Abstract

Multivariate random fields allow to simultaneously model multiple spatially indexed variables, playing a fundamental role in geophysical, environmental, and climate disciplines. This paper introduces the concept of cross-dimple for bivariate isotropic random fields on spheres and proposes an approach to build parametric models that possess this attribute. Our findings are based on the spectral representation of the matrix-valued covariance function. We show that our construction is compatible with both the negative binomial and circular-Matérn bivariate families of covariance functions. We illustrate through simulation experiments that the models proposed in this work allow to achieve improvements in terms of predictive performance when a dimple-like intrinsic structure is present.