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Comparison of Parameter Estimation Design Criteria Using a Solute Transport Model with Matrix Diffusion

Three criteria for the experimental design of parameter estimation are compared by using the criteria to develop sampling patterns for determining parameter values in one‐dimensional transport models. The models include advection, dispersion, and matrix diffusion, the latter being an important process for nuclear waste isolation. The effectiveness of various designs is assessed by studying expected errors of parameter estimates and correlation between parameters. The correlations and expected errors are computed using parameter sensitivities, and the results demonstrate that the choice of design criterion can make a significant difference in the expected estimation error of parameter values in sparse designs. The best overall choice is D‐optimality, which is a measure of the volume of the joint confidence ellipsoid of the parameter estimates. E‐optimality, which minimizes the longest axis of the confidence ellipsoid, gives somewhat similar results but is not as robust for all of the estimated parameters. It is also shown that approaches that consider parameter sensitivities, but not correlation between parameters, may result in inferior designs.