Three-dimensional plume source reconstruction using minimum relative entropy inversion

Abstract

In this paper we extend the minimum relative entropy (MRE) method to recover the source-release history of a three dimensional plume. This extension is carried out in an analytic framework, and in order to qualify as a linear inverse problem the various transport parameters such as dispersivity and the like are considered to be known. In addition, the groundwater flow system is assumed to be steady and uniform. The contributions of this paper include an explanation how MRE can be used as a measure of resolution in linear inversion, a reporting of a three dimensional analytic solution for mass transport in a steady one dimensional velocity field for a variable in-time source loading, an estimation the source-release history for synthetically generated data sets, and an application of the methodology to a case-study problem at the Gloucester Landfill in Ontario, Canada. We found that the relative entropy measure is useful in indicating the reduction in uncertainty between the posterior and prior pdfs as a result of the new information provided by the physical constraints and data. Using the individual model-parameter relative entropies as a measure of resolution, one can make quantitative judgments about which part of the history is likely to be well resolved. Comparing inversion results for synthetic aquifers with one well and two sample points with only one sample point indicates that temporal data at several wells allows for a superior reconstruction of the release history. We investigate the potential benefits of locating sample points on an spatial rather than temporal basis. Results show that early part of the release history is poorly recovered. Comparing these results with one well and two sample points indicates that temporal data at a few wells allows for a better reconstruction of the release history. An incomplete time record is also investigated. Results show that early part of the release history prior to the commencement of measurements is poorly recovered. It is essential that as much as possible of the time histories of plumes be monitored if the entire release history is to be determined. The MRE approach is used to reconstruct the release history of a 1,4-dioxane plume measured at the Gloucester Landfill in Ontario, Canada. The recovered release history is fairly narrow and generally flat in shape, although two peaks are evident. Neither peak is particularly well defined, judging from the resolution curve and analysis of the confidence ranges. One of the peaks coincides with year 1979, close to the year 1978 in which a large spill was noted. However, a considerable variation of possible source releases is possible.