Résumé
We present a method for the downscaling of low-resolution flow simulations in urban areas. The purpose is to reconstruct some flow variables over fine grids (cell size 1 m or less) from upscaled flow simulations over very coarse grids (cell size 10–50 m). The flow variables under consideration are the water depth and the norm of the unit discharge. These are two widely accepted indicators in flood hazard assessment. The method is assessed in the framework of perfect upscaling, whereby the coarse grid flow variables are exact averages of the fine grid simulation results. A simple reconstruction approach is used: the flow variables are transformed using a power law. The transform of the flow variable over a given cell in the high-resolution grid is computed as a linear combination of the transforms of the flow variables over the coarse resolution grid. The degrees of freedom in the method are the power of the transform, the number of coarse grid cells (called the neighborhood size) and the linear combination coefficients. The method is fitted by minimizing the RMSE between the exact (known) high resolution solution and the reconstructed one. The results show that (i) reconstructing the water depth is easier than reconstructing the unit discharge, (ii) flows involving shocks yield larger reconstruction errors that those involving rarefaction waves, (iii) the method is better when trained for a specific wave propagation direction.