The purpose of this research is (1) to develop a multi-objective fuzzy regression (MOFR) tool to overcome the shortcomings of the existing fuzzy regression approaches while keeping the good characteristics, and (2) to study systems with uncertain elements, using the example of rainfall-runoff process to illustrate the approach. Previous research has shown that fuzzy regression performs superior compared to statistical regression in some cases. On the other hand, fuzzy regression has also been criticized because it does not allow all data points to influence the estimated parameters, it is sensitive to data outliers, and the prediction intervals become wider as more data are collected. Here, several MOFR techniques are developed to overcome these problems by enabling the decision maker select a non-dominated solution based on the tradeoff between data outliers and prediction vagueness. It is shown that MOFR provides superior results to existing fuzzy regression techniques, and the existing fuzzy regression approaches and classical least squares regression are specific cases of the MOFR framework. The methodology is illustrated with examples from rainfall-runoff modeling, more specifically, conceptual rainfall-runoff (CRR) models are analyzed here. One of the main problems in CRR modeling is dealing with the uncertainty associated with the model parameters which is related to data and/or model structure. A fuzzy CRR (FCRR) framework is proposed herein where every element of the CRR is assumed to be uncertain, taken here as fuzzy. Parameter calibration of FCRR models using newly developed fuzzy regression techniques is also investigated. Applications are provided for a linear CRR model, the experimental two-parameter (TWOPAR) and the six-parameter (SIXPAR) models. The major findings can be summarized as follows: (1) FCRR enables the decision maker to gain insight about the CRR model sensitivity to uncertainty of the model elements, (2) using MOFR for the calibration of FCRR leads to non-convex, constrained, non-linear optimization problems, (3) fuzzy least squares regression model yields to more stable parameter estimates than the non-fuzzy regression model, (4) the methodology is applicable to any dynamic system with discrete modes.

The research described in this dissertation is predicted on the hypothesis that remotely sensed information on vegetation cover classes can be used to improve the representation of heterogeneous continental surfaces in global climate models. The problem it addressed was that current understanding of soil-vegetation-atmosphere interactions is considered only to be relevant to small plots of uniform vegetation with dimensions of the order 10-1000 m but, in order to provide realistic simulation of climate, General Circulation Models require description of such interactions for large areas of mixed vegetation with dimensions of the order 100-1000 km. The methods used to investigate this issue was to create and apply a coupled model that provided realistic representation of both surface and atmospheric boundary layer processes, and to use this model to simulate surface-atmosphere interactions with explicit representation of patches of vegetation on the one hand, and with a single, area-average representation of exchanges on the other. These modeling studies were given credibility by initiating and validating the coupled model using appropriate data from the FIFE site in Kansas and the ABRACOS site in Brazil. The results showed that when quite simple aggregation rules are used to derive the effective area-average values of the vegetation-related parameters, these parameters give adequate simulation of surface-atmosphere interactions. These aggregation rules were then applied using remotely sensed maps of land cover to derive parameter values. Significant differences were found in the resulting parameters, and in the surface energy fluxes and modeled climate calculated using those parameters. Thus, it has been shown that remotely sensed data can indeed be used to improve the representation of heterogeneous land surfaces in global climate models using the methods developed in this research, and that using these data significantly alters the simulated global climate.

In the riparian corridor of the San Pedro River in southeastern Arizona, the fluxes of water and energy over three riparian vegetation groupings were monitored and modeled in order to determine their annual water use and water sources. In situ micrometeorological and soil moisture measurements were made from 1996-1998 at a floodplain grassland site composed mainly of the perennial floodplain grass, Sporobolus wrightii (sacaton), and a tree/shrub grouping dominated by Prosopis velutina (mesquite). The results indicate that the grassland obtained water only from the near-surface (recent precipitation), while the mesquite accessed moisture from deeper in the vadose zone and/or from the water table. Both of these sites exhibited little interaction with the underlying groundwater, suggesting that the majority of the groundwater use from riparian vegetation is limited to the areas of dense mesquite and the forest gallery adjacent to the river. Measurements of the forest gallery water use composed mainly of Populus fremontii (cottonwood) and Salix gooddingii (willow) were available for some shorter term periods in 1997. These measurements were used to calibrate the Penman-Monteith model for evaporation in order to determine the water use from the forest gallery for the entire growing season. The total seasonal water use from the forest was considerably less than potential evaporation estimates. Observations of soil moisture under two rangeland sites in the San Pedro Basin were examined in order to determine the magnitude and the depth of root zone recharge characteristics in this semiarid region. Intermittent TDR observations made from 1990 to 1998 show that deeper root zone recharge occurred primarily during the wintertime, when the plants were senescent and evaporation demand was diminished. A physically-based variably-saturated flow model was used to determine the wintertime recharge. Using an automatic calibration algorithm, the model proved capable of reproducing the observations with small error. Simulated wintertime infiltration amounts indicated that substantial, deeper root zone recharge did occur during wet winters, but that the large year-to-year variability of this recharge implies that deeper-rooted plants would still need access to moisture in shallow root zone.

The transport of reactive solutes in the subsurface is influenced by a variety of physical and chemical processes. The processes are characteristically heterogeneous and often operate simultaneously at different temporal and spatial scales. In modeling reactive solute transport different models take different approaches, dependent on the scale of the system and the objective of the study. Two major approaches have been used to incorporate heterogeneous rate-limited mass transfer into mathematical models for solute transport. One focuses on processes operative at the microscopic scale and associated grain-scale heterogeneity, while the other stresses the macroscopic variability of the medium and the field-scale behavior of solute transport. In this work, I first examine the conceptual framework and model formulation of these two approaches in an attempt to evaluate potential commonality, then present a two dimensional numerical model that integrates the first approach with traditional stochastic modeling for reactive transport. In this model multiple processes are explicitly accounted for, including spatially variable flow, spatially variable sorption, locally heterogeneous diffusive mass transfer, locally heterogeneous rate-limited sorption, and locally heterogeneous first-order degradation. Finally, the model is used to (1) examine the individual and concurrent effects of multiple heterogeneous processes on reactive transport, and (2) evaluate the impact of microscopic-scale mass transfer heterogeneity on field-scale transport in systems for which hydraulic conductivity is spatially variable. The comparison of the two approaches shows that despite differences in conceptualization and formulation, both microscopic and macroscopic based models produce comparable behavior for smaller-scale systems. However, greater deviations are observed at larger scales. This suggests that caution should be taken when using mathematical modeling for elucidating the specific processes that may be influencing reactive-solute transport for a given system. Results from 2-D simulations of the new model reveal that inclusion of locally heterogeneous mass transfer does not appear to significantly influence the mean transport behavior for systems with field-scale heterogeneity. However, it does appear to influence low-concentration tailing. For simulations of reactive transport over extended distances, models with locally heterogeneous mass transfer may "preserve" the non-equilibrium effects associated with rate-limited mass transfer better than the models incorporating locally uniform mass transfer when both pore-scale and field-scale heterogeneity coexist.

Fluid flow modeling in fractured rocks is a complicated and important research and application topic in many fields such as geological, hydrogeological, environmental and petroleum engineering. Commonly used methods based on equivalent continuum assumption for fluid flow modeling can generally be applied directly to the porous geological media, but have limited applicability when the geological medium is dominated by fractures. It often happens that only limited time, cost, hydrogeological data and computer resources are available in solving a practical problem of the fluid flow modeling in fractured rocks. Therefore, it is a challenge, but necessary, to investigate the hydraulic behaviors and propose new approaches, procedures, and methodologies to build a reliable fluid flow model for fractured rocks with limited available related data. The general concepts on fluid flow modeling in fractured rocks are introduced firstly and the different ways to treat major and minor fractures in 2-D and 3-D discrete fracture fluid flow modeling are propounded. The author has investigated the relations between the hydraulic behaviors and fracture geometry parameters and found out the effect of fracture parameters on the Representative Elementary Volume (REV) for the fracture systems with statistically distributed fracture geometry parameters including the size, orientation and location. Further, a systemic procedure for fluid flow modeling in fractured rocks in two-dimensional domain is suggested and demonstrated through a 2-D case study for groundwater resources evaluation. Six 3-D conceptual linear pipe discrete fracture fluid flow models which focus on the utilization of fracture information are proposed to simulate packer or pumping tests conducted in fractured rock masses. These models can reflect channel flow in fractures, simplify and minimize the complexity of fluid flow in fractures, save computer resources and increase the possibility to solve a field problem at large scales, and implement a discrete fracture fluid flow model easily. Finally, the author has developed a practicable systemic approach to determine the REV for hydraulic properties and then the hydraulic conductivity tensor for the REV in fractured rocks using single well packer test results. These procedures are illustrated through a 3-D case study by implementing the proposed fluid flow models.

Infiltration processes on rangeland watersheds are highly variable in both space and time due to heterogeneities in soil properties and temporal variability of rainfall, as well as vegetation, cover and topographic characteristics. Infiltration processes at the plot scale are often described and modeled using a single hydraulic conductivity (Ke) parameter. In this study, the spatial variability of infiltration processes at the plot scale is examined using an integrated measurement and modeling approach. A newly developed variable intensity rainfall simulator is effectively used to measure changes in plot scale infiltration rate with changes in rainfall intensity. In addition, process-based hydrologic simulation models are used to determine the amount of complexity needed to accurately model the observed runoff response from the rainfall simulator experiments. First, a soil box lysimeter is used to measure variability of infiltration processes and runoff response due to soil texture and rainfall intensity. Second, five natural field plots in a rangeland watershed are used to measure the same processes with additional complexity in the form of cover and topographic characteristics. Steady-state infiltration rates increased with rainfall intensity on all of the plots, indicating partial area response and spatial variability of infiltration within each plot. Evaluation of the soil box lysimeter infiltration experiments showed that the location of areas with higher and lower infiltration capacities along a flow path does have an important effect on runoff response and that the response changes with changes in rainfall intensity. Using the detailed measurements of the field plot vegetative cover and surface characteristics of the plots to discretize the plots into separate overland flow planes improved the ability to model the variability of infiltration processes and the observed runoff response. Multi-plane configurations parameterized based on soil and plot characteristics resulted in a significant improvement over single plane configurations. The measurement and simulation model results show that the rainfall runoff relationship cannot be accurately described or modeled using a single Ke value at the plot scale.

Field-measured data collected from infiltration experiments conducted at the Maricopa Agricultural Center, Arizona, and one-dimensional numerical models were used in an iterative approach to develop conceptual models of unsaturated flow and transport. Conceptual models were developed using field data, estimates of hydraulic and transport properties, and assumptions regarding the types of processes occurring in the field plot. Using the field data and numerical models in an iterative approach revealed that adjustments to the parameterization of the conceptual models were necessary to allow for acceptable predictions of flow and transport. In addition, the numerical models delineated where the conceptual models needed adjustment and indicated where further analysis of the field data was necessary. Specifically, in regards to the unsaturated water flow, it was found that: (1) without increasing the laboratory determined value of Ks tenfold, it was impossible to make acceptable predictions for the infiltration experiments; (2) the laboratory-derived hydraulic properties provided a superior first approximation to texturally based hydraulic properties taken from an internal database; (3) incorporation of hysteresis into the soil hydraulic functions resulted in predictions of the water contents through time and soil water content profiles that were marginally better than not incorporating hysteresis; and (4) based on the mean square errors of the predictions and a post-audit based on the adjusted hydraulic properties, the use of a homogeneous soil profile was supported. In regard to the unsaturated solute transport, it was found that: (1) inversion techniques to estimate the unsaturated transport properties at each location (local approach) yielded the best results with respect to the fit of the data compared to the techniques which fit data from all depths simultaneously (global approach); (2) predictions using unsaturated transport properties averaged from the global approach yielded the best results compared to the average local approach properties; (3) incorporating hysteresis had little effect on the predicted bromide breakthrough curves and concentration profiles, yielding only marginally better results than predictions from models with no hysteresis; (4) it was impossible to accurately predict the breakthrough of bromide at depths deeper than 200 cm without using a retardation factor less then one.

Impacts of vegetation manipulation treatments on the hydrologic regime of ponderosa pine watersheds in Arizona were evaluated in this dissertation. First, the Seasonal-Kendall test was applied to detect trends in the precipitation and water yield of the control watershed. Then the long-term implications of two levels of forest cutting (clear cut and strip cut with thinning) on the water yield of the treated watersheds were assessed by means of the traditional paired watershed method and plots of cumulative recursive residuals (CUSUM). CUSUM plots were proposed as a complementary tool to evaluate the duration of water yield changes following treatment. Next, BROOK90, a conceptual hydrologic model, was used to assess water yield changes of ponderosa pine watersheds associated with vegetative practices. The model was optimized and verified in the control watershed to determine if the model was applicable to the environment where the experiment was conducted. Then the model was optimized for the pre-treatment period of the treated watersheds and the optimized parameters were used to simulate the water yield of the post-treatment period. Finally, results obtained with the traditional paired watershed approach were compared with those obtained with the modeling simulation. The two methods were in reasonable agreement.

Although it is one of the most difficult tasks in hydrology, delineation of aquifer heterogeneity is essential for accurate simulation of groundwater flow and transport. There are various approaches used to delineate aquifer heterogeneity from a limited data set, and each has its own difficulties and drawbacks. The inverse problem is usually used for estimating different hydraulic properties (e.g. transmissivity) from scattered measurements of these properties, as well as hydraulic head. Difficulties associated with this approach are issues of indentifiability, uniqueness, and stability. The Iterative Conditional Simulation (ICS) approach uses kriging (or cokriging), to provide estimates of the property at unsampled locations while retaining the measured values at the sampled locations. Although the relation between transmissivity (T) and head (h) in the governing flow equation is nonlinear, the cross covariance function and the covariance of h are derived from a first-order-linearized version of the equation. Even if the log transformation of T is adopted, the nonlinear nature between f (mean removed Ln[T]) and h still remains. The linearized relations then, based on small perturbation theory, are valid only if the unconditional variance of f is less than 1.0. Inconsistent transmissivity and head fields may occur as a result of using a linear relation between T and h. In this dissertation, Artificial Neural Networks (ANN) is investigated as a means for delineating aquifer heterogeneity. Unlike ICS, this new computational tool does not rely on a prescribed relation, but seeks its own. Neural Networks are able to learn arbitrary non-linear input-output mapping directly from training data and have the very advantageous property of generalization. For this study, a random field generator was used to generate transmissivity fields from known geostatistical parameters. The corresponding head fields were obtained using the governing flow equation. Both T and h at sampled locations were used as input vectors for two different back-propagation neural networks designed for this research. The corresponding values of transmissivities at unsampled location (unknown), constituting the output vector, were estimated by the neural networks. Results from the ANN were compared to those obtained from the (ICS) approach for different degrees of heterogeneity. The degree of heterogeneity was quantified using the variance of the transmissivity field, where values of 1.0, 2.0, and 5.0 were used. It was found that ANN overcomes the limitations of ICS at high variances. Thus, ANN was better able to accurately map the highly heterogeneous fields using limited sample points.

The City of Tucson, located in a semi-arid region, faces escalating pressure on its groundwater resources associated with rapid urbanization and population growth over tbe past 50 years. Because of concern that the declining water table will threaten the city's development, bringing water from Colorado River via the Central Arizona Project (CAP) was perceived as the sole solution for Tucson's water problem. As soon as CAP water arrived in Tucson in 1992, its quality provoked a quarrel over its use for potable purposes. A significant outcome of that quarrel was the enactment of the 1995 Consumer Protection Act (CPA). The primary objective of the CPA is to preclude the use of CAP water for drinking purposes at least until year 2000, unless it is treated to achieve the same quality as the groundwater previously supplied. The CPA encourages using CAP water for non-potable purposes and for replenishing Tucson aquifer through recharge. This study examines the economic and institutional issues involved in utilizing CAP water for recharge and non-potable purposes in the Tucson Basin. The economic assessment focuses on the impact of CAP water recharge on the water table, the resulting pumping cost savings, and the concomitant benefits of saving groundwater and of using CAP water instead of reclaimed water. The institutional assessment focuses on the effectiveness of using CAP water in stabilizing groundwater withdrawal and replenishing Tucson's aquifer. Four planning scenarios were designed to measure and compare the costs and benefits with and without CAP water recharge. Cost-Benefit Analysis was utilized to measure recharge costs and benefits and to derive a rough estimate of cost savings from preventing land subsidence. The results indicate that the institutional requirements can be met since one scenario relatively stabilizes groundwater and the two other scenarios will recover it. The economic benefits from reducing pumping cost and saving groundwater are not economically significant. Yet, when combing the use of CAP water for recharge and non-potable purposes, scenario 3 would not only augment the water table, but also demonstrate positive net economic benefits from savings groundwater, decreasing pumping costs and using CAP water instead of reclaimed water.