Sonar images of the Atlantic USA continental slope reveal an eroded landscape that appears remarkably similar to subaerial landscapes eroded by surface runnoff. Analysis of multibeam data reveals that they are similar in a number of quantitative aspects also, such as similar scaling between channel gradient and contributing area, they show Hack's law scaling of channel length and contributing area and tributary channels join trunk channels at the same elevation without an intervening waterfall. In modern geomorphology, the physics of river bed erosion and rules for runnoff hydrology are used to model how erosion rate varies spatially and temporally, in order to predict large-scale landscape characteristics. This paper describes attempts to adapt such an approach to submarine canyon systems eroded by sedimentary flows. The mathematical form of the erosion is studied using the vertical relief of the canyons for the net erosion depth and compared with results deduced from long-profile concavity. The rough correspondence between the two approaches lends support to the model. It is shown how the model can be used to help interpretation of canyon morphology by relating the pattern of erosion to the pattern of hemipelagic sediment supplied to the slope and other properties.
Mitchell, N. C., "Erosion of canyons in continental slopes," Geological Society London Special Publication, "Submarine slopes: processes and products," 131-140, 2004.