Spatio-temporal kriging based on the product-sum model: some computational aspects

Modeling of spatio-temporal processes is critical in many fields such as environmental sciences, meteorology, hydrology and reservoir engineering. The variogram is an important correlation measure in geostatistics and a useful tool for spatial or spatio-temporal modeling. Although many space-time covariance/variogram models are available, in practice,the generalized product-sum model is most widely used. The theoretical aspects of the generalized product-sum variogram model have been presented in other papers. However, the dissemination of software that brings the generalized product-sum variogram model to a wider group of users is undoubtedly desirable. In this paper, we describe an R routine for “spatio-temporal kriging” with hole effects, and appropriate space-time search neighborhoods. An application to ozone pollutants in an area of five counties of the US is presented. The experimental results show that the spatio-temporal random field provides more information than the purely spatial random field, because the accuracy of interpolation has been improved.