Representation of topography by porous barriers and objective interpolation of topographic data

We present a porous medium approach to representing topography, and a new algorithm for the objective interpolation of topography, for use in ocean circulation models of fixed resolution. The representation and algorithm makes use of two concepts; impermeable thin walls and porous barriers. Impermeable thin walls allow the representation of knife-edge sub-grid-scale barriers that block lateral flow between model grid cells. Porous barriers permit the sub-grid scale geometry to modulate lateral transport as a function of elevation. We find that the porous representation and the resulting interpolated topography retains key features, such as overflow sill depths, without compromising other dynamically relevant aspects, such as mean ocean depth for a cell. The accurate representation of the ocean depth is illustrated in a simple model of a tsunami that has a cross-basin travel time very much less dependent on horizontal resolution than when using conventional topographic interpolation and representation.