Struggles with stream power: Connecting theory across scales

Abstract

Two empirically consistent explanations exist for the morphology and dynamics of bedrock rivers. The stream power law appears to explain rates of rock incision at large scale (large drainage basins or landscape scale), but appears to be of limited value in predicting reach-scale morphology and dynamics. The underlying reason why stream power is such an effective tool for understanding landscape evolution is because it is an explicit representation of the inverse power relation between slope and area in rivers incising bedrock. This morphometric relation is nearly universal, subject to exogenous contingencies. Independent testing and validation of the stream power incision model is challenging because of the contingencies that exist in almost all landscapes. Mechanistic models of erosion have been tested and validated at small scales, generally below the reach scale, and opportunities exist for independent testing and validation by using them to predict reach-scale morphologies. Predicting larger scale bedrock river morphology requires the assumption that flow, sediment fluxes and bedrock erosion processes that occur at smaller scale are adequately averaged at larger scales, which is not well supported. Reconciling these two scales of explanation is one of the grand challenges of fluvial geomorphology, unless we accept that theory and explanations will be scale-delimited.