Abstract

The modeling of real-valued random fields indexed by spherical coordinates arises in different disciplines of the natural sciences, especially in environmental, atmospheric and earth sciences. However, there is currently a lack of parametric models allowing a flexible representation of the spatial correlation structure of multivariate data located on a spherical surface. To bridge this gap, we provide analytical expressions of twenty-two parametric families of isotropic p-variate covariance kernels on the d-dimensional sphere, defined for any integers p > 0 and d > 1, together with their respective spectral representations (Schoenberg matrices) and sufficient validity conditions on the covariance parameters. These families include multiquadric, sine power, exponential, Bessel and hypergeometric kernels, and provide covariances exhibiting varied shapes, short-scale and large-scale behaviors. Our construction relies on the so-called multivariate parametric adaptation approach, where a matrix-valued covariance kernel is defined on the basis of a scalar covariance to which matrix-valued parameters are applied, coupled with matrix manipulations.