1 - Applied and scientific backgrounds, project objectives Overland flow on agricultural soils induces problems of environmental resources preservation (decrease of soil thickness by erosion, nutrients losses, decrease in water quality). Overland flow events are also responsible for flooding, generating damages to goods and people. This phenomenon is highly discontinuous in time and space, making it difficult to study. To improve watershed management, a good prediction of the surface flow network is needed. However, the applied hydrologic models are quite inefficient on this issue. For agricultural areas, empirical works showed that the interaction between furrows and topography strongly controls the geometry of the flow network: at low flux, overland flow follows the furrow direction, while, at high flux, overland flow follows the topographic slope too. Due to the lack of knowledge about this interaction, this phenomenon is evaluated only through heuristic models using an on/off-type law. In this proposal, we intend to model this type of flow in order to better understand and predict the effect of surface morphology on overland flow. The final goal is to take into account the effect of the interaction between furrows and topography in Saint-Venant type models used in hydrology. 2 - Description of the project, methodology The first step of the project is a modeling work to integrate in a Saint-Venant type system the effect of the furrows on the flow properties. The challenge comes from the facts that furrows create anisotropy in the flow and that the typical height of the furrows is of the magnitude of the flow depth. This requires innovative techniques of modeling. We propose three different approaches (WP1: multi-layer, relaxation, Boussinesq) that we will compare together and with data from direct numerical simulations (WP2) and experimental measurements (WP3). Several numerical methods already used for other purposes (finite volumes, lattice Boltzmann, Arbitrary Lagrangian Eulerian…) will have to be modified to pass test cases of increasing complexity. To ensure the relevance of the targeted problems and of the proposed solutions, this project associates mathematicians and hydrologists. 3 - Expected results The close collaboration of mathematicians and hydrologists will allow for the transfer of knowledge about numerical methods recently developed in applied mathematics. During the 3rd year of the project, we will apply the results of the models set up in WP1 and validated through WP2 and 3, by integrating them in a modeling platform (to allow for an easy coupling with other hydrologic modules), by distributing a demonstration free software and by proposing modifications of existing applied hydrologic tools (WP4).