Geometric shallow water and diffusive wave approximation for basin scale coupled surface-subsurface hydrological simulations
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Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as mountain landscapes. In this work, we derive an intrinsic formulation for the diffusive wave approximation of the shallow water equations, defined on a local reference frame anchored on the bottom surface. We then derive a numerical discretization by means of a Galerkin finite element scheme intrinsically defined on the bottom surface. We aim to analyze the differences between the diffusive wave approximation and the shallow water model, both defined within a geometrically intrinsic framework and with a focus at the basin scale. Basin scale simulations on synthetic test cases show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures.