Simple models of topographically driven subsurface lateral flow: A review

math_shortcuts Explicitly simulating topographically driven lateral flow processes is important to provide realistic simulations of global water, energy, and biogeochemical cycles. We present both analytical and numerical solutions of the storage-discharge dynamics of hillslopes. The analytical solutions include saturated flow dynamics for a rectangular plane of constant slope, and solutions that quantify relationships between hillslope shape and hillslope storage and hillslope outflow. The analytical solutions presented in this paper have three primary applications in modern hydrological and land models: (1) the solutions can be used to provide an independent check for the numerical implementation of saturated subsurface flow processes; (2) the solutions increase understanding of the storage-discharge behaviour of hillslopes; and (3) the solutions provide an exact and numerically efficient way to represent flow processes in hydrological and land models. The intent of this paper is to provide a synthesis on the early analytical work on topographically driven saturated flow and hence strengthen the basis for the future development of large-domain hydrological and land models.