Predictive error analysis for a water resource management model

In calibrating a model, a set of parameters is assigned to the model which will be employed for the making of all future predictions. If these parameters are estimated through solution of an inverse problem, formulated to be properly posed through either pre-calibration or mathematical regularisation, then solution of this inverse problem will, of necessity, lead to a simplified parameter set that omits the details of reality, while still fitting historical data acceptably well. Furthermore, estimates of parameters so obtained will be contaminated by measurement noise. Both of these phenomena will lead to errors in predictions made by the model, with the potential for error increasing with the hydraulic property detail on which the prediction depends. Integrity of model usage demands that model predictions be accompanied by some estimate of the possible errors associated with them. The present paper applies theory developed in a previous work to the analysis of predictive error associated with a real world, water resource management model. The analysis offers many challenges, including the fact that the model is a complex one that was partly calibrated by hand. Nevertheless, it is typical of models which are commonly employed as the basis for the making of important decisions, and for which such an analysis must be made. The potential errors associated with point-based and averaged water level and creek inflow predictions are examined, together with the dependence of these errors on the amount of averaging involved. Error variances associated with predictions made by the existing model are compared with "optimized error variances" that could have been obtained had calibration been undertaken in such a way as to minimize predictive error variance. The contributions by different parameter types to the overall error variance of selected predictions are also examined.