Good Fit, Error-Based Observation Weights, and Sensitivity Analysis

This talk explores the importance of three aspects of ground-water model development: model fit to observations, weighting of observations, and analysis of sensitivities. Model fit to observations is one of the clearest ways to evaluate how well a model represents a system of concern. One question is, “Does a better fit always mean a better model?” This question can be addressed by considering observation errors and weighting. Theoretically, the sole function of observation weighting is to account for observation error. This talk uses synthetic test cases to show that observation error needs to be understood and quantified to identify models with good predictive ability, and that error-based weighting of observations is needed to obtain reasonable measures of uncertainty. Sensitivities (derivatives of simulated values with respect to parameters) relate the simulated equivalents of observations and predictions to model parameters, given the model as constructed. Evaluation of these sensitivities is often called a local sensitivity analysis. Local sensitivity analysis has the advantage of being very efficient. It has the disadvantage of being susceptible to erroneous results if the model is too nonlinear, but experience has suggested that this deficiency is not serious in many circumstances. When combined with error-based weighting, local sensitivity analysis can be used to determine what observations are important to predictions of interest, and, therefore, what observation errors are worth trying to reduce. The methods discussed are accessible through, for example, the computer codes UCODE_2005, OPR-PPR, and MMA, all of which are constructed using the JUPITER API.