Articles | Volume 10, issue 1
Development and technical paper
30 Jan 2017
Development and technical paper |  | 30 Jan 2017

Conservative interpolation between general spherical meshes

Evaggelos Kritsikis, Matthias Aechtner, Yann Meurdesoif, and Thomas Dubos

Abstract. 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 supermesh, 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.

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 O(NlogN) 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.

Short summary
This paper describes conservative interpolation on the sphere. A function is computed on one mesh from its values on another mesh so that the total mass is preserved, which is vital for climate modeling, and for second-order accuracy. This is done through a common refinement of the meshes, built in quasilinear time by tree sorting the mesh cells. It can be built into climate models for flexible I/O or coupling. Examples of commonly used meshes are given.