Theoretical basis of the stream-power river incision model

Abstract

The absence of explanatory literature in Portuguese on the primary mathematical model that describes bedrock channel evolution in geological time scales (>103 years), the stream-power model, is a limiting factor in training young geomorphologists in line with the international scenario of the discipline. This fact makes it challenging to develop geomorphic research in Brazil that has international insertion. This technical note fills this critical gap in Brazilian quantitative geomorphology with the first study in Portuguese that presents the derivation and implications of the stream-power model. It is reasonable to assume a recent trend of empirical studies investigating Brazilian landscapes employing sophisticated algorithms related to the stream-power model to extract quantitative information from digital elevation models. Nevertheless, the general understanding of the physical and mathematical theory behind these topographic metrics is incipient, at best. Here we present the derivation of the stream-power model from simple energy considerations using two approaches, the first based on the shear stress and the second from the rate of potential energy loss per unit area of the channel bed. We describe the simplified mechanics of different river erosion processes to clarify a pervasive notion of “river incision” due to a single process. Finally, we list the main limitations of the model.