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We provide a novel approach to model space-time random fields where thetemporal argument is decomposed into two parts. The former captures the linearargument, which is related, for instance, to the annual evolution of the field.The latter is instead a circular variable describing, for instance, monthlyobservations. The basic intuition behind this construction is to consider arandom field defined over space (a compact set of the $d$-dimensional Euclideanspace) across time, which is considered as the product space $\mathbb{R} \times\mathbb{S}^1$, with $\mathbb{S}^1$ being the unit circle. Under such framework,we derive new parametric families of covariance functions. In particular, wefocus on two classes of parametric families. The former being parenthetical tothe Gneiting class of covariance functions. The latter is instead obtained byproposing a new Lagrangian framework for the space-time domain considered inthe manuscript. Our findings are illustrated through a real dataset of surfaceair temperatures. We show that the incorporation of both temporal variables canproduce significant improvements in the predictive performances of the model.We also discuss the extension of this approach for fields defined spatially ona sphere, which allows to model space-time phenomena over large portions ofplanet Earth.

Space-Time Geostatistical Models with both Linear and Seasonal Structures in the Temporal Components