Stochastic analysis of spatiotemporal solute content measurements using a regression model

Abstract

A regression model is used to study spatiotemporal distributions of solute content ion concentration data (calcium, chloride and nitrate), which provide important water contamination indicators. The model consists of three random and one deterministic components. The random space/time component is assumed to be homogeneous/stationary and to have a separable covariance. The purely spatial and the purely temporal random components are assumed to have homogenous and stationary increments, respectively. The deterministic component represents the space/time mean function. Inferences of the random components involve maximum likelihood and semi-parametric methods under some restrictions on the data configuration. Computational advantages and modelling limitations of the assumptions underlying the regression model are discussed. The regression model leads to simplifications in the space/time kriging and cokriging systems used to obtain space/time estimates at unobservable locations/instants. The application of the regression model in the study of the solute content ions was done at a global scale that covers the entire region of interest. The variability analysis focuses on the calculation of the spatial direct and cross-variograms and the evaluation of correlations between the three solute content ions. The space/time kriging system is developed in terms of the space direct and cross-variograms, and allows the separate estimation of the regression model components. Maps of these components are then obtained for each one of the three ions. Using the estimates of the purely spatial component, spatial dependencies between the ions are studied. Physical causes and consequences of the space/time variability are discussed, and comparisons are made with previous analyses of the solute content dataset.