Contaminant release history reconstruction through empirical Bayes and Akaike's Bayesian Information Criterion

Abstract:

Contaminant release history identification has received considerable attention in the literature over the past several decades. In our review of this subject suggests that improvements are needed in terms of a reliable procedure, one that is easy to implement, with only few hyperparameters to estimate, and is able to evaluate confidence intervals. The purpose of this work is to propose an empirical Bayesian approach combined with the Akaike’s Bayesian Information Criterion (ABIC) to estimate the contaminant release history starting from concentration observations in time or space. 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 also quantifies the estimation error through confidence intervals.

We successfully test the method out on three test cases: the classic Skaggs and Kabala (1994) source, a “midnight dump” example that consists of three delta-like sources and lastly a laboratory dataset, consisting of two measurement points spatially but with synoptic observations. This experiment reproduces the response of a 2-D unconfined aquifer. The performance of the inverse method was tested with two different covariance functions (Gaussian and exponential) and also with large measurement error. Results show an excellent recovery of all sources used in the examples. Lastly, the obtained results were discussed and compared to the geostatistical approach of Kitanidis (1995).