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

Abstract

The extent to which climate and tectonics can be coupled rests on the degree to which topography and erosion rates scales linearly. The stream power incision model (SPIM) is commonly used to interpret such relationships, but is limited in probing mechanisms. A promising modification to stream power models are stochastic‐threshold incision models (STIM) which incorporate both variability in discharge and a threshold to erosion. In this family of models, the form of the topography erosion rate relationship is largely controlled by runoff variability. Applications of STIM typically assume temporally variable, but spatially uniform and synchronous runoff generating events, an assumption that is likely broken in regions with complicated orography. To address this limitation, we develop a new 1D STIM model, which we refer to as spatial‐STIM. This modified version of STIM allows for stochasticity in both time and space and is driven by empirical relationships between topography and runoff statistics. Coupling between mean runoff and runoff variability via topography in spatial‐STIM generates highly nonlinear relationships between steady‐state topography and erosion rates. We find that whether the daily statistics of runoff are spatially linked or unlinked, which sets whether there is spatial synchronicity in the recurrence interval of runoff generating events, is a fundamental control on landscape evolution. Many empirical topography—erosion rate data sets are based on data that span across the endmember scenarios of linked versus unlinked behavior. It is thus questionable whether singular SPIM relationships fit to those data can be meaningfully related to their associated hydroclimatic conditions.