A method of enhancing a geologic model of a subsurface region is provided. A bed topography of the subsurface region is obtained. The bed topography is defined by a plurality of cells with an elevation associated with each cell center. The bed topography is represented as a cell-centered piecewise constant representation based on the elevations associated with the cells. The bed topography is reconstructed to produce a spatially continuous surface. Flux and gravitational force-related source terms are calculated based on the reconstructed bed topography. Fluxes are calculated between at least two of the cells. Fluid flow, deposition of sediments onto the bed, and/or erosion of sediments from the bed are predicted using the fluxes and gravitational force-related source terms. The predictions are inputted into the geologic model to predict characteristics of the subsurface region, and the predicted characteristics are outputted.