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 first introduced in 1987 and extended in 1999 to work on the general grids of a sphere has, 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 may cause damage to the entire remapping result. However, a method's native implementation software includes a preprocessing procedure that tends to minimize or even erase the error as a side effect in many, if not most, typical applications. In this study, three alternative formulations are proposed and tested and are shown to work in a simple application.