Exponential Longitudinal Profiles of Streams

Abstract

A theoretical model is presented which shows that streams with low solids concentrations and low lateral inflows, whose bed load sediments undergo either comminution or hydraulic sorting under steady or quasi-steady conditions, have exponential profiles. Similar streams in which both communition and sorting are significant have exponential profiles only if they are short.Sediment threshold and flow depth estimates based on the theoretical model are consistent with field and laboratory data from the literature. A comparison of the model and communition and sorting data from the literature strongly suggests that hydraulic sorting and comminution dominate in short and long natural streams, respectively. No examples of natural streams of intermediate length with exponential longitudinal profiles were found, suggesting that neither sorting nor comminution is dominant in such streams.

Comparative assessment of three approaches for deriving stream power plots along long profiles in the upper Hunter River catchment, New South Wales, Australia

“…Based on sediment transport and discharge equations, theoretical models of long profile shape take an exponential form (Morris and Williams, 1997). This has been supported by laboratory and field studies (Leopold and Langbein, 1962;Morris and Williams, 1997). In this study, exponential curves were fitted to the untransformed, DEMgenerated, long profile data.…”

Effects of tectonics and lithology on long profiles of 16 rivers of the southern Central Massif border between the Aude and the Orb (France)

“…On the south edge of the Pardailhan mounts, the greatest incision takes place between 5 and 10 km from the drainage divide and often downstream an important knickzone. The exponential function appears to be the best to describe the studied river long profiles (Ohmori, 1991;Morris and Williams, 1997). The graph A (Fig.…”

Tectonic constraints on watershed development on frontal ridges: Mohand Ridge, NW Himalaya, India

“…A number of studies based on sediment transport, discharge, theoretical models, laboratory and field investigations support the idea that long profiles bear an exponential form (Leopold and Langbein, 1962;Morris and Williams, 1997). Though in some cases the exponential curve may not exactly match the long profile and a second order exponential curve better represents the long profile (Jain et al, 2006).…”