Contaminant release history identification in 2-D heterogeneous aquifers through a minimum relative entropy approach

The minimum relative entropy (MRE) method has been applied in a wide variety of fields since it was first introduced. Woodbury and Ulrych (Water Resour Res 29(8): 2847–2860, 1993, Water Resour Res 32(9): 2671–2681, 1996) adopted and improved this method to solve linear inverse problems in aquifers. In this work, the MRE method was improved to detect the source release history in 2-D aquifer characterized by a non-uniform flow-field. The approach was tested on two cases: a 2-D homogeneous conductivity field and a heterogeneous one (the hydraulic conductivity presents three orders of magnitude in terms of variability). In the latter case the transfer function cannot be described with an analytical formulation, thus, the transfer functions were estimated by means of a numerical procedure. In order to analyze the method performance in different conditions, two datasets have been used: observations collected at the same time at 20 different monitoring points, and observations collected at 2 monitoring points at several times. The observed data have been processed with and without a random error and the Boxcar and Gaussian probability distribution functions were considered as a priori information. The agreement between the true and the estimated data has been evaluated through the calculation of the normalized Root Mean Square error. The approach was able to recover the release history even in the most difficult case.