2) What variables are used to quantify downstream fining and how is downstream fining usually depicted?

3) In Figure 3, what is the physical significance of the coefficient –0.118?

4) What are the processes responsible for downstream fining?

5) What disrupts patterns of downstream fining?

6) What question(s) is(are) the paper addressing?

7) How does the geomorphology of the study rivers differ?

8) What data was collected and how was it collected? In answering this question for Riley and Gregory Creeks, you will have to understand Figure 4 and its explanation.

9) Can you relate the data in the EXCEL/MINITAB files to your answer to Q8?

10) What are the possible answers to the question(s) posed by the paper (see Q6)?

STEP 2 – Formulate an analysis that will allow you to answer the questions posed by the paper (i.e. to select the most appropriate answer from the possible answers identified in Q10). As part of this, you could consider how the sediments in Lower Riley Creek might differ from the sediments in the other reaches as a result of the buffering valley flat (see Figure 3) and how might you investigate these differences statistically?

STEP 3 – Conduct your analyses and interpret the results in the context of your answers to Q6 and Q10. Finalise a conclusion.

STEP 4 – Sketch out the analysis (i.e. the ‘story’) you want to tell. You may find it helpful to first identify the figures and/or tables needed to tell this story. You can then structure the presentation of your analysis around these.

STEP 5 – Write up the results section of the paper, integrating any Figures and Tables within the text.
BED MATERIAL TEXTURE ALONG COARSE GRAINED ALLUVIAL RIVERS

Abstract (to be completed)
Introduction
The spatial variation of bed material grain size along gravel-bed rivers has been a long-standing interest of fluvial geomorphologists and sedimentologists (Sternberg, 1875; Mackin, 1948; Church and Kellerhals, 1978; Knighton, 1980; Dawson, 1988; Ferguson et al., 1996). Theoretical arguments (Parker, 1991) and empirical evidence (Shaw and Kellerhals, 1982) suggest that grain size parameters decline gradually in a downstream direction (Figure 1). In the lowest reaches, there is often an abrupt transition from a gravel- to a sand-bed (Sambrook-Smith and Ferguson, 1995).
Figure 1. Downstream fining, the River Bollin, England (after Knighton, 1980).
The gradual longitudinal reduction in bed material size is called downstream fining and results from the combination of grain breakdown and size-selective transport. Grain breakdown occurs by abrasion whereby particles are reduced in size by grain-grain collisions as the particles roll, slide and saltate (bounce) over the bed during transport (Kuenen, 1956). This ‘wearing down’ of particles is enhanced by in situ vibration and grain fracture along pre-existing lines of weakness (Schumm and Stevens, 1973). Clearly, harder rocks are less susceptible to abrasion than softer rocks. Selective transport of finer grain sizes occurs because smaller particles are more easily transported than larger particles (Russell, 1939). Finer particles tend to move more often and at higher velocities than coarse particles leading to a longitudinal segregation or ‘fractionation’ of particle size along the length of the river.

Observed patterns of downstream fining are the results of these two groups of processes operating with different levels of significance. However, the relative importance of each process remains unresolved (see Werritty, (1992) and Mikos, (1993) for reviews) and a negative exponential model

D = Do e?L (1)

where D is some measure of particle size, L is the distance downstream, Do is the initial value at L = 0 and ? is a diminution coefficient (? < 0) has been used to describe the undifferentiated effects of both processes (Figure 1). The linear form of Equation 1 used in curve fitting procedures is

Ln D = ?L+ B (2)

where Ln is base of natural logarithms (loge), B = constant (intercept term; where B = Ln Do). Compilations of diminution coefficients indicate wide variations in downstream fining rates (Knighton, 1987). Distances within which the median particle size (D50) is halved varies from tens of kilometres in large, single thread rivers to a few hundred meters in rapidly aggrading alluvial fans.

Several researchers, however, have suggested that tributary inputs and non-alluvial sediment sources can preclude the systematic downstream diminution of bed material grain size. For example, in his study of mountain streams in the Sangre de Christo range, Miller (1958) found that grain size did not exhibit any consistent pattern with distance downstream. He attributed much of the observed scatter to the delivery of fresh rock from outcrops in or near the channel. Krumbein (1942) identified log and boulder jams, bedrock constrictions and tributary mouth cones as significant determinants of local grain size in the Arroyo Sec in the San Gabriel mountains of southern California and found evidence that debris flows and landslides introduced large amounts of colluvial material to the stream. The observed pattern of grain size was erratic and there was no overall change in grain size along the study reach. Many other workers including MacPherson (1971), Knighton, (1975), Hogan, (1986) and Benda (1990) have noted that recurrent disruption of sediment transport by large organic debris jams, and the sporadic contamination of the fluvial sediment population by colluvial and tributary inputs, preclude the development of longitudinal structure.

In this paper, it is hypothesised that non-alluvial sediment supply and storage preclude the systematic diminution of sediment texture in gravel-bed rivers. Specifically, that spatially and temporally frequent colluvial inputs (consisting of heterogeneous disparate grain size distributions), masks the effects of longitudinal sorting and abrasion processes. This hypothesis is tested using data from three Canadian rivers: the North Saskatchewan River, Alberta, and Gregory and Riley Creeks, Queen Charlotte Islands, British Columbia.
Field Sites
The North Saskatchewan River is typical of many rivers in central Canada. It flows east from the Canadian Rocky Mountains and crosses the Prairie physiographic province of Alberta and Saskatchewan (Figure 2). The headwater reaches are confined to Proterozoic and Paleozoic rocks which are predominantly limestones and quartzites. The highest reaches receive large quantities of their load directly from high altitude zones of intense periglacial rock disintegration. There is an increasing proportion of sandstone in bedrock outcrops of the foothills whilst the argillaceous sediments of the Plains contribute little to the river bed materials. For much of the river’s course, floodplain development is extensive. Since the wide valley floor effectively isolates the main stem from any colluvial inputs, it is expected that this river will exhibit a systematic fining of bed sediment downstream.

Figure 2. The North Saskatchewan River
Riley Creek and Gregory Creek are two adjacent streams that drain the western flanks of the Queen Charlotte Islands, British Columbia (Figure 3). These islands are characterised by intense rainfall, deeply weathered, fissured and jointed soft volcanic and sedimentary rocks, thin soils, glacially oversteepened slopes and frequent seismic activity. Consequently rates of sediment production and mass wasting are high. It has been estimated, for example, that of the total volume sediment mobilised by mass wasting, an average of 43 percent directly enters stream channels, testimony to the strong hillslope-channel coupling throughout the small, steep, low-order drainage networks characteristic of the islands. In contrast to the North Saskatchewan River, it is expected that the bed material of these streams will be more variable as a direct consequence of the non-alluvial storage elements and colluvial inputs.

In many respects, (geology, climate, morphometry), the basins of Riley and Gregory Creeks are similar, such that the nature of the geomorphic activity and the textural composition of weathered materials are expected to be similar. However, the strength of coupling between hillslopes and channels varies between the two streams. Whilst the entire length of Gregory Creek and the upper part of Riley Creek are strongly coupled, a valley flat in the lower 4.2 km of Riley offers some protection to the channel from hillslope failures and other colluvial sediment inputs. Therefore, the Riley and Gregory Creek data sets can also be used to test the effect of hillslope-channel coupling: all things being equal, the sediments of lower Riley should exhibit a lower level of variability than the sediments of the other reaches.

Figure 3. Location of Riley and Gregory Creeks. The indicated valley flat buffers the lower portion of Riley Creek from colluvial inputs. Mass movement information courtesy of Schwab and Hogan (pers. Comm.)

Methods
In the North Saskatchewan River, 34 samples were collected from convenient locations along a 1102 km stretch of the river. The coarsest gravel at each site was selected for sampling using the Wolman technique (Wolman 1954). The samples were taken from the top 30 cm of the river beds and as far from the bank as possible at low water.

In Riley and Gregory Creeks, surface grain size data were collected using a photographic technique. The method is based on establishing an empirical calibration curve of median grain size to the number of particles in a given area of the bed surface (Church et al., 1987). A standard area, delineated by a 1.0 m2 quadrat, was photographed at a total of 130 sites. In each case, the quadrat was placed adjacent to a riffle pool break, close to the water’s edge. At 14 of these sites, direct measurement of 100 stones within the quadrat allowed the construction of a calibration curve. The non-linear relation shown in Figure 4, fitted by eye, has the highest coefficient of determination (r2 = 0.92) and lowest standard error of any of several relations tried.
Figure 4. Photo calibration curve. The curve relates number of particles per 0.25 m2 to measured surface median grain size, and was fitted by eye. The standard error of the y estimates and r2 are noted. Number of particles is presented as log2 to provide consistent scales.
Results (to be completed)

TRANSFORMATIONS FOR LINEAR REGRESSION

Power relations
Just as a straight line relationship has an equation of the form Y=a+bX, power relations have the form Y=10a Xb. Power relations are curves, the form of which depends on the value of b.

A curve of the form Y = 10a Xb can be linearised by the transformation Y ? log10Y and X ? log10X (log10 means log to the base 10) so that the relationship between log10X and log10Y can be defined by least squares regression as

Log10Y = a+blog10X.

The equation log10Y = a+blog10X (which plots as a straight line on a graph of log10X vs log10Y) can be back-transformed to an equation of the form Y = 10aXb (which plots as a curve on graph of X vs Y)

In summary
Taking logs of both variables transforms a multiplicative relationship such as Y=10a Xb to the linear additive form log10Y=a+blog10X which can be fitted by regressing log10Y on log10X in the ordinary way.

Exponential relations
Just as a straight line relationship has an equation of the form Y=a+bX and a power relation has the form Y=10a Xb, an exponential relationship has the form Y=ea ebX. Like power relations, exponential relations are curves, the form of which depends on the value of b.

An curve of the form Y=ea eXb can be linearised by the transformation Y ? logeY (log to the base e, also known as natural logarithms, ln) so that the relationship between X and logeY can be defined by least squares regression as

loge Y= a+bX.

The equation logeY = a+bX (which plots as a straight line on a graph of X vs logeY) can be back transformed to an equation of the form Y = ea ebX (which plots as an exponential curve on graph of X vs Y)

In summary
Taking loge of the Y variable transforms a multiplicative relationship such as Y=ea eXb to the linear additive form loge Y = a+bX which can be fitted by regressing logeY on X in the ordinary way.

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