A Multivariate Approach for Modeling Spatio‐Temporal Agrometeorological Variables

One of the main issues facing agrometeorological studies involves measuring and modeling the evolution of different environmental variables over time; this often requires a dense monitoring network. Spatio‐temporal geostatistics has the potential to provide techniques and tools to estimate the spatio‐temporal multiple covariance function and define an appropriate multivariate correlation function capable of reliable predictions. This paper presents a spatio‐temporal multivariate geostatistical modeling approach based on the joint diagonalization of the empirical covariance matrix evaluated at different spatio‐temporal lags. The possibility to consider a reduced number of uncorrelated variables (lower than the number of observed variables) and separately model the spatio‐temporal evolution of these uncorrelated components represents a substantial simplification for multivariate modeling. A space–time linear coregionalization model (ST‐LCM) with appropriate parametric models for the latent components was fitted to the matrix‐valued covariance function estimated for five relevant agrometeorological variables, including evapotranspiration, minimum and maximum humidity, maximum temperature, and precipitation. The analyses highlight how to identify space–time components and choose the corresponding model by evaluating some characteristics of these components, such as symmetry, separability, and type of non‐separability. The predictive results of this multivariate study will be of interest for agriculture, in particular for addressing drought emergencies.