Identifiability criterion for solute transport parameter estimation

Date of Completion

January 1997


Statistics|Engineering, Environmental




Parameter estimation is an integral part of numerical modeling and plays an essential role in the process of investigating and remediating subsurface contamination at hazardous waste sites. The research presented in this dissertation investigates the conditions under which a given inverse problem is solvable, and examines the influence of the model formulation on the statistical reliability of the estimated parameters.^ It is evident that a parameter estimation model must take into account a wide variety of information from disparate sources. In order to accomplish that goal, this work uses a Bayesian statistical formulation to combine information obtained in the form of weighted groundwater potentiometric head and solute concentration measurements with information on expected ranges of parameter values. The resulting objective function is termed a Maximum A Posterior (MAP) estimator. Under the assumption of normal measurement error and using appropriate transformations the MAP problem is subsequently solved as a general nonlinear least squares (NLLS) problem using a modified Gauss-Newton approach.^ A series of case example inverse problems involving coupled groundwater flow and solute transport in a two dimensional flow field are investigated. The results of these case examples show that identifiability problems can manifest either as a complete inability to obtain a solution or in the form of decreased reliability of certain parameters. Further, it is shown that identifiability problems can result either from the particular set of data used to solve the estimation problem, or directly from the structural form of the model itself. A diagnostic procedure is introduced which distinguishes between identifiability problems due to model structure, and those due to the information content of the available data.^ Model nonlinearity has a significant impact upon the validity of statistical inference measures, and is an essential issue with regard to assessing the reliability of estimated parameters. Three different methods of measuring the impact of statistical nonlinearity are used in this work: differential geometric curvature measures, Monte Carlo simulations, and derived second order moment approximations. Nonlinearity is shown to be dependent both upon the monitoring network design, as well as upon the particular means of model parameterization. ^