Space–time correlation models and contaminant plumes

A contaminant plume might be described by a function defined in space–time. Spatial integrals or time derivatives of this function as well as time derivatives of spatial integrals will quantify characteristics such as the total volume of the plume, the total concentration of the contaminant in the plume, rates of change of the volume, and rates of change of concentration. The plume function usually cannot be derived in analytic form but instead must be estimated or approximated. The dual form of the kriging estimator, which is equivalent to the use of radial basis functions, provides a tool for modeling this function in analytic form. The extension of the kriging estimator, in its usual form or in its dual form, to space–time poses no problems since the estimator and the equations are essentially dimension free. The difficulty is an adequate choice of space–time variograms or covariances. The product–sum and integrated product–sum models provide an extensive array of valid models and also lead to a simple process for fitting the models by the use of marginal variograms. Examples are given and an application to air pollution data from the Milan District (Italy) illustrates the method. Copyright # 2002 John Wiley & Sons, Ltd. key words: dual kriging; space–time variograms; product–sum models; marginal variograms; radial basis functions 1