Use of an Efficient Proxy Solution for the Hillslope-Storage Boussinesq Problem in Upscaling of Subsurface Stormflow

The hillslope-storage Boussinesq (hsB) equation is a modification of the one-dimensional Boussinesq representation of saturated subsurface flow that accommodates the impact of converging and diverging flows resulting from a hillslope with nonconstant width. Here, a surrogate model, the hsB Proxy, is developed which closely emulates the results of high-quality numerical solutions of the hsB to reproduce the drainage response of a wide range of wedge-shaped hillslopes in response to a recharge time series at a fraction of the computational cost of a numerical solution and with minimal loss of fidelity. The efficacy of the Proxy in emulating the hsB response of a single hillslope and the aggregate response of a network of hillslopes is demonstrated. The Proxy applies to wedge-shaped hillslopes with homogenous hydraulic conductivity under uniform recharge, with the expectation that these hillslopes may inform future investigations into the upscaling behavior that results in the known power-law relationship between subsurface storage and outflow in a basin. The utility of the hsB as a tool for evaluating upscaling problems is demonstrated in two applications. First, the Proxy response is compared to the known basin-scale recession behavior in the Panola Mountain Research Watershed, under both transient and steady-state conditions. Second, the Proxy is applied to derive the single best effective hillslope in a basin. The Proxy is expected to be a useful tool for rapid simulation of subsurface flow from hillslopes for use in hydrological models and land surface schemes.

Automated summary

A surrogate model, the hsB Proxy, was developed in this study to closely emulate the drainage response of various wedge-shaped hillslopes to recharge time series at a lower computational cost while maintaining accuracy. The Proxy can be applied to simulate the overall response of single hillslopes and hill slope networks, and is expected to assist future investigations into upscaling issues related to subsurface storage and outflow.