Basis-spline interpolation on the sphere: Applications to semi-Lagrangian advection

Abstract

An algorithm for the interpolation of data on a colatitude-longitude grid is presented. The method employs periodic tensor product cubic basis splines (B splines) and requires no special assumptions about function derivatives at the poles. The algorithm provides significantly more accurate results than aperiodic interpolants, with only a small increase in the total number of floating point operations. The method is implemented in a semi-Lagrangian advection algorithm and a comparison is made to two other methods (spectral finite difference and cubic Lagrange semi-Lagrangian) for the advecting cone problem on a spherical shell. The B-spline solution provides the best results for shape-preservation of the original field The cubic Lagrange solution has relatively poor mass conservation but better shape preservation than the spectral finite difference.