Cokriging Transmissivity, Head and Trajectory Data for Transmissivity and Solute Path Estimation

In practical situations concerning aquifers, time and/or economic restraints often make it impossible to construct numerical models, and in these cases simple methodologies could be useful, at least for feasibility studies. In this context, the present manuscript deals with the use of a straightforward cokriging method to use data acquired from a monitoring network (transmissivity, piezometric head and trajectory data) in order to obtain useful information about the characteristics of the aquifer. Two issues have been addressed: estimation of the solute path and estimation of the transmissivity. This manuscript, compared with previous works that have applied cokriging, considers that the solute transit data originate from a source of unknown intensity and from an unknown location. The proposed cokriging systems are implemented through already developed covariance and cross-covariance functions, considering a first-order approximation in the log-transmissivity variance. For this reason, numerical Monte Carlo experiments have been performed to test the accuracy of the results of the proposed cokriging procedures in both weakly (σY2=0.16) and mildly (σY2=2) heterogeneous transmissivity aquifers. Since a prerequisite of cokriging is a linear relationship among the involved quantities, more accurate results can be expected in weakly heterogeneous transmissivity fields, where the trajectory, transmissivity and hydraulic head data relations are almost linear. Comparing the numerical results with the analytical solutions, it in fact emerges that cokriging can be very useful for the estimation of a solute path and transmissivity when a limited set of data is available for weakly heterogeneous aquifers.