Predicting spatio-temporal random fields: Some computational aspects

Modeling of spatio-temporal processes is critical in many fields such as environmental sciences, meteorology, hydrology and reservoir engineering. Nowadays spatio-temporal analysis cannot be adequately faced without considering important issues, such as: (a) modeling the spatio-temporal random field from which data might be reasonably derived, (b) choosing suitable covariance models which describe the spatio-temporal correlation of the variables of interest, (c) using adequate software packages which tackle different inferential problems. In this paper, the above aspects are properly analyzed. In particular, three different space–time random field decomposition choices are considered and the flexibility of using the generalized product–sum model is highlighted. A customized GSLib routine for kriging in space-time is proposed. This Fortran routine, named “K2ST”, is based on the use of the generalized product -sum model, with nested structures, and appropriate space-time search neighborhoods. An application to NO2 pollutant in an urban area is presented. In order to compare kriging results associated with three hypotheses of space–time random field decomposition, correlation coefficients and standardized errors between true values and predicted ones are computed. Moreover, nonparametric tests are applied to check the significance of the difference among the three approaches.

► Different space–time random field decomposition choices are considered.
► The new routine K2ST for space–time kriging is proposed.
► A modified GSLib routine for kriging is based on the product–sum models.
► Nested structures and appropriate space–time search neighborhoods can be used.
► The generalized product–sum model is fitted and used for NO2 predictions.