Controls on the patterns of topography and erosion rate in a critical orogen

We solve for the steady state patterns of erosion rate and topography in a critical wedge to understand the mutual adjustment of tectonics, erosion, and topography in the absence and presence of spatial variations in precipitation rate. We consider steady state systems in which tectonics favors a critical topographic form, assumed to be the mean elevation across the range, and in which surface erosion by rivers and hillslopes operates on a two‐dimensional landscape. We find that (1) a nonuniform critical topographic form implies a nonuniform pattern of ridge‐valley relief and hence a nonuniform pattern of erosion rate, and (2) when the system is forced by local variations in precipitation rate, maintenance of the critical topographic form requires a local response of rock uplift that greatly dampens changes in topography. We apply these concepts to the western side of the Olympic Mountains of Washington State, where mean elevation, ridge‐valley relief, and precipitation rates increase from the coast to the topographic crest of the range. We find that the main control on the erosion rate pattern is the pattern in mean elevation and the amount of precipitation. In contrast, the pattern of precipitation is only a minor control. As a whole, our work demonstrates an approach for developing the theoretical context that is necessary for interpreting spatial associations between patterns in topography, precipitation, and erosion in natural orogens.