Identifying sources of a conservative groundwater contaminant using backward probabilities conditioned on measured concentrations

If contamination is observed in an aquifer, a backward probability model can be used to obtain information about the former position, source location, or release time of the observed contamination. A backward location probability density function (PDF) describes the possible former positions of an observed contaminant particle at a specified time in the past and can be used to identify the location of the contaminant source. A backward travel time probability density function describes the possible travel times of an observed contaminant particle from a known upgradient location to the observation location and can be used to determine the time of release of contamination from the source. Neupauer and Wilson (1999, 2001, 2002) obtained backward PDFs that depend on the observation locations and sampling times, in addition to the transport properties of the aquifer and solute. We present an approach for conditioning these backward PDFs on measured concentrations. We focus on identifying the location or release time of an instantaneous point source of contamination. We derive the conditioning equations and demonstrate some important features of the technique through the use of a hypothetical example.