Centroids in second-order conservative remapping schemes on spherical coordinates

Abstract. The transformation of data from one grid system to another is common in climate studies. Among the many schemes used for such transformations is second-order conservative remapping. In particular, a second-order conservative remapping scheme to work on the general grids of a sphere, either directly or indirectly, has served as an important base in a variety of studies.

In this study, the author describes a fundamental problem in the derivation of the method proposed by a pioneer study relating to the treatment of the centroid used as a reference point for the second-order terms in the longitudinal direction. In principle, use of the original formulation has a potential to cause damage to the entire remapping result. However, a preprocessing procedure on the longitude coordinate suggested in the algorithm for other objectives tends to minimize or even erase the error as a side effect in many, if not most, typical applications. In this study, two alternative formulations are proposed and tested and are shown to work in a simple application.