Responses of chemical erosion rates to transient perturbations in physical erosion rates, and implications for relationships between chemical and physical erosion rates in regolith-mantled hillslopes

Understanding the relationship between chemical erosion rates (W) and physical erosion rates (E) is of wide interest due to their roles in driving landscape evolution, supplying nutrients to soils and streams, and modulating the global carbon cycle. Measured relationships between W and E vary around the globe, with some regions exhibiting positive correlations between W and E, some negative correlations, and others no correlation within uncertainty. Here we use a numerical model for mineral weathering in well-mixed ridgetop regolith to explore how complex W-E relationships can be generated by simple transient perturbations in E. We show that a Gaussian perturbation in E can produce positive or negative responses in W, and can result in a variety of hysteresis loops - clockwise, counterclockwise, or figure-eight - in plots of W against E. The nature of the transient response depends on the shape of the steady-state W-E relationship, which is set by regolith mineralogy, and the ratio of E to the maximum possible regolith production rate. The response time of W is controlled by the response time of soluble mineral concentrations at low E, where soluble mineral concentrations are low, and by the response time of regolith thickness at high E, where regolith thickness is low. These complex W-E relationships arise in the absence of variations in climate and lithology, which suggests that transients may account for some of the observed differences in W-E relationships among field sites, even among sites that share the same climate and lithology.