Residual mapping is an automated groundwater-model calibration technique which rapidly identifies parameter-zone configurations, while limiting tendencies to over-parameterize. Residual mapping analyzes the model residual, or the difference between model-calculated head and spatially-interpolated observation data, for non-random trends. These trends are entered in the model as parameter zones. The values of hydrologic variables in each parameter zone are then optimized, using parameter-estimation software. Statistics calculated by the parameter-estimation software are used to determine the statistical significance of the parameter zones. If the parameter-value ranges for adjacent zones do not have significant overlap, the zones are considered to be valid. This technique was applied to a finite-difference, transient groundwater flow model of a major municipal well field, located in west-central Florida. A computer conde automates the residual mapping process, making it practical for application to large, transient flow models. The calibration data set includes head values from 37 monitor wells over a period of 181 days, including a 96-day well-field scale aquifer-performance test. The transient residual-mapping technique identified five significant transmissivity zones and one leakance zone.

In this work we develop and analyze algorithms motivated by the parameter estimation problem corresponding to a multilayer aquifer/interbed groundwater flow model. The parameter estimation problem is formulated as an optimization problem, then addressed with algorithms based on adjoint equations, quasi-Newton schemes, and multilevel optimization. In addition to the parameter estimation problem, we consider properties of the parameter to solution map. This includes invertibility (known as identifiability) and differentiability properties of the map. For differentiability, we expand existing results on Fréchet sensitivity analysis to convection diffusion equations and groundwater flow equations. This is achieved by proving that the Fréchet  derivative of the solution operator is Hilbert-Schmidt, under smoothness assumptions for the parameter space. In addition, we approximate this operator by time dependent matrices, where their singular values and singular vectors converge to their infinite dimension peers. This decomposition proves to be very useful as it provides vital information as to which perturbations in the distributed parameters lead to the most significant changes in the solutions, as well as applications to uncertainty quantification. Numerical results complement our theoretical findings. / Ph. D.