The elevated Kaibab plateau in northern Arizona has an area of 88 0 square miles and lies adjacent to the Grand Canyon of the Colorado river. It is composed of a sequence of lithified Paleozoic rocks that are approximately 4000 feet thick and consist of marine sediments that contain very little permeability. The ground water system of the plateau has two principal components: 1) circulation through unfractured stratified rocks that range up to a few tens of miles wide and 2) fault controlled drains. In unfractured zones, most of the ground water circulation takes place in the upper 900 feet of the section. The water drains laterally through these rocks toward fault zones or seep faces along the canyon walls. Approximately 40 percent of the plateau surface (330 square miles) drains to canyon seeps. Fault zones provide laterally and vertically continuous large capacity conduits through the plateau. These function as drains for the ground water system as well as floodways for storm pulses that enter the faults directly from the surface. Fracturing has controlled the development of extensive karst networks in limestones that lie near the base of the Paleozoic section. These systems drain to 10 groups of karst springs that discharge an average of approximately 100 cubic feet of water per second. The karst springs drain approximately 60 percent of the plateau surface (550 square miles). The springs in Tapeats amphitheater on the west side of the plateau discharge from the extensive West Kaibab fault zone and account for approximately 70 percent of the measurable water leaving the plateau. This group of three springs drains about 40 percent of the plateau surface (380 square miles). Development of ground water supplies does not appear to be economically tenable in the unfractured portions of the plateau because the permeabilities of the rocks are very small and the depth to the small quantities of available water exceed 500 feet. Production from the large fault controlled drainage networks is equally unattractive. Although the occurrence of water is certain, the large supplies are more than 2800 feet below the land surface and exist in finite channels along the fault zones. These would be difficult to penetrate with conventional drilling methods.

Transmissivity, specific capacity, and steady state hydraulic head data collected from the Cortaro aquifer in Southern Arizona are analyzed statistically by means of regression and Kriging techniques. The statistics obtained in this manner are used to develop a stochastic model of the aquifer based on the finite element and Monte Carlo simulation methods. Three stages of generated head uncertainties are considered; (1) non-conditional, (2) conditional on transmissivity data and (3) conditional on both transmissivity and initial hydraulic head data (or inverse method). We found that simulated head values in stage 1 and 2 are associated with high variance amounting to 144.0 ft². When the statistics obtained from regression and Kriging in stage 2 are processed by means of the statistical inverse method of Neuman (1980), the result is a drastic reduction in the input head variance amounting to 75 percent reduction in the input head variance (i.e., 144 ft²). From these results, one may conclude that in order to minimize the variance of outputs generated by stochastic aquifer models, the input into such models must be created with the aid of appropriate statistical inverse procedure.

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.

Mining activity is suspected of contributing sulfate and total dissolved solids (TDS) to ground water downgradient of the Pima mining district. High ionic concentrations in tailing impoundments suggest that tailings-pond recharge may be a source of the contamination. Experiments indicated that sulfate is not significantly produced by inorganic sulfide oxidation in the tailings ponds. Tailings pond water chemistries were compared with historical water quality analyses in the Pima district. The U.S.G.S. computer program PHREEQE modeled saturation indices for anhydrite, calcite, fluorite, and gypsum in water chemistries throughout the study area. Well water downgradient of the mines had lower saturation indices than tailings pond water which discredits the claim that tailings-pond recharge is acquiring salts as it percolates to the aquifer. Evidence supports the opinion that tailings pond seepage is contributing to the sulfate and TDS content in ground water downgradient of the ponds.

A study of the Salt River Indian Reservation in central Arizona evaluated pre-development hydrologic conditions with an emphasis on simulating ground-water flow conditions within the reservation, where data was scarce before extensive aquifer pumping began in 1940 in adjoining portions of the East Salt River Valley. Water-resource development began in the valley with the completion of the Tempe Canal in 1871. Additional canals and irrigated agriculture spread quickly in areas along the Salt River, which has a mean annual flow of about 1.25 million acre-feet. Pre-development ground-water flow was horizontal and steady-state. The simulation indicated that the available water-level data, though corrupted in areas adjacent to the river, more properly described the virgin system than flow estimates. Sensitivity analyses indicated that simulated heads on the reservation were sensitive to all processes except evapotranspiration. Recharge through the riverbed, evapotranspiration, and subsurface outflow were all co-dependent.

The Arizona Nature Conservancy's Hassayampa River Preserve is 50 miles northwest of Phoenix near the town of Wickenburg. Four miles of the largely ephemeral Hassayampa River are perennial within the preserve, supporting one of the finest remaining cottonwood-willow forests in the state. Stream flows are affected by wells pumping ground water directly from the alluvial aquifer and may be influenced by wells which intercept lateral inflow from the regional basin-fill aquifer. Developing effective management strategies to protect base flow conditions (∼4 cfs) depends on a clear understanding of the surface and ground-water systems in the preserve. Provided that ground water developers near Wickenburg recognize and incorporate the interconnected nature of each hydrologic system, perennial flow within the preserve is not believed to be immediately threatened. (Abstract shortened with permission of author.)

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