Abstract
Bedrock river incision rates are thought to depend on many environmental factors, including runoff and lithologic resistance. However, evidence of the effect of lithology, and in particular lithologic heterogeneity, is varied and equivocal. To assess the relative influence of these two factors, we analyze a two-phase sediment flux-dependent stream power erosion model and derive an expression for the effective erodibility in terms of runoff rate, lithologic resistance, and parameters governing sediment transport. This expression predicts that the influence of lithologic resistance is a function of runoff. Under a wet climate, detachment-limited conditions are more common because discharge is sufficient to transport eroded sediment, leaving substantial exposed bedrock on riverbeds. As a result, local bedrock properties exert a primary control on the erodibility. Under arid conditions, transport-limited conditions dominate, leaving riverbeds largely covered by alluvium. Erodibility thus depends more on sediment transport capacity, which controls the degree of bedrock exposure, than on local bedrock properties Because channel steepness depends on erodibility, this regime transition predicts that the expected topographic manifestation of lithologic heterogeneity--steeper channels in harder rocks--should be more pronounced in wet regions than in dry regions. We confirm this prediction with numerical simulations and test its real-world applicability with topographic analysis of landscapes in contrasting climatic settings. We find that igneous and sedimentary rock units in arid Nevada show nearly indistinguishable probability distributions of channel steepness, but in the comparatively wet Oregon Coast Range, channels in igneous rocks are systematically steeper than those in sedimentary rocks. We also compile a database of >250 cosmogenic erosion rates for the southern Appalachians to directly estimate the effective erodibility, and find that basins situated in metamorphic rocks feature a consistently lower erodibility than those in sedimentary rocks in this wet region. These three regions are consistent with our theoretical predictions that lithologic control of erodibility is substantial in wetter regions but inhibited in arid regions.