Boosted robustness of semi-implicit subgrid methods for shallow water flash floods in hills

Abstract

The widespread availability of high-resolution Digital Elevation Models (DEM), has led to the development of subgrid numerical modeling techniques, based on Shallow Water Equations (SWE). Detailed DEM data is clustered as much as possible within a coarse grid cell that is preferably much larger than a raster pixel. This has considerable advantages for model efficiency, in particular for flood mapping. But overland flow on hills, key to rainfall-runoff, may have several problems with accuracy and stability. These issues arise especially during downhill flooding and with surface runoff on inclined planes. It is the focus of this paper. As robust solutions we propose: (1) a special volume correction equation with intrinsic wetting and drying but without stability constraints and, (2) a simple thin layer calculation that is accurate for runoff on coarse grids with sloping subgrids. Especially the combination (1) and (2) makes the subgrid method highly efficient on slopes, as is demonstrated by a few examples.