Intrinsic Random Function Kriging on the Sphere

Abstract Intrinsic random functions (IRFs) can be used to model spatial processes on the sphere. To perform kriging using IRFs, one needs the knowledge of the IRF order (i.e., the degree of non-homogeneity) and its associate generalized covariance function, which are challenging in Euclidean spaces and hinder its practice. On the sphere, Huang et al. [1] showed that IRFs behave differently from their counterparts in Euclidean spaces and can be characterized by their lower-frequency truncated processes. Based on this, we develop procedures to estimate both the IRF order and the associated parametric generalized covariance function. Then, a truly IRF-based universal kriging can be implemented in practice on the sphere. We demonstrate our methods through simulations, and the numerical results show that IRF kriging outperforms ordinary kriging. Additionally, we apply our procedure to a global temperature dataset to determine the IRF order.