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

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. Tectonic activity has long been known to modify climate by constructing mountain topography. Perhaps less obvious is the question of whether climatically driven erosion can also modify tectonic activity. This latter causal chain is premised on the notion that higher uplift rates can lead to steeper topography, higher precipitation rates, and thus more vigorous erosion. However, many erosion rate studies suggest that topography is only weakly sensitive to changes in rock uplift rates, thereby posing an important challenge to the climate-tectonic coupling hypothesis. Prior studies suggests that variability in daily runoff may be central to understanding this sensitivity, though historically have focused on how runoff is variable in time and not in space. As such, we developed a new numerical model of river erosion that simulates spatial patterns in runoff generation. We ran a suite of numerical experiments based on observed relationships among runoff, runoff variability, and topography to better understand how new model elements affect model sensitivity. We found that our crude representation of the size of runoff events is fundamental to model behavior. Given that event size is rarely considered in studies of climate-tectonic coupling, we argue that this property of runoff events requires more careful consideration. Relationships among mean runoff and variability with topography in mountainous terrain can explain pseudo-thresholds in channel steepness Spatial asynchronicity of similar exceedance frequency runoff events is an unrecognized control on landscape evolution Orographic patterns in variability, snowmelt, and the characteristic size of runoff events alter predictions of climate-tectonic coupling