Contaminant source reconstruction by empirical Bayes and Akaike's Bayesian Information Criterion

The objective of the paper is to present an empirical Bayesian method combined with Akaike's Bayesian Information Criterion (ABIC) to estimate the contaminant release history of a source in groundwater starting from few concentration measurements in space and/or in time. From the Bayesian point of view, the ABIC considers prior information on the unknown function, such as the prior distribution (assumed Gaussian) and the covariance function. The unknown statistical quantities, such as the noise variance and the covariance function parameters, are computed through the process; moreover the method quantifies also the estimation error through the confidence intervals. The methodology was successfully tested on three test cases: the classic Skaggs and Kabala release function, three sharp releases (both cases regard the transport in a one-dimensional homogenous medium) and data collected from laboratory equipment that consists of a two-dimensional homogeneous unconfined aquifer. The performances of the method were tested with two different covariance functions (Gaussian and exponential) and also with large measurement error. The obtained results were discussed and compared to the geostatistical approach of Kitanidis (1995).