Abstract. The exponential density function was fitted to frequency distributions of scour and fill depths derived from six single-threaded gravel-bed Channels. Scour chains and monitors were used to record the depth of bed activity in the 6 to 20 rn wide channels. Goodness-of-fit analyses indicate that the exponential function is a plausible model. Introduction of dimensionless shear stress (r*) collapses model parameters and the active proportion of the streambed of individual rivers into general trends. An exponential relation between model parameters and r* suggests a means to derive scour and fill depths to a first approximation based only on flow and channel characteristics. Exponentially distributed depths require over 400 observations to estimate the mean to within 10% with 95% confidence.
IntroductionDuring a flood event the entrainment and deposition of sediment produce a decrease and increase in the vertical position of an alluvial streambed, respectively. These fluctua- The specific objective of this paper is to describe the spatial variation of event-based scour and fill depths by a probability function, specifically the exponential density function. Results derive largely from a field program conducted in Carnation Creek, Canada [Haschenburger, 1996]. Data from previous studies [Tripp and Poulin, 1986; Carling, 1987] provide supporting evidence to suggest that the proposed probability model is applicable beyond the primary study stream.
Exponential Density FunctionThe exponential density function is formulated here to de- SelectiOn of the exponential function as a candidate model stems largely from empirical observations of magnetically tagged gravels. These observations indicate that some areas of the streambed experience little, if any, bed activity during a flood event because some tracers remain stationary at or very near the streambed surface. A limited area of the bed scours or fills relatively deeply, as documented by the few tracers buried deeply initially and later found transported downstream. It appears that the probability of the channel bed being exposed to flow at different depths controls the vertical distribution of tracer burial depths [Galvin, 1965]. Hassan and Church [1994] described this pattern by the exponential function, considering the proportion of marked particles found in a given layer of the gravel sediment body. Although alternative models such as the gamma and Weibull density functions may be applicable, the 2857