The Influence of Ecohydrologic Dynamics on Landscape Evolution: a Stochastic Approach
Abstract:The stream power incision model (SPIM) has a long history of use in modeling landscape evolution. Despite simplifications made in its formulation, it has emerged over the last 30 years as a powerful tool to interpret the histories of tectonically active landscapes and to understand how they evolve over millions of years. However, intense interest in the relationship between climate and erosion has revealed that the standard SPIM has some significant shortcomings. First, it fails to account for the role of erosion thresholds, which have been shown to be important and require an approach that addresses the variable or stochastic nature of erosion processes and drivers. Second, the standard SPIM does not address the influence of catchment hydrology, which modulates the incoming precipitation to produce discharge that in turn drives fluvial erosion. Hydrological processes alter in particular the frequency and magnitude of extreme events which are highly relevant for landscape erosion.
To address these weaknesses we introduce a new analytical stochastic-threshold formulation of the stream power incision model that is driven by probabilistic hydrology. The hydrological model incorporates a stochastic description of soil moisture which takes into account the random nature of the rainfall forcing and the dynamics of the soil layer. The soil layer dynamics include infiltration and evapotranspiration which are both modelled as being dependent on the time varying soil moisture level (state dependent). The stochastic approach allows us to integrate these effects over long periods of time to understand their influence on the longterm average erosion rate without the need to explicitly model processes on the short timescales where they are relevant. Our model can therefore represent the role of soil properties (thickness, porosity) and vegetation (through evapotranspiration rates) in the longterm catchment-wide water balance, and in turn the longterm erosion rate. We identify these catchment-wide ecohydrological dynamics as a key aspect of the model that can have a nonlinear and potentially dominant influence on the longterm rate of landscape erosion and we estimate over what climatic and ecological regimes this influence may be important.