Spatiotemporal analysis of spring water ion processes derived from measurements at the Dyle basin in Belgium

This paper deals with the study of natural variations and mapping of spatiotemporal spring water ion processes by means of stochastic analysis. Natural variations in space/time are the result of the combined effects of the physical, chemical, and topographical laws as well as the uncertainties and heterogeneities underlying the phenomenon under consideration. Maps of the space/time distribution of natural processes constitute a fundamental element of physical explanation and prediction, and are extremely valuable tools for numerous applications in environmental sciences including, e.g., water quality management, solute transport characterization, and human exposure to pollutants and hazardous substances. The spatiotemporal random field theory is applied to spring water solute contents (calcium, nitrate, and chloride ions) which are irregularly distributed in space/time over the Dyle river catchment area in Belgium. The integration of the spatial and temporal components in a space/time continuum has considerable advantages as regards the analytical investigation of solute content processes. It provides a rigorous characterization of the ion concentration data set, which exhibits a spatially nonhomogeneous and temporally nonstationary variability, in general. The physics of the situation can be expressed in terms of differential equations that emphasize the importance of space/time continuity. The characterization of the latter involves certain random field parameters. A rich class of covariance models is determined from the properties of these parameters that includes, as special cases, separable generalized covariance models. In practice, the results of the space/time analysis may depend on the scale under consideration and, thus, a scale level must be specified that reveals important features of the spatiotemporal solute content variability. The analysis leads to maps of continuity orders and covariance coefficients that provide information about space/time solute content correlations and trends. Solute content estimations and the associated estimation errors are calculated at unmeasured locations/instants over the Dyle region using a space/time estimation algorithm. The analysis is general and can be applied to various data sets from environmental, hydrogeologic, atmospheric, and meteorologic sciences.