Townley, L.R. (1987), Quantifying the uncertainty in model predictions, CSIRO Division of Groundwater Research, Mildura Modelling Workshop, 16-18 February.

The primary aim of this talk is to present a "modelling framework" in which uncertainty can be taken into account during all phases of modelling. This framework is briefly described by Townley and Wilson (1983), but is well recognised by a number of researchers. Practical applications have been limited to date, although Clifton and Neuman (1982) have demonstrated all phases of the methodology.

The intention of the talk is not to imply that this methodology can easily be applied in large-scale model studies, such as modelling of the Great Artesian Basin, the Murray-Darling system or the Swan Coastal Plain. On the other hand, it is clear that uncertainty is on the minds of many workers in Australia, hence this talk is intended to offer some hope that techniques may become available in the not-too-distant future which can deal with uncertainty.

The modelling framework is illustrated in Figure 1. At each phase of modelling (i.e. data collection, conceptualisation, parameter estimation and prediction), it is possible to quantify, at least in some intuitive way, the uncertainty in the output from that phase. In terms of the most common parameters used for model calibration, for example, it is possible to estimate the spatial distribution of transmissivities using a technique known as "kriging"; this technique quantifies the error in the estimated transmissivities, and this error can in turn be used to estimate the error in later model predictions. Incorporating measurements of heads into a weighted least squares (WLS) "inverse problem" also allows estimates of parameter error and the resulting prediction error.

Details of kriging or WLS estimation are not discussed in detail. More details about computational issues can be found in Townley and Wilson (1985). Examples of WLS applications are given by Carrera and Neuman (1986) and Cooley et al (1986) and references therein.