| Popis: |
In environmental sciences, it is common to collect and analyze spatio-temporal multivariate data concerning several variables which are measured in time over a spatial domain. The spatio-temporal data are usually sparce in space, due to the high cost of the equipment, and temporal dense since the required variables are regularly sampled in time.In the literature different methods have been proposed for the analysis of such spatio-temporal data which exhibit a correlation in space and time as well as in-between variables. Among them it is worth recalling the generalization of Blind Source Separation technique for multivariate space-time random field (stBSS) and the space-time linear coregionalization model (ST-LCM). These methods are useful to simplify the spatio-temporal multivariate analysis since by a linear transformation of the original observations only the independent components which exhibit a spatio-temporal correlation are retained (lower than the number of observed variables) and modelled.In this paper a multivariate study regarding seven environmental variables (evapotranspiration level, minimum and maximum temperature, minimum and maximum humidity, wind speed and precipitation) measured between 2000 and 2022 in Veneto region (Italy) will be proposed. Both the stBSS and the joint diagonalization of the empirical covariance matrix approach will be used to identify the hidden components, and properly chosen spatio-temporal models will be fitted to the latent components. Note that for the first approach a BSS model for the multivariate random field will be assumed, whereas for second one a space-time linear coregionalization model (ST-LCM) for the independent components will be fitted to the matrix-valued covariance function estimated for seven relevant environmental variables.Finally, the fitted models have been used to predict evapotranspiration levels and a comparison of the values obtained by using the two different techniques will be provided. |
