Parameter space methods in joint parameter estimation for groundwater flow models

The joint estimation of model parameters using hydraulic head and tracer concentration data is examined using methods based on parameter space analysis. Response surfaces and confidence regions can indicate how multiple data sets interact to reduce parameter uncertainty. Each data set produces a unique response surface and confidence region. If these surfaces are oriented differently for the two data sets, parameter uncertainties are significantly reduced when the second data set is included in the inversion. If these surfaces are similar for the two data sets, the second data set will not reduce the parameter uncertainty significantly. The axes of the linearized confidence ellipsoid are analyzed to determine the difference in orientation of the confidence regions for the two data sets. The use of confidence regions can be extended to predict the value of a second data set in reducing the uncertainty of parameter estimates, before the data are collected. Parameter space approaches are also introduced for selecting the relative weights for the individual data sets in joint parameter estimation. The conventional method based on the analysis of data residuals is compared to three other methods: with the weights selected to maximize parameter stability, to minimize the volume of the confidence region, or to minimize the longest axis of the confidence region. Each criterion can lead to substantially different weights applied to each of the data sets. The application of these methods is demonstrated using hydraulic head measurements and C-14 concentrations to calibrate a model of groundwater flow in the San Juan Basin, New Mexico.