Dynamics of the stream-power river incision model: Implications for heightlimits of mountain ranges, landscape response timescales, and research needs

The longitudinal profiles of bedrock channels are a major component of the relief structure of mountainous drainage basins and therefore limit the ele vation of peaks and ridges. Further, bedrock channels communicate tectonic and climatic signals across the landscape, thus dictating, to first order, the dynamic response of mountainous landscapes to external forcings. We rev iew and explore the stream-power erosion model in an effort to (1) elucidat e its consequences in terms of large-scale topographic (fluvial) relief and its sensitivity to tectonic and climatic forcing, (2) derive a relationshi p for system response time to tectonic perturbations, (3) determine the sen sitivity of model behavior to various model parameters, and (4) integrate t he above to suggest useful guidelines for further study of bedrock channel systems and for future refinement of the stream-power erosion law. Dimensio nal analysis reveals that the dynamic behavior of the stream-power erosion model is governed by a single nondimensional group that we term the uplift- erosion number, greatly reducing the number of variables that need to be co nsidered in the sensitivity analysis. The degree of nonlinearity in the rel ationship between stream incision rate and channel gradient (slope exponent n) emerges as a fundamental unknown. The physics of the active erosion pro cesses directly influence this nonlinearity, which is shown to dictate the relationship between the uplift-erosion number, the equilibrium stream chan nel gradient, and the total fluvial relief of mountain ranges. Similarly, t he predicted response time to changes in rock uplift rate is shown to depen d on climate, rock strength, and the magnitude of tectonic perturbation, wi th the slope exponent n controlling the degree of dependence on these vario us factors. For typical drainage basin geometries the response time is rela tively insensitive to the size of the system. Work on the physics of bedroc k erosion processes, their sensitivity to extreme floods, their transient r esponses to sudden changes in climate or uplift rate, and the scaling of lo cal rock erosion studies to reach-scale modeling studies are most sorely ne eded.