Eric Deal, Jean Braun, Gianluca Botter

• Due to the challenges in upscaling daily climatic forcing to geological time, physically realistic models describing how rainfall drives fluvial erosion are lacking. To bridge this gap between short-term hydrology and long-term geomorphology, we derive a theoretical framework for long-term fluvial erosion rates driven by realistic climate by integrating an established stochastic-mechanistic model of hydrology into a threshold-stochastic formulation of stream power. The hydrological theory provides equations for the daily streamflow probability distribution as a function of climatic boundary conditions. The new parameters introduced are rooted firmly in established climatic and hydrological theory. This allows us to account for how fluvial erosion rates respond to changes in rainfall intensity, frequency, evapotranspiration rates, and soil moisture dynamics in a way that is consistent with existing theories. We use this framework to demonstrate how hydroclimatic conditions and erosion threshold magnitude control the degree ofDue to the challenges in upscaling daily climatic forcing to geological time, physically realistic models describing how rainfall drives fluvial erosion are lacking. To bridge this gap between short-term hydrology and long-term geomorphology, we derive a theoretical framework for long-term fluvial erosion rates driven by realistic climate by integrating an established stochastic-mechanistic model of hydrology into a threshold-stochastic formulation of stream power. The hydrological theory provides equations for the daily streamflow probability distribution as a function of climatic boundary conditions. The new parameters introduced are rooted firmly in established climatic and hydrological theory. This allows us to account for how fluvial erosion rates respond to changes in rainfall intensity, frequency, evapotranspiration rates, and soil moisture dynamics in a way that is consistent with existing theories. We use this framework to demonstrate how hydroclimatic conditions and erosion threshold magnitude control the degree of nonlinearity between steepness index and erosion rate. We find that hydrological processes can have a significant influence on how erosive a particular climatic forcing will be. By accounting for the influence of hydrology on fluvial erosion, we conclude that climate is an important control on erosion rates and long-term landscape evolution.…