Overland flow modelling with the Shallow Water Equation using a well balanced numerical scheme: Adding efficiency or just more complexity?

In the last decades, more or less complex physically-based hydrological models, have been developed that solve the shallow water equations or their approximations using various numerical methods. Model users may not necessarily know the different hypothesis lying behind 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 at comparing the predictive abilities of different models and evaluating potential gain by using advanced numerical scheme for modelling runoff. We present four different codes, each one based on either shallow water or kinematic waves equations, and using either finite volume or finite difference method. We compare these four numerical codes on different test cases allowing to emphasize their main strengths and weaknesses. Results show that, for relatively simple configurations, kinematic waves equations solved with 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 we advise the use of shallow water equations solved with the finite volume method.