Completion Report / Contract No. 26-235-816-40-2-050-0735 / Arizona Department of Health Services / Bureau of Water Quality Control

This dissertation is concerned with the development of mathematical aquifer models that combine hydrological, hydrochemical and isotopic data. One prerequisite for the construction of such models is that prior information about the variables and parameters be quantified in space and time by appropriate statistical methods. Various techniques using multivariate statistical data analyses and geostatistical methods are examined in this context. The available geostatistical methods are extended to deal with the problem at hand. In particular, a three-dimensional interactive geostatistical package has been developed for the estimation of intrinsic and nonintrinsic variables. This package is especially designed for groundwater applications and incorporates a maximum likelihood cross-validation method for estimating the parameters of the covariance function. Unique features of this maximum likelihood cross-validation method include: the use of an adjoint state method to compute the gradient of the likelihood function, the computation of the covariance of the parameter estimates and the use of identification criteria for the selection of a covariance model. In addition, it can be applied to data containing measurement errors, data regularized over variable lengths, and to nonintrinsic variables. The above methods of analysis are applied to synthetic data as well as hydrochemical and isotopic data from the Tucson aquifer in Arizona and the Madrid Basin in Spain. The dissertation also includes a discussion of the processes affecting the transport of dissolved constituents in groundwater, the mathematical formulation of the inverse solute transport problem and a proposed numerical method for its solution.

The estimation of mountain-front recharge to regional aquifers is approached from a hydroclimatic standpoint. Analytical models of the seasonal water yield and streamflow are developed in this dissertation. These models are specialized for hard-rock mountainous watersheds where deep percolation occurs through fractures exclusively. Input variables are considered to be stochastic, and a relationship between precipitation and surface runoff is derived by using a deterministic physical process. Streamflow models for the summer and winter rainy seasons are developed separately in terms of known parameters of the storm process and unknown parameters of the physical process. The winter model considers the generation of surface runoff from both rainfall and snowmelt. These models include the long-term effective subsurface outflow from the mountainous watershed, or mountain-front recharge, as one of the parameters to be identified. The parameter estimation problem is posed in the framework of maximum likelihood theory, where prior information about the model parameters and a suitable weighting scheme for the error terms in the estimation criterion are included. The issues of model and parameter identifiability, uniqueness and stability are addressed, and strategies to mitigate identifiability problems in our modeling are discussed. Finally, the seasonal streamflow models are applied to three mountainous watersheds in the Tucson basin, and maximum likelihood estimates of mountain-front recharge and other model and statistical parameters are obtained. The analysis of estimation errors is performed in both the eigenspace and the original space of the parameters.