A Controlled Experiment in Ground Water Flow Model Calibration

Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.

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