A general relationship between the contributing area, slope, and mean elevation of catchments with relief declining after a tectonic uplift event is presented. This relationship is based on the continuity equation for runoff and erosion processes in the catchment. The key hypothesis underlying this relationship is that as a catchment declines, the nondimensionalized catchment approaches a constant form. This hypothesis is verified for computer simulated catchments. The area‐slope‐elevation relationship covers several cases: catchments declining toward a peneplain; catchments declining from a high slope dynamic equilibrium (resulting from a high rate of tectonic uplift) to a low slope one (resulting from a lower rate of tectonic uplift); and catchments declining from an elevated initial condition, as, for example, in the decline of a mine spoil heap. A previously published relationship between slope and area for catchments in dynamic equilibrium and based on runoff and erosion physics is shown to be a special case of this general relationship. The new area‐slope‐elevation relationship is compared with data from simulated catchments and a field catchment. It is thus shown that for declining catchments the area‐slope‐elevation relationship is a good predictor of catchment form for catchments with declining relief. It is argued that the slope‐area‐elevation relationship is sufficient, with the planiform drainage pattern, to completely define the elevation properties of the catchment such as, for instance, the hypsometric curve.
Water Resources Research – Wiley
Published: Feb 1, 1994
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