Large-Time Spatial Covariance of Concentration of Conservative Solute and Application to the Cape Cod Tracer Test

Most studies on conservative transport in stationary velocity fields have focused on the description of the concentration mean. In this work, we use a Lagrangian methodology to develop an analytical expression for the spatial covariance of the concentration, based on the central limit theorem and applicable to large times after injection. We use this expression to analyze the conservative tracer test data from the natural gradient experiment conducted at Cape Cod in 1985–1988, in which bromide was quickly injected into the aquifer and the concentration was measured at many locations at certain points in time. The parameters that determine the concentration mean had been estimated in previous studies. Here, the two-particle covariance matrix, needed to describe the concentration covariance function, is derived from the measurements through a maximum likelihood method. Then, the data are interpolated on a grid using simple kriging, and contour maps of the concentration estimates are plotted. The results of cross-validation indicate that the model is consistent with the field measurements and the kriging estimates appear realistic.