Locating
sources of groundwater contamination is an inverse problem on steroids. It is,
in fact, two inverse problems. Source locations must be back-calculated from
field measurements. The hydraulic properties of aquifer material through which
groundwater flows, and contaminants are transported, must also be inferred from
these same measurements.
Another
spice in the inverse problem soup is the nature of borehole contaminant
measurements. These data are messy, to say the least.
Yet another
problem is that numerical advection-dispersion models are slow. They are
difficult to use in inverse problem settings. Solute concentrations which they
calculate are blurred by numerical and hydrodynamic dispersion. The latter is a
surrogate for stochastic detail that they cannot represent.
We demonstrate
an innovative method to solve this two-tiered inverse problem. It is based on
particle tracking. Simulation is fast and stable. The method makes use of the
fact that, as well as carrying mass, particles carry information which is
capable of being harvested. Outcomes of the analysis are probabilistic (as they
should be). Meanwhile, uncertainties are reduced through assimilation of head
and concentration data.
In addition
to providing probabilistic maps of source location, the methodology can be used
to optimise the locations of new monitoring wells.
The focus
of our worked example report is a shallow aquifer that underlies Pavia, a city
in northern Italy. Its story is typical of countless other stories that are
told throughout the world. The aquifer is contaminated. Contamination must be
contained. Responsible parties are sought.