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The GLUE package provides tools for sensitivity analysis and uncertainty estimation using the results of Monte Carlo simulations. The starting point for the GLUE concepts is the rejection of the idea of an optimum parameter set in favour of the concept of equifinality of model structures and parameter sets which implies that it is only possible to evaluate the relative performance of the range of possible models, either qualitatively or quantitatively in terms of some likelihood measure. Note that likelihood is used here in a much wider sense than the likelihood functions of statistical estimation theory - but that traditional likelihood functions can be used within the GLUE framework. Note also that a fuzzy interpretation of the likelihood measures is also possible.

The predictions of the Monte Carlo realisations are then weighted by the likelihood measures to determine prediction limits of the required variables. Thus, those parameter set realisations that perform well in the evaluation are given the greatest weight in prediction. No distribution assumptions are made in determining the prediction limits, they are based only on the available sample of predictions. There are facilities in the software for transforming the likelihood measures input to the package (e.g. by raising to a power to make the parameter response surface more peaked) or by applying a lower threshold of acceptability. Parameter sets with likelihood measures below that threshold are then considered to be non-behavioural and have their likelihood values set to zero.

The GLUE methodology focuses attention on the subjective nature of model evaluation (e.g. choice of likelihood measure, choice of threshold value) but requires that those elements be defined explicitly and therefore made open to debate and justification. Parameter interactions and nonlinearity in the model responses (which may be extremely complex and potentially even chaotic) are handled implicitly in the GLUE methodology. In essence, the nonlinear response of a particular model parameter set is summarised by the associated likelihood value, i.e. the performance of that particular model realisation in reproducing the observations. Thus the analysis focuses on parameter sets rather than the behaviour of individual parameters and their interactions (although some facilities are provided in the Sensitivity Plots option to examine the sensitivity to individual parameters).

Errors in input data and the observation data are also handled implicitly. Thus the likelihood measure reflects the ability of a particular model to predict a particular series of observations (that may not be error free) given a particular set of inputs (that may not be error free). There is thus an implicit assumption that in prediction, error structures will be "similar" in some broad sense to those in the evaluation period.

A major limitation of the GLUE methodology is the dependence on Monte Carlo simulation. For complex models requiring a great deal of computer time for a single run, it will not be possible to fully explore high order parameter response surfaces. However, experience suggests that the upper limit of model performance is often well defined by a limited number of model realisations and that prediction intervals are reasonable in comparison with observations.

The options available in the program are as follows:

Dotty Plots

The Dotty Plot screen provides plots of any likelihood measure or predicted variable against value of each individual parameter. One dot is plotted for each Monte Carlo run in the input data file. The Dotty Plots are therefore projections of all the Monte Carlo samples onto single parameter axes. As such they should be interpreted with care as they can conceal some of the structure in the N- dimensional parameter response surface. The chosen likelihood measure or variable can be changed or transformed by choosing from the menu line options.

Sensitivity Plots

The Sensitivity Plots screen provides plots of the cumulative distributions of parameter values group according to the ranking of each Monte Carlo run for a given likelihood measure or predicted variable. Strong differences between the cumulative distributions for a given likelihood measure or variable indicates sensitivity to that parameter. Distributions plotting close together indicate a lack of sensitivity. The chosen likelihood measure or variable can be changed or transformed by choosing from the menu line options.

Uncertainty Plots

This screen provides plots of the histogram and cumulative distribution of a predicted variable, weighted by a chosen likelihood measure. 5 and 95\% sample quantiles are shown on the cumulative distribution plot. Both likelihood measure and variable can be changed by choosing from the menu line options.

List Simulations

This option provides an output of the top (or bottom) 20 simulations ranked according to either a likelihood measure or a predicted variables.

Transforming Likelihood Measures

This option provides a number of transform options, including applying a lower threshold limit, raising a likelihood measure to a power, taking the exponential of a likelihood multiplied by a coefficient, and taking the log of the measure. New likelihood measures derived in this way may be stored or edited.

Combining Likelihood Measures

The need to combine different likelihood measures arises in a number of different circumstances including: combining likelihood measures for different types of model evaluation (such as one measure calculated for the prediction of discharges and one calculated for the prediction of water table or soil moisture levels); or updating an existing likelihood estimate with a new measure calculated for the prediction of a new set of observations. Four different types of combination operator are allowed in the GLUE software: Bayes multiplication; weighted addition; Fuzzy Union; and Fuzzy Intersection (see Box 7.2).