In idealized "steady state" mountain landscapes, erosion of river beds keeps pace with tectonic uplift. The concave-upwards longitudinal profiles of such rivers have been interpreted as caused by the erosive effect of increasing water discharge down-stream being compensated by declining channel gradient to achieve spatially uniform, or gradually varying, erosion rate. Many authors have documented the existence of inverse power-law relationships between river rainfall catchment area A and channel gradient S which appear to be a consequence. In this study, similar characteristics were derived from multibeam echo-sounder data of submarine canyons in the Atlantic USA continental slope. Along-channel gradient and hemipelagic contributing area A (derived from topography in the same way as for river catchments) were also found to show declining S with A. Much of the data have power-law slopes that are comparable with river systems. However, the submarine canyon graphs show a greater diversity of forms and some are not power-law. The general decline in S with increasing A can be explained in terms of channel erosion by sedimentary mass flows, such as turbidity currents. In this conceptual model, hemipelagic sediments accumulate in the walls of canyons until they become unstable and initiate erosive sedimentary flows. The frequency and size of such flows increases down-canyon, hence with increasing A, tending to increase cumulative erosion in a way that is analogous to the effect of increasing discharge in river systems. That effect is compensated by lower S to maintain spatially balanced erosion rate. It is unclear if these canyons are in a form of steady state or if the gradient-area relationships arise in the same way as in rivers of declining orogens. However, it is speculated that a form of topographic steady state could arise from a competition between hemipelagic deposition which attempts to aggrade the slope and erosion along canyon channels. The diversity of the gradient-area graphs could have arisen from a number of mechanisms such as (1) changes in relative abundance of debris flows (matrix-supported flows), coherent mass-movements (slumps) and turbidity currents down-canyon, (2) change in erosive behaviour of individual flows as they travel down-slope, (3) transient behaviour and (4) varied lithology.
Mitchell, N. C., "Interpreting long-profiles of canyons in the USA Atlantic continental slope," Marine Geology, 214, 75-99, 2005.