Spatio-Spectral Assessment of Some Isotropic Polynomial Covariance Functions on the Sphere

Abstract

In gravity field modeling, covariance functions are mainly associated with least squares collocation. Prior to the implementation of least squares collocation, the characteristics of the selected analytical covariance function need to be well understood. In this contribution, we study four polynomial covariance functions, i.e., the spherical, Askey, C2-Wendland and C4-Wendland models. All of them are defined on the sphere and correspond to isotropic, positive definite and compactly supported functions. We examine them in the spatial and spectral domains, and assess their characteristics, such as the correlation length, the curvature parameter, the spectral maximum and the spectral decay rate. We also provide analytical expressions and numerical estimates for these parameters.