An alternative bilinear interpolation method between spherical grids

Abstract

In geoscientific studies, conventional bilinear interpolation has been widely used for remapping between logically rectangular grids on the surface of a sphere. Recently, various spherical grid systems including geodesic grids have been suggested to tackle the singularity problem caused by the traditional latitude-longitude grid. We suggest an alternative to pre-existing bilinear interpolation methods for remapping between any spherical grids, even for randomly distributed points on a sphere. This method supports any geometrical configuration of four source points neighboring a target point for interpolation, and provides remapping accuracy equivalent to the conventional bilinear method. In addition, for efficient search of neighboring source points, we use the linked-cell mapping method with a cubed-sphere as a reference frame. As a result, the computational cost is proportional to NlogN instead of N2 (N being the number of grid points), even for the remapping of randomly distributed points on a sphere.