — Slope upper 115 2 i 1.5 43 1 0.5 1 Viberg I A 5 10 Distance (m) 15 1 0.8 0.6 (u Q. 0.4 ™ 0.2 0 20 Width (m) - • — Slope 1.8 1.6 1.4 g 1.2 1 0.8 0.6 0.4 0.2 0 Viberg IB 10 15 Distance (m) 1 0.8 0.6 <u D. O + 0.4 5 5 0.2 0 20 Width (m) - • — Slope Viberg 1C 10 20 30 40 Distance (m) 50 J 1 - 0.8 - 0.6 lope - 0.4 on -- 0.2 - 0 60 -•-•-Width (m)| - • — Slope 116 1.4 -1.2 -1 I I th(m 0.8 Widl 0.6 -0.4 -0.2 -0 V • i . Viberg I D 5 10 15 Distance (m) 1 0.8 - f 0.6 „ C L O 0.4 S 0.2 0 20 Width - Current (m) - Slope Healmond Creek Lower, Mid & Upper 500 1000 1500 Distance ( m ) 1 0.8 0.6 » o 0.4 5 5 0.2 0 2000 - • - - - Width lower - A — Width mid - * — width upper H i — Slope lower - - O — Slope mid — • — Slope upper 1 1 7 4.5 i 4 3.5 -\ ? 3 iH 2 * 1.5 1 0.5 0 Hollyburn IA t 5 10 20 30 Distance (m) 40 J 1 - 0.8 - 0.6 1 - 0.4 - 0.2 - 0 50 • - -Width — Slope 118 20 15 Rapid Creek Upper S -a •B 10 o • • • 350 450 550 650 750 850 Distance (m) 1 0.8 + 0.6 • „ 0.4 5 5 0.2 0 950 Width (m) •Slope Lempke Creek Lower, Mid, Upper-mid and Upper 200 400 600 Distance (m) 800 1 0.8 0.6 » 8-0.4 5o 0.2 0 1000 . . . 4 — Width lower — A — Width mid — * Width upper — • — Slope lower — - O — Slope mid — • Slope upper 119 Sister Creek 1-5 20 10 0 1 0.8 + 0.6 „ & 0.4 M 0.2 0 500 1000 1500 2000 2500 3000 Distance (m) Width Sisters 1 - £ — Width Sisters 2 -x— Width Sisters 3 -B— Width Sisters 4 - - - A- - - Width Sisters 5 — • — Slope Sisters 5 — • — Slope Sisters 1 - -O- - Slope Sisters 2 — • — Slope Sisters 3, — 0 — - Slope Sisters 4 Hesketh Main Lower, Mid, Upper-mid and Upper 40 -i 35 -30 -? 25 -•S 20 -Wid 15 <, 10 I . 500 1000 Distance (m) 1 + 0.8 0.6 « o 0.4 K 0.2 0 1500 Width l o w e r -A— Width mid — Width u p p e r H I — S lope l o w e r • O — S lope mid — • — S lope upper 120 Hesketh Main Lower, Mid, Upper-mid and Upper 500 1000 1500 Distance (m) 2000 — • — Width lower —A— Width mid — K — Width upper — • Slope lower _ . Q Slope mid — ^ Slope upper Hesketh Main Lower, Mid, Upper-mid and Upper 100.00 80.00 £ 60.00 j | 40.00 20.00 0.00 1 0.8 0.6 0.4 ' 0.2 500 1000 1500 2000 2500 3000 Distance (m) Width lower - £ — Width mid - * Width upper -Hi— Slope lower - O — Slope mid - • — Slope upper 121 

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