Statistical methods of analyzing hydrochemical, isotopic, and hydrological data from regional aquifers

Abstract

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.