Comparative Analysis of Kinematic Approximation and Richards Equation Models for Subsurface Flow on Complex Hillslopes

Generalized solutions for the kinematic wave equation for subsurface flow have recently been derived for hillslopes of arbitrary geometry by introducing two dimensionless geometric parameters α and ε which define the hydrologic similarity between hillslopes with respect to their characteristic response (Norbiato and Borga, 2008). These solutions are derived by using a second order polynomial function to describe the bedrock slope and an exponential function to describe the variation of the width of the hillslope with hillslope distance. In this presentation we assess the behavior of this simple, one- dimensional model in comparison with a fully three-dimensional Richards equation model for a series of free drainage scenarios. For different values of saturated hydraulic conductivity, we specify the range of values of the two dimensionless geometric parameters α and ε for which the generalized solution is valid. Special attention is given to the discretization and setup of the boundary and initial conditions.