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The motivation of this paper is to deepen the theoretical foundations of the interpretation of Synthetic Aperature Radar (SAR) imagery of the coastal seas. The approach uses large-eddy simulations (LES) to study the link between bottom topography and its expression on a free surface. In particular, the focus is on situations where the flow cannot be well approximated using simple conservation of mass arguments. The full Navier-Stokes equations are solved for laboratory-scale domains. Free surface patterns are presented for three configurations: neutral flow over wavy topography, stratified flow over wavy topography, and neutral flow over three-dimensional sinusoidal topography. The extent to which each configuration produces unique and identifiable surface patterns is explored. The focus is on the fluid mechanics near the surface, for example, attachment and persistence of vortical structures, upwelling, and zones of convergence. Neutral flow over wavy topography creates a large number of powerful upwellings on the free surface. These upwellings appear to overwhelm the coherency of pre-existing vortices and vortex pairs. Consequently, the persistence of organized vortical motions on the free surface is reduced. In contrast, in stably stratified flow over a wavy boundary, upwellings are weakened, and more vortex pairs are observed. The surface signature of three-dimensional underwater topography shows elongated streaks in the streamwise direction. The above features allow these underwater topographies (at the depths presented) to be uniquely differentiated based solely on their surface signatures.