Stochastic in Space and Time: Part 2, Effects of Simulating Orographic Gradients in Daily Runoff Variability on Bedrock River Incision

Understanding the extent to which climate and tectonics can be coupled requires knowing both the form of topography and erosion rate relationships, but also the underlying mechanistic controls on those forms. The stream power incision model (SPIM) is commonly used to interpret such topography erosion rate relationships, but is limited in terms of probing mechanisms. A promising modification is a stochastic-threshold incision model (STIM) which incorporates both variability in discharge and a threshold to erosion, and in which the form of the topography erosion rate relationship is largely controlled by the variability of runoff. However, as applied STIM assumes temporally variable, but spatially constant runoff generating events, an assumption that is likely broken in regions with complicated orography. In response, we develop a unique 1D STIM based profile model that allows for stochasticity in both time and space and is driven by empirical relations between topography and runoff statistics. Testing the development of steady-state topography using spatial-STIM over a range of uplift rates highlights that coupling between mean runoff, runoff variability, and topography suggest that the development of highly nonlinear topography erosion rates should be expected. Further, we find that whether the daily statistics of runoff generating events are spatially linked or unlinked is a primary control on landscape evolution and the final resulting topography. As many empirical topography – erosion rate datasets likely sample across ranges of linked vs unlinked behavior, it is questionable whether single SPIM relationships fit to those data, without considerations of the hydroclimatology, are meaningful.