An Iterative Cokriging‐Like Technique for Ground‐Water Flow Modeling

The importance of field heterogeneities in ground‐water pollution problems has been widely recognized during the last few decades. To address the impact of field heterogeneities on ground‐water flow and solute transport, many different stochastic methods have been developed. Among all these stochastic methods kriging is the most popular one used by many practitioners to interpolate and extrapolate measured transmissivity data. However, hydraulic head measurements are generally more abundant than transmissivity data. Therefore, the cokriging technique which utilizes both the head and transmissivity measurements to estimate transmissivity and/or hydraulic head distributions has also received much attention in recent years. Classical cokriging relies on a linear predictor approach and uses covariance and cross covariance functions derived from a first‐order approximation. Consequently, it often results in head and transmissivity fields that can produce unacceptable velocity distributions. In this paper, we develop an iterative method which combines classical cokriging and a numerical flow model to obtain optimum estimates of transmissivity and head distributions and to alleviate the limitations of classical cokriging. Through several numerical examples, we demonstrate that this method is superior to the classical cokriging method in terms of producing mass conservative velocity fields. In addition, results of the study also indicate that hydraulic head measurements can improve for our prediction of ground‐water flow directions and paths in aquifers significantly.