The shallow water equation (SWE) model, while computationally efficient, has limitations in capturing complex flow phenomena accurately. One major limitation is its inability to account for dispersive effects, which can lead to inaccuracies in wave propagation and reflection. Additionally, the SWE assumes hydrostatic pressure distribution and neglects vertical velocity variations, which may be significant in certain scenarios.
To improve the approach, a more sophisticated flow model, such as the Navier-Stokes equations or a higher-order shallow water model, could be used. These models would better capture the dynamics of the flow, including turbulence, viscosity, and non-hydrostatic effects. By incorporating a more detailed flow model, the reconstruction algorithm would be able to account for a wider range of physical processes and provide more accurate bathymetry reconstructions.