Multivariate modeling for environmental spatio-temporal data

An environmental data set often concerns different correlated variables measured at some locations of the study area and for several time points. In this case, the data set presents a multivariate spatio-temporal structure; therefore appropriate modeling techniques which take into account the spatio-temporal relationships among the variables are needed. The space-time LCM (ST-LCM) based on admissible spatiotemporal models may successfully capture the spatio-temporal behaviour of the phenomena under study and can be used for prediction purposes. After a brief presentation of the spatio-temporal multivariate geostatistical framework, a case study is proposed and the following aspects are considered: 1. estimating the spatio-temporal interrelationships among the variables of interest and, consequently, identifying the basic hidden components in space and in time which characterize the same variables; the simultaneous diagonalization-based method is applied to several matrix variograms in order to detect the basic independent components which contribute to define the multivariate correlation structure of the observed variables (De Iaco et al., 2013); 2. modeling the spatio-temporal correlation among the variables under study by using the ST-LCM (De Iaco et al., 2005); in this step, the basic models at the selected scales of spatio-temporal variability have been properly chosen after the inspection of the non separability index computed for the basic components (De Iaco and Posa, 2013); 3. spatio-temporal cokriging performed by a modified version of GSLib routine to obtain prediction, over the study area, for the variable of interest. Note that the ST-LCM used in this paper is based on mixture models, i.e. the ST-LCM has been fitted by selecting different classes of spatio-temporal correlation measures, related to different scales of spatiotemporal variability.