A fully coupled superficial runoff and soil erosion basin scale model with efficient time stepping

We present a numerical model of soil erosion at the basin scale that allows one to describe surface run-off without a priori identifying drainage zones, river beds and other water bodies. The model is based on robust semi-implicit numerical techniques and guarantees exact mass conservation and positivity of the surface and subsurface water layers. Furthermore, the method is equipped with a geostatistical preprocessor that can perform downscaling of data retrieved from digital databases at coarser resolutions. Numerical experiments on both idealized and realistic configurations demonstrate the effectiveness of the proposed method in reproducing transient high resolution features at a reduced computational cost and to reproduce correctly the main hydrographic features of the considered catchment. Furthermore, probabilistic forecasts can be carried out based on soil data maps automatically generated by the geostatistical preprocessor that are distributed among the available MPI ranks to carry out simulations independently thus reducing the total cost of the simulation. The numerical experiments show the ability of the model to provide robust estimates of water levels, discharge and of the order of magnitude of the total sediment yield.