Upscaling Hillslope-Scale Subsurface Flow to Inform Catchment-Scale Recession Behavior

The subsurface flow contribution to a basin hydrograph is often conceptualized as a single lumped reservoir parameterized by a power law function fit through the observed recession behavior of the basin. However, basins may be better represented as multiple independent subsurface hillslope reservoirs characterized with variable, transient recession behavior as a function of the time history of recharge. In this work, we unify the latter, more complex understanding of the subsurface with the large-scale power law recession behavior convenient in hydrologic modeling applications. This unification is achieved by deriving upscaling relationships capable of converting simple metrics of basin hillslope topography into a signature basin response characterizing the subsurface-flow-induced recession from a single recharge event. Event superposition may then be used to simulate the application of a time series of recharge and a simple scaling relationship may be used to handle basins with homogeneous conductivity. The signature response is informed by numerical simulations of the hillslope-storage Boussinesq equation for unconfined saturated flow through sloping hillslopes applied to 30 basins in the CAMELS database. The efficacy of the upscaled signature response in replicating numerical simulations in 50 CAMELS basins is demonstrated, as is the practical efficacy of the upscaling relationships for predicting transient recession in 17 of these basins. The upscaled signature response method thus provides a tool for hydrologic modelers to estimate transient recession parameters using the insights of subsurface flow modeling, although the predictions made by this method are unable to capture the full variability of observed recession behavior.

Automated summary

The subsurface flow contribution to a basin hydrograph is often conceptualized as a single reservoir, but this study suggests that basins may be better represented as multiple independent subsurface hillslope reservoirs. In this work, upscaling relationships are derived to convert simple metrics of basin hillslope topography into a signature basin response characterizing the subsurface flow-induced recession. The efficacy of the upscaled signature response in replicating numerical simulations and predicting transient recession is demonstrated.