A 2D-SWEs framework for efficient catchment-scale simulations: Hydrodynamic scaling properties of river networks and implications for non-uniform grids generation

The application of two-dimensional shallow-water equations models (2D-SWEs) for the description of hydrodynamic-based surface runoff computations is becoming a reference approach in rainfall-runoff simulations at the catchment scale. Due to their ability in generation of flow patterns throughout the basin, they can be used not only as an advanced method for flood mapping studies and hazard assessment but also as an innovative tool for the analysis of river drainage networks, opening new perspectives for several environmental processes. In particular, in this work we put the river networks in a 2D-SWEs framework, meaning that the traditional tree-like fluvial structure, represented by a skeleton composed of a set of lines, is replaced by a collection of points discretizing the 2-D geometry of the river structure itself, for which the values of the hydrodynamic values are provided by the numerical simulations. This approach is used here to derive a new scaling property that relates the specific discharge threshold, used to identify the river network cells, to the total areas of the network cells themselves. The hydrodynamic and geomorphological interpretation of this power law function and the influence of grid resolution, on some relevant parameters of this curve, have inspired the development of a heuristic procedure for non-uniform grid generation, able to detect the most hydrodynamically active areas of the basins for which the grid refinement process makes sense. Moreover, information related to how much grid refinement is needed is provided as well. The performances of this procedure are very promising in terms of accuracy of simulated discharges, hydrodynamic behaviour of the river network and flooded areas, reducing significantly the computational times in respect to the use of fine uniform grids.