Analysis of the nonlinear storage–discharge relation for hillslopes through 2D numerical modelling

"Storage-discharge curves are widely used in several hydrological applications concerning flow and solute transport in small catchments. This article analyzes the relation Q(S) (where Q is the discharge and S is the saturated storage in the hillslope), as a function of some simple structural parameters. The relation Q(S) is evaluated through two-dimensional numerical simulations and makes use of dimensionless quantities. The method lies in between simple analytical approaches, like those based on the Boussinesq formulation, and more complex distributed models. After the numerical solution of the dimensionless Richards equation, simple analytical relations for Q(S) are determined in dimensionless form, as a function of a few relevant physical parameters. It was found that the storage-discharge curve can be well approximated by a power law function Q\/(LKs) = a(S\/(L-2(phi, theta(r))))(b), where L is the length of the hillslope, K-s the saturated conductivity,phi theta(r) the effective porosity, and a, b two coefficients which mainly depend on the slope. The results confirm the validity of the widely used power law assumption for Q(S). Similar relations can be obtained by performing a standard recession curve analysis. Although simplified, the results obtained in the present work may serve as a preliminary tool for assessing the storage-discharge relation in hillslopes. Copyright (C) 2012 John Wiley & Sons, Ltd."