A PHYSICAL EXPLANATION FOR AN OBSERVED AREA-SLOPE-ELEVATION RELATIONSHIP FOR CATCHMENTS WITH DECLINING RELIEF

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 equat ion for runoff and erosion processes in the catchment. The key hypothe sis underlying this relationship is that as a catchment declines, the nondimensionalized catchment approaches a constant form. This hypothes is is verified for computer simulated catchments. The area-slope-eleva tion 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 (re sulting from a lower rate bf tectonic uplift); and catchments declinin g from an elevated initial condition, as, for example, in the decline of a mine spoil heap. A previously published relationship between slop e and area for catchments in dynamic equilibrium and based on runoff a nd erosion physics is shown to be a special case of this general relat ionship. The new area-slope-elevation relationship is compared with da ta from simulated catchments and a field catchment. It is thus shown t hat for declining catchments the area-slope-elevation relationship is a good predictor of catchment form for catchments with declining relie f. It is argued that the slope-area-elevation relationship is sufficie nt, with the planiform drainage pattern, to completely define the elev ation properties of the catchment such as, for instance, the hypsometr ic curve.