A spectral analysis approach for the a priori generation of computational grids in the 2-D hydrodynamic-based runoff simulations at a basin scale

The increasing availability of high-resolution terrain data fostered the development of two-dimensional hydrodynamic-based surface runoff models at basin scale, for flood hazard assessment and mapping purposes. The generation of the computational domain is one of the most important preliminary steps for practical applications of this kind of modeling. Several studies can be found in the technical literature showing the influence exerted by the computational grid type used on the results in terms of water depth, flow velocity and discharge. Several approaches were proposed for the mesh generation even though, in practice, it is subject to the modeller choice and experience. In any case, the reason why a specific mesh is used is rarely discussed and its impact on the model results in terms of outflow hydrographs, runoff volumes and flooded areas extent is seldom analysed. In this work a rigorous approach for an a priori design of a computational grid is proposed. The a priori term suggests that the proposed procedure aims at generating a computational mesh, close to the optimal one, in a time-saving process which is not based on trial meshes and trial simulations. Namely, the process is based on the application of the two-dimensional Fourier analysis to a high-resolution digital elevation model in order to compute the power spectrum and finally to identify the significant waves lengths and the characteristic scales. The latter ones are located in the catchment and used for the generation of a computational grid characterized by different elements size. The simulations of surface runoff at a basin scale have shown that the application of the proposed method for the a priori construction of the grid leads to the generation of a computational mesh which reduces the calculation time by approximately 87%, if compared to a fine grid taken as reference, with negligible errors on outflow hydrographs and flooded areas extent.