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Nowadays, climate models rely on couplers. Each complete climate model isbroken into different sub-models (oceanic, atmospheric,...), each one workingon a different grid. The coupler brings these models together and interpolatesthe physical quantities between the grids. However, neither the coupler norsometimes the sub-models themselves know precisely the grid cell edges. Theyonly know the grid cell corners (vertices) and the true grid cell areas. Thus,the coupler has to make assumptions about the grid cell edges in order tocompute the grid cell intersections. For first-order schemes, the moststraightforward way to interpolate scalar quantities is to directly use theseapproximate grid cell intersections, that don' take the true grid cell areasinto account. It is the method used in the "conservative" regridding optionimplemented in the widely used spherical interpolation package SCRIP. We showthat is doesn't preserve integrals in the general case, whether the couplerusing the SCRIP-generated weights transmits directly the intensive quantity, orits extensive counterpart (that is the same quantity multiplied by the truearea of the individual source grid cell). We show how to modify theinterpolation scheme to preserve integrals in the general case.

Conservative Regridding When Grid Cell Edges Are Unknown -- Case of SCRIP