The morphology of graded gravel rivers: a network perspective

Abstract

Analytical hydraulic geometry equations are combined with a watershed model to quantify downstrem trends in equilibrium fluvial morphology in gravel streams. The hydraulic geometry equations relaet fluvial morphology to discharge, bedload transport rate and grain size; these independent variables are in turn determined by routing gravel supplied at zero-order basins through a channel network. As gravel is routed downstream, it decreases in size according to an empirical power law. The resulting model specifies the discharge, bedload transport rate, grain size, width, depth, slope and river bed elevation at every point in the drainage basin. When the downstream fining law is calibrated using data from central Pennsylvania, dowstream hydraulic geometry exponents for the width and depth are accurately reproduced. Longitudinal profiles calculated from the model fit observed profiles in largerwatersheds, but are inaccurate in smaller watersheds. The model also reproduces Hack's (1957) empirical result relating slope to the 0.6 power of A/ d s, where A is the drainage basin area and d s is the mean grain size. Unfortunately, the model requires an equilibrium time scale which is unreasonably long, suggesting that the channels of the study area are best described as systems with multiple time scales and multiple rates of response. The model probably is successful because the width and depth have relatively short relaxation times, and also because downstream trends in discharge and sediment transport rate are controlled by network topology. Thus, downstream hydraulic geometry equations do not necessarily provide strong evidence for the equilibrium of fluvial landscapes. Rather, they reflect the constancy of network topology and the rapid response times of width and depth.