UBC Theses and Dissertations
Efficient and responsible use of prior information and joint parameter estimation for estimating parameters of groundwater flow models Weiss, Richard A.
Parameter estimation problems for groundwater flow systems are often non-identifiable or unstable using only hydraulic head data. Prior information on parameters or joint parameter estimation including tracer concentrations may be used to stabilize the parameter set. Response surfaces and multiparameter confidence regions are used to identify the most efficient and responsible use of prior information and joint data sets for the purpose of parameter estimation. Prior information on some of the parameters are used to stabilize the parameter set for parameter estimation. Efficient use of prior information involves identifying those parameters for which prior information will stabilize the model parameter set the most. Responsible use of prior information involves identifying how errors in the prior information will influence the parameter estimates. The most responsible parameters for prior information are those parameters for which errors in the prior information have the least influence on the final parameter estimates. Guidelines are developed for efficient and responsible use of prior information in parameter estimation based on an analysis of the parameter space using response surfaces and eigenspace decomposition. Joint parameter estimation is used when more than one data set is available to estimate the model parameters. Response surfaces and confidence regions are used to show how multiple data sets reduce parameter uncertainty. The value of future data in reducing the uncertainty of parameter estimates is explored. For weighting data sets in joint parameter estimation, three criteria based on parameter space analysis are proposed. These three criteria are evaluated and compared to the more traditional weighting method based on an analysis of data residuals. A groundwater model for the San Juan Basin, New Mexico, is constructed and calibrated using the methods developed in this thesis. Hydraulic head data, ¹⁴C concentration data, and prior information on the model parameters is used to calibrate the model in an efficient and responsible manner. The model is calibrated in two stages. In the first stage, prior information on the hydraulic conductivity parameters for the lower model layers was found to be both efficient and responsible in stabilizing the parameter set. In the second stage, the parameter estimates and uncertainties based on the four weighting criteria were compared.
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