Abstract
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.
Highlights
Despite the simplicity and regularity of a spherical surface, there is no single ideal way to mesh it
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 be deduced efficiently
Dynamic adaptivity is not a current practice in ocean– atmosphere modelling, there is a growing body of research to this end, and dynamic adaptivity may mature in the future
Summary
Despite the simplicity and regularity of a spherical surface, there is no single ideal way to mesh it. Most recently developed methods use more flexible meshes like triangulations of the sphere and their Voronoi dual or quadrangular meshes like the cubed sphere. Such meshes avoid the polar singularity inherent to the latitude– longitude system (Williamson, 2007). Different physical components like atmosphere, land, ice and ocean typically use distinct meshes. As they are coupled together, interpolation between the various meshes is required. When interpolating fluxes between physical components coupled together, similar conservation constraints should be enforced. Assuming that the supermesh is known, formulae for second-order conservative interpolation are derived in Sect.
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