Conservative regridding when grid cell edges are unknown - Case of SCRIP
Résumé
Nowadays, climate models rely on couplers. Each complete climate model is broken into different sub-models (oceanic, atmospheric,...), each one working on a different grid. The coupler brings these models together and interpolates the physical quantities between the grids. However, neither the coupler nor sometimes the sub-models themselves know precisely the grid cell edges. They only 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 to compute the grid cell intersections. For first-order schemes, the most straightforward way to interpolate scalar quantities is to directly use these approximate grid cell intersections, that don' take the true grid cell areas into account. It is the method used in the "conservative" regridding option implemented in the widely used spherical interpolation package SCRIP. We show that is doesn't preserve integrals in the general case, whether the coupler using the SCRIP-generated weights transmits directly the intensive quantity, or its extensive counterpart (that is the same quantity multiplied by the true area of the individual source grid cell). We show how to modify the interpolation scheme to preserve integrals in the general case.