A simple geomorphic‐based analytical model for predicting the spatial distribution of soil thickness in headwater hillslopes and catchments

Abstract

Soil thickness acts as an important control for headwater hydrologic processes. Yet, its spatial distribution remains one of the least understood in catchment hydrology. Analytic methods are desirable to provide a simple way for predicting soil thickness distribution over a hillslope or a catchment. In this paper, a simple geomorphic‐based analytical model is derived from the dynamic equations of soil thickness evolution in areas with no tectonic uplift or lowering since the recent geological past. The model employs terrain attributes (slope gradient, curvature, and upstream contributing area) as inputs on grid‐based DEMs for predicting soil thickness evolution over time. The analytic model is validated first on nine abstract hillslopes through comparing 10 kyr simulation results between our proposed model and the numerical solution. The model is then applied to predict soil thickness evolution over 13 kyr in the 7.9 ha Shale Hills catchment (one of the Critical Zone Observatories in the U.S. located in central Pennsylvania). Field observed and model predicted values of soil thickness are in good agreement (with a root mean squared error of 0.39 m, R2 = 0.74, and absolute errors <0.10 m in 70% of 106 sample points). Moreover, our model verifies that terrain shape and position are the first‐order control on soil thickness evolution in the headwater catchment. Therefore, the derived geomorphic‐based analytical model can be helpful in understanding soil thickness change over geological time and is useful as a simple tool for deriving spatially distributed soil thickness needed for hydrologic modeling.