Overland Flow Modeling with the Shallow Water Equations Using a Well-Balanced Numerical Scheme: Better Predictions or Just More Complexity

Abstract

In the last decades, several physically based hydrological modeling approaches of various complexities have been developed that solve shallow water equations or their approximations using various numerical methods. Users of the model may not necessarily know the different hypotheses underlying these development and simplifications, and it might therefore be difficult to judge if a code is well adapted to their objectives and test case configurations. This paper aims to compare the predictive abilities of different models and evaluate potential gain by using an advanced numerical scheme for modeling runoff. Four different codes are presented, each based on either shallow water or kinematic wave equations, and using either the finite volume or finite difference method. These four numerical codes are compared with different test cases, allowing to emphasize their main strengths and weaknesses. Results show that, for relatively simple configurations, kinematic wave equations solved with the finite volume method represent an interesting option. Nevertheless, as it appears to be limited in case of discontinuous topography or strong spatial heterogeneities, for these cases they advise the use of shallow water equations solved with the finite volume method.