There is an urgent need to test recently constructed conceptual models of landscape evolution and geomorphology against field data. Many statistics that have commonly been used, such as Strahler statistics, are poorly suited to this testing being unable to potentially falsify the models when applied in controlled conditions. The relations between these statistics and catchment mass movement processes are, in many cases, indirect. Moreover, they are sensitive to unknowable inputs (e.g., initial conditions). One of the main differences among the competing landscape evolution models is their representation of mass movement and erosion processes, so that statistics that are directly linked to these processes, or their geomorphic signature, are needed. This paper examines the use of a log-log linear relation between catchment area, slope, and elevation. This relation has been previously derived quantitatively from the catchment erosion and hydrologic processes for dynamic and declining geomorphic equilibria. Using a catchment evolution model, this paper shows that the relation is robust against deviations from the assumptions of spatial and temporal homogeneity of erosion, climate, and tectonic uplift made in its derivation. The sensitivity of the geomorphology to time-varying tectonic uplift and climate and spatially variable soil erodability is examined. It is thus asserted that the relation between area, slope, and elevation is suitable for testing of models against field data, where spatial and temporal homogeneity of erosion, climate, and tectonic uplift are only approximately true. In the case of variable soil erodability, planar drainage patterns exhibit self-organization with the high elevation regions of the catchment having low soil erodability. Consequently, a downstream increasing erodability of the soil material, consistent with a downstream fining type of behavior, is observed. It is further argued that the equilibria relation is fundamental and uniquely defines the elevation form of catchments so that all other elevation statistics are derived from it. ¿ American Geophysical Union 1994