This subject has been an enduring theme since Lloyd Townley's PhD research on this subject between 1978 and 1983. The thesis is now available online.

Much of the thesis was not published, but some numerical results were presented at a conference in Australia in late 1983 (Townley and Wilson, 1983), the major theoretical results were published by Townley and Wilson (1985) and some further numerical examples were presented at a conference (Townley and Wilson, 1985) and later in a journal (Townley and Wilson, 1989).

The thesis resulted in preparation of a 2D finite element package for aquifer flow, with tightly integrated capabilities for calibration (of storage coefficients, transmissivities, boundary conditions and recharge) and prediction uncertainty (based on the first order second moment (FOSM) method). The package was documented in great detail (Townley and Wilson, 1984) but has been used on only a couple of projects since that time.

The FOSM method was extended in 1983-84 to cover second order corrections to the mean. Although the theory had been developed previously, what was unique about this work was development of an algorithm that is computationally efficient for large problems with many state variables. Two conference papers were published showing effects of uncertain transmissivities (Townley, 1984) and effects of uncertain recharge (Townley, 1989). This theme was continued by Townley (1988).

The fundamental ideas applicable to groundwater models apply to virtually any kind of model. Dr Bryson Bates of CSIRO was keen to calibrate a simple surface hydrological model, and our collaboration led to Bates and Townley (1985), Bates and Townley (1988a) and Bates and Townley (1988b).

Prof. Dennis McLaughlin from MIT came to Perth on sabbatical in 1991. Dennis asked me what we could work on together, and I explained that I believed there was a fundamental link between all the methods proposed to date to solve the so-called "groundwater inverse problem", and that it ought be possible to prove it. This led to years of effort, mostly by Dennis, to identify and prove the mathematical links between different methods. The work was published by McLaughlin and Townley (1996) (see also McLaughlin and Townley, 1997, in which we rejected criticisms by Peter Kitanidis). It took some years before other researchers started to reference this paper, but the paper has now received nearly 500 citations.

In 2011-12, I was invited to contribute to development of new Australian Groundwater Modelling Guidelines, with funding from the National Water Commission. I wrote Chapter 5 on "Calibration and uncertainty analysis", and others. The guidelines can be downloaded in PDF and Word formats.