Conservative interpolation between general spherical meshes

An efficient, local, explicit, second-order, conservative interpolation algorithm between spherical meshes is presented. The cells composing the source and target meshes may be either spherical polygons or latitude–longitude quadrilaterals. Second-order accuracy is obtained by piece-wise linear finite-volume reconstruction over the source mesh. Global conservation is achieved through the introduction of a <q>supermesh</q>, whose cells are all possible intersections of source and target cells. Areas and intersections are computed exactly to yield a geometrically exact method. The main efficiency bottleneck caused by the construction of the supermesh is overcome by adopting tree-based data structures and algorithms, from which the mesh connectivity can also be deduced efficiently.<br><br>The theoretical second-order accuracy is verified using a smooth test function and pairs of meshes commonly used for atmospheric modelling. Experiments confirm that the most expensive operations, especially the supermesh construction, have <i>O</i>(<i>N</i><i>log</i><i>N</i>) computational cost. The method presented is meant to be incorporated in pre- or post-processing atmospheric modelling pipelines, or directly into models for flexible input/output. It could also serve as a basis for conservative coupling between model components, e.g., atmosphere and ocean