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Bed material texture along gravel bed rivers with confluences Rice, Stephen Philip 1996

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BED MATERIAL TEXTURE ALONG GRAVEL BED RIVERS WITH CONFLUENCES by STEPHEN PHILIP RICE B.A., Oxford University, 1988 M.Sc, University of British Columbia, 1990 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF GRADUATE STUDIES (Department of Geography) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 1996 © Stephen Philip Rice, 1996 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 The University of British Columbia Vancouver, Canada DE-6 (2788) Abstract 11 Changes in bed material texture are examined along two confluent gravel-bed rivers. The work is distinguished from previous field studies by the scope and resolution of the sampling programme. A combination of 400-stone Wolman counts and photographic sampling provide surface grain size information at approximately 50 % of the bars along two 110 km reaches. The data reveal negligible overall fining and complex structure which can be explained only by reference to a large number of tributary inputs, non-alluvial sediment sources and the legacy of Pleistocene glaciation. A series of distinct sedimentary links are demarcated by significant lateral sediment inputs. Categorization of individual samples according to their location within particular sedimentary links significantly reduces unexplained variability. Texture tends to vary systematically within links and reflects the uninterrupted operation of sorting and abrasion processes. This implies that successful application of downstream fining models depends upon isolating significant lateral sediment sources and in turn the intervening sedimentary links. Therefore, guidelines for the a priori identification of significant tributary sources are developed. An empirical discriminant function based on relative basin area and a surrogate measure of distal tributary stream power is particularly successful, although its general applicability cannot be assessed for want of a suitable data set. A corresponding logistic model estimates the probability that a given tributary is associated with a textural discontinuity. Within sedimentary links downstream changes in D50 and D95 (mm) are adequately described by exponential functions, although power and linear functions of distance are equally valid in some cases. Diminution rate does not vary significantly between lithological groups, despite differences in relative abrasivity, and lithological composition is a minor control on diminution rate. An unequivocal statement concerning the relative importance of sorting and abrasion processes is not possible because relative abrasivity is confounded by a lithology-dependent size effect. However, several lines of evidence suggest that sorting is the dominant fining mechanism. Ill Second-order polynomial models describe the profile of individual sedimentary links such that slope is a simple linear function of distance. Channel slope and diminution rate are, in general, positively correlated. However, the prediction of diminution rate using slope is only marginally successful because slope and grain size, for reasons of history and circumstance, may be unadjusted within individual links. The study makes clear that extant models of textural change are inadequate when applied in all but rudimentary field situations. Greater predictive efficacy depends upon a better appreciation of, and ability to accommodate, the multiplicity of sediment sources which characterise real fluvial systems. This belies the need to consider both immanent and configurational attributes if geomorphological investigations and model building are to be applied at landscape scales. Models of contemporary fining processes must be situated within specific sedimentological networks which may not correspond with the hydrological network because sediment supply, unlike water supply, is spatially discontinuous in fluvial landscapes. Identification of the sedimentary network is dependent on careful examination of local geography and history and thereby provides a useful framework for reconciling process modeling and landscape contingency. Table of Contents Abstract List of Tables List of Figures Acknowledgement Dedication CHAPTER 1. Introduction 1.1 Definition of the study 1.2 Previous work 1.2.1 Synopsis 1.2.2 Models of fining by abrasion 1.2.3 Model s of fi ni ng by sorti ng 1.2.4 Models incorporating both processes 1.2.5 Other models of grain size change 1.3 Outline CHAPTER 2. Study Area 2.1 Climate and Hydrology 2.2 Geology and General Physiography 2.3 Quaternary History and Surficial Geology 2.3.1 Sukunka River 2.3.2 Pine River 2.4 Summary CHAPTER 3. Sediment sampling issues and methods 3.1 S am pi i ng Strategy 3.1.1 Spatial coverage 3.1.2 Site Selection 3.1.3 Vertical Sampling 3.2 Wolman sampling 3.2.1 Sample size criteria 3.2.2 Field Procedure 3.2.3 Replicate samples 3.3 Photographic sampling 3.4 Subsurface sampling 3.4.1 Construction of hybrid subsurface samples 3.4.2 Assessment 3.5 Summary CHAPTER 4. Grain size variations and spatial structure 4.1 Analysis of grain size variations 4.1.1 Analysis of variance using Chi-squared statistics 4.1.2 Within-site, between sample variability 4.1.3 Between-site variability 4.2 Spatial structure 4.3 Lateral sediment sources and grain size discontinuities 4.4 Identification of discontinuities and significant lateral sources. V 4.4.1 Distinguishing among causes of between-site variation 76 4.4.2 Significant lateral inputs and sedimentary reaches 81 4.4.3 Sukunka sedimentary reaches 82 4.4.4. Pine sedimentary reaches 88 4.5 Improvement in explanation 94 4.6 Summary 101 CHAPTER 5. A Priori Identification of Significant Lateral Sediment Sources 103 5.1 Primary controls and methodology 104 5.2 Surrogate parameters and discriminatory criteria 106 5.2.1 Determination of parameter values and tributary classification 108 5.2.2 Univariate analysis 112 5.2.3 Bivariate analysis 117 5.2.4 A discriminant function for significant tributaries 120 5.3 Anomalous tributaries 122 5.3.1 Insignificant tributaries misclassified as significant 123 5.3.2 Significant tributaries misclassified as insignificant 132 5.4 An a priori categorisation procedure for tributaries 133 5.4.1 Identification of tributary sources which affect main stem texture 133 5.4.2 Attaching probability statements to predicted classifications. 135 5.4.3 Tributary sources and sedimentary links 138 5.4 Summary and Discussion 141 CHAPTER 6. Grain Size Variations Between Significant Sediment Inputs 144 6.1 The nature of within-link fining 145 6.2 Lithology and rates of diminution 157 6.2.1 Lithology and differences in abrasivity 158 6.2.2 Compressive strength indices and the abrasivity of Pine and Sukunka gravels 160 6.2.3 Within-link diminution rates for lithologic groups 170 6.3 Channel slope and diminution rate 176 6.3.1 Mathematical description of reach profiles 177 6.3.2 Derivation of a general function for reach channel slope and implications for grain size change 184 6.3.3 Rate of change of channel slope and rate of diminution 185 6.4 Summary and Discussion 193 CHAPTER 7. Conclusion 196 BIBLIOGRAPHY 202 Appendix 1. Surficial materials along Pine and Sukunka River valleys (Maps A to J) 212 Appendix 2. Wolman samples 223 Appendix 3. Photographic estimates of D50 and D 9 5 2 3 4 Appendix 4. Notes on statistical methods 236 VI List of Tables Table 4.1. Brown-Forsythe tests of homoscedasticity for Pine and Sukunka Wolman samples. 63 Table 4.2. Within site, between sample variability. Equality of sample means at six replicate sites. 63 Table 4.3. Between-site variability. Equality of site means within each river. 69 Table 4.4. Runs tests for running mean sequences. 69 Table 4.5. Significant, downstream, between-site increases in D50 and D95 along the Sukunka River. 79 Table 4.6. Significant, downstream, between-site increases in D50 and D95 along the Pine River. 80 Table 4.7. Sampling resolution along the Sukunka and Pine study reaches. 96 Table 4.8. Improvement in residual variation following classification of grain size data by sedimentary reaches. 99 Table 5.1. Discriminatory power of absolute and relative tributary basin parameters significant and insignificant tributaries. 116 Table 5.2. Discriminatory power of basin parameters for the tributary fan group. 116 Table 5.3. Discriminatory power of bivariate functions. 121 Table 5.4. Tributaries which are misclassified by bivariate discriminant functions. 124 Table 6.1. Sukunka reaches, exponential and power model statistics for D5o and D95 versus distance downstream. 149 Table 6.2. Pine reaches, exponential and power model statistics for D50 and D95 versus distance downstream. 150 Table 6.3. Exponential model (diminution) coefficients for Pine and Sukunka sedimentary reaches. 154 Table 6.4. Sources of diminution coefficient data used in Figure 6.3. 156 Table 6.5. Analysis of variance of point load strength index Is, by lithology and b-axis size. 168 Table 6.7. Sukunka longitudinal profiles: Performance of functional mathematical models. 181 Table 6.8. Parameters for second-order polynomial models of reach profile. 182 Table A. 1 Wolman samples, summary statistics 224 Table A.2 Photographic samples 234 vn List of Figures Figure 2.1. Location, relief and principle channels of the study area 15 Figure 2.2. Annual flow regime of the lower Sukunka River. 17 Figure 2.3. Simplified bedrock geology of the study area. 20 Figure 3.1. Sample size and percentile standard errors estimated using the bootstrap technique 39 Figure 3.2. Within-site replicate Wolman samples. 41 Figure 3.3. Comparison of relations with D50 for counts derived from photographs. 45 Figure 3.4. Photographic calibration models for D50 and Dgs- 47 Figure 3.5. Surface and subsurface consecutive fraction ratios. 51 Figure 3.6. Subsurface grain size distributions and surface replicate distributions at sites STW 4b and PRD. 53 Figure 3.7. Comparison of surface and subsurface material at PRD. 54 Figure 3.8. Comparison of surface and subsurface material at STW 4b. 55 Figure 4.1. Cumulative grain size curves for the mainstem Wolman samples. 58 Figure 4.2. Skewness and kurtosis coefficients for mainline Wolman samples. 62 Figure 4.3. Stability of replicate mean grain sizes at SBP 4 and SBP 7.5. 67 Figure 4.4. Mean grain size against distance downstream for the Pine and Sukunka rivers. 71 Figure 4.5. Three-point (unweighted) running mean values for the Sukunka and Pine mean grain size sequences. 72 Figure 4.6. Downstream variation of D 5 0 along the Sukunka River. 83 Figure 4.7. Downstream variation of D50 along the Pine River. 89 Figure 4.8. Significant lateral sediment sources and the partition of Pine and Sukunka Rivers into sedimentary reaches. 95 Figure 4.9. Exponential regression models fitted to classified and undifferentiated D50 values. 98 Figure 5.1. Relation between basin area and the two-year flood discharge. 109 Figure 5.2. Frequency distributions of logarithmically transformed parameter values. 113 Figure 5.3. Identification of optimal discriminatory parameter values. 115 Figure 5.4. Bivariate scatter plots for basin area and area-slope product. 118 Figure 5.5. Bivariate scatter plots for basin magnitude and area-slope product. 119 Figure 5.6. Grain size distributions and lithological composition upstream and downstream from the Burnt/Sukunka confluence. 127 Figure 5.7. Grain size distributions and lithological composition upstream and downstream of the Sukunka/Pine confluence. 130 Figure 5.8. Probability that a tributary is a significant sediment source. Logistic models. 139 Figure 5.9. Spacing between consecutive significant and insignificant tributaries. 142 Figure 6.1. Exponential and power models of downstream changes in D50 and D95 within sedimentary reaches. 147 Figure 6.2. Comparison of exponential and power models 152 Figure 6.3. Diminution coefficients (ad) obtained in this and previous experimental and field studies. 155 Figure 6.4. Adams' experimentally determined abrasion coefficients. 159 Figure 6.5. Breakage loads versus minimum cross-sectional area for point load tests. 164 Figure 6.6. Zingg shape classification for point-load test particles 165 Figure 6.7. Distribution of compressive strength indices (Is), for each lithological group. 167 Figure 6.8. Downstream fining of sandstone and blue limestone materials. 172 Figure 6.9. Relation between lithologically undifferentiated diminution rate (D50) and percentage of sandstone. 175 Figure 6.10. Longitudinal profiles for Sukunka study reaches. 180 Vlll Figure 6.11 Comparison of exponential and linear models of downstream D50 and D95 diminution. 186 Figure 6.12 Residuals of linear relations between D50, D95 and distance. 187 Figure 6.13 Inverse relation between rate of change of slope and diminution coefficient. 189 Figure 6.14 Correlation of reach length and diminution coefficient. 191 Figure A.1. Empirical relation between R2 and p2. 238 IX Acknowledgement Primary thanks go to Dr. Michael Church, my supervisor, for his generous support, solid advice, and patient encouragement. The other members of my supervisory committee; Dr. Olav Slaymaker, Dr. Ted Hickin, and Dr. K. Fletcher, also deserve sincere thanks for their interest and encouragement. Thanks also to Brett Eaton, Drew Brayshaw, Blythe Killam, Lars Uunila, Craig Jones and Laris Grikis for their excellent and enthusiastic assistance in the field. In Chetwynd B.C. the Deck family, Nicholson family and Mayor Lasser provided local support and advice. Of all the friends at U.B.C. who should be mentioned Judy Haschenburger and Marwan Hassan must be, the former for riding the roller-coaster with me and the latter for keeping Mike busy. Thanks to Mathias Jakob for his help in translating Sternberg and to family and friends too numerous to mention for less practical, but equally important, support. Last, but of course not least, none of this would have been possible without the friendship and sacrifice of Marian Oden; Maz, I simply cannot thank you enough. This thesis is for Michael Andrew Rice CHAPTER 1. Introduction 1 1.1 Definition of the study This thesis examines the changes in grain size which occur along two confluent gravel-bed rivers in northeastern British Columbia, Canada. The principal objective of the study is to describe and explain observed spatial variations in the texture of bed materials. Such an overtly empirical exercise is somewhat atypical in contemporary studies of textural change, which have tended to focus on analytical modeling of fining processes (cf. Parker, 1991). The work is also distinguished from many previous field studies by the scope and resolution of the sampling program. These distinctions are intentional. They belie a conviction that improvements in understanding and, ultimately, the prediction of grain size changes require a better appreciation of the circumstances within which fining processes must operate. In particular, models of textural change need to accommodate the multiplicity of sediment sources which characterise individual fluvial systems including the network of channels, the contemporary land surface, and persistent palaeo-deposits. A pervasive view of textural change is that grain size becomes finer with distance downstream and that, apart from occasional interruptions by tributary inputs, diminution is relatively systematic. In contrast, textural variations along the two rivers studied here show negligible overall fining (in over 100 km), are complex, and cannot be explained without reference to a large number of tributary inputs, non-alluvial sediment sources and the legacy of Late Pleistocene glaciation. These influences are neither systematic nor predictable and must be explicitly considered in order to understand the rivers' sedimentology. They contrast with the standard model, not because they are unusual or peculiar features of alluvial systems, but because the standard view is unsophisticated. One might relate this observation to the recent focus of geomorphology upon process and the adoption of a radically reductionist mode of inquiry which encourages an overly simplistic view of spatial and temporal contingency. It is not my intention, however, to imply 2 that studies of fining processes are in any way inappropriate, but rather to suggest that progress toward modeling fluvial sedimentary systems can also benefit from a wider spatial, and longer temporal, geomorphological perspective. That is to say that adequate explanation of geomorphological phenomena demands consideration of both immanent and configurational elements (Simpson, 1963). This is a methodological cornerstone which most earth scientists are unlikely to argue against, but which geomorphology as a discipline has apparently found difficult to adhere to. Most recently the focus has been on process, mechanism, and prediction within fairly limited spatial and temporal frameworks. Following, for example Slaymaker (1987a), Richards (1990, p.196) has suggested that geomorphologists need to find ways of reconstructing explanations "at scales appropriate to landforms and the Quaternary (at least !)" and reverse the reductionist trend forewarned by some (e.g. Mackin, 1963). In Richards' exposition for a realist geomorphology (Richards, 1990, 1994) reductionist search for mechanism is seen as a fundamental element of explanation (the uncovering of ontological depth), but only if it can be situated within a realistic spatio-temporal framework. The need to accommodate the complexity of real landscapes has led Richards (1994, p.281) to suggest that "the lip-service paid to field areas needs to be reassessed". There are parallels here with Mackin's assertion that fruitful, rational, earth science depends upon careful interpretation of the data collected at specific sites (Mackin, 1963). While I hesitate to enter the realism debate (cf. Bassett, 1994; Rhoads, 1994) I intend to show that the predictive success of mechanistic models of the fining process in gravel bed rivers can only be as good as our ability to situate them within real landscapes. This may seem obvious, or worse trivial, but it is telling that, excepting the work of Pizzuto (1995), there has been no attempt to model textural change at a landscape scale. This is despite the fact that a simple mechanistic model was suggested over a century ago (Sternberg, 1875) and in spite of recognition that textural maturation is affected by specific, local circumstance. Indeed, in his seminal work, Sternberg (1875) notes that tributaries will only by chance introduce material similar to that in the mainstem (p.494). Mackin (1948, p.483) is particularly keen in his assertion that "caliber of load does not vary systematically in graded streams joined by 3 tributaries, nor in graded streams in which the rock types in the load differ notably in resistance to attrition". Recognition of the potential and actual influences of tributaries, bedrock outcrops, and non-alluvial sources is widespread in the literature (see for example Miller, 1958; Church and Kellerhals, 1978; and Dawson, 1988) but there has been little attempt to incorporate these features into models of textural change. Two processes, particle abrasion and selective deposition, are widely recognised as the dominant causes of downstream fining. Abrasion is a summary term for a range of wearing processes such as chipping, grinding and breakage, which mechanically reduce the size of individual clasts (Keunen, 1956). Selective deposition or, simply, sorting refers to the differential transport of grains as a function of their size, whereby smaller, more mobile clasts are supposed to "outrun" their larger counterparts (Russell, 1939). Considerable effort has been expended in modeling these processes yet, as Pizzuto (1995) has suggested, models of the fining process alone are of little value in field situations. The analysis presented here demonstrates that individual sedimentary links, which are analogous and sometimes equivalent to hydrologic links, provide a means of isolating fluvial maturation and lateral inputs. This provides the potential for realistic utilisation of fining models. The a priori identification of significant lateral sources and sedimentary links is examined, and some guidelines are developed. An appropriate functional model of within-link modification is defined, and controls on diminution rate are considered. My intention, then, is to demonstrate that an appreciation of local geomorphic history and the contemporary landscape, as well as of fining mechanisms, enable grain size variations to be explained, and that incorporation of these features via a framework of sedimentary links, provides a basis for modeling textural change at the basin scale. Accordingly, the research hypotheses are : i) that geomorphological history and basin physiography configure the pattern of sediment supply to a river and, in turn, preclude extended systematic downstream fining; 4 ii) that, in accordance with this configuration, the river may be divided into a series of sedimentary links, each of which routes sediment between significant sources ; iii) that within well-defined sedimentary links texture is systematically modified by fluvial processes and is readily described by a simple functional model. 1.2 Previous work 1.2.1 Synopsis Prior interest in particle size variation within fluvial systems can be considered in terms of three related issues which provide a convenient framework for an overview of previous work. Consistent with the focus of the present study, discussion is restricted to textural change in gravel-bed rivers, rather than sand-bed channels. Nor is the gravel-sand discontinuity considered. Firstly there are observations, commentaries and models of grain size change which are associated with the examination of grain size as a control on river channel morphology and behaviour, particularly longitudinal form and the concept of grade. The classic works of Sternberg (1875) and Mackin (1948) are particularly important in this group, and Sternberg's model of abrasional diminution remains the most widely cited model of textural change. Many of the ideas presented by Mackin can be traced to Gilbert's work in the Henry Mountains (Gilbert, 1877). Other contributions include those of Schoklitsch (1937), Shulits (1941), Yatsu (1955), Hack (1957), Knighton (1975), Pickup (1984) and Pizzuto (1992). Grain size is recognised as one of several variables which together, through mutual adjustment, regulate fluvial systems. Between significant tributaries, and within certain limits, bed material is expected to fine in a systematic manner with distance downstream. While Sternberg (1875) considered abrasion to be the dominant cause of fining in systems which have achieved a graded 5 condition, Mackin (1948) points out that in aggradational systems sorting must also be a significant process (cf. Russell, 1939). The second group incorporates a large number of studies that share, as a unifying theme, the examination of grain size change as an element of alluvial sedimentology. Wentworth (1919), Russell (1939), Krumbein (1941), Plumley (1948), Kuenen (1956), and McBride and Picard (1987) typify those that are concerned with the petrographical evolution of fluvial sediments. Grain size maturation is often examined along with particle shape and mineralogical composition, and attempts are made to relate a given suite of characteristics to a certain depositional environment. Schlee (1957), Mayer et al. (1984), and Els (1993) focus on the related issue of palaeoenvironmental reconstruction using alluvial grain size data. Other studies have examined bed material characteristics in a variety of contemporary alluvial systems, and emphasised the importance of sorting (Brierley and Hickin, 1985; Brewer and Lewin, 1993), abrasion (Werritty, 1992; Kodama, 1994a), weathering (Bradley, 1970), geomorphic history (Shaw and Kellerhals, 1982), and tributaries (Miller, 1958; Knighton, 1980) as causes of textural change. Church and Kellerhals (1978), Dawson (1988), and Rice and Church (1996) have examined the statistical variability of grain size characteristics in wandering, braided, and hillslope-coupled fluvial systems. Third, there has been a resurgent interest in textural change as a consequence of the equal mobility hypothesis of bedload transport (Parker et al, 1982a). This theory proposes that all grain sizes within mixed beds are transported at an essentially identical rate. Similarity is possible, despite inherent differences in inertia, because of compensating size-dependent differences in grain exposure and entrapment susceptibility. These hiding effects are augmented by the development of a surficial pavement, in which coarse material becomes concentrated and thereby rendered relatively more available for entrainment. Despite laboratory and field support (e.g. Parker et al, 1982b; Andrews and Parker, 1987) several studies question the universality of equal mobility (e.g. Komar, 1987; Wilcock and Southard, 1989; Wathen et al, 1995), and debate continues concerning the bed, flow, and scale conditions which support similar transport rates. In part, this debate has focussed on the inconsistency 6 between equal mobility and the downstream fining of bed material that is characteristic of many gravel-bed rivers. While abrasion is undoubtedly an important process in certain environments (Werritty, 1992; Kodama, 1994a) experimentally derived abrasion rates cannot account for the fining rates observed in the field (Section 5.1). In the absence of other mechanisms (cf. Bradley, 1970; Schumm and Stevens, 1973) selective deposition must be the dominant fining process in many fluvial systems. However, equal mobility suggests that grains are not preferentially entrained, transported or deposited as a function of their size, thereby precluding the intuitively attractive idea that finer grains "outrun" less mobile coarse grains (Russell, 1939). In order to try and reconcile this paradox there has been renewed interest in modeling the sorting process and examining grain size trends. Thus, Parker (1991) developed a model which produces downstream fining despite the inclusion of a significant hiding component, and tested it using data from Red Deer River, Alberta. Hoey and Ferguson (1994) have shown that rapid fining on Allt Dubhaig, a small stream in upland Scotland, can be explained by only slightly size selective transport. Most recently, Paola and Seal (1995) have suggested that lateral variations of grain size can lead to downstream fining despite the operation of perfect equal mobility. They suggest that while equal mobility may be perfectly satisfied within homogeneous patches, differences in size characteristics between patches (across a section), produce section-averaged differential mobility. A number of other fining models have been proposed. These "devices for generating predictions" (Haines-Young and Petch, 1986) are predominantly mathematical and only partially specified. Empirical coefficients, employed in all of the models, belie the fundamental complexity of the mechanisms involved and the insurmountable information requirements of a fully specified function. The models vary in their rational content, that is in the degree to which they are supported by observation or analytical argument although, as Shulits (1941) points out, this distinction is not always easily made. I am interested in examining the framework within which such models can be realistically utilised. In this respect a review of existing models is pertinent, and is organised according to the mechanism(s) that are emphasised. 7 7.2.2 Models of fining by abrasion Several models of fluvial abrasion have been proposed, of which the most widely known is often referred to as Sternberg's Law. Because work done in overcoming friction is proportional to a body's weight, Sternberg (1875) suggested that, during fluvial transport, weight loss per unit distance traveled (L) is proportional to particle weight (W), [1.1] dW/dL = -?iW which yields an exponential relation between weight and distance downstream, [1.2] W = W0.e-^L wherein Wo is the initial particle weight and X is a coefficient of abrasion. In terms of a characteri sti c parti cl e di am eter D, [1.3] D = Do.eaL wherein a = A/3, since W <x D 3. Sternberg's theoretical argument is difficult to test directly because of the difficulty of tracing individual particles in a field situation. However, a number of experimental abrasion studies demonstrate that particle size does decline exponentially with distance traveled (Wentworth, 1919; Schoklitsch, 1933; Krumbein, 1941). The extent to which these experiments simulate actual abrasion processes has been questioned (Kuenen, 1956; Kodama, 1994). Thus Keunen (1956) used a circular flume rather than the standard tumbling mill apparatus in order to better imitate bedload motion, and Kodama (1994b) used a modified concrete mixer to simulate high energy impacts between the bed load and bed material. These 8 variations produced different rates of fining, but exponential models are consistently appropriate. In contrast Adams (1979) suggested that diminution due to abrasion is best described by a power function in which the coefficient of abrasion, cid, is not constant (as in Sternberg's model) but is proportional to the reciprocal of distance downstream. He argues that close to their source pebbles are susceptible to greater rates of abrasion because they are "unsound"; that is partially weathered, angular, fractured, or heterogeneous. With transport downstream their initial weaknesses are removed, they become "sound" (homogeneous), and subsequently fine at a constant rate according to Sternberg's Law. Grain size observations from Clutha River, New Zealand are used to support this argument, and although scatter is severe the data are more adequately described by power than exponential functions. These observations are not of traced particles but rather of the bed material at a number of sites throughout the basin. It is possible therefore, that the fining pattern is partially due to selective transport, although Adams (1979) is adamant that this is not the case. There is experimental support for the power function model in the work of Dull (1930), and also in Krumbein's observation that breakage during the early stages of his experiments produced positive deviations from Sternberg's Law (Krumbein, 1941). Moss (1972) suggests that the unsound nature of quartz pebbles supplied to headwater areas leads to their rapid attrition, but that, with distance downstream, selective transport is increasingly responsible for diminution because the quartz fragments become sound. In accordance with his approach to sediment transport, Stelczer (1981) has proposed a model of particle wear that emphasizes the intermittent movement of bedload particles. Size reduction is thought to reflect a combination of attrition during periods of transport, and of grinding by overpassing particles during periods of rest. Bedload wear is therefore a function of time (in the river) rather than of distance traveled per se. He derives an analytical expression of wear which reflects these two components, [1.4] D = W(Do3.e-Klt-K2.qb.t') 9 where, D is the particle size after time T = t + t', Do is the initial particle size, t is the length of time in motion, t' is the time at rest, qb is unit bedload discharge, Ki is an abrasion coefficient for moving bedload, and K 2 is an abrasion coefficient for immobile material. The coefficients Ki and K 2 have been determined experimentally using a revolving drum, and verified by field observations of radioactively tagged bedload particles. In order to use distance as the independent variable one needs to know both the actual and virtual rate of transport of bed particles. Schumm and Stevens (1973) have also stressed the importance of particle wear without downstream movement, although the mechanism they consider to be important is vibration in place or "grain jiggling". 1.23 Models of fining by sorting Despite the problem of differentiating between abrasion and sorting effects in the field, there is little doubt that differential transport can produce significant downstream fining. In a combined field and laboratory study, Bradley et al. (1972) observed a 94 % reduction in particle size along a 16 mile reach of the Knik River, Alaska, but could simulate only an 8 % reduction in particle size by abrasion. Paola et al. (1992) reported significant downstream fining in an experimental study that unequivocally precluded abrasion as a possible mechanism. The degree to which this sedimentary fractionation (Paola et al., 1992) can occur is in part a function of the geomorphic behaviour of a particular fluvial system (Russell, 1939; Mackin, 1963). In an aggradational setting coarser particles that are left behind are likely to be buried and thereby preferentially removed from the active system. In a degradational channel or one at grade, all particles are subject to reworking. Thus, although differential transport occurs within individual events, conservation of mass demands that coarser particles are eventually able to "catch-up" with the finer material. Relatively high rates of diminution on alluvial fans (e.g. Blissenbach, 1954) support this argument (Shaw and Kellerhals, 1982), although Kodama (1994) suggests that elevated fining rates on Japanese fans may reflect vigorous abrasion. 10 The majority of sorting models are based on the standard continuity equation for conservation of mass: [1.5] aH/dT = (l/l-r|).5q s/dL where H is bed elevation, T is time, r| is bed material porosity, qs is unit sediment transport rate by volume, and L is distance downstream. Modified versions for routing individual grain size fractions are used in the most recent models (Parker 1991; Hoey and Ferguson 1994; Paola and Seal, 1995). Transport rates by size fraction are calculated with (Parker, 1991) or without (Deigaard, 1982) explicit consideration of hiding. The continuity equation is then solved by finite difference methods in order to determine changes in the grain size composition of the active layer. Grain size changes in time and space are closely related to changes in the longitudinal profile. Deigaard, (1982) found that the timescale of change for the longitudinal profile is much greater than for the development of downstream fining, and suggested that grain size is essentially dependent on slope at any point in time. Hoey and Ferguson (1994), in contrast to Parker (1991), formulated their model to incorporate transient episodes of aggradation and degradation and reached similar conclusions regarding the dependence of grain size. Paola and Seal (1995) demonstrate that fining by selective deposition is highly dependent on the depositional profile. Most sorting occurs where deposition is greatest, such that an exponential reduction in deposition rate produces an exponential decline in grain size but clearly, via a completely different mechanism than suggested by Sternberg. The approach of Troutman (1980) is distinct from the models mentioned thus far in two regards. First, following Einstein (1937), a stochastic formulation of the bedload problem is utilised. Troutman treats the randomly distributed step lengths and rest periods in Einstein's model as dependent variables, and develops probability distributions that reflect particle size and position. Secondly, he generalises his model to consider particles released from two sources so it is possible to model tributary inputs. 11 1.2.4 Models incorporating both processes The sorting model of Parker (1991) is, in fact, accompanied by an abrasion term. The continuity equation used in the sorting component is modified to account for losses of mass due to abrasion (the conversion of gravel to silt). The abrasion component is similar to that of Stelczer, in that both mobile and immobile grains are considered. Two components are analytically derived: the abrasion of saltating bedload particles as they strike the bed, and the abrasion of stationary bed material particles as they are struck. The resulting model accommodates mixtures of rock with differing (empirically determined) abrasion coefficients. This is the only model which attempts to accommodate both processes in a deterministic, analytical formulation. A more common approach, first specified by Krumbein (1937), is to accept that both sorting and abrasion tend to produce exponential reductions in particle size and, in turn, to model grain size changes functionally as [1.6] D = D0.e-(al+a2)L where cii and a 2 are coefficients of abrasion and sorting respectively (Tanner, 1971; Church and Kellerhals, 1978; Knighton, 1980). In practice aa = a.\ + a 2 is determined empirically and can be termed the coefficient of diminution. There is no claim to simulate the mechanics of abrasion or sorting. 1.2.5 Other models of grain size change A notable exception to the work discussed so far is the model of Pizzuto (1995). Like Rice (1994), Pizzuto emphasises the importance of network structure in controlling grain size change along mainstem channels. Whereas my work (Rice, 1994) was largely conceptual and sought to identify issues which are the focus of the present study, Pizzuto presents a simple 12 numerical model which allows him to examine how network structure and spatial variations in sediment supply influence fining rates. The development of this model follows an earlier result which indicated that in simple random networks the spatial pattern of tributary inputs, rather than any specific process of diminution, is largely responsible for grain size diminution (Pizzuto, 1991). Finally, Rice and Church (1996) have suggested that, in headward basins, a stochastic model of textural change is most appropriate. This arises because low-order streams are strongly coupled to the adjacent land surface and often include numerous non-alluvial storage elements. Together, these phenomena preclude the development of systematic downstream textural modification, as demonstrated by data from the Queen Charlotte Islands, British Columbia. 1.3 Outline Of these models, only the contributions of Troutman (1980) and Pizzuto (1995) explicitly consider multiple sediment sources. Pizzuto's work is particularly novel because it emphasises the importance of sediment supply from an array of zero-order basins. In this study the relevance of additional sediment sources and of sedimentological, rather than hydrological, networks are examined. In Chapter 2 the hydrology, geology, physiography and geomorphic history of the two study basins are reviewed. Detailed maps of surficial geology are presented. This is necessary in order to place my empirical observations in a meaningful context, and to introduce the historical reality within which the sedimentology of these rivers has developed. Fluvial bed texture is notoriously heterogeneous and presents significant sampling challenges. In Chapter 3 sampling methods are therefore discussed in some detail. This heterogeneity also requires that some fundamental issues of textural variability are addressed. Chapter 4 considers within-site and between-site variability and establishes the existence of spatial structure in the grain size data. The nature and causes of this structure are explored. A series of sedimentologically discrete reaches, delimited by significant lateral 13 sediment sources, are identified. Categorisation of grain size data according to location within these reaches significantly reduces unexplained variability. The identification of such reaches may provide a basis for modeling textural change in rivers. In Chapter 5 the isolation of significant lateral sources and sedimentary links is therefore considered, and some guidelines for a priori identification are presented. Finally, in Chapter 6 the nature of textural modification within these links is investigated. An exponential model is found to be adequate for functionally describing changes in grain size parameters, and lithological and hydraulic controls on the diminution coefficient cid are examined. CHAPTER 2. Study Area 14 The legacy of Quaternary glaciation is strong in British Columbia. Many rivers are incised into thick accumulations of lacustrine and morainal material, and alluvium constitutes only a thin veneer within most river valleys. Glacial deposits supply much of the clastic load carried by contemporary rivers and, because of their presence along the valleys, promote a downstream increase in specific sediment yield (Slaymaker, 1987b). In mountainous regions of the province trunk streams flow within glacially oversteepened troughs characterised by steep tributary valleys, high bifurcation ratios, and a high incidence of both episodic and slow mass movement events. In general, sediments supplied to main channels are relatively immature: that is, have undergone little fluvial modification relative to materials supplied by extended drainage networks, or those in which the channel system is not so strongly coupled to colluvial materials. One of my aims is to demonstrate the geographical and historical reality within which fluvial sedimentary processes operate. I wish to examine the nature and causes of textural variability within a historically laden landscape, but one in which the river system is not completely dominated by non-alluvial sediment supply. I am interested in the role of historical and spatial contingencies within a contemporary fluvial system, rather than in the sedimentological character of a fluvially modified Quaternary deposit. Consequently, two confluent rivers in northeastern British Columbia, with well-developed alluvial floodplains and relatively good access, were chosen for this study. Pine and Sukunka Rivers rise in the Hart Ranges of the northern Rocky Mountains and flow east and north through the Foothills toward the Alberta Plateau (Figure 2.1). They meet near the town of Chetwynd (approximately 75 km southeast of Fort St. John), and continue as Pine River to meet Peace River near Taylor, British Columbia. The rivers are intermittently, rather than continually, coupled to non-alluvial sediment sources and, in places, the main channels wander over alluvial accumulations several kilometres wide. 15 Figure 2.1. Location, relief and principle channels of the study area 56° N eo 1 I over 6000 feet I 5000 - 6000 feet I 4000 - 5000 feet 3000 - 4000 feet 2000 - 3000 feet 1000 - 2000 feet \ A l b e r t a \ P l a t e a u / ^ * \ ^ Jackfish / ' --->-• / \ M o r a i n e / I ^ V \ mVcFs X^Pme \ \ \Che twynd) / V,„ , C^^~J Q> n l / T \ #r. —-Vrrwidwell Bend ^, R o c k y M o u n t a i n F o o t h i l l s R o c k y M o u n t a i n s ( H a r t R a n g e s ) 16 My intention here is to provide an overview of the hydrology, geology, physiography and geomorphic history of the two basins. This is necessary in order to place my empirical observations in a regional context, and to introduce the historical and geographical reality within which these particular rivers entrain, transport and deposit clastic sediment. Quaternary history and the resulting assemblage of surficial materials and landforms is especially important. 2.1 Climate and Hydrology Three biogeoclimatic zones (British Columbia Ministry of Forests, 1985) are found within the study area. Boreal White and Black Spruce (at lowest elevations); Subboreal Spruce (on the lower valley slopes and hills); and Engelmann Spruce - Subalpine Fir (on higher slopes above approximately «1200 m (4000 feet)). Cottonwoods, Aspen and Lodgepole Pine are common successional species in burnt-over areas. There are no climate stations with complete temperature and precipitation records within 115 km of the study area. However, maps of various climatic parameters in the Hydrological Atlas of Canada (Fisheries and Environment Canada, 1978) are based on a regional data set from A.E.S. and the Inland Waters Branch. According to these maps mean annual precipitation varies from 500 mm in the eastern foothills, to over 1600 mm in the western foothills and mountains. Snowfall accounts for approximately 50 % of this precipitation. Mean January temperature is approximately -17° C, and mean July temperature approximately 15° C. Upstream of their confluence at Twidwell Bend (Figure 2.1)1 Pine and Sukunka Rivers have drainage areas of approximately 2500 and 2750 km2, respectively. At hydrometric station 07FB003 (Water Survey of Canada) located near the mouth of Sukunka River, but upstream of the Highhat and Dickebusch confluences, mean flow is 54 m3s-> and the mean annual flood is 480 m3s-'. The annual hydrograph (Figure2.2) shows a rapid rise in discharge during May 1. Elevations are in feet a.s.l. on the mapping used to prepare this figure and have not been converted. In the text elevations are given in both metres and feet. 17 Figure 2.2. Annual flow regime of the lower Sukunka River (monthly mean discharges and 95 % confidence intervals). 2 4 0 2 0 0 1 6 0 1 2 0 8 0 4 0 0 I X Sukunka River . near the mouth W.S.C. s tat ion 0 7 F B 0 0 3 (1 9 7 7 - 1 990 ) • J a n Feb Mar Apr May J u n Ju l Aug S e p O c t Nov Dec Month 18 which reflects the break-up of river-ice and melting of the basin snowpack. Discharges remain elevated throughout June and decline steadily through July. Approximately 56 % of the total annual flow occurs in May and June. Rainfall events maintain flow through the autumn prior to freeze-up, which gauging records indicate is usually complete by mid-December. The majority of maximum flows occur in May and June and may be associated with convective thunder storms which are common in the summer months. One such storm on July 15, 1982 produced exceptional suspended sediment yields at suspended-sediment measurement stations in the study area. On Dickebusch Creek (07FB004) this storm is associated with 73 % of all the sediment transported in a two year record (Church et al., 1989). Extreme events such as this probably have a profound effect on bed material texture, at least for a period of several years. Gauging records on Pine River above Mountain Creek (07FB010) and downstream of the Murray confluence at East Pine (07FB001) indicate that the annual regime is similar on Pine River. The Mountain Creek station is immediately upstream of the Pine study reach and there are no other stations prior to that at East Pine. Given the similarity in drainage basin area, vegetation, and climate it is likely that discharges on the Pine are similar to those on Sukunka River. Indeed, for ten stations within the Pine basin upstream of its confluence with Peace River, a strong relation between drainage area and two-year flood discharge is apparent (Section 5.2.1). 2.2 Geology and General Physiography The Rocky Mountains are at their lowest and least rugged in the Hart Ranges. Only the highest peaks exceed 2400 m (»8000 feet), although relief in the upper Pine and Sukunka valleys is impressive at approximately 900 m («3000 feet). The Mountains are distinguished from the Foothills to the east by their geology and physiography. The Mountains are composed of sedimentary rocks which accumulated on the western margin of the North American Craton, predominantly during Paleozoic times. Compression, uplift and deformation of this 19 miogeoclinal wedge (the Laramide Orogeny) occurred in response to eastward accretion of the Intermontane Superterrane between 160 and 60 million years ago (Yorath, 1990). During this orogeny subaerial weathering products were carried eastward and deposited in a shallow sea. These Mesozoic rocks were subsequently deformed in post-Cretaceous times in response to the collision of a second superterrane, the Insular Superterrane, along the Pacific margin (Yorath, 1990). They were folded, thrust faulted and uplifted to form the Foothills Belt (Hughes, 1967), with the oldest Triassic rocks cropping out furthest west along the margin of the Mountains. These rocks dip to the northeast to underlie the youngest Cretaceous and Tertiary rocks which constitute the surface of the Alberta Plateau. Figure 2.3 shows a simplified geology of the study area based on the 1:1 000 000 map of Tipper et al. (1979) and Hughes' detailed study of the Pine River valley (1967). The downstream sections of Sukunka River were mapped by Stott (1961), but information about the upper Sukunka is unpublished at the present time. The headwater valleys of both rivers are cut into Palaeozoic sediments. Although clastic sedimentary lithologies are present (shales, siltstones and sandstones), various limestone and dolomite formations distinguish these older rocks from most of the Mesozoic rocks to the northeast. Some cherts and quarzite are also present, and metamorphic rocks of Hadrynian age crop out in the uppermost tributaries of the Pine. The boundary between Paleozoic and Mesozoic rocks occurs in the vicinity of Mountain Creek on the Pine (as noted by George Dawson during his reconnaissance of the Pine valley in 1879 (Dawson, 1881)), and approximately eight kilometres upstream of Windfall Creek on Sukunka River. Upper Jurassic sandstones and shales are predominant as far downstream as the Beaudette Creek and Burnt River confluences, where they give way to Lower Cretaceous elastics. These shales, sandstones, conglomerates and siltstones (with coal and quarzite beds in some formations) underlie most of both river valleys prior to their confluence at Twidwell Bend. The uplands of the eastern Foothills and a short section of Sukunka River valley upstream of the Highhat River confluence are underlain by Upper Cretaceous elastics of the Dunvegan Formation. Limestones are present within the Mesozoic rocks only in Upper Triassic formations exposed in isolated patches along the Mountain/Foothill boundary. These Figure 2.3. Simplified bedrock geology of the study area. 20 Mesozoic E:E-E1 Upper Cretaceous } sandstone, conglomerate, shale • (Smoky Gp. and Dunvegan Fm.) Lower Cretaceous "| shale, sandstone, conglomerate, coal, siltstone, (Fort St. John and Bullhead Groups) J quartzite Upper Jurassic (L. Cretaceous) (Minnes and Fernie Groups) Upper Triassic (L. Jurassic) } sandstone, shale, coal (Gray Beds Gp. and Pardonet Fm.) Paleozoic Carboniferous and Permian ^ limestone, siltstone, sandstone, dolomite arboniferous and Per ian "I / • T J ji j i ii i /-, \ f limestone, dolomite, shale, chert, sandstone (Kundle and Ishbel Groups) J Devonian (Fairholme Gp., Besa, Perdix, Stone, Muncho-McConnell and Pine Pt. Fm.) } shale, limestone, dolomite, siltstone, sandstone Ordovician and Cambrian (Chushine, Lynx, Gog, Mural, Monkman and Beaverfoot Fm.) } limestone, dolomite, shale, sandstone, quartzite, siltstone Proterozoic Hadrynian i 1 , ,,• , • , , ,. , , . /»»• 11 J N T - i ^ r phyllite, schist, sandstone, conglomerate, limestone, dolomite (Miette Gp. and Byng Fm.) J 21 include dark blue-gray limestones of the Pardonet Formation, which are one of the few distinctive lithologies present in the alluvium of both rivers. Sandstone, shale, and low-grade metamorphic clasts constitute most of the bed material sampled along the study reaches. In general, the provenance of individual clasts is difficult to discern because of the similarity of lithotypes throughout the study area. The Pine study reach begins a short distance upstream of Mountain Creek, and the Sukunka study reach at the confluence of Dudzic Creek, within the Mountain Belt (Figure 2.1). These reaches are predominantly within the Foothills where, with the exception of the upper Sukunka, both rivers flow across the dominant structural and lithological trends. Relief declines from approximately 900 m («3000 feet) in the west to approximately 600 m («2000 feet) in the vicinity of Twidwell Bend, close to the downstream limit of sampling. Each study reach is approximately 110 km long. The Sukunka reach drops approximately 275 m , and the Pine reach approximately 150 m. In general the valleys have wide, flat floors which abut steep bedrock slopes mantled with colluvium or till. In places tributary alluvial fans and remnant Pleistocene deposits form gently sloping aprons or benches between the floodplain and valley walls. Close to the mountains these side-slopes rise to peaks which exceed 1500 m (5000 feet). Topography is more subdued in the eastern Foothills where the valley walls give way to a broken, low-relief plateau surface between approximately 900 and 1200 m («3000 and 4000 feet). Structural control is apparent within the Mountain Belt and western parts of the Foothills, where long ranges of mountains and hills are separated by valleys aligned northwest-southeast, parallel with the geological grain. The valleys follow downfaulted blocks, synclines or complex fold structures. On the Sukunka, a short distance upstream of the Burnt River confluence, a series of waterfalls occur where two tightly folded Lower Cretaceous anticlinal structures crop out in the valley bottom (Bullock and Hughes, 1953; Suska-Krusche, 1953). Such control is less striking but persistent toward the northeast where the low-relief plateau of the Outer Foothills (Hughes, 1967) is characterised by northwest-southeast trending anticlinal cuestas and escarpments. Differential erosion of shale and sandstone beds has produced stepped 22 side-wall topography in the downstream parts of both valleys. The rivers occasionally wander against bedrock exposures at floodplain level, but bedrock control on both sides of the channel is evident only in the vicinity of Sukunka Falls, and in the canyon through which Pine River flows immediately upstream of Twidwell Bend. A more detailed discussion of the physiography, landforms, and materials of the trunk valleys follows an overview of local Quaternary history. 2.3 Quaternary History and Surficial Geology Although evidence of Wisconsinan glaciation is widespread in northeastern British Columbia, the provenance and timing of Late Pleistocene events are unresolved (Bobrowski and Rutter, 1992). Mathews (1954 et seq.) established that three separate sources of ice are responsible for the morainal, glaciofluvial, and abundant glaciolacustrine deposits which mantle the Foothills and Plateau. The culmination of this work (Mathews, 1978) is a model which recognises two Laurentide glaciations (Early and Late Wisconsinan) and three of western origin (two Cordilleran events and a Late Wisconsinan Rocky Mountain advance). Mathews suggested that the later Cordilleran event was synchronous with the most recent Laurentide advance, and that the two ice sheets met along a northwesterly trending front approximately 50 km east of Chetwynd, and 25 km west of Fort St. John (Mathews, 1980, Figure 3). In contrast, Reimchen and Rutter (1972) found no evidence of ice coalescence, a view supported by Bobrowski (1991). Bobrowski suggests a simpler sequence of glacial events beginning with an Early Wisconsinan pan-provincial Cordilleran advance, which crossed the Rocky Mountains and terminated in eastern Alberta (> 40 ka BP), followed by asynchronous Laurentide and Rocky Mountain montane advances in Late Wisconsinan times (25 to 11 ka B.P.). Both Mathews and his contestors recognise the importance of Rocky Mountain ice in the period c. 15 000 to 11 000 BP. The Pine valley is singled out as a key conduit for this montane advance which consisted of valley glaciers moving out from small, local ice caps (Mathews, 1978). There is also agreement that an extensive system of ice-dammed lakes, centered on 23 Peace River valley, developed during the retreat of the Late Wisconsinan Laurentide ice. Mathews (1980) detailed several Lake Peace stages which corresponded to the changing level of the lake as retreating ice exposed lower outlets. Lake Peace probably extended into the lower reaches of the Pine valley during the highest (Bessborough) and Clayhurst stages c. 11 000 BP., but it is unclear whether the lake reached the study area, where montane glaciers may still have been present (Mathews 1980, Figure 5E). Post-glacially, Peace River and its tributaries became reestablished in exposed lacustrine materials, frequently within the limits of bedrock trenches they excavated in the Plateau surface during the last Wisconsinan interglacial (Mathews, 1978). Rapid incision has removed much of the drift from these older valleys and, beyond the Foothills, the contemporary channels have reached bedrock. In contrast, distal sections of the mountain valleys retain thick sequences of unconsolidated material. An exploratory well in the Pine valley, approximately 25 km upstream of Chetwynd (B.C. Government Pine River number 1), penetrated 1081 feet (330 m) of clays, minor silts and sands, before reaching shales of the Fort St. John Group (Hughes, 1967, Appendix 3). Cordilleran and Rocky Mountain glacier ice, deglaciation, and post-glacial excavation of the resultant fills have produced a variety of sediment sources along Pine and Sukunka Rivers, and have imposed a number of other conditions on their contemporary behaviour. Using aerial photographs and field observations the surficial materials adjacent to both study reaches have been mapped, and are discussed below. 2.3.1 Sukunka River Five maps at scales of approximately 1:25 000 and 1:40 000 show the materials along Sukunka River (Appendix 1, maps A to E). The first 10 km of the study reach, downstream from the Dudzic confluence, are characterised by a narrow and inconsistent floodplain, never more than 500 m wide (Map A). The channel is constrained in a number of places by steep bedrock slopes of folded sandstones and weak, carbonaceous shale, which have a thin veneer of colluvial and/or morainal material. Sukunka River has evidently cut through Wisconsinan drift 24 and incised a channel within these weak sedimentary rocks. Exposures of till overlying bedrock, and rock terraces adjacent to the floodplain between Twidwell Creek and McLean Creek, support this interpretation. Steep tributary fans of alluvial and glaciofluvial material further constrict the channel in this reach, and supply coarse material to the river. Several fans (for example at S 13 and S 16) have complex sets of terraces (too small to be shown on the maps) consistent with a degradational history. Downstream from McLean Creek the floodplain widens and the discontinuous benches of till over bedrock become indistinct. Extensive fluvial materials have accumulated here and the floodplain is particularly wide where the channel turns 90 degrees between Baker Creek and tributary S 27 (Map B). Steep bedrock with a thin cover of colluvium is exposed by the channel in several places. Large alluvial fans are associated with a number of tributaries, some of which have been eroded significantly by Sukunka River. From Windfall Creek downstream to Skeeter Creek, gently sloping, coalescent alluvial fans mantle the northern and eastern sides of the valley. The tributaries associated with these fans drain the high ridges around Bullmoose and Chamberlain mountains and have evidently transferred significant amounts of material (predominantly Jurassic sandstones) into Sukunka valley during the Holocene. They are responsible for pushing Sukunka River to the southern and western sides of the valley, where in places valley wall bedrock and vegetated colluvial aprons are encountered by the present channel (Map C). Windfall Creek is particularly active at the present time and, unlike some of the lower tributaries, continues to supply coarse material directly to Sukunka River. There are no terraces or other indications of degradational behaviour in this section. The channel is classically wandering rather than confined, with large complex bars, hectares in extent in places, and thick accumulations of overbank sands. Sukunka River is aggradational or, at least, at grade in this reach. The fan of Rocky Creek is the last in this section and deflects the river toward the east wall of the valley. From this point downstream to the Burnt River confluence (a distance of approximately 6.5 km) the river channel drops approximately 22 m over a series of bedrock steps, emerging at the confluence through a bedrock gorge. The course of the river follows the 25 structural grain of outcropping Bullhead Group sandstones, exploiting fault lines in the rock. Bedrock outcrops oriented parallel to the falls occur at two locations downstream of the confluence and divert the channel in each case. The exposed Bullhead sandstones, being hard weathering and fairly resistant (Suska-Krusche, 1953), control the base level of the upper Sukunka. Postglacial incision of the valley fills left in the Lower Sukunka (below the Burnt confluence) has not propagated past the bedrock barrier which the falls constitute. Adjacent to the falls and a few tens of metres above floodplain level, a terrace occupies the entire width of Sukunka valley. Beyond a deep incision cut by Burnt River, remnants of this same feature can be traced downstream for some distance. A section exposed along the Burnt reveals moderately well sorted sands and gravels with coarser cobble-boulder lenses. An apparent abandoned channel is evident within the terrace above the confluence, on the western side of the valley (Map C). The edges of this feature are somewhat scalloped and are indicative of a string of kettle lakes (J. Ryder, pers. comm.). Several terrace levels are apparent to the west of the Sukunka downstream of the confluence (Map D). The highest of these also shows evidence of ice stagnation (kettle-holes), and the feature is therefore thought to be of glaciofluvial origin. The large terrace below this bench has a smoother appearance, and well-bedded cobble-gravels and sands are exposed in a gravel pit at its surface. The surface of this terrace and those below it reflect fluvial reworking of the glaciofluvial bench during incision. A similar bench can be traced down the eastern side of the valley as far as Martin Creek, below which both features become indistinct (Map E). Several rotational bank failures close to SBP 5 (82.6) 2 reveal laminated silts and clays within the western bench, and a thick sequence of laminated silts and sands is exposed close to s93 27 (69.7) . The failure scarps of the slumps contain gravels and sands suggesting that the fines are localised. Exposures of the eastern bench in high river-side bluffs close to SBP 3.5 (76.3), SBP 4 (78.3) and SBP 5.5 (85.6), reveal complex assemblages of well sorted sands and gravels, with some silty units . Bedrock is evident at the base of these exposures and indicates that the overburden is 50 to 100 metres thick. 2. Sample site notation is explained on the legend to Appendix 1. Numbers in brackets are distances downstream in kilometres. 26 I interpret this pair of benches as the remnant of a proglacial valley-train; a braided river system which filled the width of Sukunka valley and deposited a thick layer of sand and gravel downstream of retreating and stagnating valley ice, at the end of the Late Wisconsinan Montane advance. Finer units reflect the propensity of such systems to include depositional environments for suspended load (small lakes associated with kettle-holes and abandoned channels). During the Holocene Epoch, the combined flows of Burnt and Sukunka rivers have incised into this glaciofluvial wedge and produced the terraces that are particularly well-preserved in the vicinity of the confluence. Bed material is very coarse near the confluence and represents the lag material which has accumulated during fluvial reworking and incision. Except for the large section close to the Burnt confluence no remnants of this feature are apparent in the upper Sukunka valley. Bedrock control in the vicinity of Sukunka Falls, and tributary fan progradation probably facilitated deposition of an alluvial blanket over the glaciofluvial plain. In the vicinity of Martin Creek the alluvial floodplain is significantly constricted between exposed valley-wall bedrock on the west, and Martin Creek's fan on the east (Map E). Downstream, composition of the benches changes noticeably and they are less distinct with more gently sloping upper surfaces. Glaciofluvial materials are replaced by material which has a much higher clay and silt content. In the river bank, laminated, but severely deformed lacustrine materials are frequently observed and, in places, overlie fluvial sequences with a significant organic layer at the contact. This layer is often marked by abundant tree trunks, which emerge horizontally from the current river bank. Bobrowski et al. (1991, p.354) describe a similar facies sequence in an exposure on the lower Kiskatinaw River, a tributary of Peace River, approximately 70 km east of Twidwell bend. They suggest that this sequence represents the distal portion of a slump failure in glaciolacustrine materials, which over-rode the vegetated floodplain of Kiskatinaw River. This interpretation is consistent with the deformation of clay laminae and poor drainage on the surfaces behind the Sukunka exposures. Subtle slump scarps are apparent on the hillsides between s93 37 (93.4) and the Pine confluence, although the lack of fresh scarps and presence 27 of a standing forest suggest that the failures responsible for most of these deposits are not recent. However, several small slumps in clay-rich material were noted along the lower Sukunka and Pine rivers, and failures in glaciolacustrine materials are common throughout the region (Mathews, 1978; Bobrowski and Smith, 1992). For example, Thurber Consultants (1976) report 212 sizeable slides in unconsolidated material along the Peace River valley between Hudson Hope and the Alberta border. The abundance of clays in this reach, and the apparent increase in lacustrine materials toward the distal end of the glaciofluvial benches upstream, suggest that the outwash system prograded into a lake which contemporaneously occupied the lower part of Sukunka valley. In places the clay-rich beds are juxtaposed with complex arrangements of bedded sands and gravels. These are interpreted as proximal lacustrine deposits associated with tributary deltas, beaches, or ice-rafted material. During postglacial incision clay rich benches were left above the floodplain surface. In places these have failed, while elsewhere the low angle of the upper surfaces which dip toward the channel suggests that the material is slowly deforming. The extent of this lake is unclear but the elevation of the clay rich material (approximately 2100 feet, or 640 m) suggests that it may have extended to within 10 km of the Burnt confluence. Lacustrine terraces at similar elevation are found in the valley downstream of Twidwell Bend. A large lacustrine terrace preserved at an elevation of 2300-2400 feet (700 to 730 m) immediately to the west of the Twidwell Bend and through which Pine River has incised, is probably associated with a lake which developed in the lower Pine valley (see below). If this lake was contemporaneous with that in the Sukunka then the original elevation of the latter's bed would have been several hundred feet higher than suggested above, and significant degradation must have occurred in order to leave the remnants apparent today. Such a lake may have extended as far upstream as Burnt River, such that the gravelly deposits there may be of deltaic origin. Throughout the lower Sukunka valley, large fans have built out onto the floodplain surface. The associated tributaries (Martin Creek, Dickebusch Creek, and Highhat River) are incised within the fans, and a series of terraces is apparent on the Dickebusch fan. This is 28 consistent with the generally degradational nature of Sukunka River below the Burnt confluence. 2.3.2 Pine River The Pine River study reach begins at the western limit of the Foothills and, unlike the uppermost section of the Sukunka study reach, is not constrained by bedrock (Appendix 1, Map F). The first few kilometres of the study reach are dominated by the large fans of Mountain and Lemoray Creeks, both of which are major sources of coarse sediment. Local glaciofluvial terraces indicate postglacial incision of Wisconsinan drift by Pine River. However, large complex bars, the meandering nature of the river, and its wide floodplain suggest that the river is not strongly degradational at the present time. Large tributary fans, predominantly supplied by basins eroded in the same Jurassic formations associated with high sediment yields around Chamberlain Mountain, dominate the valley as far downstream as Fred Nelson Creek (Map G). A series of small colluvial fans are strung out along the south wall of the valley. Downstream from Fred Nelson Creek, for approximately 10 km, the alluvial floodplain is confined by a pair of benches, with surfaces between 2200 and 2400 feet (670 and 730 m). These are composed primarily of sands and silts (Hughes, 1967), through which Pine River has cut to produce steep bluffs in several places. Similar terraces are evident in the valleys of some downstream tributaries (e.g., Commotion Creek, Hasler Creek), and Hughes suggests that they are the remnants of proglacial lake deposits laid down during deglaciation. The relatively coarse nature of the material suggests a location fairly close to retreating valley ice. Below tributary P 34 the alluvial floodplain widens significantly, flanked by a series of small fans and then the large fan of Hasler Creek, which forces Pine River to the northern side of the valley where bedrock is encountered (Map H). Hasler creek is an important sediment source and downstream of the confluence Pine River is characterised by large, complex bars, and an alluvial plain over 2 km wide. Immediately downstream of tributary P 47 a large slump in the lacustrine remnant associated with Hasler Creek reveals a thick sequence of clays and 29 silts. It is evident on aerial photographs taken in 1981 (e.g. BC81039, #153) that this failure diverted the course of Pine River, though the original course had been regained by 1992. The final remnants of the silt-sand lacustrine benches occur downstream of the constricting fans of Commotion and Goodrich Creeks (Map I), where a thick section of well sorted sands and silts is exposed close to PHS 2.5 (78.2). From this point downstream lacustrine materials become increasingly evident and contain a larger proportion of clay than is encountered upstream. The river banks frequently expose clay, sands and silts rather than fluvial gravels and, in several sections, fluted clays with ribbons of sand constitute the channel bed. Channel gradients are extremely low throughout the lower Pine between Young Creek and Centurion Creek, and the river is generally sluggish and entrenched. These lake-like characteristics are interrupted by injections of gravelly material at Caron Creek, P 60, and Bisset Creek, where the channel steepens and rapid fining of the introduced gravels occurs. Gravel accumulations are scarce in the intervening reaches. Lacustrine clays gently rise away from the river throughout this section and show several terrace levels in the vicinity of Chetwynd (Map J). These materials, and the coarser materials which extend as far as Fred Nelson Creek, are associated with a proglacial lake which occupied the Pine valley during deglaciation (Hughes, 1967; Mathews, 1980). Subsequent incision has removed much of the proximal material upstream, but the laminated clays in the lower Pine valley have apparently resisted fluvial erosion. Hasler Creek and the tributaries downstream are introducing coarse material to the lower Pine, but this has been insufficient to completely bury the lacustrine beds. Rather, wedges of coarse fluvial material are slowly prograding from these tributaries into the Pine valley and producing a discontinuous alluvial veneer of variable thickness. A wide, flat-floored valley runs northeast from Chetwynd toward Peace River and indicates the preglacial course of the Pine (Figure 2.1). Centurion Creek, which flows southwest within this valley, is clearly underfit (Dawson, 1881; Hughes, 1967). A morainal deposit in the vicinity of Jackfish Lake approximately 10 km northeast of Chetwynd marks a still stand in the Late Wisconsinan retreat of Pine valley ice. This feature is consistent with 30 similar moraines at Rocky Mountain Portage on Peace River and that damming Moberly Lake to the northwest. The Jackfish moraine reaches an elevation of approximately 730 m («2400 feet), which is between the levels of glacial Lake Peace at the Bessborough and Clayhurst stages. It is possible, therefore, that Lake Peace extended into the Pine valley during the montane retreat c. 13 000 to 11 000 B.P. (Hughes, 1967; Mathews, 1980). As ice retreated up the Pine and Sukunka valleys, Lake Peace, or a smaller lake impounded by the Jackfish moraine, occupied Pine valley to an elevation of between approximately 670 and 730 m (2200 and 2400 feet), within which the lacustrine sequences which mantle the valley floor were deposited. It is unclear whether water from the Pine valley joined a lake in the Lower Sukunka at a common level, but it is clear that a low point in the divide between Sukunka and Pine valleys, adjacent to Mount Wabi, was eventually exploited as an outlet for the Pine valley lake. This gradient may have developed in response to drainage of a common lake through the Sukunka's preglacial course downstream of Twidwell Bend, or simply as a result of rising water levels in the lower Pine. Rapid incision of lacustrine materials and bedrock drained Pine valley and established a new course for the postglacial Pine River. A short distance below the confluence of Centurion Creek, adjacent to Mount Wabi, the contemporary channel steepens appreciably where it enters the resulting canyon. It is flanked by lacustrine terraces and, at lower elevations, bedrock cliffs. The bed is coarse and sediment accumulations are sparse. This coarse lag deposit, and the bedrock through which the lower canyon is cut, may impose a significant base level control on the lower Pine. This control may, in turn, be responsible for preventing further incision of the lacustrine beds in the lower Pine valley, and retention of very low channel slopes throughout this section. 2.4 Summary Pine and Sukunka Rivers are confluent channels which rise in the Rocky Mountains and flow north and east through the Rocky Mountain Foothills in northeastern British Columbia. 31 Sedimentary lithologies dominate both basins. Palaeozoic carbonates in the Mountains give way to a great variety of Mesozoic sandstones and shales in. the Foothills belt. Pleistocene glaciation has left a legacy of morainal, glaciofluvial and glaciolacustrine deposits within both valleys. These deposits, along with postglacial tributary fans, are important sources of clastic material for the contemporary rivers. Along with bedrock outcrops, they are responsible for imposing vertical and lateral control at several locations. Both rivers have, however, developed extensive alluvial deposits, which makes an examination of fluvial sedimentary processes feasible. CHAPTER 3. Sediment sampling issues and methods 32 River bed gravels are strongly heterogeneous, both vertically and laterally, and obtaining representative samples of the size distribution at a particular point in space is notoriously difficult. In order to examine downstream trends and the influence of tributaries and other lateral sediment sources at a drainage basin scale, a large number of point samples is required. Obtaining the information needed to elucidate the questions raised in Chapter 1 is not, therefore, a trivial undertaking, and a review of the relevant issues and methods is pertinent. 3.1 Sampling Strategy 3.1.1 Spatial coverage The Pine and Sukunka study reaches are 107.5 and 111.8 km long (Figure 2.1). The Pine reach begins a short distance upstream from Mountain Creek, above which the relatively narrow valley-bottom carries a major highway, a railway line, and several oil and gas pipelines. Construction and maintenance of the associated river crossings, rip-rap and other engineering works continue to affect the channel bed, and this upstream section was therefore avoided. The Sukunka study reach begins a short distance upstream from the Dudzic/Sukunka confluence, above which access to the river becomes increasingly difficult. The two reaches meet at the Pine/Sukunka confluence, and sampling was continued for a short distance downstream. During 1992 and 1993 bed material information was obtained at 85 sites in the Pine reach and 143 sites in the Sukunka reach representing approximately 40% and 56% of the bars exposed during low summer flows. Samples were collected from mid-channel, lateral, and point bars (in that order of preference) which were not affected by the presence of large organic debris. In general sample sites were located equidistantly between major tributaries, the total number of samples being constrained by accessibility. Additional samples were collected in the 33 vicinity of major tributaries and sediment sources, and at places where the bed material changed noticeably. In some sections of the study reaches almost 90% of exposed bars were sampled. 3.1.2 Site Selection A river bed presents a variety of flow and textural conditions to migrating sediment. From a heterogeneous mixture, individual grains tend to settle in positions consistent with their size and shape, and as a result, substantial local sorting is evident in gravel-bed rivers (Bluck, 1982). This is apparent in the contrasting textures of pools and riffles (Keller, 1971; Milne, 1982), on simple bars with relatively coarse heads and fine tails (Smith, 1974; Bluck 1971), and within more complex assemblages of bar units which reflect a number of depositional and erosional events. Informal observation indicates that the textural variability across an individual bar often exceeds that observed between similar depositional environments separated by distances three or four orders of magnitude greater. When studying downstream variations in texture, care must therefore be taken to consistently sample material which is associated with a particular bar-scale sedimentary environment. Local-scale depositional variations are otherwise likely to confound the longitudinal scheme. This is not equivalent to collecting samples from the same relative position (e.g. the bar head) because locations of maximum turbulence, lowest velocity or minimal roughness, for example, are not located consistently. Thus, Dawson (1982) found that textural variation within braid bars is not systematic. The coarsest active material present in the bed, generally considered to exert the greatest influence on channel form, has been the focus of previous fining studies (for example, Church and Kellerhals, 1978), and for these reasons, is also considered in this study. At bars selected for sampling a reconnaissance of the surface was conducted, and the sampling site was located in that unit which consisted of the coarsest active material found. Not surprisingly these high energy sites were generally closer to the channel and the bar head than to the bank or bar tail. Inactive sediment, indicated by a substantial cover of moss or lichens, was avoided because it may have little relation to the current river regime. 34 3.1.3 Vertical Sampling A near-universal characteristic of gravel-bed rivers is a surface layer which is significantly more coarse than the bulk sand and gravel mixture which lies beneath. This layer represents a modification of the bulk material by horizontal winnowing (selective removal of fine material by flows of limited competence), vertical winnowing (preferential hiding of fine material and the consequent concentration of coarse material at the surface) or, more likely, by both processes at different times. In general, the surface layer constitutes only a tiny fraction of the total alluvial column but, because of its position at the fluid-sediment boundary, it has a disproportionate effect on channel behaviour. In particular, surface texture is a primary component of channel roughness and thereby moderates incident hydraulic stress. Also, because it is composed of the coarser sizes present in the bed, this layer provides a clear and accessible indication of local competence and, in turn, the hydraulic stress required to entrain the bulk of the bed material. For these reasons, and because representative subsurface sampling typically involves a great deal more effort, most studies of textural variation have focussed on grain size changes in the surface layer. This convention is generally followed here. However, while most field effort was directed at characterising surficial material, subsurface samples were collected at a number of sites. Representative sampling of subsurface material using conventional techniques is arduous and time-consuming. My intention here was to combine a representative sample of the finer fractions of the subsurface material, with a sample of the overlying surface material in order to reconstruct the full subsurface distribution at a site. The outcome of this endeavour is discussed in Section 3.4, following consideration of the techniques used to characterise surface materials. 35 3.2 Wolman sampling Wolman (1954) introduced grid-by-number sampling of the bed surface, a relatively straightforward and versatile field technique that is popular because it is directly equivalent to volumetric sampling of subsurface material (Kellerhals and Bray, 1971). A sample consists of the clasts lying beneath the intersecting lines of a grid laid out on the bar surface, and is representative of the areal distribution of exposed grains. The size of each individual clast, picked by hand from the surface, is determined by direct measurement or, as in this case, by passing it through gauged openings in a template (Hey and Thorne, 1983). The primary problem with Wolman sampling is its inability to represent fine materials should they be present. This arises because it is difficult to identify and handle small clasts, especially where the surface is rough and they are hidden between larger stones. Wolman (1954) suggested that particles between two and four millimetres are the smallest that can be handled in the field, while Fripp and Diplas (1993) found that particles smaller than 15 mm (the width of an average index finger) were underrepresented in samples collected subaqueously. Alternative areal sampling techniques involve measurement of all the grains exposed within a given area of the bed, and can therefore characterise finer material that is present at the surface (Diplas and Sutherland, 1988). However, areal methods are usually more time-consuming than Wolman sampling, and typically underestimate the coarsest material present. Along Pine and Sukunka Rivers very little fine material is exposed within the coarse, active units chosen for sampling. This, and the decision to focus on coarse sediment, suggest that Wolman sampling is the most appropriate method in this case. Samples were collected subaerially. Practical experience and convention suggest that such sampling allows particles larger than 8 mm to be handled without bias, and 8 mm (-3.0 phi) was therefore employed as a practical truncation limit. 36 3.2.1 Sample size criteria Accurate representation of the population grain size distribution depends on the number of particles that are sampled. Performance assessments of grid-by-number sampling have focussed almost exclusively on the population mean or median, which suggests that the distribution tails may not be adequately represented by existing sampling criteria. Mosley and Tindale (1985) monitored changes in grain-size histograms as successive particles were added to a sample, and found that on average the histograms stabilised once 70 particles had been included. In turn, they suggested that a 70-particle sample can adequately define surface grain size parameters. Other assessments using the same method (Penning-Rowsell and Townshend, 1978) or replicate sampling (Wolman, 1954; Brush, 1961; Hey and Thome 1983), indicate that 60 to 100 particles are needed to consistently estimate the mean or median. These estimates are likely to be among the most stable parameter estimates because they are generally located close to the modal class. It is unlikely that 70 particles can accurately characterise the more extreme percentiles. Sample size criteria for representative sampling of an entire grain size distribution, can be defined by examining the relation between sample size and the precision with which distribution percentiles, particularly those in the tails (D5, D95), are estimated. This requires estimates of the standard errors at those percentiles. The field effort required to construct percentile sampling distributions by replication, as suggested by Hey and Thorne (1983), and Church et al. (1987), is prohibitive. Fripp and Diplas (1993) estimated percentile standard errors on the basis of the binomial probabilities for the number of particles finer or coarser than a given percentile. This approach is appropriate only when the grain size associated with a particular proportion can be specified a priori (Rice and Church, in press). It cannot specify the precision of the grain size estimates corresponding to particular percentiles, because the reference grain sizes for the percentiles are not known in advance (hence the need to sample). However, following Deming (1950) and Yule and Kendall (1953), a percentile standard error can be calculated as 37 [3.1] sp = (V(p.(l-p)/n)).(a/yp) where sp is the percentile standard error, CT is the population standard deviation, n is sample size, p is the percentile proportion, and yp is the ordinate of the supposed population density function at the given percentile. Inman (1952) used this equation with yp values for the normal distribution to illustrate the anticipated sampling errors associated with different grain size distribution percentiles. However, experience suggests that even after log transformation onto the phi scale surface grain size distributions are poorly described by the Gaussian density function. In fact, there is no universal size distribution for fluvial sediments and values of yp are in general unknown. Absolute standard errors cannot, therefore, be specified theoretically (Rice and Church, in press). But, rearranging 3.1, it is apparent that percentile standard errors are inversely proportional to the square root of sample size: [3.2] sp = ap . a / Vn where ap = (V(p.(l-p)))/yp Thus, as sample size increases, the standard error of a given percentile will asymptotically approach a minimum value determined by the shape of the population distribution and o\ Consequently, for sample sizes larger than 300 to 400 particles, the percentile standard errors improve only slowly. This suggests that the increased effort of collecting more than approximately 400 stones is not rewarded by significant improvements in the precision of the percentile estimates nor, by extension, the precision with which the distribution is defined. A sample size criterion of 400 particles was therefore adopted in this study, and represents a reduction in confidence intervals of approximately 50% compared to a 100-stone sample, and of approximately 65% compared to a 50-stone sample. A 400-stone criterion was also suggested I 38 by Fripp and Diplas (1993) (the 1/Vn dependence holds whether one is dealing with absolute or proportional precision). An empirical method of calculating absolute percentile errors is available, and has been applied to a homogeneous gravel unit on a bar in the Mamquam River, British Columbia (Rice and Church, in press). The method is based on a statistical technique called bootstrapping which uses computational power in lieu of any distribution assumptions to estimate the standard error of a distribution parameter (Efron and Tibshirani, 1991). It is analogous to using a large number of field replicates to construct sampling distributions from which standard errors can be obtained directly. In Figure 3.1 changes in percentile standard errors are plotted against sample size for the Mamquam River unit. The theoretically expected 1/S/n dependence is apparent. More interesting is the lack of symmetry shown by percentiles equidistant from the median, which would be expected if the grain-size distribution was Gaussian. Instead, the errors associated with the coarser percentiles (D 9 5, D 8 4 and D 7 5) are generally lower than that of the D 5 0 , while the finer percentiles (D5, D 1 6 and D 2 5) have consistently larger errors. This reflects the moderate coarse skewness (in phi units) of the Mamquam grain size distribution (Figure 3.1 inset), whereby surface coarsening has produced a distribution in which the modal classes (and therefore the most stable percentiles) are shifted to one side of the median. Positive skewness (on the standard phi scale) is a common attribute of surface gravels, and it is therefore reasonable to expect that coarser percentiles are more accurately estimated than finer percentiles for any sample size (Rice and Church, in press). This is encouraging given the focus of the present study on coarse material. 3.2.2 Field Procedure At each site a grid was laid out on the coarsest active unit that could be identified. Grid dimensions varied with the shape of the unit but were designed to ensure a distance of two maximum particle diameters between sampling points and thereby assure the independence of individual observations. Typically a 500 or 750 mm interval was employed. Particles beneath Figure 3.1. Sample size and percentile standard errors estimated using the bootstrap technique for a homogeneous unit on a bar in the Mamquam River, British Columbia. Grain size distribution (inset) is based on a 3574 particle Wolman count. 40 the grid intersects were sorted using templates cut with half-phi openings. The b-axis of material larger than 256 mm was measured using a rule and sorted accordingly. In addition to classification by size, each particle was classified according to its lithology. Seven distinctive litho-types were evident in the bed material of both Pine and Sukunka Rivers; white limestones and dolomites, conglomerates, sandstones, finestones (siltstones, mudstones and shales), quartzites; blue limestone (Pardonet formation); and a miscellany of low-grade metamorphic rocks. With the exception of Pardonet limestone, these categories are not associated with individual bedrock formations, but rather identify common characteristics that can be quickly assessed in the field. Knowledge of the lithological composition of the bed, and of the size distribution within individual lithologies, is necessary to assess the role of abrasion (Chapter 6). Similar, broadly based lithological classifications have been used in previous studies of textural variability (e.g. Shaw and Kellerhals, 1982). Wolman samples of this kind were collected at the 97 Sukunka sites and 56 Pine sites indicated on the detailed maps in Appendix 1 and summary data are presented in Appendix 2. At some sites over-zealous sampling yielded more than 400 particles, while elsewhere extremely coarse sediment or sedimentary unit dimensions made samples of this size impractical. An average of 388 particles were classified at each site. At sites with moderately structured cobble-gravel surfaces, samples were collected by a crew of two or three people in less than one hour. 3.2.3 Replicate samples To assess within-site sampling error three or four replicate samples were collected at six sites (Figure 3.2). Given the dimensions of the units sampled relative to the grid dimensions necessary to ensure the independence of individual observations, the replicate grids invariably overlapped each other. Care was therefore taken to avoid excessive disruption of the surface during sampling. At site STW 4b, one of the four replicates collected (II) is noticeably different from the others, and is responsible for a large within-site variation relative to the other sites. Figure 3.2. Within-site replicate Wolman samples. Gra in . s i ze ( — phi) 42 This anomaly is difficult to explain given that the sample was collected from an overlapping position between replicates I and III. However, this was the second sample collected at the beginning of the 1993 field season, and it is possible that a significant recording or measurement error was made. This sample (STW4b 93 II) was therefore removed from the data set. Different sites were sampled in 1992 and 1993, which introduces the possibility that an unspecified temporal effect could confound the spatial variations under examination. However, two of the replicate sets (STW4b and PRD) include samples collected in 1992 and 1993 and confirm that there was very little change in the bed between field seasons (Figure 3.2). The sample collected in 1992 at STW4b is almost identical to those collected in 1993. At PRD there is some change, but comparison with the other replicates indicates that this is no greater than general within-site variability. This is consistent with observations of short term grain size stability on gravel bars in the Tulla River, Scotland, and Markarfljot Sandur, Iceland, by Bluck (1982). He suggested that over short timescales grain size composition varies relatively little on gravel bars because the surface selectively retains those bedload grains with characteristics similar to the resident material. Significant temporal changes presumably occur in response to floods capable of mobilising large portions of the bed. Between sampling periods the maximum daily discharge at Water Survey of Canada hydrometric station 07FB003 (Figure 2.1) was 383 m3s_1 which represents a return period of only 1.4 years (the mean annual flood is 500 m3s-'). An estimate of local dimensionless shear stress for the peak discharge is, [3.3] © = (prgdS)/(Dg(ps-pf)) = 0.029 where d is average channel depth (~ 2.81 m), S is measured bankfull slope through the reach (= 0.0014), D is local D50 (= 0.082 m), p s is bed material density (~ 2.65 kgnr3), pf is water density (~ 1.00 kgnr3), and g is acceleration due to gravity (= 9.8 ms2). The value of 0 = 0.029 approximates the ratio of entraining to resisting forces at the gauging site and is at the lower 43 limit of values typically associated with initial grain movements in natural gravel beds (0.03 < 0 < 0.06). For structured natural beds the effective 0 is often higher than 0.06 and general mobility (capable of changing the grain-size distribution) does not tend to occur until two to three times the entrainment threshold (Parker et al. 1982). The value of d used here is the upper 95 % confidence limit on the discharge to depth relation at the station (R2 = 0.98, n = 36) and therefore represents the maximum likely depth for a discharge of 383 irPs1 The slope estimate is derived from a longitudinal survey of bankfull slope discussed in Section 6.3 and may underestimate the true energy profile. However, it would take a 100 % increase in slope to yield a value of 0 greater than 0.06 and such an underestimation is unlikely. It is certainly unlikely that general movement occurred at this site, which supports the replicate sample evidence that significant changes in bed material did not occur between sampling periods. 3.3 Photographic sampling In order to improve sampling resolution while minimising field time, a photographic technique was used to obtain summary grain size information at 51 sites on Sukunka River and 39 sites on Pine River (Appendix 1). The method is based on establishing empirical relations between grain size distribution parameters and the number of particles exposed per unit area of the bed surface (Church et al., 1987). No attempt is made to measure grain sizes from the photographic images (cf. Adams, 1979; Diepenbroek and de Jong, 1994). At a selection of sites where Wolman samples were collected a 0.25 m2 quadrat was placed at random within the Wolman grid and photographed using a hand-held 35 mm camera. Photographs of a larger area representing more of the sampled unit may have produced better relations between measured parameters and count per unit area. However, this would have required additional equipment and more time at each site, thereby defeating the aim of obtaining useful information fairly rapidly. The number of grains exposed within each photographed quadrat, C, was counted. A clast was counted only if more than 50% of it lay within the quadrat. Where present, material 44 finer than 8 mm was not included in the count, since it is not possible to isolate individual grains accurately below this size. Scale bars included in the photographs aided in the differentiation of such material. An estimate was made of the percentage of the image which was obscured by shadow Psh, and which showed material smaller than 8 mm, Pg. Counts were then corrected for this loss of area to give the count, c, which would be expected in the absence of fines or shadow: [3.4] c=100.C/(100-(Psh + P8)) Photographs with Psh + Pg> 15% were excluded from the analysis. Bivariate scatter plots of Wolman sample surface D50 values and the associated corrected counts reveal a slight separation in the relations for photographs taken in 1992 and 1993 (Figure 3.3). For a given grain size, the count is typically a little higher for the 1993 photographs. These are not photographs of the same sites and do not therefore reflect changes in the bed surface. I made all of the counts during a single month, and operator bias is therefore an unlikely explanation. The scale bar used in 1992 is marked in 50 mm increments, which makes it somewhat difficult to distinguish material finer than 8 mm. This scale was replaced with one marked in centimetres and millimetres in 1993. This finer scale facilitated more accurate distinction of material finer than 8 mm, and I suspect that the lower counts for the '92 photographs reflect under-counting of material between 8 and 50 mm. The 1993 data set, consisting of 69 points, has therefore been define calibration relations, and is presented in Appendix 2. Least-squares linear regression was used to model the relations between D 5 0 and D 9 5 , and c, for values transformed to the base two logarithm. This transformation is convenient in order to relate count directly to grain size in phi units. Least-squares is an appropriate method of curve-fitting given that the relations are to be used for prediction (Mark and Church, 1977). Both relations are significant (Figure 3.4) and have R2 values of 0.88 and 0.79 respectively. The average standard error of the estimate is larger for D 9 5 (0.30) than for D 5 0 (0.22) which 45 Figure 3.3. Comparison of relations with D50for counts derivedfrom photographs taken in 1992 and 1993. 46 probably reflects the lower probability of including very large particles in a single 0.5 by 0.5 m quadrat. Confidence intervals (a = 0.05) for the mean response and for individual predictions, are plotted along with the models in Figure 3.4. Individual predictions are approximately ± 0.45 <I> for D50, and approximately ± 0.63 O for D95, at the 95 % confidence level. These errors are not trivial, but they are acceptable given the aim of obtaining useful information with minimal field effort. Predictions based on these models are a valuable adjunct to the Wolman samples and certainly reflect the general condition of the bed at the photographed sites. Predicted D50 and D95 values are listed in Appendix 3. For simple arrangements of equidimensional grains there is an expectation that mean grain diameter D x , is related to count c, as [3.5] D x occ- 0 5 It is not clear to what extent the slope of -0.71 observed for the D 5 0 relation reflects the average difference between D 5 0 and D x, and the non-equidimensionality and complex arrangement of clasts on these bar surfaces. That both relations have very similar slopes (-0.705 for D 9 5 , and -0.712 for D50), is a simple artifact of the relation between them, which is strong, and has a slope of 0.99. It follows that on average D5o and D95 are related by a simple additive constant (a proportional constant in original units), which in turn means that their separate relations with the same independent variable have essentially the same slope. 3.4 Subsurface sampling The weight of material (kg) needed to obtain a representative volumetric sample, is proportional to D m a x 3 , where D m a x (mm) is the size of the largest clast present. In this study, where coverage of long reaches was a priority and sampling sites are remote, coarse bed material made it impracticable to sample the full subsurface distribution at each site. Instead, representative samples of the subsurface material finer than 45 or 32 mm were collected at 61of the Wolman 47 Figure 3.4. Photographic calibration models for D,0 and D95. 95% confidence limits for the regressions and individual predictions are presented. I I i i I I I i N . 5 6 7 8 9 10 C o r r e c t e d c o u n t (log 2) 48 sites. After first removing the surface layer to the depth of D m a x , subsurface material was excavated from a small area within the Wolman grid. Excavation proceeded until approximately 150 kg of material finer than 45 mm (or 60 kg finer than 32 mm) had been removed. These sample weights exceed the 0.1% criteria of Church et al. (1987). Material coarser than 16 or 22 mm was sieved into half phi fractions and weighed at the site. A representative split of the finer material was obtained and returned to the laboratory for conventional sieve analysis. The amount of material below 0.063 mm was determined, but was not differentiated. These truncated samples are of limited sedimentological value as they stand, but it was hoped to extend them to a representative sample of the entire subsurface distribution by marrying them to the corresponding surface samples. Fripp and Diplas (1993) have used a similar technique to reconstruct hybrid surface samples from restricted areal-clay and Wolman distributions. 3.4.1 Construction of hybrid subsurface samples Here the hybrid technique is based on the premise that above some critical size, the surface distribution is simply a truncated version of the material beneath the surface. This is reasonable if one accepts that surface and subsurface materials had the same characteristics at the time of deposition, but that waning and subsequent flows have removed portions of the finer material from the surface layer, leaving undisturbed only those fractions above the competence limit of subsequent flows. Unwinnowed fractions are present in their original amounts, such that fractional proportions of surface counts and subsurface weights are equal when calculated for the range above the truncation limit. No sampling bias affects this result, because grid by number and volume by weight sampling are directly equivalent (Kellerhals and Bray, 1971). By collecting representative subsurface samples of material finer than 32 or 45 mm, and representative surface samples of material coarser than 8 mm, both counts and weights are available for the fractions between 8 and 32 or 45 mm. Wolman counts for those fractions above the winnowing limit, when normalised for the total count in that upper range, provide the 49 correct relative proportions pi, for the subsurface fractions in the same range. Thus, if the winnowing limit falls within the overlapping range, the subsurface sample gives the weight wx, of at least one of the size fractions x, for which a proportion px> is also available. The total weight of material greater than the winnowing limit wy (that would have been collected had a full subsurface sample been obtained), is therefore estimated as [3.6] wT = w x /p x and, in turn, the weights wi, for each size class above the winnowing limit can be calculated from the proportions derived from the surface counts: [3.7] Wj = wT.pi These weights can then be combined with weights obtained in the field for fractions below the winnowing limit, to reconstruct an entire subsurface distribution. Fraction x can be any size interval which is representatively sampled in both the surface and subsurface and which is above the limit of surface winnowing. To minimise the possible impact of sampling bias, a fraction which is not at either end of the sampled ranges is preferable. 3.4.2 Assessment The crux of this approach is identifying a surface winnowing limit below the upper limit of subsurface sampling (32 or 45 mm). If winnowing has occurred up to 32 or 45 mm then there is no basis for equating surface proportions and subsurface weights. Subsurface samples were designed to be representative of these fractions because I expected material of this size to be unwinnowed. However, analysis of the overlapping ranges, and of two complete bulk samples, suggest that this expectation was unreasonable, or at least that the proportions in the overlapping range are seldom equal at sites on Pine and Sukunka Rivers 50 For any pair of consecutive size classes i and i+1 above the winnowing limit, a ratio of surface counts n, will be equal to a ratio of the subsurface weights: [3.8] nj+i / ni = Wj+i / Wj In Figure 3.5 surface and subsurface ratios for the size fractions in the common range are plotted against each other for individual sites. For unwinnowed fractions the ratios should be equal and plot along the one to one lines shown. It is immediately apparent that the ratios are seldom very similar, and that in general surface ratios are higher than subsurface ratios. This indicates that reductions in the amount of material between fractions i+1 and i tend to be greater for material on the surface, which in turn reflects a relative deficiency of material in fraction i at the surface. In a number of cases the subsurface ratio reflects an increase in the amount of material in fraction i relative to i+1 (wj+i/wj < 1), yet the surface ratio records a large reduction. Widespread deficiencies in the 8 to 11 mm fraction are perhaps not surprising given the potential for underrepresentative surface sampling of this group, and the relatively high potential for significant winnowing. However, that the deficiency is apparent in larger fractions, especially the 22 to 32 mm group, is clear evidence of a surface that has been extensively modified. While there are fewer data for this group (only 19 of the 61 samples were collected to 45 mm), surface ratios are on average 1.7 times larger than subsurface ratios, and there can be little doubt that the result is real. The large size of both the surface and subsurface samples makes it unlikely that the deficiency is an artifact of unrepresentative sampling. These sites were deliberately chosen to reflect local competence and the question arises of whether any size fractions are in general undisturbed in the surface layer. Complete subsurface distributions are available at two sites and, in conjunction with the corresponding surface samples, can be used to investigate this issue. The two distributions are based on samples of 1740 and 1673 kg which, for the maximum sizes present are between the 0.1 and 0.5% criteria of Church etal. (1987). They are shown in Figure 3.6, along with the replicate Figure 3.5. Comparison of surface and subsurface consecutive fraction ratios for classes between 8 and 45 mm. 51 _o 1 01 1 00 1 00 (D O D Z3 if) 1 01 1 00 — i — > — i — i — i — >22mm / >1 6 m m 7 s . 101 8 7 6 5 6 7 TQ0 4 5 6 7 0 ' 0 ,• 1 00 h - A 5 6 7 1 0 ° >32mm / >22mm /// 4 5 0 1 S u b s u r f a c e Rat io 52 surface distributions collected at the same sites. For truncation at various grain sizes the subsurface and surface distributions at PRD are compared in Figure 3.7. There is no grain size less than 45 mm above which the surface and subsurface distributions are the same. For 8 and 11 mm truncations the surface is significantly more coarse, primarily because of excessive subsurface material below -4.5 <£> (22 mm). For truncations above 22 mm the cumulative curves are very similar but this belies excessive surficial material between -5 and -6 0 (32 and 64 mm). Above 45 mm reasonable comparisons cannot be made because the proportions being compared are restricted to a limited range. The same general result is apparent at STW 4b (Figure 3.8) where an excess of surface material between -5 and -5.5 O (32 and 45 mm) and an excess of subsurface material between -6.5 and -7.5 O (90 and 181 mm) preclude any simple conversion by truncation. These comparisons for common size ranges confirm the fundamental dissimilarity of surface and subsurface materials indicated by the ratio comparisons discussed above. The balance of evidence suggests that at most sites on Pine and Sukunka Rivers, surface and subsurface distributions are not related in a simple way. The basic assumption of the hybrid technique, that the surface material is simply a truncated version of that beneath, is apparently naive, at least for the high energy units considered here. The general deficiency of material as coarse as 32 mm in the surface layer implies that significant differential transport occurs at most sampling locations. This is prima facie evidence that fining by selective sorting is important in these rivers, an issue which is discussed further in Section 6.4. That the surface layer is not preferentially enriched with coarse material indicates that the coarsening is not associated with pavement formation and the regulation of equal mobility (cf Church et al, 1987). However, horizontal winnowing may be only one of several processes which modify surface textures relative to the subsurface. For example, migration and dissipation of gravel sheets and unit bars may add material to the surface layer without affecting the material beneath. Whatever processes are responsible, it is clear that I can have little confidence in subsurface distributions reconstructed using the hybrid technique. As with most other studies of downstream textural change my attention will therefore be limited to 53 Figure 3.6. Complete subsurface grain size distributions and surface replicate distributions at sites STW 4b and PRD. - 4 . 0 - 2 . 5 - 1 . 0 0.5 2.0 3.5 5.0 6.5 8.0 Grain s ize ( - p h i ) - 4 . 0 - 2 . 5 - 1 . 0 0.5 • 2.0 3.5 5.0 6.5 8.0 Groin s i ze ( - p h i ) 54 Figure 3.7. Comparison of surface and subsurface material at PRD. 0.30 i 0.25 0.20 0.1 5 0.10 0.05 PRD 93 8 m m Truncat ion o.oo 1 c o H — 3 o O 0.30 i 0.25 0.20 PRD 93 1 1 m m Trunca t ion 0.1 5 h 0.05 0.00 0.30 i 0.25 0.20 0.1 5 0.10 0.05 PRD 9 3 1 6 m m Trunc at ion o.oo 1 1.0 0.30 0.8 0.6 0.4 0.2 1 .0 0.8 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.25 0.20 h 0.1 5 0.1 0 0.05 0.0 0.00 PRD 9 3 2 2 m m Trunc at ion 3 4 0.40 0.35 0.30 0.25 0.20 0.1 5 0.1 0 0.05 0.00 PRD 9 3 3 2 m m Trunc at ion 1.0 0.6 0.5 h 0.4 0.3 0.2 0.1 0.0 0.0 PRD 9 3 4 5 m m Truncat ion CD Sur face 553 Subsur face — Sur face — Subsur face mm 1 .0 O.f 0.6 0.4 0.2 0.0 1 .0 CD C 0.8 0.6 A 0.4 A 0.2 0.0 Grain Size ( — phi 55 Figure 3.8. Comparison of surface and subsurface material at STW 4b. 0.30 0.25 0.20 0.1 5 0.1 0 0.05 0.00 0.30 0.25 1.0 0 .30 . 9 0.20 O O 0.1 5 0.1 0 0.05 0.00 0.30 STW4b 93 1 1 m m Truncat ion / / 1 3 4 0.00 STW4b 93 0.25 1- 1 6 m m Trunc at ion . [ 0.20 0.1 5 0.10 h 0.05 0.8 0.6 0.4 0.2 0.6 H 0.4 0.2 0.8 0.6 0.4 0.2 0.25 0.20 0.1 5 0.1 0 0.05 1 ' 0 . 0 0.00 STW4b 93 2 2 m m Trunca t ion 1 .0 1 .0 0.40 0.35 0.8 0.30 0.25 0.20 0.1 5 0.1 0 0.05 0.0 0.00 STW4b 93 3 2 m m Trunc at ion 1.0 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 STW4b 93 4 5 m m Trunc at ion • Sur face E23 Subsur face — • Sur face — Subsur face 0.£ 0.6 0.4 0.2 0.0 1.0 0.E H 0.6 0.4 0.2 a) c c o o C l o C l CD > ' 0 . 0 l ~ F Z5 o 1 .0 0.8 0.6 0.4 0.2 0.0 Grain Size ( - p h i 56 variations in surface texture. 3.5 Summary Information has been obtained about the surface bed material on approximately 50% of the bars along two 110 km study reaches. This sampling resolution is unprecedented for study reaches of this size and is intended to clarify the nature of textural variability in a fluvial system. In order to minimise the influence of local variability the coarsest units present were consistently sampled; a choice of depositional environment in accordance with previous studies of downstream change. At 153 sites, 400-stone Wolman samples provide good representations of the entire surficial grain size distribution. The lithological composition of the bed and the size distribution of each litho-type are available for each of these sites. At 90 additional sites a simple photographic technique has been used to estimate selected distribution parameters (D50 and D95). These estimates are associated with larger errors than those derived from the Wolman samples, but are nevertheless a very useful adjunct to the Wolman data. Subsurface samples, truncated at 32 or 45 mm, were collected at 61 of the Wolman sites, with the aim of reconstructing full subsurface distributions using the surface counts. However, the basic assumption of the procedure, that above some size the surface is simply a truncated version of the material beneath, appears to be untenable. While it would have been interesting to compare textural changes in the surface and subsurface materials, the surface layer is of greater interest in a geomorphological context. In general, with regard to the identification of systematic and discrete textural changes, the data sets collected along Pine and Sukunka Rivers represent an improvement over existing field data. CHAPTER 4. Grain size variations and spatial structure 57 Grain size distribution curves for the Wolman samples reveal large variations in the texture of bed material sampled within each river (Figure 4.1). My purpose in this chapter is to examine the nature of this variability within and between sampling sites, and to establish that these variations exhibit spatial structure. At this stage attention is restricted to the Wolman samples, which provide the most accurate assessments of surficial particle size. For each sample along the mainstem of the Sukunka and Pine mean grain size D x and variance s2 were calculated from the half-phi frequency counts as, [4.1] D x =>fi [4.2] s2 = I(i=.,k}fi.(Di-Dx)2 / (!<!-,*}$)-1 where, Dj is the midpoint of the ith class, fj is the frequency count of the /'th class, and k is the number ofnumber of half phi size classes. Individual grain size samples are not normally distributed and in Section 4.1.1 appropriate tests for hornoscedasticity and the comparison of means are presented. At three of six sites where replicates were collected mean grain size varies detectably between samples. This result (Section 4.1.2) is consistent with previous studies and highlights the irreducable variance often associated with visually homogeneous depositional environments in gravel bed rivers. Nevertheless, in both Pine and Sukunka rivers mean grain size varies significantly between sites (Section 4.1.3). Earlier work suggests that these variations may be systematic. Consideration of running means and a test of stochasticity reveal the presence of fine scale spatial structure in both study reaches (Section 4.2). In previous studies similar structure was found to reflect the intermittent redefinition of mainstem texture by lateral sediment inputs (Section 4.3). Significant lateral sediment inputs along Pine and Sukunka Rivers are identified in Section 4.4. Classification of grain size measurements according to their location relative to Grain s ize ( — P h i ) 59 particular sediment sources greatly improves overall explanation of textural variation (Section 4.5). 4.1 Analysis of grain size variations Two fundamental questions require attention prior to any exploration of the relations between grain size and position along the channel. First, how representative of the depositional environments that were sampled are the grain size distributions that were obtained ? Second, are the variations in grain size between sites significantly greater than those at a site ? If between-site variations are not significant, there is no basis for seeking any relation between grain size and location. Church and Kellerhals (1978) addressed these questions in their study of grain size variations along Peace River. At each of 39 sites up to four 50-particle samples were collected from within an apparently homogeneous bar-head unit. A nested analysis of variance model was then used to compare within-sample grain size measurements with replicated measurements at the same site and to compare between-site differences with the variance typical at a site. As in the present study great care was taken to collect material from sites that were uniform with regard to depositional environment, that is, to restrict sampling to sites considered to be representative of the coarsest active material present at the head of channel bars. Similar grain size analysis was conducted by Dawson (1988) and Huddart (1994). 4.1.1 Analysis of variance using Chi-squared statistics The use of a nested variance model, and indeed any ANOVA technique which is based on the calculation of Frstatistics, is predicated on a number of assumptions about the measurements involved. The three principal requirements are that samples are normally distributed, have equal variances, and are independent. 60 There is extensive evidence that nonnormality is not a serious problem, that is, that ANOVA comparisons are robust even when sample distributions are nonnormal (Box, 1953; Tan, 1982). However, the assumption of equal variances (homoscedasticity) is more problematic. Box (1954) reported that variance inequality does not seriously affect the behaviour of the F-test if samples are of approximately equal size. Wilcox (1987a) argues that it has subsequently become commonplace to ignore the homoscedasticity assumption, especially if samples are large and of equal size. However, it is not clear how large or how approximately equal sample sizes have to be in order to mitigate variance inequality. There are strong indications that too much variability adversely affects both Type I error probability and the power of F-tests (Brown and Forsythe, 1974a; Dijkstra, 1988). Monte Carlo simulations utilising values of 0 = ffmax/araiii < 4, reveal that actual Type I errors may be many times the nominal level, even if samples are large and of equal size (Wilcox, 1987a). In contrast Box's (1954) results were for a fairly narrow range of variances, 9 < V3, which explains the contradictory nature of his results. Wilcox (1987b) also suggests that the F-test becomes increasingly sensitive to heteroscedasticity as the number of samples being compared increases. Values of 9 for the Wolman samples are 9s = 3.9 (Sukunka) and 9p = 9.3 (Pine), and exceed what could be considered tolerable heteroscedacity on the basis of Box's results. In addition sample sizes are unequal and comparisons between a large number of samples are to be made. There is therefore every indication that an ANOVA procedure based on the use of F-tests is inappropriate. However, 9s and 9p utilise only two of the sample variances. Before abandoning standard ANOVA techniques, it is necessary to check the homoscedasticity of the grain size samples using a more rigorous method. The standard test after Bartlett (Bartlett, 1937) was used by Church and Kellerhals (1978), Dawson (1988) and Huddart (1994) to affirm the homoscedasticity of their respective grain size samples. In the former two cases homoscedasticity was achieved following the transformation of millimetre data onto a logarithmic scale (which, by normalising the data, minimises the dependence of variance on mean values). Cursory examination of Sukunka and Pine grain size distributions suggests that, even on a phi scale, grain size is normally distributed 61 in only a handful of samples. Because Bartlett's test is highly sensitive to nonnormality (Box, 1953) it is necessary to confirm the normality of the data prior to using the test. Skewness (a3) and kurtosis (a4) coefficients for the Wolman samples were calculated from the third and fourth moments as, [4.3] a3 = 2,i=.ijc}fi.(Di-Dx)3 / (Z{i,k}fi).s3 [4.4] a4=[I{i=,.k}fi.(Di-Dx)4/(Z,i,k}fi).s4]-3 For a symmetric distribution a3 = 0, and for a normal distribution sn = 0. The coefficients are plotted in Figure 4.2 for each river. Note that on the phi scale, positive skewness, that is a mass to the left and a tail to the right, indicates a deficit of finer material because of the negative sign associated with coarser particles (> 1.0 mm). There is a clear proclivity for the phi grain size distributions to be positively skewed, and to a lesser extent, platykurtic. An acceptance region for a null hypothesis of normality is also indicated. Even with power strongly in favour of H 0 (a = 0.01) only 12.5 % of the samples can be considered to have a normal distribution. An alternative test for homoscedasticity is therefore desireable. After comparing 56 tests, Conover et al. (1981) recommended the Brown-Forsythe test (Brown and Forsythe, 1974b) when samples are asymmetrical. This procedure compares the variance of the spread of observations within groups with that between groups using an F-statistic. The spread of the observations is measured relative to the group median rather than the mean which renders the test more robust under nonnormality. Computational details are given in Appendix 4 and results for the Pine and Sukunka samples are presented in Table 4.1. In both cases, as suggested by 9s and 9p, variances vary significantly between samples. An analysis of variance technique which is robust under heteroscedasticity, and not therefore based on F-tests, is required. Welch (1951), James (1951), and Brown and Forsythe (1974a) among others, have developed tests for comparing sample means when sample variances are unequal. Djikstra 62 Figure 4.2. Skewness and kurtosis coefficients for the mainline Wolman samples. The box delineates the acceptance region for a null hypothesis of normalcy (a = 0.01). 1 .0 o-00 in O 0.6 0.2 •0.2 •0.6 .0 • P ine o S u k u n k a Ho: Normal a = 0.01 "Ol" _o_ o o o o O c9 a • a -e-o o % ^ o o §5 o oi • o o o • • o oft' l O o O' .0 - 0 . 6 - 0 . 2 0.2 S k e w n e s s (a3 0.6 1 .0 63 Table 4.1. Brown-Forsythe tests of homoscedasticity for Pine and Sukunka Wolman samples. k N A B W = A / B Fa=o.ooi Sukunka 96 37954 4.0462 0.2862 14.14 1.54 reject Ho Pine 56 21421 4.3336 0.2577 16.82 1.71 reject Ho Where, k is the number of samples, N is the total number of observations, A is the variance of the spread of observations between samples, and B is the variance of the spread within samples. See Appendix 4 for computational details. Table 4.2. Within site, between sample variability. Equality of sample means at six replicate sites. Site Number of replicates W D C P (error) for H 0 , 1-a PLH 5.75 3 1342.098 5.534 1.001 0.25 PRD 4 2716.828 5.571 0.485 0.05 PLH 5 3 1653.835 5.484 2.989 0.75 SBP4 3 1274.827 6.001 5.762 0.90 SBP 7.5 3 1539.207 5.515 4.704 0.90 STW 4b 3 1627.721 5.244 0.059 0.025 The final column represents the probability of error associated with acceptance of Ho of no significant difference between replicate mean grain sizes. See text for definitions of W, D and C. 64 (1988) suggests the use of a simple precursor of these tests in cases where the sample sizes are large. Since sample size ranges from 150 to over 400 observations with an average of 388, the use of this chi-square test is appropriate here. In general, if there are i = 1 to k samples, consisting of n; observations, with mean grain size Dx;, and variance Si 2 , then the null hypothesis of no difference between the population means, Ho: Ui = U2 = = Uk, is tested as follows, [4.5] W = Z ( i = W Wi [4.6] D = Z{i=i,k}W,Dxi/W and [4.7] C = 2 > W Wi.(Dxi - D)2 where aj = Si 2 / nj and w; = 1 / aj. If C > y} then reject Ho and conclude that the means are significantly different (X 2 is the 1-a quantile of the chi-squared distribution with k-1 degrees of freedom). 4.1.2 Within-site, between sample variability This test was first applied to each of the replicate suites collected at sites PLH 5.75, PRD, PLH 5, SBP 4, SBP 7.5 and STW 4b. In each case the aim was to determine whether or not the mean grain size values of the individual samples vary significantly within the site. The results of this analysis are somewhat ambiguous (Table 4.2). Error probabilities for H 0 of 1-a = 0.25, 0.05 and 0.025 at PLH 5.75, PRD and STW 4b indicate the similarity of the replicate means at these sites. In contrast, at SBP 4 and SBP 7.5, 1-a = 0.90 which suggests that the replicate means are different. At PLH 5, one must be willing to accept a 25 % probability of being incorrect in order to claim that there is significant within-site variability. While this is not an insignificant error, it is acceptable given the lack of consensus among the other sites. 65 Dawson (1988) found significant within-site variations at bar-head sites along the braided Sunwapta river, which he primarily attributed to the geomorphological stratification of his sampling at the bar scale. Bar-head sampling was intended to limit within-site variability by restricting attention to a particular sedimentary environment. However, a separate study (Dawson, 1982) found that variation within braid bars is not systematic, such that bar head sites are not always the coarsest areas. This source of variability was excluded from the present study by sampling the coarsest depositional unit which could be isolated, irrespective of its location on the bar surface. Despite exercising similar judgement in the location of their sampling sites Church and Kellerhals (1978) found significant within-site variations at (predominantly) bar-head sites along Peace River. Two aspects of their sampling may have contributed to this result. Mean sizes were estimated from 50-stone samples. While a sample of this size is generally regarded as adequate for characterising mean size (Bray, 1972), larger samples would have provided more precise, stable estimates. Second, the collection of replicates along separate line transects, especially if these were perpendicular to local flow patterns, would increase the possibility that unidentified spatial structure was incorporated. During sampling along the Pine and Sukunka an attempt was made to exclude these factors. Sample sizes were much larger with an average of 388 measurements for each sample. In addition, sampling was from a grid with dimensions determined by the largest material present. Consequently, individual samples typically approached the areal extent of the homogenous unit identified for sampling and the replicate grids were to some degree overlapping (although care was taken to avoid disturbed material by offsetting the grids). Within the unit the replicates do not therefore represent spatially distinct areas. Despite these precautions, there are detectable differences in mean grain sizes at three of the six sites. These differences must reflect an inability to characterise material of this heterogeneity with a mean based on approximately 400 measurements, and/or an inability to delineate a spatially homogeneous depositional unit. In order to examine the stability of the mean values obtained, the evolution of the sample mean with increasing sample size was 6 6 examined for each of the replicate samples at SBP 4 and SBP 7.5 (Figure 4.3). In aggregating the observations within a given sample it was not possible to reconstruct the spatial order encountered in the field. Rather, the observations were randomly sampled, and the mean calculated after each addition of five observations. The stability of each mean is evident in the rapid development of a horizontal trend. The samples which are responsible for the significant variability at each site (sample I at SBP 4, and C at SBP 7.5) are adequately characterised by 399 and 408 observations respectively. Thus they differ from their companions because of real differences in the populations being sampled, not because of vagaries in the sampling procedure, i.e., the unfortunate admission of one or two extreme measurements. The homogeneity of the sampled units at these and other sites is therefore in question. The operational problem of visually delineating a homogeneous unit is significant. Despite an operator's best intentions, subtle facies boundaries may go unrecognised. If the areal unit required in order to ensure adequate representation and the independence of individual observations is large, as it is here, limiting sampling to a single depositional unit is especially difficult. One can question the rationale for expecting to find an area in which the grain size population reflects a single, uncompromised depositional process. Subtle variability in bar topography and therefore in the bed stresses during flow events, may produce subtly different depositional conditions within the boundaries of accreting gravel sheets or unit bars. Marginal variations in the resulting grain size population within the larger recognisable unit may be impossible to see, but could be detected by large samples which vary slightly in their position. Furthermore, genetically distinct grain size populations may occur concurrently within the same areal unit. Bluck (1982) has pointed out the amalgamation of depositional flow events which may be represented by a single volumetric sample of bar-head material. Such samples may be deconstructed into component distributions which relate to particular modes of transport and deposition (Inoue, 1992). A similar palimpsest of generically distinct grain size populations may characterise a given area on the bar surface. For example, relatively mobile fine material arriving as a unit bar at the head of an older, larger barform may dissipate 67 Figure 4.3. Stability of replicate mean grain sizes at SBP 4 and SBP 7.5. Observations were randomly aggregated in steps of five. 100 200 Sample size 68 among the fabric of the pre-existing coarser bed unit such that the two populations become indistinguishable at a large scale. However, small changes in the alignment of a sampling grid which has a resolution similar to that of the surface structure could fortuitously differentiate the constituent distributions. There is clearly scope for work in this area (cf. Church and Kellerhals, 1978) and it is unlikely that much progress can be made without an improved understanding of small scale textural variabilty within visually homogeneous units. For the present study the implication is that some of the between-site variability is a reflection of irreducable site scale variations. It should be remembered however, that three of the six sites show no significant difference in mean value despite the highly sensitive nature of the test (large degrees of freedom). 4.1.3 Between-site variability We now turn to the question of whether there are significant grain size variations between sites. That is, are the mean grain sizes which occur at different sites drawn from the same or different populations. The chi-square procedure was applied to the Pine and Sukunka data (Table 4.3). For those replicate sites which showed no significant variability, the median mean size and the associated variance were chosen to represent the site. At the other replicate sites (SBP 7.5, SBP 4, and PLH5) samples were pooled in order to define the most representative mean and variance of the unit sampled. For both Pine and Sukunka Rivers C greatly exceeds X 2 oooi, and there is no doubt that the mean grain sizes vary significantly between sites. This analysis does not take into account the relative locations of the sites. It does however, provide a basis for exploring the question of whether grain size exhibits any spatial structure. 69 Table 4.3. Between-site variability. Equality of site means within each river. Number of W D C P (error) sites for H 0 , 1-a Sukunka 90 47703.84 5.703 9629.897 » 0.999 Pine 49 29916.27 5.249 13049.007 » 0.999 The final column represents the probability of error associated with acceptance of H 0 of no significant difference between replicate mean grain sizes. See text for definitions of W,D and C. Table 4.4. Runs tests for running mean sequences. Number of Number of Number of Probability of negative positive runs, r obtaining fewer changes, nn changes, np runs, P (%) Sukunka 49 38 33 1.2 Pine 20 26 19 10.6 See Appendix 4 for computational details. 70 4.2 Spatial structure Theoretical arguments and empirical evidence indicate that grain size distribution parameters can decline systematically in a downstream direction, particularly between tributary junctions in the absence of coupling and non-alluvial sediment sources. However, it does not appear that any simple model could adequately describe the covariance of mean grain size and distance shown in Figure 4.4. Some structure is apparent, though, and can be seen more clearly if the sequences are filtered using an unweighted three-point running mean (Figure 4.5). This removes some of the high frequency scatter associated with bar-to-bar scale variability. Several strong fining trends are evident, for example between 40 and 55 km on the Sukunka, and between 50 and 60 km on the Pine. Gradual coarsening sequences are also visible, for example between 30 and 40 km on the Sukunka. In general the sequence of mean sizes along the Pine appears to be less well organised than along the Sukunka. Runs tests (Appendix 4) were used to determine whether or not structure is present, that is, whether the changes in grain size from site to site exhibit a non-random pattern. Results for the running means are given in Table 4.4. Along the Sukunka there is only a 1.2 % chance of obtaining fewer runs than the number observed, which confirms the presence of low frequency structure. Along the Pine the same probability increases to 10.6 %, which is less conclusive but still indicative of a non-random, low frequency pattern. This structure suggests that a categorical variable is responsible for a significant portion of the grain size variability observed in the field data. Classifying individual grain size samples according to their location relative to particular sediment sources, each of which is responsible for redefining mainstem texture, has reduced unexplained variability in previous studies (e.g. Church and Kellerhals, 1978; Dawson, 1988). The remainder of this chapter is concerned with the identification of these lateral sediment inputs and the improvement in explanation which they afford. A thorough investigation of the variation of grain size parameters along the two study reaches is required. It is therefore appropriate to use a high resolution data set including both Figure 4.4. Mean grain size plotted against distance downstream for the Pine and Sukunka rivers. In each case a simple model is clearly inadequate. 71 Q_ I CD N CO C o C o CD 1 | - 1 1 1 ' | -1 • • - ( - 1 1 1 p - ! | . S u k u n k a — 1 1 •• 1 — r 1 1 1 1 1 1 1 - o o O O o o o °°° o o o o o ° O OO o o • ° O Q O n Q> o n ° o ° ° § o o ° o o ° ° ° ocsP o o o °o o o o o % o 0 ° o o o o o Q o o -o 1 . 1 , 1 , 1 , 1 , 1 , 1 1 , 1 , 1 , 1 . 1 . 0 1 0 20 30 40 50 60 70 80 90 1 00 1 1 0 1 20 Dis tance d o w n s t r e a m (km) I CD N l CO C O CP c o CD P ine o oo o o oo Oo o o o o o o ° ° o 00 0 10 20 30 40 50 60 70 80 90 1 00 1 1 0 1 20 Dis tance d o w n s t r e a m (km) 72 Figure 4.5. Three-point (unweighted) running mean values for the Sukunka and Pine mean grain size sequences showing fine structure. JZ CL c o CD c c c ZS 7.0 6.5 6.0 5.5 5.0 h 4.5 n > r - I 1 1 ' 1 1 1 1 -S u k u n k a ° o ° c % o o „ o o o « o o o o o o o O O Q 8 o o o 1 o o °OQ0 Oo _l i I i I i L_ J i I j I i L 0 10 20 30 40 50 60 70 80 90 1 00 1 1 0 1 20 Dis tance downs t ream (km) CL I • c o CD CP C C c 7.0 6.5 6.0 5.5 r-5.0 4.5 i 1 r P ine ' O o QD O O o o o o o o o o o o o o -o o o J i _ l i L 0 10 20 30 40 50 60 70 80 90 100 110 120 Dis tance downs t ream (km) 73 Wolman samples and photographic parameter estimates. Variations of median grain size (D5o) and D95 are examined. Given the asymmetry of the grain size distributions, D 5 0 is more appropriate than the mean as a measure of central tendency. D95 approximates the upper competence limit at a given location, and may therefore define stronger downstream trends (cf. Brierley and Hickin, 1985). Identification of significant lateral sources relies upon the isolation of discontinuities in grain size trends (Section 4.3). It is necessary to differentiate grain size steps caused by lateral sources from those caused by sampling problems, bar-to-bar scale variability, and distance downstream. This is difficult operationally, but in Section 4.4.1 a suitably flexible method is developed. Potential discontinuities are then identified and, by examining grain size trends, a series of discrete "sedimentary reaches", or "links", is defined (Sections 4.4.3 and 4.4.4). Classification of the grain size data according to the sedimentary links within which samples are located greatly reduces unexplained variability in both study reaches (Section 4.5). Explanation of textural variations is clearly improved by the identification and consideration of significant lateral sediment sources. 4.3 Lateral sediment sources and grain size discontinuities. Previous empirical studies show that the sediment supplied to a river by tributaries and other sources may redefine bed material and disrupt downstream fining trends. Miller (1958) suggested that coarse sediment supplied by tributaries was in part responsible for the grain size fluctuations he observed along streams in the Sangre de Cristo Mountains of New Mexico. Subsequent studies have identified disruptions in downstream maturation in response to sediment inputs at confluences (Church and Kellerhals, 1978; Knighton, 1980; Ichim and Radoane, 1990, Brewer and Lewin, 1993), at tributary fan contacts (Bradley et al, 1972; Dawson, 1988), and downstream from outcrops of non-alluvial materials such as glacial drift and bedrock (Bradley et al, 1972; Werritty, 1992). 74 I refer to such features as lateral sediment sources because they inject material which has characteristics independent of processes operating longitudinally within the recipient channel. Previous studies indicate that particularly large or dissimilar lateral inputs delimit a series of distinct reaches, within which sorting and abrasion processes modify the redefined throughput population to produce relatively systematic fining trends. In turn it has been demonstrated that a series of discrete size-distance relations are best suited to the description of changes in bed material texture along a fluvial system. For example, a series of negative exponential models, each delimited by clear breaks at tributary junctions, significantly reduced unexplained variation along the Peace River in British Columbia (Church and Kellerhals, 1978), various upland streams in England (Knighton, 1984), and part of the Sunwapta River in Alberta (Dawson, 1988). Rice (1994) and Pizzuto (1995) have suggested that realistic models of textural change must incorporate lateral sediment inputs. However, identifying which of many potential sources have a persistent downstream influence on bed material is not straightforward. Beyond unspecified references to relative tributary size, sediment load and sediment calibre, there are no existing theoretical or empirical guidelines for making a priori distinctions. Consequently, one must focus on the grain size information and isolate the important lateral sources on the basis of their effect rather than their cause. This procedure hinges on the identification of discontinuities, that is, on displacements or steps in the grain size signal that reflect a hiatus in downstream textural modification (the "sediment character jumps" of Brewer and Lewin (1993)), and is complicated by the spatial variability of bed material texture. 4.4 Identification of discontinuities and significant lateral sources. The studies cited above are characterised by few data or consideration of a limited number of lateral sediment sources. Consequently, examination of the data and identification of discontinuities was relatively straightforward (cf. Knighton, 1984, Figure 3.10 p.79), especially after local variability was removed (cf. Church and Kellerhals, 1978, Figure 7, p. 1157). In 75 contrast, there are a large number of potential sediment sources along both Pine and Sukunka Rivers and data resolution is high. According to 1:50,000 National Topographic Survey (N.T.S.) mapping there are 79 tributaries to the Sukunka and 76 to the Pine, and it is clear from the maps in Appendix 1 that the potential for coarse sediment input from non-alluvial contacts is considerable. Samples were collected at a high resolution in order to facilitate identification of all significant lateral sources, and any form of smoothing is undesirable. The identification of discontinuities is therefore significantly more difficult in the present study. Within a series of observations, one might model the value of an observed grain size parameter D, as [4.8] D =/(L s) + ew + sB where/is a function describing the cumulative effects of fluvial abrasion and sorting processes, L s is distance downstream from a major sediment source, ew is a within-site error term associated with the location of sample sites at a bar scale (particularly the (in)ability to isolate genetically discrete populations), and E B is a between-site (within-trend) error term associated with inherent bar-to-bar scale variability. The vagaries of local sediment mobilisation, transfer and deposition, and reworking of floodplain units produced by the same channel regime, but by distinct bar-scale hydraulic conditions, contribute to 8 B . The two error terms are assumed to be normally distributed random variables and, in the absence of additional sediment inputs, Ew + £ B account for the total residual variance about an empirical relation between grain size and distance. The initial problem here is to take an unclassified sequence of data and identify those between-site variations that are caused by intervening lateral sediment sources, rather than by sampling errors, inherent between-site variation, or distance. Where a lateral source does provide a likely explanation, one must then determine whether or not it has a persistent or transient effect on bed material texture. 76 4.4.1 Distinguishing among causes of between-site variation Distinguishing among the possible causes of a between-site difference is not straightforward. Comparing the magnitude of observed differences with estimates of 6w, S B and f (Li), where Li is the distance between sites, might indicate unusually large steps, but only the within-site variance term (sw) can be quantified (using replicate samples). The magnitude of the distance effect (f (Li)) cannot be defined prior to the isolation of any size-distance relations, and is therefore unknown until discontinuities are identified. An estimate of inherent between-site variability (SB), might be obtained by considering variations between closely spaced bars along input-free reaches. However, along these rivers, where bar spacings typically range between 102 and 103 m, one cannot assume that samples from consecutive bars are unaffected by distance. A flexible, somewhat involved method which uses statistical testing, reasonable assumptions, and careful examination of the situation at each sample site, is required. The problem is simplified if one assumes that discontinuities tend to be positive, such that [4.9] D D -Du>0 where D D is the value of a grain size parameter and Du is the value of the parameter at that site immediately upstream. If the volume of an influx of relatively fine sediment is sufficiently large, a step decrease in grain size is possible (see, for example, Andrews, 1979). However, such an input is less likely to persist than a relatively coarse input, because the relative coarseness of the mainstem is indicative of a transport regime capable of removing the finer material. Although the volume of the input is important, it is therefore reasonable to focus on downstream increases in size when searching for discontinuities. If one also assumes that sorting and abrasion processes tend to produce a downstream reduction in gross grain size parameters, then by focussing on positive changes one is also excluding distance as a potential cause of observed between-site differences Frostick and Reid (1980) have shown that this is 77 not neccessarily true for individual lithologies, but the majority of empirical evidence indicates that downstream fining is the norm in alluvial systems. Individual samples provide best estimates of the mean D50 and D95 at a site, and standard errors can be defined using the replicate samples. In those cases where a positive downstream change is identified, a t-test can be used to establish whether the difference in the mean value of a given parameter between consecutive sampling sites exceeds that expected on the basis of sampling chance. Pairs flagged by this test provide a starting point for further investigation. Within-site variance estimates are required for both percentiles, for each of the two sampling methods. For an individual Wolman sample the standard errors awP, are approximated using the best estimate of within-site variance based on the six sets of replicate samples, [4.10] a W p = V(2ii=1,6)Spi2/6) where spj2 is a variance estimate for percentile p based on the /th set of replicates. Each standard error is associated with l(i=i.6)ni -6=13 degrees of freedom. For the photographic estimates of D50 and D95 the within-site term must incorporate the variance due to site selection, and that due to the calibration error associated with the relation between count and the given parameter. The former element is equal to the Wolman within-site term ctwp, and the latter is the mean standard error associated with the prediction of an individual observation, a{Dp}c (section 3.3). The combined error term for photographic estimates is then [4.11] o-Pp = A/o-wp2 + c7{Dp}c2 with 13 + (69-2) = 80 degrees of freedom (each photographic calibration is based on 69 data points). In making a comparison of consecutive D50 or D95 values (which are assumed to represent mean values for the site) a t-value is calculated as [4.12] t = (D p D - D p U) / V (0-pD2 + CTpU2) 78 where the subscript D refers to the downstream sample and U to the upstream sample. Depending on whether the percentile estimates are based on Wolman or photographic sampling, the appropriate standard error estimates are substituted for <jpD and apu. If two Wolman samples or two photographic samples are being compared, the relevant degrees of freedom are simply 2n-2, where n is the number of degrees of freedom associated with the given technique's error estimate. For comparisons of Wolman with photographic estimates the degrees of freedom are given by [4.13] [(o-po + CTpu)2 / ((o-pD2/nD-l) + (o-pu2/nu-l))] - 2 where no and nu are the numbers of degrees of freedom associated with the downstream and upstream errors repectively. Table 4.5 lists those downstream increases in D50 and D95 along the Sukunka which exceed within-site variance with a probabililty of more than 95 percent. Table 4.6 lists similar increases along the Pine. Having isolated between-site changes which are not the result of distance or sampling effects it remains to distinguish inherent between-site variability from lateral source effects. The association of the latter with potential sediment sources (tributaries and streamside outcrops of non-alluvial material) makes this possible. All tributaries and non-alluvial contacts are considered to be potential sources of sediment, and are shown along with the sample sites in maps A to J, Appendix 1. All of the mainstem tributaries encountered in the field are shown on 1:50,000 N.T.S. maps, which are therefore considered to be adequate for identifying potential Table 4.5. Significant, downstream, between-site increases in D50 and Dg5 along the Sukunka River. Upstream site Downstream Difference in Difference in Potential source of sediment in intervening site D50 W TWU TWU 2 0.49(1) 0.26(1) Glaciofluvial fan exposed in RB TWU2 s94 5 1.78(1) 1.53(1) Twidwell Creek (S 12) SML U3 STW 1.5 0.42(1) 0.55(1) Till & b/rock (RB), McLean fan (LB) STW 1.5 s93 12.5 0.68(1) 0.62 (4) McLean Creek (S 17) & fan S20 U2 STW 2 0.19(3) 0.44(1) Morainal bench (LB), S 19 STW 2 S20U1 0.25 (2) - Fan, b/rock exposed in RB S20U1 S20D1 0.68(1) 0.42(1) S20 s93 2 SLTU1 0.42 (4) - ? No apparent source SLT U2 s93 3 0.80(1) 0.68 (3) ? No apparent source SLT U3 s93 4 0.65(1) - Lean-to Creek (S 22) s93 7 BKR4 0.50 (3) 0.55 (4) ? No apparent source BKR3 BKR2 0.71 (1) 0.33 (1) ? No apparent source STW 4.25 s93 19 0.76(1) 0.62 (4) Steep b/rock slope (LB) STW 4.5 S31 U2 0.31 (1) 0.33 (1) Fan exposed in RB, S 28 STW 5 STW 6 0.22 (3) - B/rock (RB), S 30 WFU WFD 0.44(1) 0.86(1) Windfall Creek (S 34) SCH U2 SWB 4 0.20 (3) 0.12(4) Colluvial apron exposed in LB SWB 5.5 SWB 6 1.63(1) 1.80(1) Rocky Creek fan exposed in LB SWB7 SWB 7.5 0.21 (3) - Glaciofluvial terrace over b/rock, LB SWB 7.75 SWB 8 - 0.36(1) Fan, S 48, S 49 s93 26 BND 2.54(1) 2.73 (1) Burnt River (S 50) s93 29 SBP 2.5 0.68(1) 0.68 (3) ? Boulder Creek fan SBP 5.5 s94 6 0.94(1) 1.04(1) Glaciofluvial terrace over b/rock, RB SMAU1 SMA U2 - 0.25(1) ? No apparent source SBP 7 s93 36 0.48 (3) - ? Martin Creek fan (RB) SBP 8 SHD Ul 0.37(1) 0.18(2) Dickebusch fan (RB) SHD U2 s93 39 0.76(1) 0.96(1) Dickebusch / Highhat fans s93 39 s93 44 0.62 (4) - Dickebusch / Highhat fans, S 70, S 71 SBP 9.5 s93 46 - 0.57 (4) ?S73 Within-site standard errors are a = 0.0636 0>, a = 0.0473 O, or = 0.2312 0, and a = 0.3125 <D. Levels of significance are shown brackets, where 1: a < 0.005, 2: tj.005 < a < 0.010, 3: 0.010 < a < 0.025, 4: 0.025 < a < 0.050. Table 4.6. Significant, downstream, between-site increases in D and D along the Pine River. Upstream site Downstream site Difference in D50 W Difference PMU 1 PMU 1.45(1) 1.52(1) PMU3 PMD 1 0.26(1) 0.21 (1) PMD 1 PMD 0.52(1) 0.52(1) p93 1 p93 2 0.85 (2) 0.84 (4) p93 3 PLU2 0.99(1) 1.23(1) p93 4 p93 5 1.07(1) 1.07 (2) p93 32 p93 33 0.57 (4) -p93 34 p93 35 1.25(1) 1.23(1) p93 37 p93 38 0.76 (3) 0.75 (4) PLH 3 PLH 4 1.27(1) 1.39(1) PLH 4.9 PLH 5 0.33 (1) 0.23(1) PLH 5 PLH 5.5 - 0.29(1) p93 42 PLH 6 0.85(1) 0.84(1) PLH 8 p93 30 0.64(1) 0.76 (2) PLH 9 p93 17 2.90(1) 2.78(1) PCMU2 p93 20 3.12(1) 3.18 (J) p93 24 p93 25 1.65(1) 1.64(1) PHS3.15 p93 16 2.01 (1) 2.29(1) PHS 3.2 PHS 3.23 2.29(1) 1.65(1) PHS 3.25 p93 13 0.80(1) 1.16(1) PHS 3.75 PHS 3.9 0.54(1) 0.58(1) PHS 4.5 p93 10 1.74(1) 1.61 (1) p93 12 PHS 5 1.25(1) 1.75(1) Potential source of sediment in intervening reach Glaciofluvial terrace exposed in RB Mountain Creek (P 2) Mountain fan, Cairns Creek (P 3) Lemoray fan in RB Lemoray fan in RB Lemoray Creek (P 4) ? P 8, Colluvial fans (RB) Big Boulder Creek fan ? Big Boulder Creek fan Beaudette Creek, Fisher Creek, fans Crassier Creek fan ? p 23-26, lacustrine terrace (LB) P 35 fan, b/rock(LB) P 43 fan, b/rock (LB) Hasler Creek (P 45) and P 44 fan Goodrich Creek (P 49) and fan Caron Creek (P 56) P60 Bisset Creek (P 62) B/rock cliff, RB ? no apparent source Canyon reach (see text) Canyon reack (see text) Within-site standard errors are cr,.,„ = 0.0636 <D, a 0.005, 2: 0.005 < a < 0.010, 3: oM% < a < 0.025, 4^ 6.025 = 0.0473 O, o <a<0.050 = 0.2312 <D, and a p 9 5 = 0.3125 G>. Levels of significance are 1: a < 81 tributary input sites. For each pair of significant between-site differences identified above, possible sources of sediment in the intervening reach are indicated in the final columns of Tables 4.5 and 4.6. Non-alluvial materials and/or tributaries which currently supply or may have recently supplied sediment are present in all but five cases along the Sukunka and one on the Pine. In the absence of reasonable exogenous explanations, these six steps reflect inherent between-site variability within alluvial reaches. 4.4.2 Significant lateral inputs and sedimentary reaches The effect of a given lateral source depends on the delivery rate and textural characteristics of the material supplied. Redefinition of the throughput population is dependent upon an influx that is sufficiently voluminous or which exhibits a decidedly dissimilar grain size distribution. Consequently, not all of the sources identified in Tables 4.5 and 4.6 have a persistent effect on bed material texture. Those which do can be identified by their association with the beginning and/or end of a reasonably systematic fining trend. Those which do not are presumably sufficiently small and/or texturally similar as to be accommodated by the throughput population within a few channel widths. The former sources define a series of sedimentologically distinct reaches which provide a meaningful framework for examining textural change along the mainstem. In contrast, the smaller inputs simply augment residual variability due to within and between-site variance. The identification of significant lateral sources is thus dependent on the identification of fining trends and vice versa. In light of the scatter which exists in most reaches and the large number of potential sediment sources, recognising trends is seldom straightforward and a significant degree of judgement is usually required. An absence of grain size data because of access problems further complicates the task in some reaches. Careful evaluation of the potential sediment sources in terms of their sediment delivery capabilities is fundamental in order to decide whether or not a given source can reasonably explain a coincident step. Field notes and observations are used to inform these decisions, which are often difficult to make 82 given the lateral instability of the wandering channels and the possible persistence in the mainstem of sediments derived from historically active sources. Nevertheless, a number of sedimentologically discrete reaches can be identified. They are demarcated upstream and/or downstream by significant, between-site, downstream increases in grain size, that are reasonably explained by coincident lateral sediment sources. In most cases they exhibit fining trends of variable strength, within which scatter about a relation with distance is attributable to site and bar scale variability, the latter incorporating lateral effects which are insufficient to redefine mainstem texture. 4.4.3 Sukunka sedimentary reaches Along Sukunka River seventeen discrete reaches have been defined. These are indicated with the associated discontinuities and significant between-site steps in Figure 4.6 which shows downstream variations in D50. The procedure by which these reaches have been identified is, as suggested above, somewhat complex and it is therefore useful to briefly review my reasoning on a reach by reach basis. Refer to maps A to E in Appendix 1 for clarification of sample site locations. Three very small reaches (numbers 2, 4 and 6) which contain only one or two sediment accumulations are not explicitly considered. 1. The identification of Dudzic Creek confluence with the upstream end of the first reach requires some explanation given that a significant step is not observed between s94 2 (0.5) and s94 3 (1.4). There are no notable sediment accumulations in the 700m immediately downstream of the Dudzic Creek confluence, and samples collected at DZU (0.5) and DZD (1.2) in the first days of the 1992 field season were subsequently rejected upon revision of sample site selection criteria. Marked coarsening of the bed material below the confluence was observed during the profiling exercise in 1994 and I assume that it is only the lack of samples between s94 2 (0.5) and s94 3 (1.4) which precludes the identification of a significant step at the confluence. Thus, depite the lack of a t-test flag, the Dudzic confluence is taken as the 83 Figure 4. 6. Downstream variation of D along the Sukunka River. Significant between-site steps (shaded), discontinuities {dashedlines), and sedimentary reaches are indicated. Error bars are 95% confidence intervals. 1 o 11 1 2 ! i i i o i $ 4 • Photo samp le o Wolman samp le 40 45 50 55 60 65 70 75 8 0 1 4 1 5 1 6 i 80 85 u C c 90 95 t5~s If _ X I"* p 1 7 1 00 1 05 1 1 0 1 1 5 1 20 Dis tance downst ream (km) 84 upper end of this link. Adjacent to TWU Sukunka River is actively eroding the toe of a large glaciofluvial fan and a 30m high, largely unvegetated cutbank constitutes the river's right bank. Coarse bouldery material litters the base of this cutbank and the bed of the river. There is subsequently a significant grain size step between TWU (8.3) and TWU 2 (8.5) (the bar immediately downstream), and the fan input is therefore taken to demarcate the end of the first reach. 3. Twidwell Creek enters the Sukunka between TWU 2 (8.5) and s94 5 (8.8) where a significant step occurs. Large active bars in the tributary and in the reach downstream of the confluence attest to Twidwell's unequivocal role as the significant sediment source responsible for this step. Fining is apparent prior to the next significant step and termination of the third reach between SML U3 (14.1) and STW 1.5 (14.4). McLean Creek fan, and an unstable roadcut exposing till and bedrock above the right bank, both produce coarse material at this point. It is unclear which is primarily responsible for the step but either provides a reasonable explanation for the observed step and the identification of a discontinuity is clear. 5. The subsequent step between STW 1.5 (14.4) and s93 12.5 (14.6) is attributable to McLean Creek and its fan, which is subject to active erosion by Sukunka River downstream of the confluence. Fining is then observed as far as S20 U2 (16.3), after which a significant step is apparent. A morainal bench within a few tens of metres of the left bank may have introduced coarse material to the river in the recent past, but is heavily vegetated and stable today. S 19 is a more likely source of coarse material between S20 U2 (16.3) and STW 2 (16.7), and confirms this step as a discontinuity. 7. The unnamed tributary, S 20 enters the main stem at the site of the next discontinuity between S20 Ul (17.2) and S20 Dl (17.5). Although there is a significant between-site increase between STW 2 (16.7) and S20 Ul (17.2) the influx of sediment from S 20 immediately downstream is a more important sediment source. The next two steps are not readily explained, 85 but the third, between SLT U3 (19.1) and s93 4 (19.3), occurs at the confluence of Lean-to Creek. The latter therefore demarcates the end of a poor fining trend. Without s93 3 (19.0) the data would define a better trend, but there is no basis for excluding this sample and one must assume that it is an extreme example of bar to bar scale variability. 8. Between the discontinuity at Lean-to Creek and STW 4.25 (27.4) there are two unexplained steps and an absence of any fining trends, which may reflect intermittent hillslope-channel coupling in the upper part of the reach. The three subsequent steps between STW 4.25 (27.4) and s93 19 (28.4), STW 4.5 (29.2) and s31 U2 (29.8), and STW 5 (30.6) and STW 6 (32.3) are each associated with potential sediment sources. However, only the alluvial fan between STW 4.5 (29.2) and S31 U2 (29.8) appears to be an active source. Data resolution is relatively poor in this section because of access problems and the consecutive occurrence of the steps makes it difficult to define any trends. The entire reach between Lean-to and Windfall is best characterised as a single reach within which grain size is essentially independent of distance. 9. The step between WFU (36.9) and WFD (38.2) is attributable to Windfall creek which is the most significant sediment source upstream of Burnt River. The tributary enters the Sukunka as a braided channel flowing across a very large alluvial apron. An exceptionally clear fining trend is subsequently observed as far as SWB 5.5 (53.9). There is a small step between SCH U2 (47.6) and SWB 4 (47.9) which is associated with an exposure of coarse colluvial material in the left bank. However, statistical confidence in this step is relatively low for both D50 and D 9 5 , and it does not appear to significantly interrupt an otherwise excellent trend. Immediately upstream of SWB 6 (54.6) a 5m high exposure has been cut in the margin of Rocky Creek's fan. The exposure reveals cobble-boulder materials which are also evident in the adjacent channel, and the bar from which sample SWB 6 (54.6) was collected. This active contact is clearly responsible for the observed discontinuity between SWB 5.5 (53.9) and SWB 6 (54.6). 86 10. The next break occurs in the D50 signal between SWB 7 (56.5) and SWB 7.5 (57.0), and is marginal statistically. The potential sediment source at this site, a glaciofluvial exposure overlying bedrock, does not appear to be very active. There is no clear break in an otherwise decent fining trend between SWB 6 (54.6) and SWB 7.75 (57.5), and this step is consequently not identified as a discontinuity. Indeed the trend continues essentially uninterrupted in the D 5 0 data at least as far as s93 26 (58.8). However, a significant break is observed in the D95 data between SWB 7.75 (57.5) and SWB 8 (58.3). Rocky Creek and the smaller S 48 enter Sukunka River in this reach and either could reasonably explain the increase in D 9 5 . Although an uninterrupted trend could be envisioned it is therefore appropriate to demarcate this step as a discontinuity and the end of reach 10. 11. Downstream of SWB 8 (58.3), as far as the Burnt River confluence, there are very few sediment accumulations and these are largely inaccessible because of a series of rapids and waterfalls. Fining may continue between the bars downstream of s93 26 (58.8), the final sample collected prior to Burnt River, but this remains unknown. 12. The significant step in grain size between s93 26 (58.8) and BND (65.6) is associated with the Burnt River confluence. The Burnt is approximately the same size as the Sukunka at this point and supplies a large amount of coarse material, much of it derived from large glaciofluvial terrace exposures within a few kilometres of the confluence. Fining is observed until the next significant between-site step at s93 29 (73.2). 13. The step between s93 29 (73.2) and SBP 2.5 (74.0) lacks a very convincing explanation in terms of a coincident lateral sediment source. However, the data do suggest that this step separates two distinct fining trends, albeit weak ones. At the present time Boulder Creek enters Sukunka River a few hundred metres upstream of SBP 2 (72.2), over a very steep cobble-boulder fan. The margins of the fan are difficult to determine, in part because of the various terrace levels which are apparent on the valley floor throughout this reach, and it is feasible that 87 the mainstem is entraining coarse fan material in the vicinity of s93 29 (73.2). Given this potential explanation I am unwilling to accept that the step is a consequence of inherent between-site variability, and am confident that it can be classified as a discontinuity. Downstream of the step a moderate fining trend continues until SBP 5.5 (85.6). Immediately below this site an almost vertical glaciofluvial terrace scarp with bedrock exposed at its base constitutes the right bank of the channel. Downstream, cobble-boulder material covers the bed for approximately 800 m, and a significant increase in size is observed at the next bar, where photograph s94 6 (87.1) was taken. The terrace scarp is clearly a significant sediment source and demarcates the end of reach 13. 14. A significant step in the D 9 5 data between SMA Ul (88.7) and SMA U2 (89.4) is not apparent in the D50 series. Both banks are alluvial here and there are no intervening tributaries. No sediment source is apparent and the step is therefore regarded as indicative of between-site variation. The next step occurs between SBP 7 (91.7) and s93 36 (92.4) and is coincident with the margins of Martin Creek fan, which provides a reasonable explanation for the step. The fining trend here is not very strong, which may reflect the mainstem's confinement between bedrock cliffs on the left bank and Martin Creek fan on the right. 15. Downstream from s93 36 (92.4) fining is apparent until SBP 8 (97.2) where initial contact with Dickebusch Creek's large, degraded fan provides an explanation for the step up to SHD Ul (97.5). 16. Grain size subsequently increases between the extant sediment accumulations (samples SHD U2 (98.2), s93 39 (99.3), s93 44 (100.3)). This coarsening can be attributed to inputs from Highhat River, Dickebusch Creek, and their fans, between which Sukunka River is sandwiched in this reach. 88 17. The final fining sequence continues downstream of Dickebusch Creek as far as the Sukunka's confluence with Pine River. Although a significant step does not occur between the final Sukunka sample at SKU (110.8) and the first post-confluence Pine sample at PRD (109.0), a break in the trend is apparent, and the confluence is designated as the end of the final Sukunka reach. The lack of a discontinuity at this confluence is considered in some detail in Section 5.3.1. Within this section, between SBP 9.5 (103.0) and s93 46 (104.0), there is a marginally significant step in the D 9 5 data, which although not statitically significant (a > 0.05) also shows up in the D 5 0 sequence. Good fining trends could be defined upstream and downstream. However, a reasonable trend is apparent without this break, and there is no convincing explanation in terms of a coincident sediment source. S 73 is a small tributary which does not supply a significant amount of sediment to the mainstem, and the exposure of Dickebusch fan adjacent to s93 45 (102.3) appears to be too far upstream to have an impact downstream of SBP 9.5 (103.0). There is the possibility that the step is associated with a former position of Dickebusch fan. However, my inclination is to classify this as a disruption rather than a discontinuity. A second internal disruption is apparent in the vicinity of s93 48 (107.9), but again there is no reasonable explanation for it, it does not satisfy the between-site difference criteria, and it is best regarded as indicative of inherent bar-to-bar scale variation. 4.4.4. Pine sedimentary reaches Sixteen discrete sedimentary reaches can be identified along Pine River. These are shown, along with discontinuities and significant between-site steps in D50 in Figure 4.7. Refer to Appendix 1 (maps F to J) for clarification of site locations relative to tributaries and other sediment sources. One very small reach (number 11) is not explicitly considered in the following discussion. 1. Upstream of .Lemoray Creek confluence texture varies erratically with large between-site differences and no systematic fining trends. The end of this reach is defined by the grain Figure 4. 7. Downstream variation of D along the Pine River. Significant between site steps (shaded), discontinuities (dashed Tines), and sedimentary reaches are indicated. Error bars are 95% confidence intervals. 7 h 7i 6 40 IT h I 4-o in Q 5 1 o -H "5 45 1 2 50 55 60 65 70 75 80 i 3 1 4 1 5 1 6 h-r1-C a n y o n 80 85 90 95 100 105 D i s t a n c e d o w n s t r e a m ( k m ) 1 5 20 90 size step between p93 4 (4.9) and p93 5 (5.4) which is adequately explained by the coincident entrance of Lemoray Creek, and which is associated with a subsequent fining trend. 2. Fining is observed as far as p93 32 (10.1), at which point a weak step is observed. In the intervening reach neither tributary P 8 nor the colluvial apron close to the right bank are very active, and an adequate explanation of this step is not forthcoming. A more significant step occurs immediately downstream between p93 34 (12.9) and p93 35 (13.6) and is reasonably explained by the juxtaposition of Big Boulder Creek fan. This is therefore taken as the downstream discontinuity of the second reach. 3. A subsequent step between p93 35 (13.6) and p93 36 was noted in the field but the photograph taken at p93 36 did not develop, and there is therefore no quantitative evidence. Immediately downstream is a small step (p93 37 (14.8) to p93 38 (15.5)) which is reasonably explained by historical contact with Big Boulder fan, and is therefore defined as a discontinuity. The resulting reach is very short, and difficult to assess. 4. Downstream, a fining trend continues at least as far as PLH 3 (24.5). Lack of data in this reach due to accessibility problems hampers interpretation, but given the dominantly alluvial nature of the channel it is reasonable to expect fining to continue until Beaudette Creek confluence. Of the three possible sources of the step between PLH 3 (24.5) and PLH 4 (30.8) (Beaudette Creek, Fisher Creek, and Falling Creek fan), Beaudette is the most active and therefore the most likely to redefine mainstem texture.' A discontinuity and the termination of reach 4 is therefore defined at this confluence. 5. Fining is subsequently observed as far as the step between PLH 4.9 (35.9) and PLH 5 (36.1) (a replicate site where mean D50 and D 9 5 were used in the t-tests). The step is small but can be explained by contact with Crassier Creek fan. It is therefore defined as a discontinuity and the termination of sedimentary reach 5. 91 6. The small step between PLH 5 (36.1) and PLH 5.5 (42.8) could be associated with any of several potential sources. Lack of data precludes a reasonable association with any one source. Indeed, lack of data as far as p93 42 (53.0) precludes the formulation of any reasonable statement regarding the nature of bed material changes in this reach. 7. The significant step between p93 42 (53.0) and PLH 6 (53.7) can be attributed to the fan of tributary P 35 and/or bedrock contact along the left bank. From here fining is apparent as far as PLH 8 (60.0), after which there is a significant step to p93 30 (61.9). Contact of the left bank with a steep bedrock exposure, the fan of P 43, and Hasler Creek fan provide feasible explanations for this step. Disruption of the fining trend is clear and a discontinuity is defined. 8. Data are available only in the upper part of the reach between p93 30 (61.9) and Hasler Creek confluence. Downstream of PLH 9 (62.7) there are no sediment accumulations to sample. It is therefore difficult to know whether the fining trend indicated by the three available data points continues, especially in light of potential non-alluvial supply by bedrock and fans. 9. The significant step between PLH 9 (62.7) and p93 17 (65.4) is adequately explained by coarse sediment input from Hasler Creek, its fan, and perhaps the fan associated with P 44 too. An excellent fining trend is then observed as far as PCM U2 (72.3) after which a large positive step is observed. This is coincident with the confluence of Goodrich Creek (P 49) and may also reflect sediment input from Commotion Creek which is presently confluent a short distance downstream. 10. Subsequently, a strong fining pattern is again observed and continues as far as PLH 2.5 (78.2). Within a few hundred metres of this site Pine river enters the first of several sections in which bed and banks are composed of sands, silt and clay, rather than gravel and sand. 92 Sediment accumulations are generally absent in these reaches, sand ripples and clay flutings are characteristic of the bed, and the channel gradient is very low. The last of these sections extends to the canyon through which the Pine now descends to the Sukunka confluence. Except for the injection of coarse gravelly material at several points between PHS 2.5 (78.2) and the canyon, it is likely that the low gradient section would be continuous. The presence of gravel on the bar where sample p93 24 (80.8) was collected suggests that P 54 is the first of these injection points. This tributary is therefore associated with a discontinuity and the end of reach 10, even though a significant step is not observed between PHS 2.5 (78.2) and p93 24 (80.8). 12. A second injection of coarse material by Caron Creek is responsible for the significant step between p93 24 (80.8) and p93 25 (81.8). Fining is then observed as far as PHS 3.15 (85.8), a bar composed of fine gravels close to the beginning of the second clay/sand reach. A significant step between this site and p93 16 (87.4) is associated with a gravel input by tributary P 60 which demarcates the end of reach 12. 13. This gravel input persists for only a short distance (from p93 16 (87.4) to PHS 3.2 (88.5)) but a significant decrease in grain size is observed. The channel then enters a third clay/sand reach which is interrupted by a large influx of gravel at Bisset Creek confluence, as indicated by the significant step between PHS 3.2 (88.5) and PHS 3.23 (91.3). Although there are only two data points, it is reasonable to designate the reach between P 60 and Bisset Creek as sedimentary reach 13. 14. Fining is evident downstream of Bisset Creek confluence but only for a short distance. A significant step occurs between PHS 3.25 (92.8) and p93 13 (94.3), and is reasonably explained by the presence of a high, unstable bedrock cliff approximately 300 m upstream of p93 13 (94.3). Despite a lack of exposed sediment accumulations the bounding discontinuities of a sedimentary reach are clear, and the available data suggest strong fining. Reach 14 is therefore defined between Bisset Creek and the bedrock cliff. 93 15. Downstream of the bedrock cliff fining proceeds as far as PHS 3.75 (95.8), where a small step to PHS 3.9 (96.7) is observed. There is no apparent reason for this step in terms of a sediment input and it is therefore attributed to inherent between-site variability. The channel enters a fourth and final sand/clay reach which contains gravel accumulations at PHS 4 (97.5) and PHS 4.5 (99.2). A significant step occurs between PHS 4.5 (99.2) and p93 10 (100.8), which also delimits the beginning of the canyon produced by the incision of Pine River into glaciolacustrine and bedrock units following re-routing during deglaciation. Bed material throughout the canyon is very coarse, and is unlikely to have passed through the low gradient channel of the Pine upstream of p93 10 (100.8). It is a lag deposit created by the aforementioned incision, and can be viewed as the remnant of a diffuse non-alluvial sediment source. The upstream extent of the lag material therefore delimits the end of reach 15. 16. There is evidence of fining within the canyon between p93 10 (100.8) and p93 12 (103.5) and subsequently beyond PHS 5 (103.7). However, it is clear from field inspection that the accumulations of material available for sampling at p93 11 (102.6) and p93 12 (103.5) are not representative of the channel bed, which is consistently bouldery. The canyon section is defined as a distinct reach because of its unusual history. Downstream from the canyon the Pine/Sukunka confluence is marked by the somewhat unexpected absence of a discontinuity, and in fact, a fining trend is apparent from PRU (107.0, the final sample upstream of the confluence) to PR3 (113.2, the sample collected at the end of the study reach). However, I am not confident that this trend reflects fining of material supplied by the canyon source. There is some evidence (considered further in Section 5.3.1) that Sukunka River is introducing a relatively fine load and causing a reduction in median size along the Pine. This complication precludes the definition of a disinct reach below the canyon. 94 4.5 Improvement in explanation Discontinuities associated with significant sediment sources delineate 16 reaches along Pine River, and 17 on Sukunka River (Figure 4.8). Downstream fining trends are apparent in twenty one of these, representing 67 % of the Pine study reach and 75 % of the Sukunka study reach. In two sections (upstream of Lemoray Creek on the Pine, and between Lean-to Creek and Windfall Creek on the Sukunka) no trends are apparent, and in the reach adjacent to Dickebusch and Highhat fans, downstream coarsening occurs. The canyon reach of Pine river is a special case in that the bed is a lag deposit and contains little mobile sediment. Three reaches (upstream of Burnt River on the Sukunka, downstream of Crassier Creek on the Pine and upstream of Hasler Creek on Pine) contain too few data to allow a reasonable assessment of the textural changes within them. The latter two could conceivably contain several fining reaches. The five remaining reaches are very small sections with only one or two sediment accumulations (reaches 2,4 and,6 on Sukunka, and 3 and 11 on Pine). Identifying these discontinuities and sedimentary reaches involves a certain degree of judgement. My interpretations are not the only ones possible, but I have been consistent and meticulous in my attempt to distinguish among possible sources of variance on a site by site basis. The classification described represents a sound definition of the sedimentological character of these two alluvial systems. Without sampling the active bed, rather than exposed bars, additional information is largely unavailable. Difficulties of interpretation reflect the natural complexity of the system rather than an inability to accurately characterise it. In several sections almost 90 % of exposed bars were sampled and on average 63 % of bars on the Sukunka and 51 % on bars on the Pine were sampled (Table 4.7). Two relatively inaccessible sections from Big Boulder Creek to P 35 on the Pine and immediately upstream of Windfall Creek on the Sukunka, are the only two reaches where a significant improvement in sampling resolution could be made. 95 Figure 4.8. Significant lateral sediment sources and the resulting partition of Pine and Sukunka Rivers into sedimentary reaches. R e a c h 6, d o w n s t r e a m of C r a s s i e r ; poo r da ta I f e a c h u \ " [ R e a c h 1 5 ; / ' I R e a c h 9 | " - " \ • R e a c h 2 R e a c h 1, ups t ream of L e m o r a y ; no t rend R e a c h 16 C a n y o n 7 R e a c h 17| R e a c h 16, D i c k e b u s c h & Highhat fans ; c o a r s e n i n g R e a c h 15 R e a c h 131 v J R e a c h 10 R e a c h 9 Significant Lateral Sediment Sources Pine 1 • Lemoray Creek River 2. Big Boulder fan (upstream) 3. Big Boulder fan (downstream) 4. Beaudette Creek 5. Crassier Creek fan 6. P35 / bedrock 7. P43 / bedrock 8. Hasler Creek 9. Goodrich Creek 10. P54 11. Caron Creek 12. P60 13. Bisset Creek 14. Bedrock cliff 15. Canyon 1. Dudzic Creek 2. Glaciofluvial exposure Sukunka 3. Twidwell Creek River 4. Till exposure 5. McLean Creek 6. S19 7. S20 8. Lean-to Creek 9. Windfall Creek 10. Rocky Creek fan 11. S 48 / Rocky Creek 12. Burnt River 13. Boulder Creek fan 14. Glaciofluvial scarp 15. Martin Creek fan 16. Dickebusch Creek fan 17. Highhat River fan 96 Table 4.7. Sampling resolution along the Sukunka and Pine study reaches. Sedimentary reach Length Number Number Percentage (km) of of of bars samples exposed sampled bars Sukunka 1. Dudzic Ck. - glaciofl. exposure 7.77 9 30 30 3. Twidwell Ck - till exposure 5.42 11 16 69 5. McLean Ck. - S 19 2.17 4 5 80 7. S 20 - Lean-to Ck. 2.04 7 8 88 8. Lean-to Ck. - Windfall Ck. 18.00 28 44 64 9. Windfall Ck. - Rocky Ck. fan exp. 17.00 20 46 43 10. Rocky Ck. fan- S 48 3.60 6 8 75 11. S 48 - Burnt River 6.02 2 5 40 12. Burnt River - Boulder Ck. fan 8.60 7 14 50 13. Boulder Ck. fan - Fluviogl. scarp 12.60 12 23 52 14. Fluviogl. scarp - Martin Ck. fan 6.10 7 8 88 15. Martin Ck. fan - Dickebusch fan 5.40 5 8 63 16. Dickebusch / Highhat 2.73 3 4 75 17. Dickebusch Ck. - Pine River 11.60 14 20 70 Pine 1. PMU - Lemoray Ck. 5.27 13 17 76 2. Lemoray Ck. - Big Boulder fan 8.43 7 19 37 4. Big Boulder fan - Beaudette Ck. 15.02 5 29 17 5. Beaudette Ck. - Crassier Ck. fan 7.28 3 15 20 6. Crassier Ck. fan - P 35 / bedrock 17.30 4 34 12 7. P 35 / bedrock - P 43 / bedrock 7.60 8 17 47 8. P 43 - Hasler Ck 3.92 3 5 60 9. Hasler Ck - Goodrich Ck. 7.73 8 19 42 10. Goodrich Ck. - P 54 8.00 7 15 47 12. CaronCk. - P 60 5.51 5 6 83 13. P 60-Bisset Ck. 3.73 2 2 100 14. Bisset Ck. - bedrock cliff 3.03 2 5 40 15. Bedrock cliff - canyon entrance 6.00 8 9 89 16. Canyon 6.00 4 9 44 The total number of Wolman and photographic samples in each sedimentary reach is compared with the number of sediment accumulations exposed during summer low flows. 97 Categorisation of grain size parameters according to the reaches in which they are located greatly reduces unexplained textural variability on both rivers. This is clear when one compares the total residual variance about a single regression model with that associated with a set of models fitted to the individual reaches. Exponential models, which have been widely utilised in studies of textural change, are used to make this comparison (alternative fining models and their applicability to Pine and Sukunka sedimentary reaches are discussed in detail in Section 6.1). If D' is a grain size parameter measured arithmetically, for example in mm, then according to the exponential model, [4.14] D' = D'o.e a L where L is distance downstream, D'o is the value of D' at L = 0, and a' is a coefficient of diminution. If grain size is measured on a logarithmic scale, for example using phi units, [4.15] D = D 0 + cx.L where, D is grain size = log2(D'), Do is the value of D at L = 0, and a is a coefficient of diminution = a'.log2(e). Thus for phi data the relation takes a linear form. Exponential models of the relations between distance and D5o are shown in (Figure 4.9). Reaches which include less than three data points were excluded from the analysis. For Pine River, the use of reach-scale models reduces the total residual sum of squares by approximately 75 %, from 39.32 phi2 to 9.96 phi2, and on Sukunka River there is a similar reduction in residual variance of approximately 78 %, from 36.63 phi2 to 8.10 phi2 (Table 4.8). These results provide the most thorough confirmation to date that explanation of textural change in alluvial systems is dependent on identifying significant lateral sources. In turn it is clear that models of fining processes, whether empirical or theoretical (e.g. Parker, 1991; Hoey and Ferguson, 1994), will be most successful when applied within the reaches delimited by 98 Figure 4.9. Exponential regression models fitted to the classified and undifferentiated D50 values for a) Pine River and b) Sukunka River. Sedimentary reaches are numbered, and discontinuities are indicated by dashed vertical lines. 0 b) Sukunka li ii, ii ii h . i i i n i L_j i i — L J — u u 1 0 20 40 60 8 0 1 0 0 1 2 0 Distance downstream (km) 99 Table 4.8. Improvement in residual variation following classification of grain size data by sedimentary reaches. Exponential models relating D50 (-pni) to distance downstream (tan) were used in this comparison. Pine n SS R2 Sukunka n SS R 2 Residual Residual All data 80 39.32 0.02 All data 139 36.63 0.02 u/s Lemoray 13 3.18 0.00 Reach 1 9 0.16 0.89 Reach 2 8 0.75 0.61 Reach 3 11 1.13 0.79 Reach 4 5 0.01 0.98 Reach 5 4 0.19 0.73 Reach 5 3 0.05 0.91 Reach 7 7 1.33 0.29 d/s Crassier 8 0.03 0.04 d/s Lean-to 30 2.05 0.04 Reach 7 8 1.16 0.72 Reach 9 20 0.78 0.86 u/s Hasler 3 0.10 0.77 Reach 10 6 0.22 0.84 Reach 9 8 0.75 0.88 Reach 12 7 0.14 0.88 Reach 10 7 1.07 0.81 Reach 13 14 0.36 0.70 Reach 12 5 0.39 0.92 Reach 14 7 0.34 0.30 Reach 15 8 1.17 0.26 Reach 15 7 0.32 0.71 Canyon 4 1.16 0.02 Dickebusch 3 0.06 0.83 Reach 17 14 1.02 0.66 All sections 80 9.96 0.55 139 8.10 0.66 Sections with fewer than three data points were excluded from this analysis. Values are given to 2 d.p.. 100 lateral sources. It is evident however, that fining does not occur in all reaches, and that rates are highly variable between reaches. Using their own model, Hoey and Ferguson (1994) were able to produce a reasonable simulation of the grain size changes along a 2.5 km reach of Allt Dubhaig, a small stream in upland Britain. This confirms the value of their modelling approach, but also reflects the idealised conditions of the study reach which is free of any lateral sediment inputs (Ferguson and Ashworth, 1991). In the sense that significant lateral sources represent points of adjustment within the sedimentary system, an analogy can be drawn with tributary junctions in the channel network. Adjustment is to an input of clastic material rather than of water, and by extension the intervening reaches are analogous (and may be equivalent) to channel network links. Reaches such as those identified above might then be regarded as sedimentary links, within which fluvial processes operate relatively free of lateral interruptions, just as network links are supposed to be closed to significant hydrologic inputs. The sedimentary link is a useful concept which can be used to describe the framework within which alluvial textures are produced. Realistic models of textural variation must focus on the network of sedimentary links which characterise any fluvial system. The work of Dawson (1988) has been cited in this chapter in support of my argument concerning the importance of lateral sediment inputs. His work also indicates, however, that a model based on fining within sedimentary links may not everywhere minimise unexplained variations. Using covariance analysis, he confirmed the impact of three potential sediment sources on textural maturation along a 10 km reach of the Sunwapta River, Alberta. However, clear grain size discontinuities and sediment inputs are associated with only two of the three tributary fans. At Wooley Creek, which is not a significant source of sediment, there is a subtle change in the slope of the size-distance relation, but no textural step. This indicates that changes in the nature of the fining process can occur within sedimentary links. In this case one can hypothesise that the change in fining rate is an adjustment to the new hydraulic conditions below the Wooley Creek confluence. Tributaries which introduce water, but not sediment, may therefore be an important consideration in refining classifications based primarily on lateral 101 sediment inputs. It is also possible, however, that the observed change in slope is in fact unrelated to the tributary and reflects the unsuitability of exponential models in braided streams, as has been demonstrated by Frostick and Reid (1980) and by Brierley and Hickin (1985). 4.6 Summary This chapter has examined grain size variability at several scales along the two study reaches and identified spatial structure associated with lateral sediment inputs. Significant within-site variations are apparent at three of six replicate sites despite every effort to minimise sampling error. This result confirms the findings of Church and Kellerhals (1978) and Dawson (1988). Identifying genetically distinct grain size populations on depositional surfaces which constitute a palimpsest of depositional and erosional events is clearly problematic. Huddart (1994) reports no significant within-site variability for sites on the Morsardalur-Kjos sandur, southeast Iceland, but gives no details of his sampling procedure. Between-site variations are significant in both rivers and there is therefore a basis for seeking a relation between grain size and distance. General (exponential) models fit neither data set but significant structure is apparent at a finer spatial scale. Previous empirical studies suggest that this structure is related to tributaries and lateral sources of sediment. Data from the Pine and Sukunka rivers demonstrate the improvement in explanatory power afforded by classifying a river into a series of discrete reaches separated by significant lateral sediment sources. Most of these reaches exhibit fining trends which reflect the modification of material by fluvial processes in the absence of disruption by major lateral inputs. An important implication for models of textural change is that models of downstream fining will only be as successful as the isolation of significant lateral sediment sources and thereby the links within which fining processes can operate unhindered. The successful identification of discontinuities and sedimentary links on Pine and Sukunka Rivers is not surprising given that grain size data were at hand. However, in order to apply fining models in 102 a predictive mode, it will be necessary to identify significant lateral sediment sources a priori. This problem is considered in the following chapter. Shaw and Kellerhals (1982) noted a high degree of variability and general downstream coarsening in the mountainous portions of several Albertan gravel-bed rivers. Examination of the undifferentiated grain size data for Sukunka and Pine Rivers supports their observation. They suggest that, "an explanation for these observations lies in the complex historical and present-day geomorphological processes in these reaches" (Shaw and Kellerhals, 1982, page 48), and I maintain that the analysis presented in this chapter confirms that this is indeed the case. Careful examination of tributaries and other lateral sources, often with an eye to the recent past, has yielded a reasonable explanation of textural changes that initially appear unstructured. 103 CHAPTER 5. A Priori Identification of Significant Lateral Sediment Sources The occurrence of lateral sediment sources is clearly an important control on the pattern of grain size change along gravelly alluvial systems. In particular there is an association between some lateral sediment sources and discontinuities in the downstream maturation of bed texture. One can reasonably explain this association in terms of the contamination of mainstem sediments by influxes of distinct material at tributaries and non-alluvial contacts. In certain cases these discontinuities demarcate sedimentary links, within which fluvial processes operate relatively free of lateral disruption. By identifying lateral sediment sources and sedimentary links one achieves a degree of simplification which facilitates the measurement and description of the grain size changes produced by fluvial processes, that is, of downstream fining. Empirically derived descriptive models and theoretically derived mechanistic models of fining processes may then be tested in a rigorous, meaningful manner. However, in order to capitalise on these conceptual constructs (lateral sediment sources, sedimentary links) and improve our ability to predict textural change in rivers, one must first be able to identify them without the benefit of grain size observations. This chapter is therefore concerned with the a priori identification of significant lateral sediment sources. Potential sediment sources (tributaries and non-alluvial contacts) can be identified reliably using maps, aerial photographs and field reconnaissance. The problem is then to distinguish those sources which are likely to disrupt fining processes from those which are not. My principal aims in this chapter are to provide a predictive tool capable of making this distinction, and also to examine the limits of predictive power that can be achieved in the light of contingent factors and simplifying assumptions. Tributary sources are more amenable to assessment because surrogate data about sediment yield and other relevant characteristics can be gleaned from maps and aerial photographs. Appraisal of significant non-alluvial sources is more complex because sediment yield is more difficult to estimate. I shall therefore concentrate on identifying tributary sources here. This simplification is a reasonable one for an exploratory 104 study given that the majority of lateral sources along Pine and Sukunka Rivers are tributary streams. The primary controls of tributary behaviour are discussed and a suitable set of surrogate variables identified. Values are determined for all tributaries along both rivers and, on the basis of the grain size analysis in Chapter 5, tributaries are independently classified as significant or insignificant. The success of univariate and bivariate criteria for discriminating between these two groups is then assessed (Sections 5.2.2 and 5.2:3). A bivariate function involving relative basin area and absolute slope-area product is found to be most useful (Section 5.2.4) but its performance is not superlative. To try and improve the discriminant function an examination of consistently misclassified tributaries is undertaken (Section 5.3). Most anomalies are explained by historical circumstances and are not easily identified without detailed investigation. Given this uncertainty it is useful to attach probability statements to a priori predictions of tributary significance. A logistic model provides an appropriate means of doing so because the dependent variable is dichotomous (Section 5.4.2). Finally, the influence of tributary spacing on the classification, as significant or insignificant, of individual tributaries within a sequence of tributaries is considered (Section 5.4.3). 5.1 Primary controls and methodology Knighton (1980) and others have suggested that the relative volume and relative size characteristics of an input determine whether or not it redefines bed texture in the recipient channel. In particular, the larger the volume of an input and the greater the grain size disparity between it and the mainstem material the greater is the expectation that the mainstem texture is changed significantly. At confluences the situation is complicated by the concomitant influx of water which, if sufficiently large, modifies ambient stresses and thence the bed material. It is possible that a tributary which introduces a significant quantity of water but little sediment could, by increasing mainstem competence, produce a significant change in texture. Therefore, the relative volume of a sediment input, its size characteristics relative to the recipient channel 105 and, at tributaries, the relative contribution of water, are likely controls on the occurrence of grain size discontinuities. One approach to the problem of discriminating between significant and insignificant sources would be to simulate the mixing process at injection sites and, in turn, compare the resultant downstream texture with that upstream. However, the development and testing of such a model would be a major undertaking given the spatial and temporal complexities of the mixing process. These include asynchronous arrival of material at the mixing site (cf. Reid et al., 1989), the difficulty of differentiating input components within the downstream mix (Church and Kellerhals, 1978) (although natural tracers may be useful in this regard (Chaumont et al., 1994)), and the pattern of vertical and lateral mixing in the bed downstream. Beyond its development it is likely that the information requirements of such a mechanistic model would be extensive and necessitate field measurements. An alternative method that is more appropriate for a large-scale model of downstream change is pursued here. It is based on identifying surrogate measures of the primary controls suggested above and, in turn, using independently classified significant and insignificant sources to define discriminant parameter values. Although physical explanation is eschewed in favour of predictable associations, this approach serves more than a pragmatic goal since it may provide empirical confirmation of the suggested controls. It is most amenable to the assessment of potential tributary sources, because morphometric and hydrological basin parameters can serve as useful surrogate measures. Surrogate parameters are more difficult to define and ascertain in the case of non-alluvial contacts like bedrock cliffs or fluvioglacial exposures. Herein, I shall therefore focus on differentiating between significant and insignificant tributaries. Tributary fans are also considered since it may be possible to assess their significance using the same criteria. Discriminatory criteria will be established using the tributaries of Pine and Sukunka Rivers, which can be classified as significant or insignificant according to whether or not they are associated with a grain size discontinuity (Section 4.4). Both sets of data are used to maximise the generality of results. 106 5.2 Surrogate parameters and discriminatory criteria The grain size characteristics of the sediment supplied by a tributary stream ultimately depend on the origin of the clastic load and its subsequent modification within the basin (Knighton, 1980). Lithology of source rocks and of alien unconsolidated materials, climatic and biotic controls on weathering processes, and the dimensions and structure of the drainage network are important in this regard. The volume of material carried by a tributary depends upon the amount of sediment supplied to the channel and the ability of the channel to transfer it downstream. Geomorphic history, climate, vegetation, basin area and hypsometry are important considerations. The volume of water leaving a basin is primarily dependent on its climate, vegetation and size. My aim is to identify one or more basin parameters which subsume the complexity of these multiple controls, and which, in turn, can be used as a basis for discriminating significant and insignificant tributaries. To simplify the problem one can initially assume that geomorphic history, lithology, vegetation characteristics and climate are homogeneous between the tributary basins of a given network. Lithological homogeneity is perhaps the least reasonable of these, but it is also the easiest to check in most places. Fundamental consideration of scale then indicates that a measure of basin size is an appropriate starting point. Knighton (1980) suggests Shreve magnitude or stream length, and one might also consider basin area. Although Walling (1983) and Church and Slaymaker (1989) have exposed the unreliability of simple relations between basin area and sediment yield, it is reasonable to expect that both sediment and water yield are, to some degree, conditioned by tributary size. In the field it was apparent that several large tributaries had no impact on main stem sediments despite evidence of extensive sediment production and mobilisation within the tributary basin. For example, Chamberlain Creek is a large tributary of the Upper Sukunka which is crossed by the Sukunka access road several kilometres from its confluence with the main channel close to where the stream emerges from the mountain front. At this point the 107 stream is braided and shows evidence of recent avulsions and depositional floods. It is clearly transporting large quantities of gravel and cobble sized material into the Sukunka valley. However, the large fan which the tributary has built during the Holocene has forced Sukunka River to the opposite side of the valley. Aerial photographs show that, between the mountain front and river, a large braided channel gives way to a number of small low-gradient distributaries which flow into an organically rich, marshy area close to the river. This suggests that Chamberlain Creek deposits the majority of its coarse load close to the mountain front and that little, if any, coarse sediment reaches the Sukunka. Indeed, along the main river there are only a few small sandy entrants and no evidence of gravel inputs. The diffuse nature of the distributaries precludes any hydraulic impact. This example indicates the important role which storage plays in moderating tributary sediment yield and suggests that a measure of sediment delivery, rather than production, would be useful. Estimates of bed load yield are not feasible given the information requirements of mechanistic and morphological predictive methods. However, the nominal ability of a stream to transport sediment is reflected by the gross power which it possesses (Q = pgQS), for which a surrogate variable is the product of tributary basin area and channel slope. This follows from the assumption, which will be assessed below, that discharge Q is related to basin area, such that [5.i] n*pgsm On the basis of these considerations, three variables were chosen for analysis; drainage basin area, network magnitude, and area-slope product. In addition to absolute values, these parameters were examined relative to those for the mainstem channel. One would expect that, where sediment and water yields are very small relative to the main channel, the tributary has little effect on texture because inputs are easily accommodated by the main stream, but that as the relative tributary inputs increase, an impact is more likely to occur. Petts (1984) and others have shown that tributary influence is increased by upstream impoundment of a recipient channel and the subsequent reduction of its relative sedimentary contribution. 108 5.2.1 Determination of parameter values and tributary classification According to 1:50 000 N.T.S. mapping 78 tributaries enter the Sukunka study reach, and 77 enter the Pine study reach prior to their confluence. No additional tributaries were identified in the field and I am therefore confident that all perennial tributaries are included in the analysis. The Shreve magnitude of each basin M t , was determined from the blue-line network on these maps, and drainage basin areas A t , were measured from them using a digital planimeter. The validity of the area-slope product as a measure of stream power primarily depends upon the relation between area and discharge Canadian Water Survey gauging records were used to assess the relation between drainage area A, and discharge Q, for rivers draining the eastern flank of the northern Rocky Mountains. In addition to ten stations within the Pine basin, eleven stations in the Muskwa, Sikanni, Wapiti and Halfway drainages were used. It is assumed that climatic and vegetational controls on stream hydrology are similar in these basins. In a majority of Albertan gravel bed rivers, bedload is mobile at or near the two year flood discharge which, in turn, is most consistently related to channel morphology (Bray, 1972). The discharge with a return period of two years Q2, was determined from maximum daily discharge records and, after logarithmic transformation, least-squares regression was used to define a power relation with basin area. The data and the regression are shown in Figure 5.1. Four of the stations have short records of less than five years but do not appear to adversely affect the relation which is significant, has R 2 = 0.96 and a mean standard error of 0.17 (log units). In the original units of m3s-' and km2 the relation is [5.2] Q 2 = 0.155 A 0 9 * 109 Figure 5. J. Relation between basin area and the tM'o-year flood discharge for rivers draining the eastern flank of the northern Rocky Mountains. O CD cn i_ O JZ o to. T5 o O D CD o 2 1 0 3 3 2 1 0 2 3 2 1 O 1 3 9 - . O P ine s ta t i ons • Other s ta t i ons : • < 5 year r e c o r d - r - H 1 1—I I I I I | 1 1 1 I 1 1 I i l l I I I I I I I I 1 > ' I O _J L I I I I I I 02 = 0.1 55 * AO.96 I ' I I . I I I I I I I I I I I I I 1 0 1 2 1 0 2 2 1 0 3 2 1 0 4 2 Drainage basin a r e a , A ( k m 2 ) 110 That the exponent in this relation is so close to unity is unusual. Reported values are usually lower, in part because of the potential for increased water storage within the valleys of larger basins (Knighton, 1987). The almost linear relation for these drainages may reflect a lack of floodplain storage during flood events. This is consistent with these rivers' headward containment within glacially eroded mountain valleys and their downstream entrenchment in the relatively soft Mesozoic and Cretaceous sedimentary rocks of the Rocky Mountain Foothills and Alberta Plateau. The strong relation between area and discharge is somewhat surprising given the steep precipitation gradient between the Continental Divide and Foothills (Section 2.1). One might expect runoff and therefore discharge, for basins of a given area, to vary signficantly with distance from the divide (i.e. with position within the gradient). For gauging stations within the Pine basin a plot of Q2/A against distance from the divide to basin centroid does reveal a reasonable inverse relation. Thus discharge per unit basin area does decline with distance from the divide such that tributary basin position, as well as area, control runoff and discharge. Residual scatter in Figure 5.1 may largely reflect this position effect but it does not preclude a significant relation between area alone and Q2. While a correction for position might improve discharge estimates the simple formulation involving area alone is appropriate as a first approximation and is used here. The exponent of 0.96 indicates that increases in discharge are almost exactly proportional to increases in area so that, [5.3] Q = pgQ2S * pg(0.15A)S and therefore, that D. cc AS, the area-slope product which I shall denote VF. Many of the Pine and Sukunka tributary basins are smaller than those used here, which range in size from 23 km2 to 20300 km2. However, there is no indication in Figure 5.1 that either the relation deviates, or that error terms increase for smaller basins. I l l The Chamberlain Creek example suggests that transport capability in the distal reaches of a tributary is of primary importance and that channel slope close to the tributary mouth is therefore pertinent. Approximate energy gradient was derived by estimating average channel slope from 1:50 000 N.T.S. maps. Confluence elevation was determined by linear extrapolation along the mainstem profile, then distance to a convenient contour close to the confluence (typically 500 to 1000 m upstream) was measured using a digital planimeter. Area-slope product was then calculated for each tributary basin. For each parameter, relative values M t /M m , A t /A m , were calculated as the ratio of the tributary value (subscript t) to that for the mainstem basin upstream of the confluence (subscript m). Slope estimates along Pine and Sukunka Rivers were based on profiles constructed using 100 ft contours from the 1:50 000 maps. Between contour crossings the profile was assumed to be linear. Surveyed bankfull slopes are available for the Sukunka but these were not used in order to maintain consistency, and because such detailed information is rarely available. Of 156 tributary confluences along the Pine and Sukunka Rivers (including the confluence of the two rivers), 21 are associated with grain size discontinuities. In many cases local erosion of fan alluvium may also contribute to the observed grain size step. Four additional discontinuities close to Rocky Creek, Boulder Creek, Martin Creek and Crassier Creek are unequivocally associated with fan exposures. Although tributary channels do not play a contemporary role in causing these steps, they are included as a separate group in this analysis because production of fan deposits may be related to the characteristics of the tributary basin. The role of P35 and P43 in causing local discontinuities is unclear because of the presence of bedrock outcrops nearby and these two tributaries are therefore excluded from the analysis. The remaining 129 tributaries are assumed to have no impact on texture. This is a reasonable assumption given the high resolution of mainstem grain size information and its examination in Chapter 4. 112 5.2.2 Univariate analysis How well do the six selected parameters distinguish the two main tributary types? For each parameter under consideration, Figure 5.2 shows the distribution of values for the 21 "significant" and 129 "insignificant" tributaries. Because of strong positive skewness, the original values have been logarithmically transformed to facilitate examination. Two separate populations are apparent in each case, although the degree of separation varies with the parameter used and in all cases the two distributions overlap. Therefore, none of the parameters unequivocally distinguishes between tributaries of the two types. That is, there is no single parameter value which isolates the two groups. A discriminatory criterion based on one of these parameters can correctly identify only a proportion p of the significant tributaries and will incorrectly classify a proportion q of the insignificant group. Optimal discrimination is achieved using a criterion which maximises p while minimising q. The optimal discriminatory criterion for a given parameter can therefore be defined as that parameter value which is associated with the maximum difference between p and q. As one would expect, the mode of the significant group is greater than that of the insignificant group for each parameter. If ns is the number of significant tributaries which have a parameter value greater than a potential discriminatory value v, and r\\ is the corresponding number for the insignificant group, then [5.4] p = ns/21 and [5.5] q = rij / 129 Figure 5.3 shows the variations in p, q and p - q for each parameter, for values of v from the observed minimum to the observed maximum in steps of 0.1 logarithmic units. The optimal discriminatory values, as defined above, are indicated by the peaks of the p - q plots. Each parameter's discriminatory power can be assessed in terms of the proportions p (significant 113 Figure 5.2. Frequency distributions of logarithmically transformed parameter values for Pine and Sukunka "significant" (shaded) and "insignificant" (blank) tributaries. 0.25 - 1 — i — i — i — i — i — i — i — i — i — i — r Basin Area 0.20 0 .15 0.1 0 0 .05 0 .00 - 1 . 5 - 0 . 7 0.1 0.9 1.7 2.5 3.3 4.1 0 .25 0.20 -0.1 5 0.10 0 .05 0.00 - 4 . 5 - 3 . 9 - 3 . 3 - 2 . 7 -2 .1 - 1 . 5 - 0 . 9 - 0 . 3 0.3 0.5 0.4 0.3 0.1 0.0 -1 1 r~ Shreve Magnitude 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 0.40 0.32 0.24 0.1 6 0.08 0.00 Relative Magnitude - 3 . 0 - 2 . 6 - 2 . 2 - 1 . 8 - 1 . 4 - 1 . 0 - 0 . 6 - 0 . 2 0.2 0.6 0 .25 0.20 0 .15 0.10 0 .05 Area-S lope Product o.oo - 3 . 0 - 2 . 4 - 1 . 8 - 1 . 2 - 0 . 6 0.0 0.6 0.40 0.32 0.24 0.1 6 0.08 0.00 - i — i — i — v Relative A rea -S lope Produc t - 3 . 5 - 2 . 9 - 2 . 3 - 1 . 7 -1 .1 - 0 . 5 0.1 0.7 Signi f icant t r ibutar ies Not s ign i f icant 114 tributaries identified), and q (insignificant tributaries incorrectly identified), corresponding to these optimal values. A useful additional measure, denoted u, is the proportion of significant tributaries in the subset of tributaries which exceed the optimal criterion. The criteria and corresponding proportions p, q and u, are presented in Table 5.1. In all cases p exceeds 0.81, and is 0.95 for relative area, q varies between 0.08 for relative magnitude and 0.22 for relative area. That these single parameter criteria isolate between 81 and 95 % of significant tributaries is encouraging. However, the concomitant isolation of between 8 and 22 % of the insignificant tributaries is problematic, since this represents between 10 and 29 incorrect, extraneous, classifications. Unfortunately, higher values of p are not associated with lower values of q, and the proportion of isolated tributaries that are significant never exceeds 0.63 (relative magnitude). Somewhat surprisingly the relative parameter criteria do not significantly improve discrimination. The criteria in Table 5.1 can be applied to the group of four tributaries whose fans are important sources. Relative area-slope product, relative magnitude and tributary magnitude do not perform very well but relative area and relative area-slope product successfully isolate the entire group (Table 5.2). If these four tributaries are included in the significant group the proportion of significant tributaries identified p', is reduced slightly in most cases. The proportion of isolated tributaries which are significant u', improves slightly for all parameters. In general, the inclusion of these four tributaries in the significant group does not markedly alter the performance of the criteria defined using the two major groups. This indicates that discontinuities associated with fan exposures can be identified on the basis of their source basin characteristics about as reliably as significant contemporary channels. Individually these six parameters distinguish a large proportion of the significant tributaries, but they also isolate an unhelpful proportion of those which have no influence on main stem texture. It is possible that an improvement in discriminatory power might be accomplished by using them in combination, and this is considered below. 115 Figure 5.3. Identification of optimal discriminatory parameter values. See text for discussion. 1 .0 0 .8 0 .6 0.4 0 .2 - --I ' Basin Area - • —i I . — _ — , - 1 1 .0 0 .8 0 .6 0.4 0 .2 0 .0 -• 4> Relative Area -• - 1 1 .0 0 .8 0 .6 0.4 0 .2 0 .0 O O O O Q 1 1 ' 1 1 Shreve magnitude -[ V M • 0.8 0 .6 0 .4 0 .2 0 .0 1 QOOOQ6 aQQQQf l f lQQQQOOOOOOOQ i . 1 Re Arec Pr - S l o p e \J I oduct • 'A \\ * A ± * * 3 -1 - e - Signif icant tributaries c lassi f ied correct ly , p -E3— Insignificant tributaries incorrect ly c lassi f ied, q -A— Difference, p — q 116 Table 5.1. Discriminatory power of absolute and relative tributary basin parameters: significant and insignificant tributaries. Parameter Optimal Proportion p Proportion q Proportion u Criterion, (and count) (and count) log and original Magnitude > 0.8 (6) 0.86 (18) 0.12 (16) 0.53 Area (km2) > 1.3 (20) 0.86 (18) 0.14 (18) 0.50 Area-Slope product >-0.2 (0.63) 0.86 (18) 0.19 (24) 0.43 Relative Magnitude >-1.5 (0.03) 0.81 (17) 0.08 (10) 0.63 Relative Area >-2.0 (0.01) 0.95 (20) 0.22 (29) 0.41 Relative Area-Slope >-0.4 (0.40) 0.81 (17) 0.13 (17) 0.50 product Criteria are based on the optimal differentiation between significant and insignificant tributaries, p is the proportion of the 21 significant tributaries which meet (exceed) the criterion, q is the proportion of the 129 insignificant tributaries which exceed the criterion, u is the proportion of values exceeding the criterion which are significant. Table 5.2. Discriminatory power of basin parameters for the tributary fan group, and the effect of including this group with significant tributaries. Parameter Proportion exceeding Revised Revised criterion, fan group proportion p' proportion u' (and count) Magnitude 0.50 (2) 0.80 0.56 Area 0.75 (3) 0.84 0.54 Area-slope product 1.00 (4) 0.88 0.47 Relative Magnitude 0.25 (1) 0.72 0.64 Relative Area 1.00 (4) 0.96 0.45 Relative Area-Slope product 0.25 (1) 0.72 0.51 Discriminatory criteria are those given in Table 5.1 which are based on optimal differentiation of significant and insignificant groups, p' and u' are calculated following the inclusion in the significant group of the four tributaries with fans that are important sources. 117 5.2.3 Bivariate analysis The two "delivery" variables (area-slope product and the associated relative term) are plotted against the four "production" parameters, in Figures 5.4 and 5.5. The former consists of the four plots involving area, and the latter the four plots involving Shreve magnitude. Significant and insignificant tributaries are differentiated, and the four tributaries with fans that are important lateral sources are also indicated. In all cases the significant and insignificant tributaries plot in distinct but never completely separate areas of the bivariate space. Consistent with the larger values one would expect for significant tributaries, the corresponding points are located toward the upper right corner of each plot. Lines which bisect the two main groups were drawn on to the logarithmic scatter plots by eye. In most cases several lines were fitted before those which optimise p, q and u were identified (Figures 5.4 and 5.5). Formal discriminant function analysis was not used because of the non-normality of the parameter values. Each line represents a discriminatory function, the equation of which (in original units) is noted on the respective plot. Because there are fewer significant tributaries, the inclusion or exclusion of one such tributary in the region above a potential discriminatory line has a larger effect on p, q and u, than including or excluding a member of the insignificant group. No account of this was taken when fitting the lines and it is reasonable to assume that these functions would be different if the group sizes were different. The ability of these functions to differentiate between the two types of tributary can be gauged by the values of p, q and u associated with them (Table 5.3). Here, p is the proportion of significant tributaries for which y >/(x), where y is the ordinate value for the tributary, x is the abscissa value, and/is the relevant discriminatory function. As before, q is the corresponding proportion of (incorrectly identified) insignificant tributaries, and u is the proportion of significant tributaries in the subset of all tributaries for which y >/(x). Compared to the univariate approach values of p are slightly lower and represent the omission of an additional one to three significant tributaries. However, the number of incorrectly classified insignificant tributaries is drastically reduced (by at least 50 %), and Figure 5.4. Bivariate scatter plots for basin area and area-slope product showing optimal discriminatory functions. x Ins igni f icant A S ign i f i can t Fan re lated 1 2 Log Area 1 1 1 1 - - - v^>fc" 1 1 1 J A ^ X v x *k x x x x 1 1 1 1 A 1 . 1 1 : X * x % - x \ x $ X A X. IBv". .X A XX > Xs X X X v|/t = = 0.1 4 A t / Am -0.51 ; 1 " x , , , , , , , , - 4 - 3 - 2 -1 0 Log Relative Area CD > CD cr C P O CD > CD cr o 0 1 2 Log Area vh/vkm = 0.021 A t / A m " 1 -4 - 3 - 2 -1 0 Log Relative Area 5 Loq Relative ^ $ t>5 611 120 values of q are therefore significantly lower. The net result is a significant improvement in the proportion of tributaries which are selected that are significant sediment sources; values of u range from 0.70 to 0.75 compared with 0.41 to 0.63 for the univariate criteria. 5.2.4 A discriminant function for significant tributaries The bivariate criteria are not as successful at isolating significant tributaries as the univariate criteria, but they are more successful at differentiating between the two major groups. They identify the majority of important tributaries while minimising the number of extraneous, incorrectly isolated, insignificant tributaries. Consequently, a bivariate function is likely to be more effective as the basis of a procedure for categorising tributaries a priori. In choosing between the eight bivariate functions there are several considerations. If the four tributaries with fans that are important sources are included in the significant group, the bivariate results are not markedly affected, even though the discriminatory functions were defined using the two larger groups. Values of p' are generally lower, and values of u' increase slightly (Table 5.3). Inspection of Figures 5.4 and 5.5 indicates that the absolute area-slope relations are in general better at identifying this group. Choosing a function which is best able to isolate this fan group, as well as the significant tributary group, is desirable since it improves the overall proportion of significant lateral sediment sources that are identified. In assessing the relative performance and merits of the eight empirical functions it is therefore pertinent to consider the revised values (p' and u'). These show that, in general, the functions vary little in their performance. Differences in p', q and u' reflect only small changes in the number of tributaries involved. In light of this the effort needed to define the parameters involved becomes a relevant factor. In addition, in order to maximise the unknown generality of the chosen function, it is appropriate that it includes at least one relative measure. Relative area-slope product is more onerous to determine than the absolute value for a tributary. The four relations involving the former are no more powerful than those that utilise the latter, and a relation involving is therefore preferable. Of these, the relation with relative 121 Table 5.3. Discriminatory power of bivariate functions. Function p (and q (and u Revised, Revised, counts) counts) P* u' = 422.67 A,-i-79 0.81 (17) 0.05 (7) 0.71 0.80 0.74 ¥ t / ¥ m = 2.92 A,-0-" 0.76 (16) 0.05 (6) 0.70 0.72 0.72 ¥ t = 0.14 A t/Am-°-5i 0.81 (17) 0.05 (6) 0.74 0.80 0.77 W m = 0.021 A,/Am-'oi 0.62 (13) 0.04 (5) 0.72 0.56 0.74 *Ft = 18.03 M f 1 1 1 0.67 (14) 0.04 (5) 0.74 0.64 0.76 W'Fm = 7.83 M t -°" 0.71 (15) 0.04 (5) 0.75 0.64 0.76 % = 0.0017 Mt/Mn,-1-94 0.76 (16) 0.05 (7) 0.70 0.68 0.71 ^,7^= 10- 6M t/Mm- 3- 9 1 0.81 (17) 0.05 (7) 0.71 0.72 0.72 Discriminatory functions y = fx), fitted by eye. p is the proportion of the 21 significant tributaries where y >J{x). q is the corresponding proportion of the 129 insignificant tributaries, u is the proportion of significant tributaries in the subset for which y >fx). Revised values are for the same criteria following inclusion as significant the four tributaries whose fans are important sources. ¥ is area-slope product, A is area (km2) and M is Shreve magnitude. The subscript t applies to tributary values and m to mainstem values upstream from the confluence. 122 area is particularly powerful, with high values of both p' (0.80) and u' (0.77), and q = 0.05. The absolute area relation performs almost as well (u' = 0.74), but this relation is probably of less general value given that it does not include a relative term. There is no advantage in using magnitude rather than area (as a more easily determined parameter), because the area-slope product necessitates area measurements. The discriminant function involving relative area and absolute slope-area product is therefore recommended for use in the tributary categorisation procedure. 5.3 Anomalous tributaries I have argued that basin size and the energy of the distal channel are useful surrogate measures for the amount of water and sediment produced and delivered by a tributary basin. That several pertinent variables provide fairly good discriminatory functions for significant and insignificant tributaries attests to this argument. Relative basin area and slope-area product have been selected as particularly useful variables upon which to base an a priori categorisation scheme. However, if their performance here can be used as a yardstick of predictive capability, identifying 80% of the significant tributaries along a study channel is hardly superlative especially if 23% of those isolated do not in fact have any impact. Examination of the consistently anomalous tributaries from the preceding analysis may reveal ways of improving the discriminant function. In particular it is useful to search for the reasons behind the consistent misclassification of individual anomalies and, perhaps more importantly, to determine whether the anomalous tributaries share any common characteristics. If they do then inclusion of parameters which isolate these characteristics would bolster predictive performance. Alternatively, the existing criterion may represent a limit of generality such that additional performance is gained only at the expense of field investigations or measurements. The relevant tributaries are listed in Table 5.4 along with the number of bivariate relations for which they are anomalous. Each tributary listed, including those which are 123 anomalous only one or two times, is considered below. These marginal anomalies are considered because they tend to plot close to the discriminant functions in cases where they are correctly classified. The four tributaries with fans that are important sources are not considered here because the bivariate criteria were established using the significant and insignificant tributary groups. 5.3.1 Insignificant tributaries misclassified as significant Of ten insignificant tributaries misclassified as significant, the anomalous nature of three of them is in doubt (Falling Creek, Fisher Creek, and Little Boulder Creek). Each case is characterised by insufficient or ambivalent local grain size information which leaves open the possibility that their original classification as insignificant is, in fact, incorrect. The discontinuity between PLH 3 (24.5) and PLH 4 (30.8) (Figure 4.7 and map G, Appendix 1) could reasonably be attributed to either Falling Creek or Fisher Creek. Without additional grain size data Beaudette Creek was designated as the site of the discontinuity in Section 4.4 because it is the most obvious contender in terms of size and sediment load (as indicated by confluence and tributary channel morphology). It is possible that Fisher Creek and Falling Creek are "anomalous" only because of my somewhat arbitrary classification of Beaudette as the significant source, rather than any singular attributes. At Little Boulder Creek there is a significant between-site change in D50 but not in D95 (samples p93 32 and 33). Because the stream did not appear to be very active, and because only D5o showed a significant change, I regarded this step as noise during link identification in Section 4.4. Given Little Boulder Creek's categorisation as significant by two discriminant functions, it is possible that my decision at that time was incorrect. This anomaly indicates the difficulty of classifying marginal cases rather than any unusual circumstance. In contrast, adequate grain size information upstream and downstream of the seven remaining tributaries suggests that these certainly are misclassified by the discriminant functions. I can offer no good explanation for four of these anomalies (Wildmare Creek, 124 Table 5.4. Tributaries which are misclassified by the bivariate discriminant functions. The numbers of functions which misclassify them are indicated in brackets. Insignificant misclassified as significant Significant misclassified as insignificant Sukunka River (8) P54 f8) Mountain Ck.. P2 (S) S19 (S) Centurion Ck.. P67 (S) S48 (8) Falling Ck..P20 (S) P60 (S) Fisher Ck.. P19 (8) Goodrich Ck., P49 (2) Wildmare Ck., P65 (2) S20 (2) Bluff Ck., S56 (1) Lean-to Ck., S22 (2) P14 (2) McLean Ck., S17 (1) Little Boulder Ck, P8 (2) Dickebusch Ck., S71 (1) S25 (2) Caron Ck,P56(\) Commotion Ck.,P50(l) Tributaries are listed in general order of distance from the discriminant line, those further away appearing at the head of each list. Those misclassified by the preferred discriminatory function are underlined. 125 Bluff Creek, P14, and S25) and can find no general reason why they should be misclassified. For example, they do not exhibit unusual morphometryor lithological characteristics. They simply reflect the imperfection of the assumptions and surrogate variables which are the basis of the discriminant functions. One methodological assumption may also be relevant. Linear extrapolation between contour line crossings was used to estimate confluence elevations which, in turn, were used in calculating distal tributary gradients. In fact, main stem gradients tend to be lower upstream of confluences and greater downstream (Section 6.3.1) such that linear interpolation may underestimate confluence elevation and overestimate distal tributary slope. It is possible, then, that overestimation of slope is responsible for the misclassification of these tributaries as significant. Examination of the three remaining anomalies (Sukunka River, Centurion Creek and Mountain Creek) which are misclassified by all eight functions, provides more substantive insight. Before considering these it is worth noting one difference between Wildmare Creek and several similarly sized significant basins such as Bisset Creek, a short distance upstream. Wildmare's fan does not reach the Pine in its present position. This suggests a lack of coarse material in the distal reaches of the tributary and might explain the lack of a discontinuity. Examination of fan positions might therefore be useful in distinguishing between marginal tributaries, i.e. those which plot on or very close to discriminant functions. Sukunka River was treated as a tributary of the Pine primarily because the subsequent channel retains the Pine name. In fact, the Sukunka has a slightly larger drainage area at the confluence; 2746 km2 compared with 2513 km2 for the Pine. If instead Pine River is defined as the tributary, the confluence is still misclassified by all eight functions and is still the furthest insignificant case from the discriminant lines. Knighton (1980) suggests that as tributaries approach the size of the mainstem the volume and texture of their input is likely to be similar to that in the main channel. This in turn suggests that the influence of tributaries diminishes as their relative size approaches 1.0. The discriminant functions do not take this into account. The lack of a significant step at the Pine/Sukunka confluence (along both rivers) supports Knighton's hypothesis, which in turn offers an explanation for the misclassification. 126 Verification of Knighton's explanation would suggest that monotonically decreasing discriminant functions are inappropriate and that an alternative function, or ancillary "rule" could be used to improve tributary classification. Some additional support is provided by the lack of a large discontinuity at the Dudzic/Sukunka confluence. Here, the relative parameter ratios are closer to 1.0 than in most cases (e.g. A t /A m = 1.36), although as explained in Section 4.4 sampling problems in this reach complicate interpretation. However, at the Burnt/Sukunka confluence where A t /A m = 0.87, the most striking grain size discontinuity of all those observed provides solid contradictory evidence. Surface grain size distributions from the tributary and from the main channel upstream and downstream of the input are shown in Figure 5.6. In contrast to Knighton's suggestion that similar-sized basins have similar distal textures there is clearly no similarity between the two samples collected upstream of the Burnt/Sukunka confluence (BNT and SWB 8 (58.3)). Furthermore, the size distribution of the material at the downstream site BND (65.6) is similar to that of the Burnt River sample. This suggests unequal mixing of the input populations and in turn a difference in bedload yields. This inference should be treated with caution since it inherently assumes that the surface bed material texture is representative of the bedload texture. In the long term this is a reasonable assumption because the surface material downstream must reflect the coarser material supplied from upstream, which in turn is indicated by the surface material found there. Additional arguments can be made in support of the dominance of Burnt River at its confluence. Approximately 2 km from the confluence an unvegetated terrace scarp, some 500 m long and 30 to 50 m high, constitutes the left bank of the river. It is associated with the highest of several glaciofluvial terraces, supplies a large amount of coarse, unconsolidated material, and instigates a braided channel pattern. Lower terraces of fluvially reworked fluvioglacial material continue to supply material as the river approaches the confluence. In contrast, Sukunka River upstream of the confluence exhibits an almost complete absence of bars and riffles indicating minimal transfer of coarse material. It is possible that all coarse 127 Figure 5.6. Grain size distributions and lithological composition of the surficial material upstream and downstream from the Burnt/Sukunka confluence. 9.1) Grain size class (-phi) Grain size c lass (-phi) Grain size class ( — phi) 128 material moving into this canyonised section is rapidly flushed through, but at the confluence the pattern of bar development strongly suggests that the Burnt input is dominant. A comparison of the lithological composition of the bed materials around the confluence supports this argument. The right hand side of Figure 5.6 shows the lithological composition of the surface material at the three sites around the confluence. The composition of the sample at BND (65.6) (downstream from the confluence) is very similar to that for the Burnt River sample BNT, and quite different from that collected at SWB 8 (58.3). The sandstone, bluestone, and quartzite fractions are especially telling. So, the sediment supplied by Burnt River is not only coarser, but there is also more of it. In producing the large Sukunka discontinuity the Burnt input does not so much modify, as reconstitute the Sukunka grain size distribution. Given the similar sizes of the Burnt and Sukunka rivers at their confluence, this example refutes Knighton's claim, and indicates that an alternative explanation is needed to account for the misclassification of the Pine/Sukunka confluence. However, several contingencies complicate the nature of relative sediment supply at the Burnt/Sukunka confluence, and some caution is therefore needed in a science where "laws" are judged by their generality rather than by a single falsifying instance. Bedrock control of the distal Sukunka reach presumably affects sediment transfer to the confluence, and the fluvioglacial terraces which supply a large proportion of the Burnt's load are located within the Sukunka valley, and may have little to do with the characteristics of the Burnt River basin. Thus, the Burnt/Sukunka confluence could be regarded as an exceptional case; anomalous, and not therefore useful for assessing the verisimilitude of Knighton's hypothesis. However, despite the lack of a discontinuity the surface samples collected around the Sukunka/Pine confluence do not support Knighton's argument either. The two samples collected upstream from the confluence, PRU (107.0) and SKU (110.8), are significantly different. The Sukunka sample shows a distinctive lack of material coarser than 6.5 <D (Figure 5.7). The coarseness of the Pine material is consistent with the steep canyonised nature of the channel immediately upstream of the confluence. Of four replicates collected downstream from the confluence at PRD (109.0) the two most different are overlain in Figure 5.7. Surface 129 material at this downstream site has more in common with that from the Sukunka than would be expected if the rate of input of the two populations were equal. The cautionary note sounded above regarding surface material and bed load characteristics is again pertinent. However, the very low energy, gravel-deficient conditions which characterise the Pine upstream of the canyon support the contention that, relative to its size, the Pine supplies little coarse material to the post-confluence channel. Once again the legacy of Late Pleistocene and Early Holocene events (the creation and subsequent draining of the lake which occupied the Pine valley) are a primary determinant of the contemporary river's sedimentological character. Unlike the Burnt/Sukunka confluence, dominance of Sukunka material does not create a discontinuity along Pine River (Figure 4.7), because the Sukunka input is finer than that which is evident at the downstream end of the steep Pine canyon. The Sukunka's dominance ensures that there is no discontinuity in the Sukunka signal, although the fining trend apparent downstream from Dickebusch does seem to be arrested slightly (Figure 4.6). Lithological evidence (Figure 5.7) neither supports nor discredits this argument. Individual lithological proportions in the downstream sample show affinity with one or other of the input populations. So, the lack of a discontinuity at the Pine/Sukunka confluence has little to do with the similar size of the two basins, and casts additional doubt on Knighton's intuitively attractive hypothesis. Basins of equal size do not necessarily have similar distal textures or similar bedload yields, and where two such basins meet one would be wrong to assume that a discontinuity is unlikely. Additional data are needed in order to decide whether they are however, significantly less likely than elsewhere, especially given the unusual conditions affecting one or both of the upstream channels in these two cases. Indeed the importance of geomorphic history, both in terms of limiting the generality of Knighton's argument and in terms of explaining the Sukunka's anomalous classification by the discriminant functions, is clear in these examples. The evidence here suggests that use of alternative functions or of an ancillary rule based on Knighton's hypothesis would be inappropriate. The singular history of Centurion Creek also explains its consistent misclassification. Centurion Creek flows within the trough which at one time carried Pine River in the opposite 130 Figure 5.7. Grain size distributions and lithological composition of the surficial material upstream and downstream of the Sukunka/Pine confluence. Grain size class (-phi) Grain size class (-phi) 131 direction, toward Peace River. It is decidedly underfit (Dawson, 1881; Hughes, 1967) and flows across the bed of a drained post-glacial lake which was at one time impounded by the Jackfish Lake moraine (Section 2.3.2). Despite its large basin area, it is clear in the field that the stream carries very little coarse sediment. This is a consequence of more than just the low gradient imposed by the underlying lake-bed. Lack of coarse bedload reflects the preponderance of lacustrine materials within the valley and deposition of tributary sediment loads along the margins of the wide, flat, valley floor. Because the width of the valley is not related to Centurion Creek's drainage area lateral channel migration must seldom reach these coarse accumulations. Kettle lakes within the morainal blanket may also hinder coarse sediment transfers. Coarse bedload is consequently lacking in comparison to similarly sized basins characterised by a common history of glacial and fluvial erosion and relatively consistent morphometry. The general association between basin size and sediment production, manifest in the discriminatory functions, is of little value in this particular case. The misclassification of Centurion Creek is a consequence of its atypical history and unusual morphometry relative to other tributaries within the Pine and Sukunka drainages, and in this sense Centurion Creek is a true anomaly. Without actual bed load measurements only careful consideration of a tributary basin's history and relative character might indicate such tributaries a priori. Mountain Creek was not defined as an important lateral source in Section 4.4 despite the fact that it is associated with a significant downstream increase in grain size (samples PMU 3 (1.3) to PMD 1 (1.7)). The categorisation of Mountain Creek as a significant source by the discriminant functions is not therefore surprising. It is "incorrectly" classified because in addition to injecting a sediment population capable of redefining mainstem texture, the definition employed in Section 4.4 specifies that a significant sediment source must also be associated with a fining pattern. This working definition was necessary because the identification of discontinuities within a grain size signal cannot be separated from the identification of the fining trends which indicate sedimentary links. No fining trends occur in the vicinity of Mountain Creek and it was not therefore defined as a significant source. 132 Trends are lacking as a result of the abundance of proximal lateral inputs, which disrupt textural modification along the main stem. Significant between-site differences occur immediately upstream (PMU 1 (0.4) to PMU (0.8)), immediately downstream (PMD 1 (1.7) to PMD (2.5)) and between four of the remaining six sites prior to the significant input at Lemoray Creek (Table 4.6 and Map F, Appendix 1). The proximity and abundance of other lateral sediment sources relative to the spacing of mainstem depositional sites is not considered by the discriminatory functions, but could be incorporated in a tributary classification procedure. 5.3.2 Significant tributaries misclassified as insignificant Two of the eleven significant tributaries misclassified by the discriminant functions may not be anomalous. S19 and S48 were identified as significant sources in Section 4.4, but in both cases a degree of doubt was involved. In the latter case the associated grain size step (samples SWB 7.75 (57.5) and SWB 8 (58.3)) is only in D95, and the confluence of Rocky creek offers an alternative explanation for the discontinuity (Table 4.5). In the former case a morainal bench on the left bank may be responsible for the discontinuity observed between S20 U2 (16.3) and STW 2 (16.7). In light of these doubts classification of S19 and S48 as significant tributaries and, in turn, their anomalous status, should be regarded as marginal. The remaining tributaries certainly are significant. There is no obvious reason for the incorrect classifications by some of the discriminant functions, of McLean Creek, Lean-to Creek, S20, Dickebusch Creek, Goodrich Creek, Caron Creek and Commotion Creek. That is, the misclassifications do not reflect any real basin attributes which facilitate unusually low sediment yield relative to other significant tributaries. Rather, these anomalies simply reflect the imperfection of the discriminatory criteria in the face of natural variability. The fact that S20, Lean-to and McLean are misclassified by the two functions involving absolute magnitude, suggests that this variable is not sensitive enough to discriminate marginal cases. In contrast P54 and P60 are exceptional. These tributaries are relatively small and not very steep, yet they are associated with significant steps because they introduce some coarse 133 material to reaches otherwise devoid of gravel concentrations. An input that would elsewhere be of limited significance is crucial in the lower Pine because the river transports very little coarse bedload in this section. As outlined in Chapter 2 the lower Pine flows over the bed of a glacial lake which once occupied the valley. Alluvial aggradation downstream of major tributaries like Commotion Creek has produced an alternating series of gravel and clay/sand reaches. P54 and P60 inject material into low gradient sand/clay reaches and consequently produce textural discontinuities. The discriminant functions are not sensitive enough to pick up on the relative difference in the transfer characteristics of tributary and mainstem, and misclassify the two tributaries. To an unknown degree overestimation of mainstem channel slope along the lower Pine contributes to the misclassification. This overestimation arises because the contour interval from which average slope is calculated, encompasses both the very steep canyon section and the much gentler section upstream. As with the exceptional cases discussed in the previous section, only detailed knowledge of local geomorphic history or absolute measurements could aid in the a priori categorisation of tributaries such as P54 and P60. 5.4 A n a priori categorisation procedure for tributaries A tentative procedure for categorising significant tributaries is presented below. The discriminant function identified in Section 5.2.3 should be used to identify tributaries likely to cause steps in a mainstem grain size signal. Subsequently, the proximity and abundance of other lateral sources should be considered so that tributaries which may cause significant mainstem perturbations, but which are unlikely to be associated with fining trends (e.g., Mountain Creek), can be recognised. 5.4.1 Identification of tributary sources which affect main stem texture The bivariate discriminant function, 134 [5.1] ¥ t >0.14A t /A m -° -5i , where A t /A m is relative basin area and 4 \ is tributary area-slope product, is successful in classifying the significant and insignificant tributaries of Pine and Sukunka Rivers. It is recommended here as a means of predicting which tributaries are likely to affect mainstem texture and which are unlikely to do so in other river systems. While the underlying arguments regarding sediment production and yield are general it is unclear how general this discriminant function is. Regional geomorphic history is clearly important and it is unlikely that the Pine/Sukunka function is transferable to areas of markedly different physiography or climatic history. Lithology is also likely to be a limiting factor and restrict the use of the function defined here to areas of deranged sedimentary and low-grade metamorphic rocks. The generality of the function cannot be assessed because a suitable set of mainstem grain size observations does not, to my knowledge, exist. This relatively simple approach, whereby the complex array of factors which determine water and sediment yield are represented by two surrogate variables, is not capable of unequivocal discrimination. If the Pine and Sukunka data are used as a gauge for the discriminant function's predictive power, then one can expect it to correctly classify approximately 80% of the significant tributaries and incorrectly classify 5% of insignificant tributaries. Because insignificant tributaries are likely to be more numerous, the latter could represent a large number of extraneous identifications. However, examination of anomalous tributaries has not revealed an additional general factor which could be parameterised and included in the discriminant function to improve its performance. The majority of anomalies remain unexplained or are explained by singularities, rather than any common, identifiable attribute. Results should therefore be regarded as guidelines rather than final statements and, if at all possible, tributaries should be examined in detail to improve confidence in categorisations. Where field visits are impractical mapping of surficial materials and geomorphic features will 135 be useful. Patterns of sedimentation and channel stability gleaned from aerial photographs are likely to be particularly valuable. In marginal cases the position of a tributary's fan relative to the main channel may indicate the likelihood of coarse bedload yield and, in turn, facilitate final classification. It is worth noting that following careful examination of the sixteen surely anomalous confluences encountered on the Pine and Sukunka, only four could be explained by contingent effects. This indicates that, depending on the scale of the reach being examined, the improvement in overall classification gained by detailed examination of individual basins may not justify the additional effort required. 5.4.2 Attaching probability statements to predicted classifications. As a useful adjunct to the discriminant function, the Pine and Sukunka data can be used to develop a relation between basin parameters and the probability that a given tributary is significant (or insignificant). This relation does not add new insight (it is based on the same empirical data used to define the discriminant function) but rather provides an assessment of the uncertainty associated with a given categorisation. That is, it provides an additional piece of information which can be used to help finalise tributary classification. The dependent variable in such a relation is dichotomous (a tributary is either significant or insignificant), while the independent variables (A t/Am and %) vary continuously on interval scales. If significant tributaries are represented by a value of 1 and insignificant tributaries by a value of 0, then the dependent variable can be viewed as a probability. A fitted relation between tributary characteristics and tributary status (1 or 0) then indicates the probability that a given pair of A t /A m and T t are associated with a significant tributary. An appropriate model is the logistic function in which the dependent variable (P) is constrained to a value between 0 and 1 for an independent variable (x) varying in the range -oo to +<x>. [5.2] p = [ eo + Px] / [ l + e a + p x ] 136 The function describes a sigmoid curve that, for positive values of P, is asymptotic to P = 0 as x—»-oo, and to P = 1 as x—>+oo. It takes the value P = 0.5 at x = -a/p. The logistic function is easily linearised by rearranging and taking logarithms to the base e: [5.3] loge(P/1-P) = a + Px The left hand side of this equation is called the logit transformation of the probability P and the model is known as a linear logit model. In this case there are two independent variables and the model has the form [5.4] log e(P/l-P) = Po + Pix1 + p2x2 where, by convention, the intercept term is denoted po, xi = log(At/Am) and x2 = log^t) (the logarithmic transformation introduced earlier is retained here in order to reduce non-normality of the data). For continuously varying, as opposed to grouped independent data, the maximum likelihood method is appropriate for estimating p0, Pi, and p2 (Wrigley, 1985, p35). Relevant statistics for assessing the significance and overall fit of logit models are the likelihood ratio test and p2 (Wrigley, 1985). Details are given in Appendix 4. The likelihood ratio test is used to assess the significance of the model parameters and is equivalent to the F-test used in least-squares regression. A chi-squared statistic (x2) is used to test the null hypothesis that Pi = p2 = ... = PK = 0 General goodness-of-fit is assessed using p2 which is analogous to R2 in least-squares regression. Although p2 ranges from 0 to 1, with higher values indicating a better fit, it tends to take on lower values than the R2 index and p2 should not be judged by the standards associated with R2. McFadden (1979) has suggested that p2 values of between 0.2 and 0.4 represent a very good fit and an empirical graph presented by Domencich and McFadden (1975) indicates that values of p2 close to 0.6 are equivalent to R 2 values close to 1.0 (Figure A. 1). 137 In the light of the examination of discriminant function anomalies the Pine and Sukunka data were modified prior to model fitting. First the six tributaries which may have been misclassified (i.e. which may not be anomalous) were removed. This was done in order to improve overall confidence in the observed classifications and therefore in the fitted model. Also the classification of Mountain Creek was changed from insignificant to significant since it is associated with a significant grain size step. Initially, all explained and unexplained anomalies are included in the analysis. The four tributaries with fans that are important sources were classified as significant in this analysis. The resulting relations therefore describe the probability that a tributary or the associated fan is a significant source. The logit model, [5.5] loge(P/ 1-P) = 2.74+ 1.92.x, + 3.33. x2 [5.6] .". P = [e( 2 7 4 + 1- 9 2 x l + 3.33.X2)] / [1 + e(2.74+ 1.92.XI+3.33.X2)] was fitted to this data set using the maximum likelihood method and is shown with the observed values in Figure 5.8A. Significant tributaries lie on the horizontal plane where P = 1, and those classified as insignificant on the horizontal plane where P = 0. Drop lines from the observed points to the model plane indicate the deviations between observed and modeled values. While these are large in some cases, (for the anomalous tributaries identified earlier) the parameter estimates are significant (a « 0.001), and p2 = 0.508 which, according to McFadden (1979), indicates a very good fit. For values of log(At/Am) and log(vFt) the model predicts the probability that the associated tributary is a significant sediment source which disrupts mainstem texture. Predicted probabilities reflect the empirical relation between basin parameters and tributary significance that exists in the basins of the censored data set. Since this set includes several tributaries which are known to be anomalous for specific reasons of geomorphic history, the role of contingent historical events is to some extent incorporated and moderates the 138 probabilities which the model predicts. The question then arises whether this model is appropriate for use elsewhere? Singularities are, by definition, unpredictable and cannot be assumed to be of a similar nature and extent in other systems. Therefore, it is more appropriate to fit a model in the absence of those anomalous tributaries which have been explained (Sukunka River, Centurion Creek, P54 and P60). Unexplained anomalies remain in the analysis. Predicted probabilities then reflect the likelihood of a tributary being significant, while assuming that it is not affected by peculiar historical conditions. The validity of this assumption must be determined for individual predictions by examination of the tributary basin. The significant logit model, fits the censored data set less the four tributaries mentioned, with p2 = 0.81. The proportion of the predictions close to either 0 or 1 increases dramatically, as indicated by the reduced curvature of the fitted surface (Figure 5.8B). As with the discriminant function the generality of this model is unknown and is probably constrained by historical, climatic and lithological conditions. 5.4.3 Tributary sources and sedimentary links Not all significant grain size steps are associated with the beginning or end of a fining sequence. Where lateral sources occur in close proximity to one another texture may be disrupted to such an extent that fining does not develop. Following the identification of tributaries that are likely to have an impact on texture their spacing should be considered in order to help with the identification of sedimentary links. Using data from several catchments in the United Kingdom, Jarvis and Sham (1981) [5.7] loge(P/ 1-P) = 9.41 + 5.73.x, +9.91.X2-[5.8] 140 showed that the arrangement of tributaries along one side of a mainstem channel is not random. While small tributaries tend to be followed downstream by other small tributaries, large tributaries tend to be separated from each other by large distances and numerous smaller tributaries. This is a simple corollary of the spatial requirements of tributary basin development; larger basins preempt the formation of other large basins in their vicinity as they bifurcate away from the mainstem and enlarge their catchments. From the above examination of Pine and Sukunka tributaries it is clear that tributary size is a critical determinant of impact on mainstem bed material texture. The implication is that significant tributaries do not join the mainstem in close proximity to one another, at least from the same side of the basin. Furthermore, the importance of relative size suggests that with increasing distance downstream, the size of significant tributaries increases. This implies that with distance downstream significant tributaries become more widely spaced along any one side of the channel. Spacing of significant tributaries along the Sukunka River (Figure 5.9A) supports these arguments. In general, significant tributaries are more widely spaced than insignificant tributaries and, for entry from any one side of the basin, inter-tributary distance increases downstream. When both sides of the basin are considered together this pattern breaks down, as exemplified by the Highhat and Dickebusch confluences close to kilometre 100. Along Pine River spacing does not continue to increase downstream (Figure 5.9B) and significant tributaries occur at a spacing similar to that of insignificant tributaries in the distal, low gradient section. Here relative size is less important than relative slope as a cause of grain size discontinuities and arguments based on Jarvis and Sham's work do not hold. However, despite the proximity of the significant tributaries in this reach, strong fining patterns are observed, which may reflect a lack of active fan margins and incompetence of the mainstem. Thus, both the spatial requirements of tributary development and empirical evidence suggest that, as around Mountain Creek, non-fluvial sources and tributary fans, rather than other tributaries, are most likely to complicate the grain size signal close to significant tributaries. The problem of identifying those significant sources that are unlikely to be associated with strong fining then becomes one of determining the degree of coupling between channel and 141 non-alluvial materials. In small mountainous streams strong hillslope-channel coupling may be a general feature (Rice and Church, 1996), and mask the effect of tributary inputs (Rhoads, 1989), but the spatial distribution of coupling in larger systems is more difficult to characterise (Rice, 1994). 5.4 Summary and Discussion Although potential fluvial and non-fluvial lateral sources may be identified from maps and aerial photographs, significant tributary sources are more conducive to a priori identification because tributary basin parameters can be used as surrogate variables for sediment and water production and delivery. Basin idiosyncrasies and oversimplification of a complex set of controlling factors preclude criteria which can unequivocally distinguish tributary types. However, it has been possible to develop operational guidelines for tributary classification based on relative basin area and the product of tributary area and tributary channel distal slope. Generality of specified discriminant and logistic functions cannot be assessed because of the lack of a suitable data set, but geomorphic history and lithology are likely to be primary constraints on the application of these functions elsewhere. Beyond these practical guidelines an important implication of this chapter is that sedimentological networks and hydrologic networks do not necessarily correspond. Sedimentologically, Sukunka River is more important than Pine River, and Burnt River is more important than Sukunka: the main sediment pathway is distinct from the hydrologic mainstem, and certainly has little to do with the hierarchy of geographical names. A number of relatively small tributaries are highly significant sediment sources either because of internal circumstances or relative conditions on the mainstem that are often associated with local geomorphic history. Contemporary singular events may also be important, such as the exceptional sediment fluxes recorded on Dickebusch Creek in 1982 (Section 2.1). These observations reflect the spatially discontinuous nature of sediment supply within fluvial landscapes, which contrasts with the essentially homogeneous distribution of water supply. 142 Figure 5.9. Spacing between consecutive significant and insignificant tributaries along (A) Sukunka and (B) Pine Rivers 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 D i s t a n c e d o w n s t r e a m ( k m ) 4 0 ^ 3 0 D 3 s 2 0 E o <v o c o If) Q 1 0 0 t i i r i r B. P i n e Insignificant — © — Significant .{\ Right side only 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 D i s t a n c e d o w n s t r e a m ( k m ) 143 This patchy, somewhat unpredictable, arrangement of important sediment sources in turn reflects local geomorphic history, lithologic heterogeneity and local contingencies. Models based solely on hydrological network order may be fundamentally inappropriate for understanding sediment fluxes and sediment characteristics within fluvial systems. Having identified the importance of lateral sediment sources for understanding textural change and provided some guidelines for their discrimination, the description and prediction of changes within sedimentary reaches is considered in my final chapter. 144 CHAPTER 6. Grain Size Variations Between Significant Sediment Inputs Within sedimentary links changes in bed material texture are predominantly the result of fluvial processes. Disruptions due to minor sediment inputs may augment residual variability associated with site and bar-scale noise, but sedimentary links provide an essential framework for applying models of fluvial textural modification. Particle abrasion and sorting processes are generally regarded as the most important causes of textural change, although debate continues as to their relative importance. Cursory inspection of Sukunka and Pine grain size data (Figures 4.6 and 4.7) indicates that diminution rates and the association between size and distance vary between links. My aim in this chapter is to examine these differences and in turn the reach-scale controls of within-link modification. It is not my intention to develop or test a model of the fining processes, but rather to identify a suitable descriptive function for Pine and Sukunka links and explore the reach-scale controls on its specification. In particular, what functional model is generally applicable and what controls the rate of diminution within any given link ? The former query is addressed by examining the appropriateness of exponential and power models for describing grain size changes within Pine and Sukunka sedimentary reaches (Section 6.1). Exponential models are suitable, and lithological and hydraulic controls on the diminution coefficient ad are examined in Sections 6.2 and 6.3. Analysis of published data reveals that differences in abrasion resistance between lithological groups are not necessarily significant. Point load strength tests are therefore used to index the relative abrasivity of the lithological groups in the study area (Section 6.2.2). Significant differences are observed between several groups, in part because of weathering susceptibility, and fining rates for these groups are compared within links in order to assess the influence of litho-type on the diminution coefficient aa (Section 6.2.3). Although interpretation is complicated by lithology-dependent differences in size characteristics several lines of evidence suggest that lithological composition plays a minor role in within-link diminution. 145 Consideration of the hydraulic forces acting on individual particles and of the adjustments which occur within fluvial systems on land-forming timescales suggest that channel slope and bed material size are interdependent. This is particularly true between major sediment sources. Rate of diminution may therefore be related to rate of change of channel slope and this possibility is examined in Section 6.3. In contrast with the balance of previous work simple polynomial models describe the longitudinal profiles of individual sedimentary reaches (Section 6.3.1). This implies that channel slope varies as a linear function of distance downstream. In some reaches linear models are adequate for describing changes in grain size too and this indicates that size and slope are at least correlated (Section 6.3.2). In turn, examination of the relation between diminution and rate of change of slope (which is constant for a given reach) reveals a reasonable relation. However, an independent test of this relation's predictive capability highlights the importance of local geomorphic history and contingent conditions for controlling reach scale diminution. 6.1 The nature of within-link fining The existing fining models discussed in Chapter 1 become relevant in this context because, excepting Troutman (1980), the authors explicitly or implicitly consider bed material changes in the absence of lateral sediment inputs. It will be recalled from Section 1.2 that a number of partially specified analytical models purport to simulate sorting and abrasion processes. Exponential reduction of average particle size is predicted by most models and has been verified by experiment for Sternberg's abrasion Law (e.g. Schoklitsch, 1933) and for unconstrained selective deposition (Paola et al., 1992). It will also be recalled that a simple exponential model adequately describes the undifferentiated effects of abrasion and sorting in a number of field situations (Church and Kellerhals, 1978; Knighton, 1984; Dawson, 1988). This is to be expected if both sorting and abrasion processes are independently described by exponential relations (Krumbein, 1937; Tanner, 1971). 146 In contrast, Adams (1979) suggests that the unsound nature of particles close to their source elevates abrasion rates in headwater areas, such that a negative power function is better suited to the description of the abrasion process. Plumley (1948) reports downstream fining in terrace gravels of the Black Hills, South Dakota, that is best described (in at least one of three cases) by a power function, although selective transport is held to be largely responsible for the fining. Diminution on Squamish River, British Columbia, primarily due to sorting downstream from a major sediment source, is also described most appropriately by a negative power function (Brierley and Hickin, 1985). Recent theoretical work by Paola and Seal (1995) indicates that fining profiles due to sorting depend on the distribution of deposition within a reach and that exponential reductions are to be expected only where the depositional profile is also described by a negative exponential function. This is to some extent verified by their observations on the North Fork Toutle River (Seal and Paola, 1995) where fining occurs most rapidly in the distal portion of the study reach upstream from a sediment retention dam where measured deposition rates are highest. Pizzuto (1992) utilises a power function to describe grain size changes in his model of graded river morphology. The pattern of fining within links is therefore uncertain and it is appropriate to examine the validity of exponential and power functions for describing grain size change. Lateral sources delimit a series of 16 reaches along Pine River and 17 along Sukunka River (Figure 4.8). Excluding the canyon reach on Pine River, five reaches that contain too few data to allow a reasonable assessment of textural change, and the five very short reaches (see section 4.5), one is left with 22 reaches. For these reaches exponential and power functions were fitted to downstream variations in D50 and D95 (Figure 6.1). Although my purpose here is to determine descriptive parameters, least-squares regression is an appropriate technique. because the independent variable L (distance downstream within a reach) is known within a small error (Mark and Church, 1977). Base two logarithms were used to linearise the data such that the equations yield grain size D on the phi scale for L specified in km (exponential model) and in log2km (power model). Model significance and other statistics are given in Tables 6.1 for the Sukunka and 6.2 for the Pine. 147 Figure 6.1. Exponential (solid) and power (dashed) models of downstream changes in D50 and D95 within sedimentary reaches. SR 1. -L , A 1 9 SR 5 9 -SR 7 8 8 1 — 7 i 7 -| 6 > •K I -6 -1 ' A "* * 5 5 L A D 9 5 • D50 4 0 CD N 00 c o 6 12 16 20 - 6 1 SR 1:3. . p . i 1 2 D i s t a n c e d o w n s t r e a m ( k m 148 Figure 6.1 continued. Exponential (solid) and power (dashed) models of downstream changes in D50 and D95 within sedimentary reaches. 1 I :"5. T \ \ * T 5 4 0 I l J 1 1 s R 1 7 **• 1 < < A - — i -I 5 2 0 PR 4 T -1 i •a \ -r j • % PR i 1 0 : -P R 5 $ T O i ! PR 1 5 D i s t a n c e d o w n s t r e a m ( k m ) 149 Table 6.1. Sukunka reaches, exponential and power model statistics for D50 and D95 versus distance downstream. Reach n R 2 Exponential model S.E. {y} (phi) Signif. R2 Power model S.E.{y} (phi) Signif. SR 1 9 0.89 0.15 0.83 0.19 0.73 O.J 8 0.66 0.20 -SR3 11 0.73 0.35 0.90 0.21 0.78 0.33 •/ 0.85 0.27 SR 5 4 0.73 0.31 X 0.55 0.40 X 0.73 0.22 X 0.51 0.30 X SR 7 7 0.29 0.52 X 0.36 0.49 X 0.23 0.43 X 0.39 0.35 X SR 8 30 0.04 0.27 X 0.01 0.28 X 0.02 0.28 X 0.00 0.25 X SR 9 20 0.86 0.21 0.70 0.30 0.92 0.76 0.85 0.23 SR 10 6 0.84 0.24 _ 0.87 0.22 _ 0.95 0.14 0.90 0.21 SR 12 7 0.88 0.17 _ 0.76 0.24 _ 0.93 0.75 0.87 0.20 SR 13 14 0.70 0.17 0.55 0.21 0.78 0.14 0.62 0.20 SR 14 7 0.30 0.26 X 0.49 0.22 _ 0.25 0.32 X 0.41 0.25 X SR 15 7 0.71 0.25 _ 0.96 0.10 V 0.68 0.27 - 0.94 0.11 V SR 16 3 0.83 0.25 X 0.42 0.46 X 0.79 0.35 X 0.35 0.59 X SR 17 14 0.66 0.29 0.69 0.27 •/ 0.66 0.30 0.70 0.27 For each reach the top row refers to the D 5 0 relation and the second, italicized row, to the D 9 5 relation. Models were fitted using least-squares regression. The reported standard error term is the average standard error of the y estimates (= \MSE). The significance of each relation is indicated as follows: S significant at a = 0.005; - not significant at a = 0.005; * not significant at a = 0.10. 150 Table 6.2. Pine reaches, exponential and power model statistics for D50 and Dg5 versus distance downstream. Exponential model Power model Reach n R2 SE. {y} Signif. R 2 SE.{y} Signif. (phi) (phi) PR 1 13 0.00 0.54 X 0.00 0.56 X 0.00 0.56 X 0.00 0.58 X PR 2 8 0.61 0.35 _ 0.58 0.37 _ 0.55 0.35 - 0.61 0.32 -PR 4 5 0.98 0.06 0.69 0.22 0.99 0.04 0.68 0.22 -PR 5 3 0.91 0.23 X 0.98 0.11 0.90 0.28 X 0.98 0.14 -PR 7 8 0.72 0.44 _ 0.80 0.37 0.69 0.44 - 0.82 PR 9 8 0.88 0.35 0.91 0.31 0.88 0.38 0.91 0.33 PR 10 6 0.89 0.23 0.92 0.20 0.81 0.32 - 0.86 0.28 -PR 12 5 0.92 0.36 _ 0.64 0.75 X 0.92 0.40 - 0.67 0.75 -PR 15 8 0.26 0.44 X 0.56 0.34 _ 0.13 0.47 X 0.40 0.39 -For each reach the top row refers to the D 5 0 relation and the second, italicized row, to the D 9 5 relation. Models were fitted using least-squares regression. The reported standard error term is the average standard error of the y estimates (= VMSE). The significance of each relation is indicated as follows: S significant at a = 0.005; - not significant at a = 0.005; * not significant at a = 0.10. 151 Negative exponential and/or negative power models are significant (a < 0.10) in all but six cases, demonstrating the prevalence of downstream fining within sedimentary links. In Sukunka Reach 16 bed material coarsens downstream, presumably as a consequence of extended sediment supply by both Highhat and Dickebusch fans. In SR 5, SR 7, and SR 14 weak fining trends can be observed (and in fact the power model for D50 is significant at a = 0.10), but the small number of sites and degree of scatter preclude significant relations. Upstream of Windfall Creek on Sukunka (SR 8), and of Lemoray Creek on Pine (PR 1), grain size varies independently of distance. In the latter case this is easily explained by a large number of active non-fluvial sources adjacent to the channel (glaciofluvial terrace and alluvial fan exposures in the south bank) and by Mountain Creek tributary; inputs which must be of sufficient magnitude and frequency to prevent the development of any downstream trends. In contrast it is difficult to account for the lack of fining in the reach upstream of Windfall. There is intermittent coupling in the upper part of the reach but the lower section is dominantly alluvial (Appendix 1, map B), although data resolution is poor in this lower section. In two reaches on Pine River (PR 5 and PR 15) exponential models are not significant (a = 0.10), while power relations are. The lack of data in reach PR 5 makes this result less convincing than in PR 15. In PR 12 the D50 power model is not significant while the other three models are at a = 0.10, but not at a = 0.005. In all other reaches both models are significant at a = 0.10 and in many cases at a = 0.005. There are no systematic differences in their applicability to D50 and D95 (Tables 6.1 and 6.2) and if R 2 and standard error values for each D 5 0 model are plotted against one another (Figure 6.2) it is apparent that, in general, there is little to choose between them in terms of their ability to describe within-link textural modification. In a few cases textural change within individual reaches is best described by power models (eg PR 7, SR 15) or by exponential models (e.g. SR 9, PR 12), but in general either model provides a reasonable fit to the data. Reaches which do show a tendency toward one model rather than the other are not distinctive in any other way. None of the grain size profiles exhibit deviation from these models as extreme as reported by Seal and Paola (1995) on the North Fork Toutle River, where recent inundation 152 Figure 6.2. Comparison of exponential and power model standard errors and R2 values. L L J GO CD " O O O Q _ 0.6 0.4 0.2 0.0 + : / / / / / : / Q •/ • : • / x • ^ * ' / • / / 0.0 • 0.2 0.4 0.6 Exponential model S.E.ty} o C L 1.0 0.6 CM ID O E CD 0.4 0.2 / 0.0 / / + • Bo th signif . O Nei ther signif . -f Exponent ia l signif . X Power signif . 0.0 0.2 0.4 0.6 0.8 1.0 Exponential model R 2 153 by debris from Mount St. Helens is a dominant factor. In summary there is no empirical imperative here for preferring either model. However the balance of theoretical and empirical evidence in the literature suggests that exponential models are more appropriate. Furthermore, Adams' argument concerning elevated weathering rates close to source materials (Adams, 1978) is unlikely to apply to individual sedimentary reaches along a mainstem channel. Most tributaries deliver material that has already been transported some distance and has therefore become sound. The major non-alluvial sources in this case are glaciofluvial deposits consisting of well rounded, mature material (although weathering during storage may weaken some clasts). In the absence of a complete analytical description of the fining process, exponential models are therefore used to describe changes in grain size parameters within the Pine and Sukunka sedimentary reaches. Model coefficients ad (*1), are presented in Table 6.3. For significant models cia has an average value of -0.245 for D50, and -0.255 for D95 with respective standard deviations of 0.156 and 0.180'. In most previous studies loge has been used to linearise grain size data for exponential modeling, and yields coefficients with rates in units of the original measurements (usually mm.km1). The coefficients in Table 6.3 can be adjusted for comparison by dividing by log2(e)-= 1.443. The values obtained for D 5 0 (-0.43 < ad < -0.05) correspond closely with rates previously obtained for reaches delimited by significant sediment sources and more generally with values in rivers where sorting is thought to dominate the fining process (Figure 6.3). For example, Dawson (1988) reports values of -0.6919 < otd < -0.1579 for sedimentary reaches on Sunwapta River, Alberta, and a single sedimentary reach on Allt Dubhaig has a coefficient for surface D 5 0 of ad = -0.528 (Ferguson and Ashworth, 1991). Rates are significantly higher than those obtained in most abrasion experiments and for the central sections of several Albertan rivers where abrasion alone is thought to control diminution (Shaw and Kellerhals, 1982). There is an indication, then, that sorting is the predominant fining process within the Pine and Sukunka sedimentary reaches. Sources of the diminution coefficients presented in Figure 6.3 are given in Table 6.4. 154 Table 6.3. Exponential model (diminution) coefficients for Pine and Sukunka sedimentary reaches. D 5 0 D 9 5 Reach aa p (F) aa p (F) ( ( SR 1 SR 3 SR 5 * SR7 x SR8 x SR 9 SR 10 SR 12 SR 13 SR 14 x SR 15 SR 16 x SR 17 PR 1 x PR 2 PR 4 PR 5 x PR 7 PR 9 PR 10 PR 12 PR 15 x -0.167 -0.315 -0.570 -0.468 +0.014 -0.115 -0.449 -0.158 -0.074 -0.085 -0.237 +0.452 -0.106 +0.013 -0.143 -0.093 -0.198 -0.285 -0.359 -0.307 -0.620 -0.146 0.0001 0.0009 0.1436 0.2156 0.2607 0.0000 0.0099 0.0016 0.0002 0.1993 0.0167 0.2746 0.0004 0.8894 0.0227 0.0012 0.1911 0.0079 0.0005 0.0049 0.0107 0.1976 -0.110 -0.344 -0.407 -0.339 +0.009 -0.125 -0.528 -0.188 -0.080 -0.088 -0.229 +0.543 -0.107 +0.005 -0.124 -0.093 -0.231 -0.272 -0.375 -0.315 -0.680 -0.101 0.0034 0.0003 0.1447 0.2744 0.4486 0.0000 0.0008 0.0004 0.0000 0.2755 0.0233 0.3065 0.0004 0.9565 0.0369 0.0005 0.2004 0.0104 0.0006 0.0141 0.0108 0.3805 Mean -0.245 -0.255 &Std. dev. 0.156 0.180 for p(F)>1.0 Models that are not significant at a = 0.10 are indicated by a cross (x). For grain size D in mm, and distance downstream L in km, models are of the form, log2(D) = log2(D0) + a d . L such that aa is in units of For aa in divide by log2(e) = 1.443. For prediction of grain size in mm a bias correction is also necessary. 155 Figure 6.3. Diminution coefficients (a J obtained in this and previous experimental and field studies, for median or mean size. NJ 'U) c o E o c o T J CD E E ^E "D 8 I 1 02 1 01 1 00 1 0 -1 1 0 - 2 1 0 - 3 1 O " 4 o o o E • o-- e en o "ct: <u V Q. o o ABRASION EXPERIMENTS FIELD STUDIES 156 Table 6.4. Sources of diminution coefficient data used in Figure 6.3. All coefficients are for D50 or mean size and are expressed in mm. km-1 Source - ad (mm.krrr1) Abrasion mills / barrels Daubree(1879)* 0.00130, 0.00036 (n=12) Wentworth(1919)* Marshall (1927)* 0.00090 0.00014 Krumbein(1941)* 0.01000 Adams (1978), means 0.00059-0.01944 Brewer & Lewin (1993) 0.00300 Keunen-type flume Keunen(1956)* Bradley (1970)* 0.00006 - 0.00320 (n=18) 0.00028 - 0.000420 Brewer & Lewin (1993) 0.06700 ERC Mixer Kodama (1992), means 0.01555 -0.04057 (n = 6) Sorting experiment Paola et al. (1992) 13.2 (n=l) Rivers - abrasion Shaw & Kellerhals 0.00165 -0.00177 dominated (1982) (n = 4) Rivers - undifferentiated Heyne (Leliavsky, 1966) * 0.00600 (n=12) Sternberg (Leliavsky, 1966)* 0.00400 - 0.00850 Hack (1957)* 0.01390 Leopolds al. (1964)* 0.03270 Church & Kellerhals 0.00494, 0.00975 (1978)* Knighton (1980) 0.04200-0.11800 Rivers - sorting Brierley and Hickin (1985) 0.03900 dominated Dawson (1988) 0.15790-0.69190 (n = 8) Ferguson & Ashworth (1991) 0.52800 Brewer & Lewin (1993) 0.03520, 0.06780 Japanese fans Yatsu(1957)* 0.01040-0.11000 (n = 15) Kodama (1992) 0.08900 Upland ephemeral Mayer et al. (1984) 0.34000, 0.44000 streams (Arizona) Rhoads(1989) 0.40000 - 0.76000 (n = 5) Pine and Sukunka this study 0.07400 - 0.62000 sedimentary reaches (n=14) * data from Shaw and Kellerhals (1982), Tables 11 and 12 (p 148 -150). 157 While the observed rates for significant exponential models are fairly homogeneous relative to the entire range of previously recorded values, they vary over an order of magnitude. The variation is much greater if non-significant reaches are also considered. In a predictive mode the successful application of a functional exponential model will depend on the choice of an appropriate value of ad. The query which arises, and that I wish to address in the remainder of this chapter, is whether fining rates can be identified a priori on the basis of reach scale information. That is, can aa be predicted for a given sedimentary reach ? My examination of this issue will focus on two possible determinants of fining rate at the reach scale: lithologic control; and hydraulic control, particularly channel slope. 6.2 Lithology and rates of diminution Despite their shortcomings in terms of simulation of field conditions (cf. Keunen, 1956; Kodama, 1994b) controlled abrasion experiments confirm that the rate of mechanical breakdown by attrition, chipping, grinding and breakage is dependent on rock type. Quartzitic and igneous rocks are generally more resistant than sandstones, which in turn are more resistant than many fine-grained clastic rocks (mudstone, siltstone) and carbonates (limestones and dolomites). A fortuitously convenient arrangement of bedrock types, exhibiting markedly different abrasion rates, allowed Werritty (1992) to examine the relative contribution of abrasion and sorting to downstream fining along River Dunajec in southern Poland. In the present context, if the abrasivity of the lithologies is sufficiently diverse, differences in the lithological composition of material supplied to the head of individual reaches (from upstream and from lateral sources) would produce different fining rates for the lithologically undifferentiated populations. Within individual reaches this would be reflected in different fining rates for the different lithological groups, or at least for those groups with differing resistance to abrasion. If fining rates do not, in general, differ between groups one can conclude that lithological composition is not a control on fining rate between reaches. If they do differ significantly then an examination of differences in lithological composition would be pertinent. 158 This analysis also assesses the relative importance of abrasion as a significant cause of size reduction. For gravels and larger particles that are composed of many different minerals, gross density differences are unlikely to have a significant effect on entrainment and deposition thresholds. In the absence of significant shape differences, sorting processes therefore operate essentially independently of rock type (assuming that there are no lithology-dependent differences in size). Thus, differences in fining rate between clasts of different lithologies would indicate that abrasion is an important process, while similar rates would indicate that it is not. 6.2.1 Lithology and differences in abrasivity Prior to comparing fining rates it is necessary to establish that resistance to abrasion varies between the lithological groups used to categorise field samples. Although large experimental samples do demonstrate lithology-dependent variations in average rates of abrasion, close inspection of experimental data reveals that rates are highly variable within groups and that differences are often marginal. This is apparent in Adams' (1978) tumbling mill data for pebbles from rivers on South Island, New Zealand. In Figure 6.4 mean values for logarithmically transformed abrasion rates (logioaa) are plotted along with standard deviations and standard errors for each of seven lithological groups (I have split Adams' "sedimentary" group into sandstones and fine-grained elastics). The transformed data are normally distributed, have equal group variances (a = 0.05), and standard analysis of variance is therefore applicable. ANOVA reveals that significant differences are present and the Newman-Keuls test, which compares ranges and is more conservative than a standard Least Square Difference test, was used to examine the contrasts. With a strict criterion for difference (a = 0.01) silica is significantly more resistant than all other lithologies. However, the only other significant difference is between extrusive igneous (second most resistant) and fine sedimentary (least resistant) pebbles. With a more relaxed criterion (a = 0.05) the three softest lithologies (carbonates, metamorphics and finestones) are all significantly less resistant than extrusive 159 Figure 6.4. Adams' experimentally determined abrasion coefficients for distinct lithological groups (after Adams, 1978). -0.8 •1.4 -Data from Adams (1978) UJ o u_ UJ O O z O CO < OQ < o -2.6 -3.2 -3.8 -4.4 +Std. Dev. +Std. Err. • Mean Ex t rus i ve S i l i ca F i n e c las t i c M e t a m o r p h i c Intrusive S a n d s t o n e C a r b o n a t e LITHOLOGY 160 igneous pebbles, and the abrasion rate of sandstone pebbles (third hardest) is significantly less than that of finer grained elastics. This analysis indicates that only the resistant silica rocks (predominantly quartz pebbles) have unequivocally distinct abrasion characteristics. Fine-grained sedimentary rocks (siltstone and argillite) are significantly less resistant than extrusives, and marginally less resistant than sandstones, but not different from limestones, metamorphics and intrusive pebbles. There are no igneous materials in the Pine and Sukunka study area (apart from very rare Shield erratics), and Adams' data suggest that differences in abrasion may be at best marginal between the predominantly sedimentary materials that are present, at least at the level of lithological classification employed and supposing that Adams' New Zealand particles are representative of their petrographical groups. A lack of detectable differences would preclude any expectation that lithological composition is an important control on fining rate. It is therefore important to assess the relative abrasivity of the seven lithological groups identified in the field. 6.2.2 Compressive strength indices and the abrasivity of Pine and Sukunka gravels Experimental equipment was not available to conduct standard abrasion tests so an alternative method was employed. The point load strength test was used to assess the compressive strength of gravel particles within each lithological group. Point load strength is a strength index which is highly correlated with uniaxial compressive strength (Broch and Franklin, 1972) but in contrast involves a relatively inexpensive and straightforward procedure which can be applied to irregularly shaped specimens (Cargill and Shakoor, 1990; Selby, 1982). It has been used by Huddart (1994) in examining textural changes along Morsardalur-Kjos sandur, southeast Iceland and by Kodama (1994b) in his experimental work, although in both cases few details are presented. Moss (1972) used a related technique to assess the strength of fluvially transported quartz grains. The use of point load strength as a surrogate for abrasion rate is based on the assumption that the compressive strength of a sedimentary particle (that is, its ability to resist deformation without failure) is directly related to the rate at which 161 breakdown occurs due to abrasion processes (attrition, breakage, chipping, etc.). While compressive and tensile pressures are perhaps most directly associated with fracturing and breakage (cf. Moss, 1972), experimental evidence demonstrates that frictional attrition is also highly correlated with compressive strength. A relation between low-energy abrasion in water (cm.hr1) and compressive strength (kgf.cnv2) obtained by Sunamura et al. (1985), has a correlation coefficient of -0.96 for the logarithmically transformed data. Similarly strong inverse relations have been observed experimentally for abrasion of concretes by water-borne steel particles (Liu, 1981) and for aeolian abrasion of a variety of rock types by sand (Suzuki and Takahashi, 1981). The standard test procedure (ISRM, 1985) involves breaking test specimens by applying a concentrated load between two cone-shaped platens. The index of strength Is (Pa) at the moment of failure is defined as [6.1] IS = P / A where A (m2) is the minimum cross-sectional area through the loading points and P (N) is the applied load at failure. P is measured using a hydraulic pressure gauge attached to the loading ram. In engineering practice A is approximated using a representative area D e 2 , where D e is the diameter of a cylinder with the same cross-sectional area as the test piece used (ISRM, 1985). This convention stems from the widespread testing of drilled cores, but there is no such imperative in this study, and minimum cross-sectional area is used to calculate Is. The load required to break a specimen is a function of A and, more specifically, of the volume affected by the applied load (Brook, 1985). A size correction is therefore required in order to compare the strength of rocks for which test piece size varies. Standard practice is to report IS(50), the value of Is that would be obtained by testing a core of diameter D e = 50 mm. A suggested method for obtaining IS(50) involves establishing an empirical relation between P and D e, and interpolating that value of P corresponding to D e = 50 mm (ISRM, 1985). This approach yields a single estimate of strength which is overly simplified in the present context. 162 The character of lithological groups, rather than individual formations or very discrete petrographical units, is being assessed and an appreciation of within-group heterogeneity is useful. Corrections to Is are not therefore made. However, analysis of variance indicates that the mean sizes (b-axis) of test particles varies significantly between some of the lithological groups (a = 0.01). In particular the white limestones and fine-grained sedimentary specimens are smaller than the sandstone and quartzite test pieces. To ensure that observed differences in strength can be unequivocally attributed to lithology, comparisons between lithology are made for narrowly defined grain size fractions. Test particles were collected from exposed, vegetation-free bar surfaces in the vicinity of the Windfall Creek confluence and on the first major bar downstream of the Pine/Sukunka confluence. Several hundred particles from each lithological group, except conglomerate (which is scarce), were returned to the laboratory for testing. Handling this volume of material in the field necessitated ignoring the larger sizes and most particles tested range from 22 to 64 mm (b-axis). It is appropriate to measure the strength of wet gravels, but point load strength varies with water content (particularly for saturation levels below 25 %), and it is therefore necessary to standardise saturation. Particles were submerged in water for approximately 48 hours prior to testing, a procedure used by Kodama (1994b). The exact degree of saturation was not determined but weighing tests indicated that for all lithologies the majority of water uptake occurred within 2 hours of submergence and thereafter at a relatively low and decreasing rate. Within 48 hours water content was probably close to the final saturation content for all lithologies, and was almost certainly greater than 50 %. At saturations above 50 % water content has little influence on strength (ISRM, 1985). Approximately 50 particles from each group were selected for testing. Visibly fractured particles and those with a c-axis dimension less than 0.3 times the b-axis dimension were not tested (ISRM, 1985). Particles were placed with their smallest (c-axis) dimension between the platens of a standard point load testing machine, and load was steadily increased until failure occurred. For a majority of breakages, minimum cross-sectional area through the platens corresponded with the failure plane. Values of A were obtained by tracing the outlines of 163 failure planes onto paper and measuring their enclosed area using a digital planimeter. When the failure plane did not coincide with the minimum cross-sectional area, a careful approximation of the latter was made. In Figure 6.5 breakage load is plotted against cross-sectional area for each lithology and two features characterise each set of results. First there is significant scatter and correlation coefficients are in general very low. This contrasts with similar plots in the engineering literature where power functions with exceptionally high R2 values are presented, typically with P cc A 0 7 5 (e.g. Brooks, 1985, Figures 3,6,7)). The 0.75 exponent indicates that load is not very sensitive to area and that, in turn, for the fairly narrow range of sizes tested here one should not expect a strong systematic relation. The degree of scatter may also reflect the natural heterogeneity of strengths within my rather broad lithological groupings. Second, there is a marked bimodality in the observed breakage loads with a higher mode between 10 and 30 kN and a lower mode between 0.4 and 1.0 kN. The presence of this pattern in all six groups suggests that inadvertent combination of two distinct petrographic groups is not responsible. All six lithological groups are ultimately of sedimentary origin and it is possible that the orientation of bedding laminae within the test particles is responsible for the bimodality. However, examination of sandstone breakage loads classified by laminae orientation (massive, perpendicular to load, normal to load (Figure 6.5)), indicates that this is not the case. Moss (1972) demonstrated that the fragmentation load of quartz grains (0.5-5 mm) increases with distance downstream, a finding that he attributes to the selective breakage of weaker members of the initial population with distance traveled (cf. Adams, 1978). Individual test particles were not identified with the site where they were collected. One might suspect that the bimodality observed here is a result of test clasts being collected at two separate sites, one much further downstream than the other. However, the upstream collection site is far enough from source areas that the gravel population has had ample opportunity to become rich in predominantly sound clasts. This is supported by a lack of bimodality in the shape indices of test particles (Figure 6.6), which would be expected if sound and unsound subpopulations were present. In addition the white limestone particles, which exhibit strong bimodality, were almost 164 Figure 6.5. Breakage loads versus minimum cross-sectional area for point load tests. 1 o 2 1 01 4 3 2 1 00 1 o- i F Limestone r=0.69 • o O' o 'O - o ( B O O o«x>: o 1 02 1 0' 4 3 2 1 0° 3 2 1 0"1 • ' 111 • I ' ' ' ' : \ Finestone ": - r = 0.15 '• : - O -0 : 03 o • : : oooo 0 <5B> !o -'.O ' • 1 • ' • ' — i i r w r c r r t . i O O 1Q2 2 3 1 Q3 2 3 1 04 1 02 2 3 1 03 2 3 1 02 101 I 1 04 1 0-1 1 02 2 3 1 Q3 2 3 o massive parallel A normal 1 o 4 1 02 r O Q_ 3 2 1 01 4 3 2 1 0° I Metamorphic r = 0 .36 • o 1 0-1 a n o o O o • o OQ 1 02 1 01 4 3 2 1 0° i ) i 11 ' 1 1 i Quartzite: r = 0.41 o o .©-••• o o 1 02 3 2 1 01 3 2 1 00 1 Q2 2 3 1 Q3 2 3 1 04 1 02 2 3 1 Q3 2 3 1 ( 10-1 . ' i ' I' " I — II — 1 ;Bluestone \ • r = o.38 : ; 1° : 3 : O o 0 \ € 0 o ! , , — i i 1 1 1 1 1 02 2 3 1 Q3 2 3 1 04 T O S S —sect ional area ( m m 2 Figure 6.6. Zingg shape classification for point-load test particles 1 .0 OA 0.6 0.4 0.2 0.0 BLADE o White limestone A Quartzite Finestone o Blue limestone V Sandstone X Metamorphic 0.0 0.2 0.4 0.6 1 .0 c / b 166 entirely collected at the upstream site. It is therefore unlikely that spatial separation is the cause of the bimodality. Although I have not attempted a detailed assessment of each test particle, differences in degree of weathering provide a reasonable explanation of the observed bimodality. In order to explain such discrete subpopulations a critical weathering condition would have to be invoked. Such a condition may reflect the length of time an exposed particle has remained undisturbed. Alternatively the two modes may represent particles that have recently been excavated from subsurface storage (lower mode) and material that has been active recently (upper mode). Numerous studies have noted the importance of weathering (e.g. Keunen, 1956; Bluck, 1964) which has been clearly demonstrated by Bradley (1970) in his examination of the middle Colorado River, Texas. More recently Johnsson and Meade (1990) have discussed weathering of sand in alluvial deposits, and Dobrovolskaya et al. (1991) have suggested that subaqueous biochemical weathering of gravels is intense, and varies between lithological groups. Whatever the cause of the bimodality, it presents a problem in terms of examining differences in the point load strength index. Values of Is are far from normally distributed, and cannot therefore be assessed using standard ANOVA. There is no way of transforming the data to achieve normalcy. However, a logarithmic transformation improves the normalcy of each subpopulation, which in turn can be considered separately. For each subpopulation the total variance in logio(Is) was partitioned in a two-factor design using six lithological groups and three groups based on b-axis size (< 40 mm, 40 -50 mm, > 50 mm). Variances are heterogeneous between the sub-groups of this design. In each case, the two subpopulations were easily identified and there was no need to use special procedures to isolate them (Figure 6.7). ANOVA results are reported for each subpopulation in Table 6.5. For the upper mode both lithology (a « 0.01) and size (a = 0.01) significantly affect Is. There is no significant interaction such that each effect, in general, holds for all levels of the other independent variate. With unequal group sizes, and a desire to ensure that observed differences are real, the relatively conservative Scheffe's test is appropriate for comparing group means (Milliken and Johnson, 1984). With regard to lithology white limestone is significantly Figure 6.7. Distribution of compressive strength indices (IJ, for each lithological group. Upper and lower modes and subpopulation means are indicated. 1 -0.209 L imestone =43 0.771 -1 .0 -0 .5 0.0 0.1 4 0.12 0.10 0.08 0.06 0.04 0.02 0.00 Finestone n = 40 1 .068 -0 .5 0.5 Sands tone n = 51 -0.330 0.853 I .5 0.1 4 0.12 0.1 0 0.08 0.06 0.04 0.02 0.00 l e tamorph ic n = 46 -0.1 47 At AA AAt AA AAt AA/ A/A A '/ yaAAAA^ AAAAA/ 1 .1 32" -0 .5 0.5 1.5 Quartzi te n = 59 -0.1 64 1 .1 32 -1.0 - 0 . 5 0.0 0.5 0.18 0.16 0.1 4 0.12 0.1 0 0.08 0.06 0.04 0.02 0.00 Bluestone n = 50 0.051 4 A A A A At Aa AAAAA //A/A///A//VA/A 1 .055 -1 .0 - 0 . 5 0.0 0.5 1.0 1.5 L o g ( P o i n t L o a d S t r e n g t h Index, l s ) 168 Table 6.5. Analysis of variance ofpoint load strength index 75, by lithology and b-axis size. Source d.f. Sum of Squares Mean Square F P Upper Mode 0.0000 • Lithology 5 2.412 0.482 10.78 Size 2 0.569 0.285 6.36 0.0022 • Interaction 10 0.578 0.058 1.29 0.2391 Error 160 7.159 0.045 Lower mode Lithology 5 1.795 0.359 4.45 0.0011 • Size 2 0.193 0.096 1.19 0.3075 Interaction 10 0.799 0.080 0.99 0.4569 Error 93 7.499 0.081 Six lithological groups (white limestone, fine-grained clastic sedimentary, sandstone, metamorphic, quartzite and blue limestone) and three b-axis size groups (< 40 mm, 40-50 mm, > 50 mm) were used in the analysis. The dependent variable, point load strength index (Is), is bimodally distributed and each subpopulation is considered separately, following logio transformation. Sindicates significance at a = 0.01. 169 weaker than all other groups except sandstone (a = 0.01), and sandstone is significantly weaker than the metamorphic and quartzite groups (a = 0.01), blue limestone (a = 0.05), and fine-grained elastics (a = 0.10). For the lower mode there is no size effect, but once again, lithology is important (a = 0.01). In this case both the fine-grained elastics (a = 0.01) and sandstones (a = 0.05) are significantly weaker than the blue limestones. These results indicate that there is at least the potential for lithologically dependent wear in Pine and Sukunka links. In order to see whether this has an effect on diminution rates, and in turn whether lithological composition is a determinant of within-link fining rate, the fining behaviour of two particularly dissimilar lithologies should be examined. The balance of information garnered above suggests that a comparison of white limestone or sandstone with quartzites, metamorphics, or bluestones would be useful. Unfortunately white limestones are scarce and grain size parameter estimates are therefore likely to be unreliable. However, the equally weak sandstones occur in abundance and are well represented in my Wolman samples. Quartzites are also relatively scarce, but metamorphics and blue Pardonet limestones occur in fairly equal proportions within most samples. Blue limestones are most readily distinguished in the field and may therefore be a more homogeneous group. Sandstone and blue limestone may therefore be the most appropriate groups to compare. In addition to the differences within the two subpopulations, the proportion of test pieces falling in each mode varies by lithology (Figures 6.5 and 6.7). Thus the lower mode constitutes 14 % of the entire quartzite population and 28 % of the blue limestone group, but 65, 51 and 43 % of finestones, white limestones and sandstones respectively. There is no reason to doubt that the random samples collected in the field (of visibly unweathered clasts) are representative of the bed material as a whole. In turn, it is reasonable to suppose that a greater proportion of the latter three groups are present in a weakened state within Pine and Sukunka gravels. This will act to reinforce the lithological differences identified for the individual subpopulations because the groups with lower compressive strength indices in the upper mode are also those which are proportioned in favour of the lower mode. This reinforcement effect helps to further distinguish the sandstone and bluestone groups. Median values for the bimodal distributions are 3.13 MPa 170 and 8.52 MPa respectively. A Mann-Whitney U-test was used to compare the positions of the two bimodal, untransformed distributions, and confirmed that the compressive strength indices are significantly different (a < 0.001). Before going on to compare the diminution rates of these two groups, the influence on abrasion of particle size should be considered. Theoretical and empirical evidence demonstrates that large particles abrade at a higher rate than small particles because of their greater surface area and weight (Sternberg, 1875; Krumbein, 1941; Keunen, 1956; Kodama, 1992; Werritty, 1992). The above ANOVA reveals that pebbles in the coarsest fraction of the upper mode (> 50 mm) consistently record lower values of Is than the central group (a = 0.05) or the fraction below 40 mm (a = 0.01.) which appears to support the contention that larger rocks are less resistant. However, this result should not be interpreted literally, because it indicates only that the rate of change of A is greater than that of P with respect to increases in b-axis dimension. While higher Is = P / A values for a given size (between lithologies) give an indication of relative abrasivity, comparisons of P (which reflects the inherent strength of the particle rather than a size-normalised index) are more appropriate for examining the influence of size. Given the extant experimental confirmation of Sternberg's proposition no further analysis is presented here; It is sufficient to remark that large differences between the grain size distributions of the lithological groups being compared could lead to false interpretations regarding the importance of abrasivity as a control on fining. Differences in grain size characteristics should therefore be considered during the following analysis. 6.2.3 Within-link diminution rates for lithologic groups In Table 6.6 sandstone and bluestone D50 diminution coefficients are presented for the 11 sedimentary reaches that contain at least three Wolman samples and exhibit significant general fining (size distributions by lithology can be constructed only for sites sampled using the Wolman technique). In three of these there are too few bluestone clasts to allow one to 171 Table 6.6. Diminution coefficients for sandstone and blue limestone within several sedimentary reaches. Reach n -aa sand -ad blue Different ? SR 1 7 0.207 0.172 no SR 3 5 0.213 0.122 no SR 9 14 0.124 0.095 a = 0.05 SR 10 6 0.457 0.221 no SR 12 4 0.146 0.092 no SR 13 9 0.070 0.036 a = 0.10 SR 17 9 0.091 0.035 a = 0.05 PR 7 5 0.276 0.170 no PR 9 5 0.230 - -PR 10 3 0.202 - -PR 12 3 0.692 -Reaches PR 9, PR 10, and PR 12 contain insufficient bluestone particles to allow reasonable calculation of D50. Coefficient differences are tested according to the method detailed by Sachs (1982; p.440). 172 Figure 6.8. Downstream fining of sandstone and blue limestone materials within four sedimentary links on Sukunka River. Exponential models have been fitted. O IT) Q 1 "A \ ' ! 1 A A » i S R 1 D50Sand = 7.27 - 0 .207*L DsoBlue = 6.71 - 0.1 72*L 2 4 6 ' I ' \ . • • 1 • • m . D50 Sand = 6.76 -1 1 ; - 0.1 24*L - A * A T ~"~ "A •' • "~ A. : D50 i Blue = - 6.1 45 - 0 .095*L i , i , i w ^ ^ : * i SR 9 0 2 4 6 8 1 0 1 2 1 4 1 6 1 • 1 1 ! 1 - • • • -A A~ — -~ A - ~ _.. A • -1 ~ ~ — — — _A A "~ i A SR 1 3 Dsosand = 6.76 - 0 .070*L D50Blue = 5.97 - 0 .036*L 0 2 4 6 10 12 SR 1 7 Dsosand = 6.75 - 0.1 27 *L _ DsoBlue = 5.71 - 0 .035*L 0 2 4 6 8 10 D i s t a n c e d o w n s t r e a m ( k m 173 reasonably calculate D50. For the eight remaining reaches it is immediately apparent that there are differences in diminution rate; the sandstone group fining more rapidly than the bluestone group in every case (Figure 6.8 shows four examples). However, when the diminution coefficients are critically compared, significant differences (a < 0.10) are present in only three reaches (see Sachs, 1982, p440 for details of the test procedure). Although the error probabilities associated with accepting a difference generally exceed a = 0.10, the fact that the rate for sandstone is higher in every link suggests that the differences are not fortuitous. It is difficult to avoid the conclusion that the weaker sandstone group fines at a higher rate than the more resistant blue limestones. In turn this suggests that abrasion is a significant fining process within these links. However, it is also apparent that in each case the sandstone group is significantly coarser than the blue limestone group. This introduces the possibility that observed differences in cxa are due to disparate grain size distributions rather than the inherent abrasivity differences identified by the compressive strength tests. It was noted above that coarse material is expected to abrade at a higher rate than fine material, which is consistent with the more rapid fining of the coarser sandstones. In general, none of the lithological groups which show a significant difference in compressive strength exhibit similar size distributions within the mainstem, and it is therefore difficult to critically assess the role of initial particle size. One can only conclude that differences in size characteristics, as well as in inherent resistance, may control the diminution rate of individual lithologies. In the light of my compressive strength tests and examination of Adams' data, which show that abrasivity differences are often marginal, it is possible that lithological influences are primarily size-related; an observation not explicitly addressed in previous studies. Unfortunately, because observed differences may be due to size rather than abrasivity, these results cannot address the question of whether abrasion is a relevant process in these reaches. With different grain size populations sorting cannot be excluded as a cause of different fining rates, since preferential transport is dependent on the size characteristics of the material involved. Coarser (and generally more heterogeneous) inputs are expected to exhibit higher 174 fining rates. An unequivocal field test of the kind proposed above, requires two lithologic groups of distinct abrasivity, but similar grain size characteristics. Contrary to my initial expectations these conditions are not met along Pine and Sukunka Rivers. Returning to the question of whether lithological composition is an important determinant of link-scale diminution, it is apparent that individual lithologies may fine within links at different rates. However, it is also clear that these differences are not very large and one must wonder whether input composition significantly affects diminution of the lithologically undifferentiated population. Sandstone is consistently the most coarse and, as shown above, least resistant lithology. If lithologic composition is an important control on ad, then it is reasonable to anticipate some relation between abundance of sandstone in an input, and fining rate in the downstream reach. Figure 6.9 shows that a weak relation (R = 0.34) does exist between undifferentiated diminution rate and the proportion of sandstone in the bed of a reach (determined from the Wolman samples). There is an indication that fining rates are higher in links where sandstone is predominant, but in general percent sandstone cannot be regarded as a viable indicator of diminution rate. Finally, a comparison of between-link and within-link variations in lithologically differentiated diminution coefficients is useful. The variance of diminution coefficients within links reflects the role of lithology alone, while variance between links encompasses the impact of all link-scale factors other than lithology. Sandstone and blue limestone are the most dissimilar lithologic groups and therefore provide a reasonable estimate of within-link variance. A one-way analysis of variance for diminution coefficients in the eight links examined above (Table 6.6), indicates that between-link variance is greater than that within links at a = 0.10. This implies that link-scale factors other than lithology are largely responsible for the variability of diminution coefficients. It is reasonable to conclude that, in general, the influence of lithology on undifferentiated within-link diminution is relatively minor. 175 Figure 6.9. Relation between lithologically undifferentiated diminution rate (D50) and percentage of sandstone in the bed material. C L T3 I c o -+-> c £ 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1 r- 1 • • R - 0.34 P" R1 2 -S • R1 0 -• • PRO • . . SR3 • PR7 PR.1 0 • SR1 • SR1 7 # • SR1 2 -SR9 c • 5R1 3' i 1 0 20 30 • 40 50 60 Average p e r c e n t a g e s a n d s t o n e 70 176 6.3 Channel slope and diminution rate Following Gilbert (1877, 1914), Rubey (1952) suggested that for "large, adjusted streams", [6.2] S3 = k.(Qs2.D / Q2.X) where S is channel slope, Q s is sediment load, D is grain size, Q is discharge, and X is cross-sectional shape. Slope and grain size are thus recognised as two of several key variables which together, by mutual adjustment, govern the behaviour and form of fluvial systems. On time scales of individual particle motion channel slope may be viewed as an independent variable which in part determines the size of particles that are entrained, transported and deposited at any given location. On longer, land-forming timescales, local channel slope is adjusted in accordance with grain size (among other variables), and may be regarded as a dependent variable (Mackin, 1948). There is therefore a basis for anticipating some relation between grain size and channel slope, and in turn a relation between the rate of change of grain size and the rate of change of channel slope. Hack (1957), for example, found that channel slope is correlated with bed material size in a number of streams in Virginia and Maryland, but only if individual or lithologically similar streams are considered. He observed a more general correlation between channel slope and the ratio of bed material size to drainage basin area (which can be viewed as a surrogate for discharge). Hack (1957) also made the observation that more rapid changes in grain size are associated with greater profile concavity. It is clear from equation 6.2 and Hack's results that additional factors preclude a straightforward relation between slope and grain size. However, the situation is significantly more simple between major tributaries, where discharge and sediment load are fairly constant. Thus, Mackin (1948) argues that one can expect to observe systematic changes in channel slope only between major tributaries, since it is only between tributaries that grain size can vary in a systematic manner. This statement is to some extent reflected in the conclusion of Penning-177 Rowsell and Townsend (1978) that, "at a local scale", slope is more closely correlated with grain size than with discharge or cross-section form. The contribution of Sternberg (1875) also supports Mackin's caveat concerning the simplification afforded by channel links. After considering changes in cross-sectional form and discharge, Sternberg (1875) concluded that grain size is the dominant control of channel slope along the middle Rhine between Basel and Mannheim. He was the first to suggest that the longitudinal profile develops in response to a systematic reduction in grain size caused by fluvial abrasion, such that velocities sufficient to move the coarsest debris at any given point are maintained. In support of this argument he showed that downstream changes in both particle size and elevation are adequately described by negative exponential functions, which is to be expected if slope is directly proportional to grain size. However, as Woodford (1951) pointed out, there are few major tributaries in the section of the Rhine which Sternberg examined. This is presumably the reason for the consistent relation between channel slope and grain size. Shulits (1941) and Yatsu (1955) confirmed Sternberg's result for homogeneous reaches in the United States and Japan. There is a strong possibility then, that grain size and channel slope are related within Pine and Sukunka sedimentary reaches and that, in turn, rate of grain size diminution is related to rate of change of channel slope. Here the homogeneous reaches are defined in terms of lateral sediment sources, rather than by tributaries per se. 6.3.1 Mathematical description of reach profiles It is first necessary to determine the pattern of slope variation within individual reaches, and to this end detailed profiling of the Sukunka River study reach was carried out in 1994. A simple "leap-frog" surveying procedure utilising an automatic level was used to obtain the bankfull profile along 98.5 km of the channel. Two sections, surrounding the falls above Burnt River confluence and the extensive log jams upstream of Windfall Creek, were not surveyed. At each survey point the high water line was approximated using the vegetation trim line on bars and along the channel banks. Driftwood and accumulations of sand were sometimes used 178 to aid in the definition of this feature. Despite every effort to be consistent, difficulties in identifying the high-water line produce a degree of scatter in the derived elevation (H) and distance (L) co-ordinates. Occasionally, especially where channel slopes are low, positive downstream elevation changes were recorded. These kinds of error are inevitable given the nature of the task, but they are minor relative to the overall fall within any given reach and are safely assumed to be randomly distributed about the actual high-water profile. Gradients can be determined for the short distances between profile co-ordinates but the small errors mentioned produce a significant amount of scatter. A more appropriate method of describing changes in channel slope is to determine a mathematical description of the profile H =J{L) and obtain the first derivative/'(L) = dH / dL = S. Various models have been used functionally to describe longitudinal profiles (Woodford 1951; Snow and Slingerland 1986), the most widely accepted being exponential, power and logarithmic forms. Shulits (1941) suggested that the exponential model has a rational basis (S oc D, and dD/dL cc D), a view not shared by Rubey (1941). Other equations were formulated empirically using elevation data (Jones, 1924), by examining relations between several variables in Rubey's equation (Hack, 1957), or by heuristic approaches based on principles such as landscape entropy (Leopold and Langbein, 1962). Each of the proposed models has been fitted to actual river profiles with some success. Ohmori (1991) tested a variety of functions along 50 Japanese rivers, and found exponential and power functions to be most useful. Longitudinal profiles for the links examined are shown in Figure 6.10. Least squares regression is an appropriate fitting technique and was applied to the longitudinal profiles of each Sukunka reach except SRI6, where lateral sources are abundant and are known to complicate the pattern of textural change. In Table 6.7 mean standard errors and R 2 values for exponential, power, logarithmic, second order polynomial and linear models are presented. To facilitate comparison, mean standard errors are calculated for the back-transformed values of the exponential and power models. Mean standard errors are therefore in metres in each case. For power and exponential models the usual measure of statistical concordance R2, is replaced by a similar measure for the original variates called the Index of Variation, I2 (cf. Ezekial and 179 Fox, 1959). This expresses correlation between the dependent variable and the predicted dependent variable. In sharp contrast with the balance of previous work polynomial models are consistently the most appropriate. In every reach a quadratic equation of the form [6.3] H = p0 + Pi .L + p 2.L 2 is associated with the lowest standard error and highest R 2 of the five models considered. The success of this model reflects the limited concavity of the reach profiles, which in some cases are very close to linear (e.g. SR10, SR14). Model parameters (Table 6.8) indicate that two of the reaches (SR7 and SRI4) are mildly convex. Church (1972) found that polynomial models are most appropriate for describing the profiles of several rivers in Lewis and Ekalugad valleys, eastern Baffin Island. For simple reaches that are hydraulically homogeneous and do not encounter significant sediment sources (as here, and on the Baffin Island sandurs), but which are aggrading, Church argues that polynomial profiles are to be anticipated. If channel slope is adjusted to move the load supplied w(L), then [6.4] dH/dLoc W (L) and in turn the rate of change of slope is proportional to the rate of change of load: [6.5] d/dL (dH/dL) oc dw(L)/dL If the reach is in equilibrium, such that the total load supplied is moved through and out of the reach, then w(L) is constant and height is related to distance by a simple linear function. This result expresses Mackin's (1948) observation that graded streams should possess a linear profile. Mackin suggests that graded streams (or at least links) tend to have a slightly concave profile only because of systematic grain size diminution between major tributaries. This 180 Figure 6.10. Longitudinal profiles for Sukunka study reaches. 0 4000 8000 1 2000 0 4 0 0 0 8 0 0 0 D i s t a n c e d o w n s t r e a m wi th in r e a c h ( m ) 181 Table 6.7. Sukunka longitudinal profiles: Performance of functional mathematical models. I2 R2 Mean Standard Error (m) Reach Exp. Pow. Log Poly. Lin. Exp. Pow. Log Poly Lin. SR 1 0.93 0.43 0.87 1.00 0.99 5.21 19.85 4.22 0.43 1.04 n=37 SR 3 0.86 0.33 0.88 1.00 0.99 7.37 24.10 2.66 0.26 0.90 n=45 SR 5 0.97 0.73 0.94 1.00 0.99 0.67 2.04 0.66 0.15 0.24 n=12 SR 7 0.88 0.67 0.88 0.99 0.98 0.72 1.26 0.56 0.19 0.21 n=12 SR 8 0.93 0.39 0.79 1.00 0.99 4.05 14.45 4.10 0.48 0.68 «=63 SR 9 0.92 0.38 0.92 1.00 0.96 1.83 25.62 2.65 0.34 1.83 n=59 SR 10 0.90 0.69 0.84 0.94 0.94 0.35 0.69 0.40 0.26 0.26 n=22 SR 12 0.95 0.60 0.88 1.00 0.99 2.72 8.05 2.81 0.39 0.72 n=47 SR 13 0.96 0.45 0.89 1.00 0.98 2.01 9.65 2.01 0.33 0.78 «=65 SR14 0.88 0.56 0.82 0.99 0.99 1.27 2.66 1.15 0.26 0.29 n=31 SR 15 0.94 0.47 0.82 0.99 0.98 0.77 3.09 1.00 0.24 0.29 n=22 SRI 7 0.93 0.59 0.93 1.00 0.98 2.11 5.89 1.18 0.31 0.59 «=27 Exponential, power, logarithmic (base 10), polynomial and linear models are considered. To facilitate comparison mean standard errors are given in metres for all five models, that is, they are calculated for the residuals of the curvilinear relations using back-transformed values. Index of variation I2, for the power and exponential models, is equivalent to the usual measure of statistical concordance, R2, but are calculated for the curvilinear relations. The highest R2 (or I2) values and lowest standard errors are underlined for each reach. 182 Table 6.8. Parameters for second-order polynomial models of reach profile. Reach Po Pi P2 SR 1 39.44 -0.0067 2.142 x 10-7 SR 3 24.38 -0.0066 3.793 x 10-7 SR 5 9.55 -0.0053 5.846 x 10-7 SR 7 5.46 -0.0019 -3.874 x 10-7 SR 8 31.30 -0.0032 4.786 x lO-8 SR 9 35.16 -0.0037 9.581 x 10-8 SR 10 4.05 -0.0010 2.268 x 10-8 SR 12 28.12 -0.0040 1.062 x 10-7 SR 13 22.69 -0.0026 6.809 x 10-8 SR 14 10.46 -0.0012 -4.954 x 10-8 SR 15 8.23 -0.0021 9.758 x 10-8 SR 17 16.41 -0.0022 6.485 x 10-7 Parameters are for models of the form H = (30 + Pi-L + P2L 2 , where both height (H) and distance downstream (L) are in metres. 183 diminution, he points out, must be solely due to abrasion, because in a graded reach all sizes of material must move through, albeit at different rates. The slow reduction in size generated by abrasion leads to a systematic reduction of channel slope as the velocity necessary to maintain particle motion declines downstream. In contrast, in aggrading streams, real sorting is possible as less mobile (coarser) material is selectively buried and, to use Mackin's phrase, permanently withdrawn from circulation (Mackin, 1948, p. 173). Downstream fining is then much more rapid and channel slope must adjust more radically to the imposed grain size changes. Mackin (1948) argues that the slope of an aggrading reach is therefore likely to be significantly steeper than that of a graded reach. If the downstream reduction in load in an aggrading reach is proportional to e-kL (as Sternberg's abrasion model and selective sorting models suggest), then Church (1972) points out that [6:6] d2H/dL2 = Ce- k L where C is a constant of proportion. The solution of this equation for height is [6.7] H = (C/2) e-kL + C 2 L + C 3 which represents an exponential decay function superimposed on a straight line (Church, 1972, p 79). The linear component can be interpreted as adjustment of the channel profile to that load associated with a graded condition and the exponential component as the result of aggradation. Using the Taylor's series expansion of ekL, Church goes on to show that this function is approximated by a polynomial function and is satisfactorily expressed by the second-order polynomial (equation 6.3) if P„>2 are small. 184 6.3.2 Derivation of a general function for reach channel slope and implications for grain size change From equation 6.3 one can derive a general expression for channel slope within Sukunka links: [6.8] S = SH/dL = pi + 2p2.L Thus, channel slope varies as a simple linear function of distance downstream. Although the coefficient 2p2 is generally small (Table 6.8), significant reductions in slope are accomplished within most links. For example, in reach SR 9 channel gradient declines from -0.0037 (mm1) immediately below Windfall Creek confluence to -0.0002 (m.nr1) immediately above the Rocky Creek fan exposure some 18 km downstream. Ferguson and Ashworth (1991) suggest that in the absence of a significant increase in discharge such a reduction of slope implies a rapid reduction in shear stress, To °c S.d, and in turn stream competence. Their argument is based on the supposition that mean depth d, is likely to vary less than channel slope within simple reaches such as that studied on Allt Dubhaig. In turn they argue that the rapid reduction in grain size observed within the Dubhaig study reach is not surprising. Grain size variations are therefore seen as a direct reflection of changes in channel slope, rather than of a more complex adjustment. In this regard the argument is similar to that of Sternberg or Mackin, except that Ferguson and Ashworth treat slope as the independent variable. In the context of Sukunka reaches one might anticipate a similarly simple relation between tributaries, and possibly non-alluvial lateral sources, such that, following equation 6.8, grain size would vary as a simple linear function of distance downstream. Indeed, linear models for the downstream reduction of D50 and D95 within the Sukunka reaches are surprisingly successful. In Figure 6.11 standard errors (mm) for exponential and linear models are plotted against each other. There is a tendency for the exponential models to have marginally smaller mean errors, especially for D 9 5 , but in general the linear fits are very 185 good. Upon inspection of model residuals, however, it is apparent that in several cases small mean standard errors belie inappropriate linear models. Most of these cases (six of nine) pertain to D 9 5 relations, as exemplified by reach SR 9 (Figure 6.12). The pattern in the residuals makes it clear that a curvilinear relation is more appropriate for describing downstream changes in D95 whereas the linear relation appears to be reasonable for D50. This pattern is present in two other reaches. In several cases then, material close to the limit of movement deviates systematically from a simple relation with slope, while median grain size exhibits a simple proportionality with slope. This observation presumably reflects the fact that material closer to the competence limit is increasingly sensitive to subtle changes in depth. While median grain size can, in some reaches, be related to slope alone, D 9 5 deviates in a systematic way. The generality of this phenomenon is uncertain since not all of the Sukunka reaches behave in the same way. There is an indication in these observations that particle size and channel slope are at least approximately proportional to one another within Sukunka reaches. This implies that diminution rate may be related to the rate of change of slope within sedimentary reaches such that the latter might be used to predict 6.3.3 Rate of change of channel slope and rate of diminution The coefficient 2(32 in equation 6.8 expresses the rate of change of slope with respect to distance downstream, and is constant for a given reach. In Figure 6.13 202 is plotted against diminution coefficients of D50 and D95 (ccd(5u) and Od(95)) for each Sukunka reach which exhibits fining and has a concave profile. Ignoring reach 10 for the moment a reasonable inverse relation is apparent for both D 5 0 (R2 = 0.88) and D95 (R2 = 0.77). More rapid changes in slope are associated with greater rates of downstream fining, as one would expect if slope and grain size are approximately proportional to one another. For ad in phi.kirr1 and 2(32 determined for elevation in metres and distance in kilometres, the simple linear relations, 186 Figure 6.11 Comparison of mean standard errors (mm) for exponential and linear models of downstream D50 and D95 diminution. 50 o 40 i_ CD O 30 D CD -o 20 o o CD C O Q_ X L d 1 0 0 O D50 A D95 / A / / / / t A / i / / linear better P° £ A p \ Q P o / & • exponential better A p / / 0 10 20 30 40 50 Linear model, standard error (mm) 187 Figure 6.12 Residuals of linear relations between D5(y Dp5 and distance for Sukunka Reach 9. in o D X ) If) CD ~o o E o CD C 40 30 20 1 0 0 -1 0 - 2 0 - 3 0 V 1 1 • 1 1 • i 1 I SR 9 - A 6 * o o A A O A A 0 _ ^ 9 .Q — -O-o A 2 . o O O A . A A A . -A A O A 1 , 1 , 1 , 1 , 1 . 1 . 1 , 1 , 0 4 6 8 10 12 14 16 1 Distance downstream (km) o D50 A D 9 5 188 [6.9] ad(50) =-0.06-399.20 (2p2), and [6.1.0] ad(95) = -0.09 -281.58 (2p2) are highly significant (p < 0.005) and have mean standard errors of 0.058 and 0.062' respectively. These relations could provide a reasonable estimate of within-reach diminution rates for a reach where longitudinal profile data are available and p2 has been determined. One must admit, however, that each relation depends very much on two points. Reach SR 10 is clearly anomalous: very strong fining is apparent yet the channel gradient is low and does not vary significantly down the reach (Figures 6.1 and 6.10). A straightforward explanation is apparent. The reach is initiated at an actively eroding exposure in Rocky Creek fan, where a significant amount of coarse material is being delivered to the main stem without a concomitant addition of water. It is evident in Figure 6.10 that the profile of SR 10 is essentially a continuation of the profile of SR 9 immediately upstream. It is therefore reasonable to suggest that slope conditions in SR 10 are associated with the hydrological and sedimentological influence of Windfall Creek, and are essentially independent of the input of coarse material by Rocky Creek fan. This implies that the fan exposure is a recently activated source to which Sukunka river is still adjusting. Currently, discharge in the distal portion of SR 9 is incompetent to transport the coarse material eroded from the fan margin. A significant grain size step therefore occurs and strong selective deposition produces rapid downstream fining. This reach is anomalous because it does not share the degree of alluvial adjustment which has been attained in the other Sukunka reaches, and it highlights the importance of local circumstance in controlling fining rates. Still, the general relation is encouraging and equations 6.9 and 6.10 (or locally defined equivalents) may provide a means of predicting diminution coefficients for sedimentary reaches. From a practical standpoint, however, the detailed profile information collected along Sukunka River is seldom available, and equivalent cartographic information is typically unreliable. Equations 6.9 and 6.10 are therefore of limited predictive value. 189 Figure 6.13 Inverse relation between rate of change of slope and diminution coefficient for concave Sukunka reaches which exhibit fining. "D c CD o CD o u c o 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 Slope c o e f f i c i e n t , 2(32 190 In this regard it is interesting that logarithms of reach length, L r (which is easily derived from maps), are inversely correlated with logarithms of 2p2 (R = 0.82), and that, in turn, a spurious correlation exists between log (Lr) and log (-ad) (Figure 6.14). For D50 the correlation coefficient is -0.89 and for D95 it is -0.85. Bluck (1987) reports a stronger correlation for alluvial fans. Without intending to imply a causal relation least-squares regression yields the significant (p < 0.01) statistical relations, [6.11] -Od(50)= 1.10 Lr- 0 - 8 8 and [6.12] -ad(95) = 0.83 L r - 0 7 8 which have mean standard errors of 0.044 and 0.063 respectively (i.e. when calculated using back-transformed estimates of ad). Pine River was not surveyed, and the predictive performance of equations 6.11 and 6.12 can be independently assessed using observed reach lengths and diminution coefficients from Pine sedimentary reaches. In Figure 6.15 observed and predicted ad(5o> and ad(95) are plotted for comparison. Although predicted values are acceptable in several cases (PR 2, 5, 7, 15) there is a clear tendency toward significant underprediction for higher values of ctd. It is interesting that these higher values are associated with reaches in the Lower Pine valley where mainstem slope is inherited from the former bed of glacial lake Pine. Thus, ad values for reaches PR 9 and PR 12 fall significantly below the 1:1 line. The trend indicated by these two reaches is continued by PR 14 and PR 13 which are also in the lower Pine section. From my traverses of these reaches I can confirm that diminution rates are very high, but observed ad values are suspect because only two measurements were made within each reach. PR 13 values plot far to the right and are not shown in Figure 6.15, but PR 14 ad values are plotted for comparison using a distinctive symbol. Underprediction of diminution coefficients along the lower Pine is indicative of the atypical history and current condition of this stretch. Steep tributaries introduce relatively 191 Figure 6.14 Correlation of reach length and diminution coefficient (which belies the rational correlation shown in Figure 6.13). E C L 1 00 7 6 5 1 0-1 7 6 5 O A R = - 0 . 8 9 for D50 R = - 0 . 8 5 for D95 o. A o A _ l I I [_ O D50 A D95 O A 100 2 3 4 5 6 1 CP-Length of r e a c h (km 192 Figure 6.15 Observed and predicted values of adfor sedimentary reaches on Pine River. Predictions are based on equations 7.11 and 7.12. I CD o CD CL 0.75 O D50 A D95 0.50 0.25 O / / A°<^ °A PR 9 PR 1 4 " O A PR 1 2 0.00 0.00 0.25 0.50 O b s e r v e d —ad 0.75 193 coarse material to a mainstem which is not competent to transport it. Aggradation is ongoing, but the early Holocene lacustrine platform still dominates the bed profile and very rapid fining by selective deposition is the result. An analogy can be drawn between these reaches and the experimental arrangement of Paola et al. (1991) whereby sediment supply greatly exceeded the competence and capacity of the contrived flow, resulting in rapid fining by selective deposition. If profile information were available I expect that the lower Pine reaches would plot close to SR 10 in Figure 6.13, and that equations 6.9 and 6.10 would provide little additional predictive power. So, although a general relation between fining rate and rate of change of slope can be identified, it is clear that the simple empirical correlations are of little value in reaches which are not adjusted to relatively recent contingencies (SR 10) or a recalcitrant geomorphological legacy (Lower Pine). In turn one cannot presume that the relations discussed in this section provide a general means of predicting diminution rates, even within a limited geographical area. 6.4 Summary and Discussion Within sedimentary links fluvial processes dominate the modification of bed material texture and systematic changes in grain size parameters are typically observed. Downstream changes in D 5 0 and D 9 5 (mm) are adequately described by exponential functions, although power functions and linear functions of distance are equally valid, statistically, in a number of cases. The influence on diminution rate of lithological composition and of reach slope was considered. Point load testing indicates that several of the lithological groups have distinct abrasion characteristics, in part because of differences in susceptibility to weathering. Observed differences in diminution rate, are however, confounded by concomitant differences in grain size distribution, such that lithology-dependent diminution may be a function of size rather than inherent petrographical resistance. Differences are minor between the most distinct lithological groups, and it is clear that lithological composition plays a minor role in within-link particle size reduction of the lithologically undifferentiated population. 194 An unequivocal statement concerning the relative importance of sorting and abrasion processes is not possible because of the confounding size effect. However, diminution rates observed within these reaches generally exceed those observed in abrasion experiments (including high-energy ERC tests) and in rivers where abrasion is thought to dominate. In fact, observed diminution rates are similar to values for rivers where, on the basis of geomorphic evidence, sorting processes are thought to be dominant. Polynomial profile forms suggest that most reaches are in general slightly aggradational, and although several sections of Sukunka river are flanked by degraded fans and terraces, numerous active sediment sources have been identified, and bed material is in general abundant and fresh. Moderate aggradational behaviour is conducive to selective deposition, and supports the contention that sorting processes are predominantly responsible for textural modification. In several reaches very high rates of size reduction can be reasonably explained only by selective deposition within unadjusted, rapidly aggrading systems. That extensive horizontal winnowing of the surface layer is a general feature of Pine and Sukunka gravel bars (Section 3.4 on surface versus subsurface texture) also indicates that selective transport is the dominant fining process. In the majority of reaches examined channel slope declines as a simple linear function of distance, such that a basic correlation between particle size and slope occurs. This is to be expected, especially within sedimentary links, given the mutual dependence of these variables at any given point: slope determines hydraulic stress and in turn competence; while particle size, in the light of local hydraulic stress, facilitates vertical adjustments and in turn channel slope. For the majority of Sukunka reaches this mutual adjustment, which is ultimately driven by sediment and water supply, is at least approaching some form of equilibrium and a reasonable correlation between diminution rate and rate of change of slope is apparent. The predictive value of this relation was assessed on Pine River using reach length as a convenient surrogate for rate of change of slope. Although diminution rates for several reaches are predicted with reasonable accuracy it is clear that, in general, predictive power is limited. Examination of the data indicates that poor predictions are associated with those reaches where, for reasons of history and circumstance, slope and grain size are presently unadjusted. These "anomalous" 195 reaches could be "explained away" in terms of their atypical geomorphic situations, but this would be inappropriate because they are neither rare nor unrepresentative of real alluvial landscapes. 196 CHAPTER 7. Conclusion Information about the size of surficial bed material was obtained at a total of 218 sites, representing approximately 50% of exposed bars, along two 110 km study reaches. The high sampling resolution and quality of the samples constitute an unprecedented field data set. This data has facilitated detailed description and explanation of the textural changes along two large, gravel-bed rivers in terms of lateral sediment inputs, local history and downstream fining mechanisms. Despite every effort to minimize sampling error and consistent with previous work, significant within-site variations in mean size are apparent. Identifying genetically distinct grain size populations on depositional surfaces which constitute a palimpsest of depositional and erosional events is clearly problematic. High resolution site scale sampling, capable of monitoring the temporal modification of texture, may help to elucidate this problem. Between-site variations are significant in both rivers and there is therefore a basis for seeking a relation between grain size and distance. It is immediately apparent that simple fining models explain very little of the observed variability and are wholly inappropriate. Further examination confirms hypothesis (i) (Section 1.1) that extended systematic fining is precluded by multiple lateral sediment inputs. Finer structure is apparent and a series of distinct sedimentary reaches, or links, was identified using the grain size data and detailed consideration of local geomorphological history and circumstance (hypothesis (ii)). Most of these reaches exhibit fining trends which reflect the modification of material by fluvial processes in the absence of disruption by major lateral inputs. Simple fining models applied to individual sedimentary links improve overall explanation by approximately 75 %. This result provides the most thorough confirmation to date that explanation of textural change in alluvial systems is dependent on identifying significant lateral sources. An important implication for models of textural change is that models of downstream fining will only be successful if they can be situated within reaches where fining processes operate unhindered. In turn it is clear that the identification of sedimentary links and, at a basin 197 scale, the sedimentary network, must be the basis of any attempt to model textural change using fining models. In this context the a priori identification of significant lateral sources becomes important. While it is relatively easy to identify potential sources, distinguishing those which are likely to have an effect on texture is more difficult. By way of an initial examination of this problem, criteria for the classification of significant tributaries are developed. Basin idiosyncrasies and oversimplification of a complex set of controlling factors preclude criteria which can unequivocally distinguish tributary types. The best discriminant function is based on relative basin area and a surrogate measure of distal tributary stream power, parameters gleaned from topographic maps and regional hydrometric data. It identifies 80 % of the significant tributaries along the study reaches but 23 % of the nominally significant group are, in fact, insignificant. Detailed consideration of tributaries that are misclassified by the discriminant function does not reveal any commonality that might facilitate an improvement in predictive performance. Rather, the examination of anomalous cases suggests that greater performance can only be achieved through detailed consideration of local history, again highlighting the importance of geography and contingency. In the light of this, logistic functions are developed which provide the probability that a given tributary is a significant sediment source. Generality of the discriminant and companion logistic functions cannot be assessed because of the lack of a suitable data set. While the formulation of the bivariate discriminant function may be of general merit it is unlikely that the actual function is of value outside the region. Physiography, geomorphic history and lithology are likely to be primary constraints on the application of these functions elsewhere. Exploration of these issues is an obvious avenue for future research. An important implication of this analysis is that sedimentological networks and hydrologic networks do not necessarily correspond. Sedimentologically, Sukunka River is more important than Pine River, and Burnt River is more important than Sukunka: the main sediment pathway is distinct from the hydrologic mainstem. A number of relatively small tributaries are highly significant sediment sources either because of internal conditions or 198 relative conditions on the mainstem that are often associated with local geomorphic history. These observations reflect the spatially discontinuous nature of sediment supply within fluvial landscapes, which contrasts with the essentially homogeneous supply of water. Models based solely on hydrological network order may be fundamentally inappropriate for understanding sediment fluxes and sediment characteristics within fluvial systems. Significant advances in modeling the fluvial modification processes which operate within links have been made in recent years. As yet, however, these contain unreasonable information requirements for a model which is to be applied at a drainage basin scale. In lieu of the development of a more appropriate model, grain size changes within links can be described by a purely functional equation based on empirical observation. Downstream changes in D50 and D95 (mm) are adequately described by exponential functions, although power functions and linear functions of distance are equally valid in a number of cases (hypothesis (iii)). Diminution rate varies significantly between sedimentary links and the question of what controls this variation arises. The influence of lithological composition and channel slope on diminution rate was considered. Differences in diminution rate are minor between lithological groups despite observable differences in abrasivity. In general, the role of lithological composition in controlling the within-link fining rate of the lithologically undifferentiated population is minor. The longitudinal profile of individual links is in all cases most accurately described using a second-order polynomial function, such that channel slope varies as a simple linear function of distance. For the majority of Sukunka reaches a basic association between grain size decline and slope decline is apparent and reflects mutual adjustment on post-glacial timescales. A reasonable correlation between diminution rate and rate of change of slope is observed. The predictive value of this relation was assessed on Pine River using reach length as a convenient surrogate for rate of change of slope. Although diminution rates for several reaches are predicted with reasonable accuracy, it is clear that, in general, predictive power is limited. Poor predictions are associated with those reaches where, for reasons of history and circumstance, slope and grain size are presently unadjusted. A simple method of predicting the diminution coefficient in functional exponential models is not, therefore, forthcoming. 199 Many previous studies have discussed the relative importance of sorting and abrasion as fining processes and some comment is warranted here. Despite lithological classification of every clast collected during Wolman sampling, which allows comparison of diminution rate between lithological groups, an unequivocal statement is not possible. This is because relative abrasivity is confounded by a lithology-dependent size effect. Thus, while the relatively soft litho-types do appear to fine more rapidly than their harder counterparts they also tend to be larger and lithology dependent sorting, rather than abrasion, could be responsible for the difference in diminution rate. However, diminution rates observed within these reaches generally exceed those observed in abrasion experiments (including high-energy ERC tests) and in rivers where abrasion is thought to dominate. This suggests that sorting is the dominant fining process. Support comes from two additional lines of evidence. First, polynomial link profiles are indicative of moderate aggradation which is conducive to selective deposition and sorting. Second, an attempt to combine surface and subsurface bed material samples revealed that the surface layer is subject to extensive horizontal winnowing (not surface enrichment) and therefore that size selective transport is widespread. A general theme which permeates this work is the necessity in geomorphological investigations, and in the endeavour of model building, to consider both configurational and immanent aspects of explanation (cf. Simpson, 1963). In Chapters 2, 3 and 4 my focus is primarily on explanation. Textural variations are described and explained in terms of fining processes, local history and lateral sediment sources. The sedimentary link is identified as a fundamental component of the fluvial system that provides a basis for understanding textural change. In Chapters 5 and 6 guidelines for the discrimination of significant and insignificant tributary inputs are established and the nature of, and controls on, fining within sedimentary links are examined. Through the thesis my emphasis thus shifts from explanation to prediction, although a complete predictive model is not developed. This approach reflects a conviction that existing fining models are inadequate when applied in all but the most rudimentary of field situations and that greater predictive efficacy can only be obtained by seeking to understand and incorporate historical and spatial 200 contingencies. I am not suggesting that the fining models are themselves simplistic or analytically naive, but rather that there has been little attempt to develop a framework within which models of fluvial processes can be realistically applied. I do not claim to have achieved such a predictive scheme, nor did I set out to do so. Rather, it is my hope that this study has provided a basis for integrating investigations of fining processes with the spatial and temporal complexities that constitute the geomorphological landscape. As Simpson (1963) makes clear, geologic (or geomorphological) phenomena are fully explained only by consideration of both configurational circumstances and the immanent processes which operate within their confines. While the disruptive effect of lateral inputs has been widely acknowledged, the resolution of previous empirical data sets is generally too low to reveal the extent of configurational influences, certainly at the scale considered here. The inappropriateness of modeling grain size changes using models of immanent processes alone is starkly revealed. Sternberg's "Law" is incapable of describing grain size changes on Pine and Sukunka Rivers, not because it is an unreasonable model of process, but because law-like statements are rarely tenable in a discipline where, at least at a landscape scale, contingency is a primary consideration (cf. Bradley, 1963; Gould, 1988). The degree to which field history and immanent modeling can be combined is unclear, and must ultimately be related to the objectives and resources associated with individual applications. While some guidelines for the identification of significant tributaries have been suggested, it may not be possible to develop similar guidelines for non-alluvial sources. While potential non-alluvial sources may be identified from reconnaissance photographs, the existence of a grain size discontinuity is difficult to establish without information about the volume and characteristics of the material involved. Even for tributary sources, where some information about sediment yield can be presumed, the analysis in Chapter 5 indicates that historical singularities are important. Similarly, general controls on link-scale fining rate are difficult to identify given the unadjusted condition of some links. 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Alluvial fans : bedded sands and rounded gravels, bouldery lenses. Glac io f luv ia l : complex arrangements of rounded cobbles, gravels, and sands , with local silt and clay sequences . M o r a i n a l : unsorted gravels and boulders in silty matrix. Colluvial fans : angular cobbles and boulders. Bedrock : bare, or with thin veneer of colluvium or till. Proximal glaciolacustr ine : bedded sands and silts with local c lay and gravel units. Distal glaciolacustr ine : frequently laminated and deformed c lays with gravels and sand units. P64 Tributary creeks with identifier Major (high, steep) terrace scarps Smal ler terrace Uncertain fan margin Unit boundary Cartographic boundary Steep bedrock with colluvial or morainal veneer (valley wall) Low gradient, c lay and sand reaches on Lower Pine p93 10 Photographic sample site (Pine) s93 26 (Sukunka) P H S 4.5 Wolman sample site with (99.23) distance downstream (km) A . D u d z i c c o n f l u e n c e t o S 2 0 Twidwell Creek Lean-to Creek S22 Baker Creek S24 Sukunka River J B K R 2 (21.95) \Sukunka River B K R 4 {20.53) S T W 2.5 r I S L T J3_4 S L T D 1 C (19.40) i93 U2X (18.72)\ S L T U 3 (19.11) S21 S23 B . L e a n - t o C r e e k t o W i n d f a l l C r e e k B K R 1 (22.78) S25 S T W 3.5 S93 15 ' B K R 3 (22.20) (21.75) 3 2 (23.72) S93 161 S 2 5 D l , (24.47) S26 . S T W 4b (25.14) S T W 4 a (24.94) s 9 3 17 S T W La rge c o m p l e x bars in c h a n n e l 214 1 km (Approximate scale, 1:25 000) \ S T W 4 . 5 (29.17) W F T , \ N S 2 8 (29.79) ( S 3 ? 215 C . W i n d f a l l C r e e k t o B u r n t R i v e r (Approximate scale, 1:40 000) Burnt River S53 Blind Creek S54 T h i c k s e q u e n c e of sor ted silts a n d s a n d s Sukunka River D . B u r n t R i v e r t o S B P 5 . 5 (Approximate scale, 1:40 000) S56 Bluff Creek S61 Sukunka River La rge fa i lures with o rgan ic contact su r face S 70 Highhat River S63 Martin Creek s 7 1 \ Dickebusch Creek S 73 S75 Higher su r face , L a k e P i n e ? Pine River 1 km E . S B P 5 . 5 t o P i n e c o n f l u e n c e (Approximate scale, 1:40 000) F . M o u n t a i n C r e e k t o B e a u d e t t e f a n 1 km (Approximate scale, 1:40 000) N A Big Boulder Creek P10 P16 PLH 2 (18.43) p93 40\ Poor access CK PLH 3 (24.48) Little Boulder Creek P8 p93 36. p93 3J p93 /p93 38 J93 3E P13 P15 P14 P3 Cairns Creek PLH 1 (8.48) p93 31 P12 P11 P9 Pine River J ™ " 0 PMD PMD 1 ( <3^?> (1.67) PMU 3/ (1.311 PLU (4.75U p934_ p93 1~ p933 (3.94) >LU: PLD 46.02) v p936, ^593 5 PLT PMT \ P4 Lemoray Creek P 2 Mountain Creek P5 P6 P7 219 Fisher Creek P19 P 17 Fred Nelson Creek P24 P25 Fur Thief Creek P27 Silt s a n d bluffs P33 Crassier Creek P23 G . B e a u d e t t e C r e e k t o P 3 3 P 2 0 Falling Creek (Approximate scale, 1:40 000) P 18 Beaudette Creek Pine River • • • * > • A • • ft c • • • • • V P 3 4 P 3 7 P 3 8 P 3 9 H . P 3 3 t o C o m m o t i o n C r e e k 1 km (Approximate scale, 1:40 000) 220 N A P 3 5 'p93 41 (53.65P PLH 6.5 (54.68) PLH 7 J55.83) 393 27 P 4 0 \PLH 7.5 fe7.39> PLH 8/ (59.98)\ p93 28s! P47 P 4 3 P L H r P 4 2 Ivorline Creek ^ - H S U p93~30/ /p93 29 / • HST( P44 P46 C • C ; p9317 HSD* (66.53;" p93 18 Commotion Creek P50 c? c i PHS 1, (7f.76> PCM U1 J71.73) PCM D1 (7402,) PHS 1.5 {69.05) PCM U2 (72.34) Kp9319 33 20 p93: P 4 5 Hasler Creek P47 P48 Recent rotational slump in clays P49 Goodrich Creek 221 I . C o m m o t i o n C r e e k t o P H S 3 . 9 1 km (Approximate scale, 1:40 000) N • Bisset Creek P62 Wildmare Creek P65 L ~-PHS 3.9 (96.69) PHSy3.25\ (92\77) ~ pg!&75 3 15 'PHS 3.5) I', (94.66) / • , p9313 11 1 P64 P51 P93 22, Stone Creek P55 P53 High cutbank in well-sorted sands and silts /PHS 2.5 (78.19) \ p93; ^ N (p93 25| p93 24i Pine River >>) {((76.06), p93 23) < . V , P 5 7 PHS 3 (82.91) PHS 3.1 (84.31) P59 •PHS 3.1! i v P 5 8 \ 1 1 - - - - J > 9 3 1 § - > = ; PHS 3.23. (91*6). ' V-\PHS3.2 (88.50) r ( P 6 0 Low gradient reaches, bed and banks of clay and sand, little gravel P61 P63 P52 Young creek P54 P56 Caron creek 222 Appendix 2. Wolman samples 223 Table A l contains summary information for the 157 Wolman samples which were collected at 143 sites along Pine and Sukuna Rivers. Sampling rationale and method are discussed in Chapter 2. Single samples collected on the mainstems are followed by the replicate suites, and finally tributary mouth samples. Sample locations are indicated on the maps in Appendix 1. For the mainstem samples (including the replicates) distances are given in kilometres from the start of the study reaches. The Sukunka reach begins at a bridge over Sukunka River a short distance upstream from the Dudzic Creek confluence. The Pine reach begins a short distance upstream from Mountain Creek confluence. For samples below the Pine/Sukunka confluence distances are for the Pine reach. Each entry contains two rows of data. The upper row contains the number of clasts in each half phi fraction between -3.0 and -9.5 (although these are labelled in -phi). Counts for the class -9.5 to -10 phi are included in the final column, separated from the -9.0 to -9.5 count by a comma. The first seven columns of the second row contain the counts for each of seven litho-types. Labels are as follows: LI white limestones and dolomites; L2 finestones (siltstones, mudstones and shales); L3 sandstones; L4 conglomerate; L5 miscellaneous low-grade metamorphics; L6 quartzites; L7 blue-grey limestones (Pardonet Formation). Individual grain size distributions by litho-type are not presented. Subsequently the second row contains summary statistics; mean size, standard deviation, D50 and D95. Mean size D x, and standard deviation o\ are calculated from the half-phi frequency counts as D x = S(i=i,k} / Z{i=i,k}fi ° = V [I{i=i.k}fi.(Di-Dx)2 / (Zji=i.k}fi)-1] where D; is the midpoint of the /th class, f| is the frequency count of the ;'th class, and k is the number of half-phi classes. D50 and D95 are the median and 95th percentiles of the cumulative percent finer size distribution. For those sites used to define the photographic calibrations (Section 2.3), the corrected number of clasts per 0.25m2, c, is the final entry in the second row. Table A. 1 Wolman samples, summary statistics Sample ID Distance Total >3 >3.5 >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 d/s (km) count L 1 L2 L3 L4 L5 L6 L 7 D X a c D Z U 0.462 404 19 39 45 79 61 65 65 22 9 0 0 0 0 70 108 22 49 14 747 - - 5.76 6.75 -D Z D 1.185 408 12 37 36 48 49 64 63 38 31 22 8 0 0 57 92 68 0 41 46 704 - - 5.67 7.72 -S D T 1 2.879 312 0 4 5 14 26 43 51 76 64 22 6 1 0 35 58 30 0 58 55 76 6.45 0.85 6.59 7.80 -S D T 2 4.011 394 0 4 18 29 39 58 80 56 58 39 12 1 0 36 57 39 0 704 65 93 6.28 7.09 6.37 7.91 -S D T 3 5.239 404 9 12 37 33 48 60 75 64 45 21 0 0 0 52 43 59 1 90 77 88 5.88 7.23 6.02 7.52 -S D T 4 6.332 363 11 33 39 33 35 44 40 58 55 15 0 0 0 50 51 57 ; 58 66 80 5.72 7.67 5.85 7.47 -S D T 5 6.844 362 1 10 23 35 56 66 76 64 26 4 1 0 0 37 63 77 1 69 49 72 5.84 0.85 5.92 7.25 -T W U 1 7.859 410 5 8 31 54 81 79 81 37 30 4 0 0 0 10 112 74 0 (53 27 724 5.66 0.84 5.66 7.22 778 T W U 8.277 397 16 26 36 63 69 64 58 39 23 2 1 0 0 24 59 (54 1 59 77 779 5.47 7.77 5.42 7.73 -T W U 2 8.456 400 2 7 20 40 51 97 72 54 47 10 0 0 0 11 75 90 0 58 54 772 5.92 0.87 5.91 7.39 273 T W D 9.275 252 4 6 10 15 15 30 45 41 36 24 23 3 0 17 34 54 0 36 53 58 6.44 7.48 6.51 8.29 -S T W 1 11.252 402 7 17 29 31 54 45 38 57 92 28 4 0 0 3 44 85 0 66 86 720 6.07 7.48 6.24 7.77 -S M L U 1 12.634 390 11 14 32 72 67 65 56 45 28 0 0 0 0 8 91 44 0 86 57 770 5.57 0.99 5.49 7.75 -S M L U 2 13.669 431 3 28 32 54 54 80 58 55 44 17 1 0 0 6 80 (58 0 707 50 726 5.77 7.26 5.75 7.46 288 S M L U 3 14.139 453 15 27 37 55 73 108 98 34 4 2 0 0 0 4 98 53 0 702 65 737 5.43 0.86 5.59 6.76 -S T W 1.5 14.391 406 5 9 20 30 56 82 93 67 38 5 1 0 0 11 76 104 0 49 72 94 5.97 0.86 6.01 7.37 -S T W 1.75 15.492 276 1 2 3 18 32 44 40 40 45 42 8 1 0 0 40 38 0 93 28 77 6.44 7.07 6.48 7.94 773 S20 U 2 16.308 414 4 14 35 75 70 73 57 55 25 6 0 0 0 6 98 65 0 90 47 708 5.90 1.32 5.56 7.27 229 Continued - : . K> 4i. Table A. 1 (continued) Wolman samples, summary statistics Sample ID Distance Total >3 >3.5 >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 d/s (km) count LI L2 1 3 L4 1 5 L 6 Z, 7 D X CT ^ c S T W 2 16.683 400 10 22 32 49 56 63 42 60 38 27 1 0 0 7 92 74 2 76 85 64 5.75 7.59 5.75 7.65 -S 2 0 U 1 17.168 416 10 23 28 26 55 66 57 77 52 21 1 0 0 6 61 55 0 756 59 707 5.90 7.52 6.00 7.55 200 S 2 0 D 1 17.483 186 1 2 7 6 14 18 32 37 30 33 6 0 0 6 26 57 0 55 54 56 6.55 7.09 6.68 7.95 97 S L T U 1 18.536 429 1 6 19 41 66 79 123 74 20 0 0 0 0 77 79 55 0 705 85 98 5.86 0.64 6.07 6.99 189 S L T U 2 18.720 389 4 25 34 60 67 80 64 46 9 0 0 0 0 9 94 45 0 95 74 74 5.46 0.85 5.55 6.89 241 S L T U 3 19.109 332 18 39 43 67 59 46 35 21 4 0 0 0 0 7 71 55 0 75 70 76 5.05 0.95 4.99 6.70 406 S L T D 1 19.404 401 1 11 31 69 65 92 72 47 13 0 0 0 0 4 120 58 7 776 87 55 5.58 0.72 5.65 6.95 258 S T W 2.5 20.528 390 3 13 33 54 70 98 59 43 16 0 1 0 0 22 49 55 0 107 87 78 5.56 0.78 5.67 6.97 226 B K R 4 21.280 414 0 5 17 30 61 77 85 87 39 13 0 0 0 21 55 55 0 756 77- 70 6.04 0.77 6.70 7.40 209 B K R 3 21.749 401 20 40 53 66 49 57 63 40 13 0 0 0 0 11 67 86 7 92 60 84 5.25 7.75 5.22 6.97 597 B K R 2 21.954 421 2 13 26 43 58 80 77 85 33 4 0 0 0 17 39 129 0 96 47 99 5.84 0.88 5.95 7.24 767 S T W 3.2 22.197 398 4 19 22 47 72 97 81 36 19 1 0 0 0 10 60 60 0 95 64 709 5.67 0.78 5.68 7.00 -B K R 1 22.783 399 14 23 40 57 57 77 73 39 19 0 0 0 0 7 76 65 106 87 60 5.44 7.07 5.56 6.99 507 S T W 3.5 23.719 403 3 8 23 47 53 74 87 76 26 5 1 0 0 15 57 57 0 106 61 707 5.85 0.85 5.96 7.25 -S 2 5 D 24.470 402 4 7 17 31 54 83 102 71 30 3 0 0 0 7 55 58 0 98 52 754 5.97 0.75 6.02 7.27 754 S T W 4 A 24.936 399 5 15 30 53 90 114 72 17 2 1 0 0 0 7 60 61 0 102 70 99 5.45 0.60 5.55 6.50 -S T W 4.25 27.390 391 11 18 32 64 69 75 71 40 9 2 0 0 0 4 (52 67 0 86 80 98 5.45 0.89 5.57 6.89 222 S T W 4.5 29.170 420 8 17 36 55 65 74 87 61 17 0 0 0 0 21 84 87 0 74 77 85 5.59 0.97 5.70 6.97 252 Continued Table A. 1 (continued) Wolman samples, summary statistics Sample ID Distance Total >3 >3.5 >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 d/s (km) count L 1 L2 L3 L4 L5 L6 Z, 7 D X cr c S 3 1 U 2 29.792 398 4 9 14 41 56 74 94 65 35 6 0 0 0 73 58 78 0 705 68 76 5.90 0.83 6.01 7.30 747 S31 U l 30.024 406 1 3 10 34 56 83 71 88 55 4 1 0 0 6 52 80 0 772 42 774 6.07 0.74 6.77 7.36 742 S T W 5 30.590 399 3 3 32 46 77 75 74 60 25 4 0 0 0 16 50 95 0 72 82 84 5.74 0.80 5.76 7.78 -S T W 6 32.284 399 4 14 14 48 55 67 88 81 21 1 0 0 0 3 44 130 0 53 98 77 5.83 0.85 5.98 7.75 -W F U 36.905 404 2 9 31 56 68 91 91 43 13 0 0 0 0 27 46 66 0 33 134 98 5.62 0.69 5.70 6.92 -W F D 38.227 395 2 4 12 29 62 73 54 63 58 33 4 1 0 14 78 149 0 29 52 73 6.77 1.03 6.14 7.78 -S W B 0.5 39.266 436 1 4 11 21 54 86 95 75 70 18 1 0 0 3 34 222 0 52 43 82 6.19 0.76 6.22 7.48 726 S W B 1 40.815 406 2 3 14 30 38 82 89 89 51 8 0 0 0 27 45 162 0 47 47 84 6.77 0.75 6.79 7.38 -S W B 1.5 42.564 399 3 9 16 42 53 66 100 88 22 0 0 0 0 11 26 178 0 74 37 79 5.88 0.76 6.05 7.05 756 S W B 2 43.914 399 0 10 18 30 68 84 101 69 18 1 0 0 0 2 82 208 2 35 29 47 5.84 0.66 5.94 6.98 -S W B 2.5 44.499 387 2 20 27 59 74 89 76 27 12 0 1 0 0 7 31 183 0 77 44 57 5.50 0.74 5.56 6.88 274 S W B 3 45.726 377 0 8 30 56 76 109 74 20 4 0 0 0 0 12 30 156 0 30 52 97 5.57 0.53 5.58 6.63 -S C H U 1 46.843 380 3 8 37 60 82 98 72 20 0 0 0 0 0 7 37 112 0 81 52 97 5.42 0.56 5.50 6.53 293 S C H U 2 47.595 401 9 30 64 88 71 96 38 5 0 0 0 0 0 5 36 112 0 702 49 97 5.06 0.62 5.07 6.30 536 S W B 4 47.946 400 3 15 42 91 92 88 58 9 2 0 0 0 0 16 34 723 0 38 89 700 5.26 0.55 5.27 6.42 -S W B 4.5 50.509 397 5 52 67 80 74 92 25 2 0 0 0 0 0 5 39 100 0 775 56 82 4.95 0.67 4.97 6.74 547 S W B 5 51.277 405 3 26 54 113 97 79 31 0 1 1 0 0 0 14 59 707 0 55 118 58 5.05 0.49 5.03 6.27 -S W B 5.25 52.352 416 32 71 89 80 94 47 3 0 0 0 0 0 0 3 77 73 0 772 45 46 4.59 0.56 4.60 5.87 638 Continued On Table A. 1 (continued) Wolman samples, summary statistics Sample ID Distance Total >3 >3.5 >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 d/s (km) count LI L2 L3 Z 4 L 5 L6 Z, 7 £> c S W B 5.5 53.931 428 6 48 103 115 100 49 7 0 0 0 0 0 0 8 41 94 0 700 99 86 4.75 0.42 4.75 5.85 -S W B 6 54.552 401 3 8 13 16 27 63 93 86 64 26 2 0 0 7 84 245 11 33 14 73 6.28 0.90 6.38 7.65 -S W B 6.25 55.262 441 6 16 41 72 71 58 61 85 29 1 1 0 0 2 61 191 73/ 37 75 5.63 1.03 5.63 7.75 203 S W B 6.5 56.070 436 4 8 23 60 78 112 94 5.5 6 0 0 0 0 6 65 218 5 65 27 52 5.63 0.62 5.70 6.85 292 S W B 7 56.485 399 16 30 59 81 82 84 39 8 0 0 0 0 0 4 42 123 3 75 90 62 5.04 0.68 5.08 6.35 -S W B 7.5 56.960 393 6 32 46 66 79 90 61 12 1 0 0 0 0 10 48 155 3 44 59 74 5.22 0.70 5.29 6.45 -S W B 7.75 57.466 400 8 46 69 94 103 58 16 6 0 0 0 0 0 4 49 117 2 775 67 46 4.88 0.55 4.97 6:06 525 S W B 8 58.286 404 14 38 82 73 75 56 54 11 1 0 0 0 0 77 50 142 58 77 62 5.00 0.78 4.97 6.42 -B N D 65.638 313 1 2 3 7 . 15 13 33 63 53 57 47 13 6 0 40 193 5 39 14 22 7.77 7.75 7.78 8.63 -S B P 1 67.868 400 0 1 0 9 23 65 69 97 82 43 10 1 0 0 82 218 3 44 24 29 0.66 6.62 6.67 7.90 -S B P 1.5 70.796 370 1 4 4 15 21 48 62 91 84 33 1 0 0 0 27 238 11 47 76 37 6.48 0.78 6.63 7.73 774 S B P 2 72.232 411 2 1 23 36 54 58 90 102 38 1 0 0 0 1 75 174 6 48 39 68 5.97 0.82 6.74 7.24 -S B P 2.5 74.024 400 0 5 10 20 22 64 79 77 85 36 2 0 0 2 35 214 7 77 19 52 6.41 0.84 6.50 7.75 129 S B P 3 75.185 401 0 4 6 20 26 31 78 87 98 48 3 0 0 0 39 212 5 58 36 57 6.56 0.82 6.70 7.82 -S B P 3.5 76.332 403 3 7 16 31 31 64 84 79 66 19 2 0 1 0 51 195 6 65 29 57 6.78 0.98 6.29 7.55 783 S B P 4.5 80.437 400 2 6 26 47 44 46 48 82 84 14 1 0 0 0 39 187 3 85 38 48 6.09 7.73 6.30 7.47 201 S B P 5 82.585 398 1 3 17 31 55 83 104 76 28 0 0 0 0 7 90 120 0 53 57 77 5.95 0.63 6.04 7.74 -S B P 5.5 85.620 390 4 14 34 45 64 99 90 33 7 0 0 0 0 2 49 114 5 97 33 90 5.55 0.77 5.67 6.87 254 Continued Table A. 1 (continued) Wolman samples, summary statistics Sample ID Distance Total >3 >3.5 >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 d/s(km) count L 1 L2 13 L4 L 5 L6 Z, 7 D X (7 D P5 c S B P 6 87.638 399 6 8 11 24 54 73 70 95 50 7 1 0 0 6 67 145 0 70 50 67 6.06 0.89 6.77 7.38 -S M A U 1 88.710 391 2 12 38 43 43 78 111 53 8 0 0 0 0 2 43 119 3 704 44 76 5.65 0.80 5.85 6.89 798 S M A U 2 89.430 394 2 9 23 32 60 85 88 68 27 0 0 0 0 2 27 129 704 43 85 5.83 0.75 5.92 7.74 767 S M A U3 90.742 393 0 1 8 26 69 112 103 60 13 1 0 0 0 7 29 138 4 707 23 97 5.90 0.45 5.97 6.95 738 S B P 7 91.732 401 2 12 11 22 52 66 87 88 49 12 0 0 0 7 86 181 0 49 39 45 6.09 0.86 6.20 7.42 -S B P 8 97.189 389 4 13 36 67 72 79 76 36 6 0 0 0 0 2 47 737 7 63 66 79 5.47 0.72 5.52 6.87 -S H D U l 97.534 402 2 8 26 44 53 88 101 61 18 0 0 1 0 1 44 141 5 99 30 82 5.78 0.74 5.89 6.99 -S H D U2 98.202 387 3 11 14 41 54 98 100 59 7 0 0 0 0 0 42 777 4 708 40 82 5.75 0.64 5.86 6.90 738 S H D D l 100.835 444 1 6 15 16 53 54 81 113 81 24 0 0 0 7 73 310 5 34 8 73 6.30 0.84 6.48 7.54 107 S B P 9 101.632 399 3 4 8 20 43 56 102 98 54 10 1 0 0 5 65 200 3 60 28 38 6.27 0.73 6.32 7.42 -S B P 9.5 103.034 436 0 2 8 15 42 71 92 101 89 16 0 0 0 0 82 257 P 63 6 79 6.35 0.65 6.43 7.47 747 S B P 10 105.554 350 6 6 6 18 57 52 64 85 50 6 0 0 0 7 33 188 7 53 38 30 6.70 0.87 6.23 7.38 -S B P 10.5 107.403 435 8 21 42 55 79 99 78 41 10 2 0 0 0 7 83 148 0 87 40 82 5.47 0.83 5.56 6.88 -S B P 11 109.265 397 3 5 20 36 59 71 121 69 13 0 0 0 0 8 60 176 3 66 39 45 5.84 0.66 6.02 6.95 -S B P 11.5 109.711 386 1 10 20 39 67 99 74 57 15 4 0 0 0 2 48 166 4 70 36 60 5.75 0.77 5.78 7.00 -S K U 1 110.258 415 1 5 26 54 83 107 95 40 4 0 0 0 0 0 59 167 4 77 29 79 5.62 0.54 5.68 6.79 278 S K U 110.770 408 6 6 26 71 76 98 92 29 4 0 0 0 0 7 42 168 0 84 59 54 5.52 0.67 5.60 6.72 -Continued Table A. 1 (continued) Wolman samples, summary statistics Sample ID Distance Total >3 >3.5 >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 d/s (km) count LI L2 L3 L4 L5 L6 7, 7 D X c P M U O 0.000 278 4 14 25 39 56 73 41 21 5 0 0 0 0 5 65 46 0 67 20 87 5.41 0.73 5.57 6.79 287 P M U 1 0.356 392 10 42 53 68 68 57 74 18 2 0 0 0 0 73 82 43 0 770 33 777 5.76 0.86 5.77 6.57 267 P M U 0.789 211 2 4 8 6 13 28 35 39 40 25 8 3 0 0 35 ' 43 0 78 28 27 6.50 7.20 6.62 8.03 -P M U 3 1.316 390 10 23 42 54 62 83 85 29 2 0 0 0 0 4 89 75 0 103 46 73 5.38 0.82 5.52 6.70 275 P M D 1 1.668 420 2 10 43 58 52 80 100 66 9 0 0 0 0 3 66 69 0 730 68 84 5.65 0.78 5.78 6.97 -P M D 2.526 399 3 5 13 17 39 69 88 104 48 12 1 0 0 1 69 54 0 104 61 7/0 6.78 0.77 6.30 7.43 -P L U 1 3.939 420 4 15 26 41 71 96 101 54 12 0 0 0 0 12 72 51 0 735 62 88 5.67 0.73 5.78 6.92 226 P L U 2 4.596 399 2 8 22 28 49 62 86 75 40 22 5 0 0 1 60 106 0 775 56 67 6.07 7.00 6.77 7.66 747 P L U 4.749 419 0 2 10 24 35 87 91 98 62 10 0 0 0 2 69 186 0 69 49 44 6.22 0.65 6.28 7.47 -P L D 6.015 399 2 4 10 19 36 57 60 115 85 10 1 0 0 0 46 165 7 70 53 64 6.33 0.79 6.55 7.45 -P L H 1 8.476 392 0 5 10 24 36 57 94 89 60 14 3 0 0 i 24 58 0 757 56 702 6.25 0.77 6.34 7.48 -P L H 2 18.457 390 5 11 35 50 77 85 74 42 10 0 0 0 0 i 58 109 7 702 65 54 5.54 0.75 5.60 6.89 -P L H 3 24.479 400 5 23 60 91 81 88 42 10 0 0 0 0 0 4 35 140 0 773 56 52 5.73 0.59 5.73 6.38 -P L H 4 30.774 310 6 14 12 8 27 42 57 57 55 30 2 0 0 0 69 767 3 48 14 9 6.24 7.26 6.40 7.77 -P L H 4.9 35.934 399 11 33 49 58 82 89 60 16 1 0 0 0 0 0 96 181 7 66 30 25 5.20 0.76 5.30 6.48 -P L H 5.5 42.757 420 14 23 31 40 70 63 84 74 20 1 0 0 0 2 118 145 4 98 37 22 5.62 7.06 5.75 7.00 -P L H 6 53.650 335 3 8 8 12 25 58 55 70 67 27 2 0 0 0 69 152 2 88 7 77 6.34 0.98 6.49 7.73 -P L H 6.5 54.683 401 3 6 9 19 38 48 85 115 64 14 0 0 0 0 70 236 70 57 70 78 6.28 0.79 6.46 7.45 92 Continued K> to _ . , \o Table A. 1 (continued) Wolman samples, summary statistics Sample ID Distance Total >3 >3.5 >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 a7s(km) count L 1 L2 L3 14 L 5 L6 L 7 D X CT ^ D 9 5 c P L H 7 55.83 336 5 43 55 87 78 56 12 0 0 0 0 0 0 3 77 135 2 77 32 76 4.85 0.50 4.87 5.96 476 P L H 7.5 57.391 399 14 38 76 105 87 61 18 0 0 0 0 0 0 0 67 777 2 97 47 75 4.84 0.53 4.84 5.98 333 P L H 8 59.984 399 18 64 88 99 89 38 3 0 0 0 0 0 0 2 82 165 7 70 53 26 4.63 0.47 4.65 5.78 448 H S U 62.341 399 20 37 44 69 76 104 44 5 0 0 0 0 0 0 95 180 74 34 73 5.07 0.74 5.79 6.33 -P L H 9 62.683 384 33 75 92 95 65 21 3 0 0 0 0 0 0 7 89 776 0 69 47 2 4.46 0.48 4.45 5.81 522 H S D 66.532 396 3 6 12 30 78 93 93 58 23 0 0 0 0 0 106 228 0 50 9 3 5.83 0.63 5.87 7.07 -P H S 1.5 69.048 351 3 19 42 64 88 94 40 1 0 0 0 0 0 0 54 209 6 56 77 9 5.79 0.57 5.27 6.29 -P H S 1 71.159 401 5 21 71 101 108 81 13 1 0 0 0 0 0 0 82 242 2 57 77 7 4.98 0.43 5.07 5.96 -P C M U 1 71.729 402 16 60 85 97 82 54 8 0 0 0 0 0 0 0 94 219 3 65 78 3 4.70 0.52 4.77 5.89 547 P C M U2 72.345 378 39 105 88 86 48 12 0 0 0 0 0 0 0 0 94 213 5 46 77 3 4.30 0.43 4.26 5.43 777 P C M D 1 74.022 375 4 10 30 50 101 120 54 6 0 0 0 0 0 0 56 267 2 34 73 3 5.37 0.46 5.46 6.38 273 P H S 2 76.063 407 5 23 50 66 122 90 49 1 1 0 0 0 0 0 69 269 2 43 75 9 5.78 0.53 5.24 6.37 -P H S 2.5 78.194 411 23 57 98 122 83 28 0 0 0 0 0 0 0 0 77 267 3 40 79 5 4.58 0.47 4.62 5.63 566 P H S 3 82.914 393 9 18 23 47 71 108 90 24 3 0 0 0 0 0 110 219 2 53 8 7 5.49 0.69 5.63 6.65 -P H S 3.1 84.309 407 1 29 47 49 102 94 65 12 2 0 0 0 0 0 67 298 9 27 72 0 5.26 0.68 5.35 6.45 307 P H S 3.15 85.760 353 103 156 63 30 1 0 0 0 0 0 0 0 0 0 89 795 3 33 32 7 3.78 0.27 3.74 4.72 -P H S 3.2 88.500 257 44 54 54 44 33 24 4 0 0 0 0 0 0 0 73 140 0 37 72 7 4.36 0.66 4.28 5.82 673 P H S 3.23 91.256 345 0 3 9 9 22 38 77 111 62 12 2 0 0 0 54 280 0 6 0 5 6.42 0.64 6.57 7.47 58 Continued Table A. 1 (continued) Wolman samples, summary statistics Sample Distance Total >3 >3.5 >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 d/s (km) count L 1 L2 L3 L4 L5 L6 7, 7 D X a D50 c P H S 3.25 92.771 395 4 9 32 63 96 137 49 5 0 0 0 0 0 0 96 264 2 25 5 3 5.35 0.44 5.47 6.35 -P H S 3.5 94.661 421 2 11 28 66 96 105 85 25 3 0 0 0 0 0 119 276 2 75 4 5 5.47 0.56 5.54 6.64 -P H S 3.75 95.794 302 21 57 48 69 67 34 5 1 0 0 0 0 0 0 57 228 0 8 7 4.63 0.59 4.68 5.87 -P H S 3.9 9 6 6 9 399 12 31 47 75 80 93 46 9 6 0 0 0 0 0 106 260 5 23 4 3 5.16 0.74 5.22 6.45 372 P H S 4 97.548 399 29 47 55 56 79 69 45 18 1 0 0 0 0 7 120 211 7 50 11 5 4.99 0.93 5.08 6.49 P H S 4.5 99.227 423 15 42 67 76 73 81 52 16 1 0 0 0 0 0 150 222 7 27 73 70 5.06 0.80 5.08 6.46 373 P H S 5 103.746 157 2 4 3 1 4 10 8 21 24 31 15 21 10,3 0 24 775 2 74 7 7 7.34 7.88 7.52 9.26 37 P R U 106.964 396 2 5 17 29 50 66 79 87 55 6 0 0 0 0 75 188 3 78 34 18 6.07 0.83 6.18 7.37 -P R 2 111.507 399 11 14 35 33 58 35 85 12 24 2 0 0 0 - - - - - - - 5.71 1.02 5.87 7.73 -P R 3 113.167 399 19 27 42 58 74 80 79 19 1 0 0 0 0 - - - - - - - 5.25 0.85 5.36 6.50 -D Z T _ 306 7 16 27 47 68 58 41 24 16 2 0 0 0 78 120 29 0 35 24 20 - - 5.47 7.08 -T W T - 250 8 6 6 12 15 23 28 39 39 36 21 12 3,2 9 23 40 7 68 59 50 - - 6.85 8.69 -W F T - 393 4 15 25 50 64 61 78 57 23 11 4 1 0 5 74 216 0 77 16 65 - - 5.82 7.42 -B N T - 361 1 3 4 13 24 42 50 56 60 57 34 16 1 3 56 210 14 36 75 27 - - 6.89 8.48 -P M T - 377 3 1 19 44 80 103 92 34 1 0 0 0 0 7 34 70 0 779 62 97 - - 5.70 6.74 -P L T - 344 3 3 3 17 23 32 41 50 61 37 45 28 1 0 21 290 0 26 3 4 - - 7.00 8.77 -H S T - 346 5 15 26 38 35 38 54 49 57 24 5 0 0 0 58 202 2 65 7 72 - - 6.75 7.74 -Continued -Table A. I (continued) Wolman samples, summary statistics Sample ID Distance Total >3 >3.5 . >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 d/s (km) count LI L2 L3 L4 L 5 L6 Z, 7 D X CT c S T W 4 B 25.144 408 9 18 51 84 73 93 64 13 3 0 0 0 0 (1992) 6 60 96 0 62 80 104 5.25 0.68 5.29 6.47 -S T W 4 B 1 25.144 407 14 26 44 60 97 83 66 12 5 0 0 0 0 (1993) 9 93 44 0 779 80 62 5.24 0.76 5.57 6.47 227 S T W 4B 2 25.144 407 16 37 62 75 62 87 55 11 2 0 0 0 0 (1993) 75 85 59 0 707 89 78 - - 5.77 6.45 -S T W 4B 3 25.144 407 23 21 37 60 88 94 61 19 3 1 0 0 0 (1993) 10 98 69 0 76 62 92 5.25 0.85 5.56 6.57 -S B P 4 i 78.315 399 5 5 11 31 58 58 67 97 60 6 1 0 0 1 74 164 0 56 46 58 6.09 0.89 6.24 7.59 -S B P 4i i 78.315 397 3 10 28 31 49 73 62 87 52 2 0 0 0 . 2 61 752 2 48 50 82 5.94 0.96 6.04 7.55 -S B P 4i i i 78.315 403 4 10 22 43 42 61 78 87 49 7 0 0 0 5 59 158 5 62 45 77 5.97 0.98 6.72 7.57 -S B P 7.5 94.788 424 14 20 44 58 60 98 74 47 9 0 0 0 0 3 104 112 2 85 43 77 5.44 0.91 5.58 6.87 762 S B P 7.5b 94.788 426 7 19 34 68 74 79 97 44 4 0 0 0 0 0 60 138 5 90 52 705 5.49 0.78 5.57 6.80 -S B P 7.5c 94.788 408 3 26 21 57 61 88 101 44 7 0 0 0 0 i 65 127 2 103 58 72 5.57 0.77 5.70 6.85 -P L H 5i 36.121 401 7 25 24 45 58 118 85 34 5 0 0 0 0 0 82 187 2 81 20 29 5.52 0.76 5.68 6.78 -P L H 5ii 36.121 399 3 24 31 39 76 92 104 27 3 0 0 0 0 1 74 202 7 65 26 52 5.57 0.70 5.64 6.69 -P L H 5i i i 36.121 403 15 12 27 65 68 108 78 29 1 0 0 0 0 7 66 208 7 75 27 57 5.42 0.75 5.57 6.67 -P L H 5.75a 48.278 421 8 21 34 50 89 58 76 73 12 0 0 0 0 0 44 • 195 6 88 57 57 5.56 0.92 5.57 6.94 773 P L H 5.75b 48.278 405 8 23 38 51 67 65 78 58 17 0 0 0 0 0 53 190 75 55 46 5.54 0.97 5.62 6.97 -P L H 5.75c 48.278 450 9 30 39 61 74 75 86 63 12 1 0 0 0 0 75 190 7 85 25 72 5.50 0.96 5.58 6.92 -P R D 109.041 399 10 17 32 45 51 87 102 49 6 0 0 0 0 (1992) 0 72 130 6 727 50 54 5.58 0.85 5.76 6.86 -P R D A 109.041 434 1 8 36 53 85 108 96 42 5 0 0 0 0 (1993) 0 81 180 2 74 57 60 5.59 0.60 5.66 6.80 227 Continued Table A. 1 (continued) Wolman samples, summary statistics Sample ID Distance Total >3 >3.5 >4 >4.5 >5 >5.5 >6 >6.5 >7 >7.5 >8 >8.5 >9 dVs(km) count LI L2 L3 L4 L5 L6 L 7 D X a Dso D95 c P R D B 109.041 429 1 12 22 75 79 103 96 40 1 0 0 0 0 (1993) 0 81 175 3 85 29 56 5.55 0.58 5.62 6.74 220 P R D C 109.041 423 0 7 31 63 11 116 90 38 1 0 0 0 0 (1993) 0 84 154 3 92 28 62 5.57 0.54 5.64 <5.75 239 234 Appendix 3. Photographic estimates of D 5 0 and D 9 5 Table A.2 contains estimates of D 5 0 and D 9 5 obtained using the photographic method described in Section 2.3. Sample locations are indicated on the maps in Appendix 1, and distances downstream are from the head of each study reach. For grain size in -phi units, and corrected count per 0.25 m2, c (log2 units), D 5 0 = 11.22 -0.71 (count) D 9 5 = 12.41 -0.71 (count) Table A.2 Photographic samples Sample ID Distance d/s (km) c ( log 2 ) D 5 0 (-phi) D 9 5 (-phi) s94 1 0.188 87 6.63 7.87 s94 2 0.462 79 6.73 7.97 s94 3 1.355 74 6.80 8.04 s94 4 2.478 131 6.21 7.46 s94 5 8.847 31 7.69 8.92 s93 8 11.701 146 6.10 7.35 s93 9 12.154 227 5.64 6.90 s93 10 12.992 269 5.47 6.73 s93 11 13.130 196 5.80 7.05 s93 12 13.509 175 5.91 7.16 s93 12.5 14.623 82 6.69 7.93 s93 13 16.008 122 6.28 7.53 s93 1 17.679 171 5.94 7.19 s93 2 18.006 240 5.59 6.84 s93 3 18.959 117 6.33 7.57 s93 4 19.343 229 5.64 6.89 s93 5 19.522 243 5.57 6.83 s93 6 19.942 179 5.89 7.14 s93 7 20.914 237 5.60 6.85 s93 14 23.143 233 5.62 6.87 s93 15 24.154 269 5.47 6.73 s93 16 24.325 231 5.63 6.88 s93 17 26.056 221 5.67 6.93 s93 18 27.162 333 5.25 6.51 s93 19 28.350 124 6.27 7.51 . s93 20 41.730 183 5.87 7.12 s93 21 43.321 207 5.74 6.99 s93 22 46.426 262 5.50 6.75 s93 23 48.381 651 4.56 5.83 s93 24 49.305 489 4.86 6.12 s93 25 500.15 420 5.01 6.27 s93 26 58.782 603 4.64 5.90 s93 27 69.697 84 6.67 7.91 s93 28 71.570 126 6.25 7.50 s93 29 73.236 191 5.82 7.07 s93 30 74.419 111 6.38 7.63 s93 31 77.454 95 5.94 7.78 s93 32 79.360 130 6.22 7.46 s93 33 81.456 218 5.69 6.94 s93 34 83.265 163 5.87 7.12 continued 235 Table A. 2 (continued) Photographic samples Sample ID Distance d/s c ( log 2 ) D 5 0 (-phi) D 9 5 (-phi) (km) s94 6 87.050 89 6.61 7.85 s93 35 91.363 194 5.81 7.06 s93 36 92.448 83 6.68 7.92 s93 37 93.284 154 6.04 7.29 s93 38 95.703 267 5.48 6.73 s93 39 99.250 88 6.62 7.86 s93 44 100.255 48 7.24 8.48 s93 45 102.289 147 6.09 7.34 s93 46 103.966 74 6.80 8.04 s93 47 106.377 171 5.94 7.19 s93 48 107.878 178 5.89 7.15 p93 1 3.292 503 4.83 6.09 p93 2 3.661 220 5.68 6.92 p93 3 4.233 358 5.18 6.43 p93 4 4.925 260 5.51 6.76 p93 5 5.372 91 6.58 7.83 p93 6 5.741 84 6.67 7.91 p93 31 9.201 278 5.44 6.69 p93 32 10.138 265 5.49 6.74 p93 33 11.871 152 6.06 7.31 p93 34 12.906 246 5.56 6.81 p93 35 13.647 73 6.81 8.05 p93 37 14.804 337 5.24 6.50 p93 38 15.529 160 6.00 7.25 p93 39 16.088 183 5.87 7.12 p93 40 17.458 201 5.77 7.02 p93 41 32.224 196 5.80 7.05 p93 42 53.009 228 5.64 6.89 p93 27 56.393 364 5.16 6.42 p93 28 58.621 443 4.96 6.22 p93 28 59.484 584 4.67 5.93 p93 30 61.884 322 5.29 6.54 p93 17 65.393 43 7.35 8.59 p93 18 68.13 157 6.02 7.27 p93 19 70.234 378 5.12 6.38 p93 20 72.622 42 7.38 8.61 p93 21 73.143 123 6.27 7.52 p93 22 75.207 293 5.38 6.64 p93 23 77.087 610 4.63 5.89 p93 24 80.825 655 4.56 5.82 p93 25 81.790 131 6.21 7.46 p93 26 82.058 100 6.49 7.73 p93 16 87.429 204 5.75 7.01 p93 13 94.313 124 6.27 7.51 p93 14 95.158 411 5.03 6.29 p93 15 95.319 279 5.43 6.69 p93 10 100.799 72 6.82 8.07 p93 11 102.618 140 6.14 7.39 p93 12 103.507 124 6.27 7.51 p94 1 115.264 199 5.78 7.03 Apppendix 4. Notes on statistical methods. 236 Brown-Forsythe test for homoscedasticity under nonnormality Details of this test, which is a derivative of a test proposed by Levene (1960), can be found in Brown and Forsythe (1974b), and Wilcox (1987b). The procedure compares the variance of the spread of observations within groups with that between groups using an F statistic. The spread of the observations is measured relative to the group median rather than the mean, which renders the test more robust under nonnormality. See Conover et al. (1981) for a review of various procedures. If there are j = 1 to k groups, each with i = 1 to nj observations X ;J , and medians Mj, then the null hypothesis of equal variances: Ho: cr2i = cr22 = - v\ is tested as follows, Zy = Ixjj - Mj I Z.j - Z{i=l,nj} Zjj / ^ z.. = £{j=i,k> z.j/k A = Zu-ijcjnj(z.j-z..)2/(k-l) B = Zfj-ljc} Sii=l.nj} (Zij - Z.j)2 / (N-k) N = Zy=i,k} nj W = A / B If W > F, where F is the 1-a quantile of the F distribution with k-1 andN-1 degrees of freedom, reject Ho and conclude that variances are unequal. Runs test for identifying structure in a sequence of observations. A run is defined as an unbroken series of positive or negative changes in the values occuring within a sequence. A runs test (Bradley, 1968:p 277-281; Draper and Smith, 1963:p95-99) assesses the likelihood that the observed pattern of runs is non-random. If nn is the number of negative changes in a sequence, and np is the number of positive changes, then for nn > 10 and np > 10, u = [(„+np)]+l a 2 = [(] / [(nn+np)2.(nn+np-l)] and P, the probability of obtaining r or fewer runs, where r is the number of runs observed, is approximated as, P = P{ Z < [(r-u+0.5)/Vcr2] } where Z is a unit normal deviate obtained from tables. An unusually low number of runs will yield a small value of P, and is indicative of low frequency structure. An unusually high 237 number of runs is indicated by a value of P which approaches 1.0, and is indicative of high frequency structure on a scale similar to that of the sampling. Assessing the significance and fit of logit models. Because logit regression models are fitted using the maximum likelihood procedure, the standard F-test and R 2 parameter are not appropriate. Suitable tests are detailed in Wrigley (1985). The significance of the model parameters is assessed using an equivalent of the F-test called the joint likelihood ratio test, with the null hypothesis: H 0 : p , = p2 = ... = f3K = 0 and test statistic, -2 [lGge A(Po)-log eA(P)] where loge A(p\>) is the maximised log likelihood of the fitted model which includes only the constant term Po, and loge A(P) is the maximised log likelihood of the fitted model which includes all of the parameters (Po, Pi, P2, PK) If the null hypothesis is true, the test statistic is distributed as chi-square with K degrees of freedom (where K is number of independent variables). Thus, if the test statistic exceeds the critical value of y}, at a given level of significance a, the null hypothesis is rejected with a (100.a)% chance of error. The overall fit of a logit model is assessed using p2, which is equivalent to the coefficient of determination R2 used in least-squares regression, p2 uses a ratio of maximised log likelihood values rather than a ratio of sums of squares, and is calculated as P = 1- [l0ge A(P)/ l0ge A(p0)] (i.e using the maximised log likelihood values defined above). The closer the ratio is to zero, the greater the value of p2, and the better the fit of the model. Like the coefficient of determination, p2 ranges from 0 to 1, but it tends to take on values much lower than R 2 and should not be judged according to the standards associated with R2. Domencich and McFadden (1975, p. 124) provide a graph of the empirical relation between R 2 and p2 which is reproduced in Figure A.l McFadden (1979) has suggested that p2 values of between 0.2 and 0.4 represent a very good fit. 238 Figure A. 1. Empirical relation between R2 and p2. Reproduced from Domencich and McFadden (1975, p. 124). 


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