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Exact Scheffé-type confidence intervals for output from groundwater flow models: 2. Combined use of hydrogeologic information and calibration data

Richard L. Cooley
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Abstract

Calibration data (observed values corresponding to model-computed values of dependent variables) are incorporated into a general method of computing exact Scheffé-type confidence intervals analogous to the confidence intervals developed in part 1 (Cooley, this issue) for a function of parameters derived from a groundwater flow model. Parameter uncertainty is specified by a distribution of parameters conditioned on the calibration data. This distribution was obtained as a posterior distribution by applying Bayes' theorem to the hydrogeologically derived prior distribution of parameters from part 1 and a distribution of differences between the calibration data and corresponding model-computed dependent variables. Tests show that the new confidence intervals can be much smaller than the intervals of part 1 because the prior parameter variance-covariance structure is altered so that combinations of parameters that give poor model fit to the data are unlikely. The confidence intervals of part 1 and the new confidence intervals can be effectively employed in a sequential method of model construction whereby new information is used to reduce confidence interval widths at each stage.

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Richard L. Cooley. 2010-07-09. Exact Scheffé-type confidence intervals for output from groundwater flow models: 2. Combined use of hydrogeologic information and calibration data. https://doi.org/10.1029/92wr01864

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