• Nonlocal and localized finite element solution of conditional mean flow in randomly heterogeneous media

      Guadagnini, Alberto; Neuman, Shlomo P.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1997-09)
      This report considers the effect of measuring randomly varying local hydraulic conductivities K(x) on one's ability to predict deterministically, without upscaling, steady state flow in bounded domains driven by random source and boundary terms. Our aim is to allow optimum unbiased prediction of hydraulic heads h(x) and Darcy fluxes q(x) by means of their ensemble moments, , and c, conditioned on measurements of K(x). It has been shown earlier that these predictors satisfy a deterministic flow equation which contains an integro-differential "residual flux" term. This term renders c nonlocal and non-Darcian so that the concept of effective hydraulic conductivity looses meaning in all but a few special cases. Instead, the residual flux contains kernels which constitute nonlocal parameters that are conditional on hydraulic conductivity data and therefore nonunique. The kernels include symmetric and nonsymmetric second -rank tensors as well as vectors. We derive exact integro-differential equations for second conditional moments of head and flux which constitute measures of predictive uncertainty. We then develop recursive closure approximations for the moment equations through expansion in powers of a small parameter ay which represents the standard estimation error of In K(x). Finally, we solve these nonlocal equations to first order in a by finite elements on a rectangular grid in two dimensions. We also solve the original stochastic flow equations by conditional Monte Carlo simulation using finite elements on the same grid. Upon comparing our nonlocal finite element and conditional Monte Carlo results we find that the former are highly accurate, under either mean uniform or convergent flows, for both mildly and strongly heterogeneous media with a as large as 4 - 5 and spatial correlation scales as large as the length of the domain. Since conditional mean quantities are smooth relative to their random counterparts our method allows, in principle, resolving them on relatively coarse grids without upscaling. We also examine the quc on under what conditions can the residual flux be localized so as to render it approximately Darcian. One way to achieve such localization is to treat ' "draulic conductivity as if it was locally homogeneous and mean flow as if it was locally uniform. This renders the flux predictor Darcian according to c _ - Kc(x) \7c where Kc(x) is a conditional hydraulic conductivity tensor which depends on measurements of K(x) and is therefore a nonunique function of space. This function can be estimated by means of either stochastically- derived analytical formulae or standard inverse methods (in which case localization coincides with common groundwater modeling practice). We use the first approach and solve the corresponding localized conditional mean equation by finite elements on the same grid as before. Here the conditional hydraulic conductivity is given by the geometric mean KG(x). Upon comparing our localized finite element solution with a nonlocal finite element solution and conditional Monte Carlo results, we find that the first is generally less accurate than the second. The accuracy of the localized solution deteriorates rel tive to that of the nonlocal solution as one approaches points of conditioning and singularity, or as the variance and correla': ^n scale of the log hydraulic conductivity increase. Contrary to the nonlocal solution, locàlzation does not yield information about predictive uncertainty.
    • ON THE THEORY AND MODELING OF DYNAMIC PROGRAMMING WITH APPLICATIONS IN RESERVOIR OPERATION

      Sniedovich, Moshe; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1976-12)
      This dissertation contains a discussion concerning the validity of the principle of optimality and the dynamic programming algorithm in the context of discrete time and state multistage decision processes. The multistage decision model developed for the purpose of the investigation is of a general structure, especially as far as the reward function is concerned. The validity of the dynamic programming algorithm as a solution method is investigated and results are obtained for a rather wide class of decision processes. The intimate relationship between the principle and the algorithm is investigated and certain important conclusions are derived. In addition to the theoretical considerations involved in the implementation of the dynamic programming algorithm, some modeling and computational aspects are also investigated. It is demonstrated that the multistage decision model and the dynamic programming algorithm as defined in this study provide a solid framework for handling a wide class of multistage decision processes. The flexibility of the dynamic programming algorithm as a solution procedure for nonroutine reservoir control problems is demonstrated by two examples, one of which is a reliability problem. To the best of the author's knowledge, many of the theoretical derivations presented in this study, especially those concerning the relation between the principle of optimality and the dynamic programming algorithm, are novel.
    • Optimal Operation of Water-Supply Systems

      Clausen, George S.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1970-06)
      The traditional metropolitan water -supply planning problem is characterized by two main steps: (a) project future water requirements based on present rates of economic growth,, and (b) schedule water development projects to be introduced into the system on time to meet these predicted requirements. The City of Tucson plans its water supply essentially in this manner. The prime objective of this phase of our research was to formally review the above problem and to formulate it in terms of concepts of management science. Implied commitments to accept Colorado River water and gradual changes in quality of Tucson's groundwater force serious consideration of the economic tradeoffs between alternative sources and uses of water. These alternatives lead to a need for a restatement of water - supply planning objectives in more precise forms than have heretofore been put forth. The doctoral dissertation by G. Clausen addresses itself to the above restatement with actual data on the Tucson basin. The various water -supply planning objective functions including the traditional one are all expressions which maximize the difference between gains and losses involved with water development. They can be expressed mathematically and differentiated on the basis of how these gains and losses are defined. In the traditional sense, gains derived from meeting projected requirements are assumed to be infinite, and losses are taken to be actual project costs and not social costs associated with undesirable economic growth. Therefore, maximization of net gains is accomplished by minimizing project costs, and gains do not even have to be expressed. Consideration of alternatives, however, requires that gains be expressed quantitatively as benefits to individuals, communities, or regions, i.e., primary, secondary, or tertiary benefits. The same logic holds for the expression of total costs. An objective function, used to express the water- supply problem in the Tucson Basin, considers gains as cash revenue to a hypothetical central water - control agency which sells water to the users within the basin. Losses are considered as marginal costs to the agency for producing, treating, and distributing water. The concept of economic demand is used to estimate the amount of water that municipal, industrial, and agricultural users will purchase at different prices. Linear demand functions are postulated. The possible sources of supply considered are groundwater from within the basin, groundwater from the neighboring Avra Valley Basin, reclaimed waste water, and Central Arizona Project water from the Colorado River. Constraints are formulated to allow for limits on water availability, for social limits on water prices, and for minimal requirements of each user over a specified time period; these permit a determination of optimal allocations of water under different conditions to answer "what if' questions, given the assumptions of the model. The resulting static model is termed a pricing model and is optimized by first decomposing the objective function into component parts with each part representing terms involving only one source of water. In instances involving inequality constraints, quadratic programming is used. In other instances where equality constraints or unconstrained conditions exist, Lagrange multipliers and calculus methods are used. These latter conditions arise when it is determined at which point certain constraints become inactive. In the completely general case, this type of decomposition is not possible, but it appears that in many specific uses objective functions of this nature can be profitably decomposed and optima determined much more conveniently than otherwise possible. The model clearly identifies the opportunity costs associated with the required use of Colorado River water in lieu of the cheaper Tucson groundwater.
    • PLANKTONIC DYNAMICS AS AN INDICATOR OF WATER QUALITY IN LAKE MEAD

      Staker, Robert Dale; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1974-06)
      The purpose of this investigation was to identify the zooplankton arc. phytoplankton found in Lake Mead, to quantify their presence, to elucidate some temporal and spatial patterns, and to investigate some of the planktonic responses to physical, chemical, and biological parameters. Phytoplankton and zooplankton population samples were collected from eight different sites at 11 depths at six times over an annual period. These samples were collected with a 6 -liter Van Dorn sampler. Phytoplankton samples were preserved in Lugol's solution and the zooplankton were placed in formalin preservative. The 503 zooplankton population samples were scored in a ruled counting chamber using a stereomicroscope. Eighteen species of zooplankton were identified. The 274 phytoplankton samples were placed on Millipore filters and slides were prepared for examination with phase contrast microscopy. A total of at least 79 algae were found to comprise the phytoplankton flora. The zooplankton for the most part were rotifers, cladocerans, and copepods. Keratella, the principal rotifer, was found to be diacmic and Bosmina, Daphnia, the calanoid, cyclopoid, and nauplii copepods were monacmic. Spatial relationships across the reservoir indicate that Bosmina and cyclopoid copepods are water quality indicators. The late summer phytoplankton were mostly Cyanophyta with populations as large as 5 X 106 cells /liter occurring in Boulder Basin. Winter samples contained mostly diatoms and cryptomonads, while the spring phytoplankton was mainly Chlorophyta. The early summer flora showed a mixture of Chrysophyta, Chlorophyta, and Cryptophyta. Biomass determinations were made from average cell volumes and population counts. The blue -green alga Oscillatoria had the greatest biomass during the late summer period. Bacillariophyta reached a volumetric peak in late winter and the Chlorophyta in spring. The Cryptophyta showed a peak in winter while the Chrysophyta, represented mostly by the presence of Dinobryon, showed greatest population sizes in early summer. The Euglenophyta and Pyrrophyta were relatively unimportant groups of the biomass. Weak nocturnal migrations were exhibited by Asplanchna sp., Keratella cochlearis, and Bosmina longirostris. This conclusion was derived from an analysis of variance of the diurnal data. The copepod groups showed no migration patterns. Since this study was performed when the lake was isothermal, it is inferred that migration is a phenomenon not influenced by temperature. A transect study in Boulder Basin during the winter showed that Daphnia, Asplanchna, Chydorus, and Polyarthra, and possibly calanoid copepods, appear to be littoral, and are found mostly in the Las Vegas Wash area. Phytoplankton counts showed evidence for decreases in Bacillariophyta, Chlorophyta, Cyanophyta, and Cryptophyta across the basin from the wash to the dam area. Pyrrophyta, Chrysophyta, and Euglenophyta were not important in the phytoplankton flora at this season. Nygaard's and Pearsall's ratios and Palmer's pollution -tolerant algae indices were applied to the phytoplankton data. Results of the Nygaard and Pearsall ratios, the migration study, the transect study, and the population studies indicate that Boulder Basin is eutrophic.
    • Preference Criterion and Group Utility Model for Reservoir Control Under Uncertainty

      Krzysztofowicz, Roman (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1978-03)
      From the standpoint of real -time reservoir operation, the multipurpose control problem may be reduced to a dual purpose problem of (1) flood control under uncertain inflow and (2) conservation control (water supply, power generation, low flow augmentation, recreation, etc.) after the flood has receded. A preference criterion for real -time flood control under the conditions of uncertainty is developed in accordance with three postulates: (1) The input to the control process is a probabilistic forecast of the inflow hydrograph, (2) The control decisions are based upon the decision maker's value judgments concerning preferences over operating attributes, trade -offs between reservóir purposes, and attitude toward risk. (3) The conservation control is imbedded into the flood control through the attribute space of the preference criterion allowing thus for explicit consideration of the trade -offs between reservoir purposes. The preference criterion is developed within the framework of utility theory. The value judgments of the decision maker are quantified in terms of a two -attribute disutility function. It is argued that minimization of expected disutility is a plausible and well motivated criterion for multipurpose real -time reservoir control under uncertainty. A suitable disutility model is developed. The case of a group decision maker is analyzed in depth. Common group utility models based on aggregation of individual utility functions and interpersonal utility comparisons are critically reviewed. An alternative approach based on direct group value judgments is suggested, and a general group utility model for decision -making in engineering systems is developed. The disutility assessment procedures are analysed, and response biases that may be introduced into the decision maker's preference structure by the use of an inappropriate assessment scheme are identified. Some principles and novel techniques for assessing disutility functions are advocated; they are motivated by results of psychological research in human decision behavior, and are further supported by experimental evidence. Results of assessment of the reservoir control disutility function for several single and group decision makers are presented.
    • Preferential Reservoir Control Under Uncertainty

      Krzysztofowicz, Roman (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1978-11)
      A model for real -time control of a multipurpose reservoir under the conditions of uncertainty is developed. The control model is formulated as a multistage decision process. It is conceptualized in the form of two sub -processes. The first level process is a Forecast - Strategy Process which performs as an open-loop feedback controller. It is defined by a sequence of forecasts and optimal release strategies against these forecasts. At each forecast time (time of issuing the forecast), the optimal release strategy is computed for the time period equal to the lead time of the forecast, and it remains in execution until the next forecast time. The second level process, defined for each forecast time, is a Control Process which for the given forecast generates the release strategy satisfying the preference criterion (minimization of expected disutility). This process is formulated as a truncated Markovian adaptive controller performing on a finite set of discrete times --the same set which indexes the forecast inflow process. To evaluate the past performance of the control, a set of measures of effectiveness is proposed. Computational aspects of the control model are analyzed. Structural properties of the reservoir control process are explored in the main theorem which assures the monotonicity of the optimal strategy with respect to one of the state variables. Also, the properties of the optimal strategy for the case of a categorical forecast are proven. Next, two suboptimal strategies are derived: (1) partial open -loop strategy and (2) naive /partial open-loop strategy. Finally, a'discretization procedure which guarantees convergence of the numerical solution is discussed, and the computational requirements of the optimal and two suboptimal strategies are compared.
    • PRELIMINARY VEGETATION AND HYDROLOGIC ANALYSES FOR BINGHAM CIENEGA

      Baird, Kathryn J.; Ronayne, Michael J.; Maddock, Thomas, III; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1997-01)
      This report is in two parts. The first part covers the ecological processes pertinent to the restoration of Bingham Cienega. The second part presents a subregional groundwater flow model for analyzing the water budget, stream and spring behavior, and water table configuration. Because of the sparsity of ecological and hydrologic data, both parts must be considered as preliminary studies.
    • THE QUANTITATIVE FEATURES OF CHINA'S WATER RESOURCES: AN OVERVIEW

      Changming, Liu; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1983-02)
      China has a long history of hydrological development. According to Chinese legends, famous projects of flood water diversion were developed by the Great Yu as early as the year two thousand B.C. The earliest hydrological record appeared in 256 B.C., when Mr. Lipin and his son constructed the Dujiangyan irrigation system in the upper reach of the Mingjiang River in Sichuan Province. At Baopingkao, the water intake point of the Dujiangyan irrigation system, a water staff gage was carved on a stone for the measurement of water levels. Although hydrological studies in China started early, hydrology and water resources as modern sciences have been developed only in the last several decades, particularly rapidly in the last 30 years. For instance, the number of hydrological stations has increased 45 times, from about 350 to more than 16,000. Of these, about 3300 stations also take flow velocity measurements. The average density of the hydrological stations is about one per 530 km2 and that of discharge measurement stations about one in 3,000 km2. These stations are highly concentrated in eastern China. The longest records of precipitation are maintained in the large cities in eastern China, including Beijing, Shanghai and Tianjing. Beijing has 140 years of precipitation records. The Hankao hydrological station on the Changjiang (Yangtze) River has the longest discharge record spanning 117 years (1865- 1982).
    • Rainfall estimation from satellite infrared imagery using artificial neural networks

      Hsu, Kuo-Lin; Sorooshian, Soroosh; Gao, Xiaogang; Gupta, Hoshin Vijai; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1997)
      Infrared (IR) imagery collected by geostationary satellites provides useful information about the dirunal evolution of cloud systems. These IR images can be analyzed to indicate the location of clouds as well as the pattern of cloud top temperatures (Tbs). During the past several decades, a number of different approaches for estimation of rainfall rate (RR) from Tb have been explored and concluded that the Tb-RR relationship is (1) highly nonlinear, and (2) seasonally and regionally dependent. Therefore, to properly model the relationship, the model must be able to: (1) detect and identify a non-linear mapping of the Tb-RR relationship; (2) Incorporate information about various cloud properties extracted from IR image; (3) Use feedback obtained from RR observations to adaptively adjust to seasonal and regional variations; and (4) Effectively and efficiently process large amounts of satellite image data in real -time. In this study, a kind of artificial neural network (ANN), called Modified Counter Propagation Network (MCPN), that incorporates these features, has been developed. The model was calibrated using the data around the Japanese Islands provided by the Global Precipitation Climatology Project (GPCP) First Algorithm Intercomparison Project (AIP-I). Validation results over the Japanese Islands and Florida peninsula show that by providing limited ground-truth observation, the MCPN model is effective in monthly and hourly rainfall estimation. Comparison of results from MCPN model and GOES Precipitation Index (GPI) approach is also provided in the study.
    • RAINFALL-RUNOFF MODELING OF FLASH FLOODS IN SEMI-ARID WATERSHEDS

      Michaud, Jene Diane; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1992-06)
      Flash floods caused by localized thunderstorms are a natural hazard of the semi -arid Southwest, and many communities have responded by installing ALERT flood forecasting systems. This study explored a rainfall- runoff modeling approach thought to be appropriate for forecasting in such watersheds. The kinematic model KINEROS was evaluated because it is a distributed model developed specifically for desert regions, and can be applied to basins without historic data. This study examined the accuracy of KINEROS under data constraints that are typical of semi -arid ALERT watersheds. The model was validated at the 150 km2, semi -arid Walnut Gulch experimental watershed. Under the conditions examined, KINEROS provided poor simulations of runoff volume and peak flow, but good simulations of time to peak. For peak flows, the standard error of estimate was nearly 100% of the observed mean. Surprisingly, when model parameters were based only on measurable watershed properties, simulated peak flows were as accurate as when parameters were calibrated on some historic data. The accuracy of KINEROS was compared to that of the SCS model. When calibrated, a distributed SCS model with a simple channel loss component was as accurate as KINEROS. Reasons for poor simulations were investigated by examining a) rainfall sampling errors, b) model sensitivity and dynamics, and c) trends in simulation accuracy. The cause of poor simulations was divided between rainfall sampling errors and other problems. It was found that when raingage densities are on the order of 1/20 km2, rainfall sampling errors preclude the consistent and reliable simulation of runoff from localized thunderstorms. Even when rainfall errors were minimized, accuracy of simulations were still poor. Good results, however, have been obtained with KINEROS on small watersheds; the problem is not KINEROS itself but its application at larger scales. The study also examined the hydrology of thunderstorm -generated floods at Walnut Gulch. The space -time dynamics of rainfall and runoff were characterized and found to be of fundamental importance. Hillslope infiltration was found to exert a dominant control on runoff, although flow hydraulics, channel losses, and initial soil moisture are also important. Watershed response was found to be nonlinear.
    • A RANDOM-WALK SIMULATION MODEL OF ALLUVIAL-FAN DEPOSITION

      Price, Williams Evans, Jr.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1972-06)
      A digital model based on a random walk was used in an experiment to determine how well such a model is able to simulate alluvial - fan deposition. The model is in three dimensions and is dynamic with respect to both time and space. Two principal stochastic events were employed, (1) a relative uplift of the mountain area that is the source of the fan sediments, and (2) a storm event of sufficient magnitude to result in the deposition of material on the fan. These two events are assumed to follow independent Poisson processes with exponentially distributed interoccurrence times. The pattern of deposition is determined by a random walk from the canyon mouth at the mountain front, and each depositional event is assumed to occur instantaneously. The direction that each step in the walk takes is determined probabilistically by the gradient in the direction of flow, the momentum of flow, and the boundary conditions stipulated in the model. The type of flow, whether a depositing debris or water flow, or eroding water flow, depends upon the thickness of erodible material in the source basin. Deposition is assumed to occur over the entire route of flow either as a bed tapered in the direction of flow or as a bed of uniform thickness. The particle -size distribution of the water -flow deposits is governed by the slope in the direction of flow. Erosion is considered negative deposition and results from the exponential decline in elevation of the main stream channel at the fan apex during periods of no uplift, or from water flows containing little basin sediment. Results from the computer runs were printed as geologic maps of the fan surface, and geologic sections through the deposits; these indicate that, at least qualitatively, a random -walk model provides a reasonable basis for simulating alluvial -fan deposition.
    • RESPONSE FUNCTIONS IN THE CRITICAL COMPARISON OF CONJUNCTIVE MANAGEMENT SYSTEMS IN TWO WESTERN STATES

      Lacher, Laurel Jane; Maddock, Thomas, III; Lord, William B.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1993-04)
      Conjunctive management of surface and ground -water resources on state and local levels is a relatively new political phenomenon. This type of management has evolved, in part, in response to growing populations with ever -increasing, and often conflicting, water demands. In addition, a more sophisticated technical understanding of the physical link between groundwater and surface waters has led water managers to reconsider historical strategies for solving water supply problems. In light of growing demand and improved technology, some western states have begun the transition from crisis- oriented water management to one of long -term planning for population growth and environmental protection. This planning process requires that the constituents of a region define their water use goals and objectives so that various approaches to conjunctive management may be evaluated for their suitability to that particular physical and socio- political environment.
    • REVIEW OF MODELING OF WATER FLOW AND SOLUTE TRANSPORT IN THE VADOSE ZONE: Stochastic Approaches

      Yeh, T.-C. Jim; McCord, J. T.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1994-11-10)
      Hydrologic properties of the vadose zone are heterogeneous at many different scales. An accurate prediction of water flow and solute transport in the vadose zone requires detailed information about spatial distributions of the properties. Collecting such detailed spatial distribution of hydrologic properties of geological formations is a formidable task. As a result, hydrologic modelers face a difficult challenge: to make the best prediction with little information. During the past few decades many approaches and theories based on stochastic concepts have been developed in an attempt to overcome this difficulty. These stochastic approaches and theories provide ways not only to predict flow and transport processes in large -scale, heterogeneous vadose zones, but also to assess uncertainties in our predictions. One widely -investigated stochastic approach involves the use of effective flow and transport properties. The effective property approach essentially represents a generalization of the well -known equivalent homogeneous media approach discussed in most hydrology textbooks (e.g., using the arithmetic mean conductivity and harmonic mean conductivity for flow parallel to and normal to stratification, respectively, in layered media). This approach is a valuable tool in many practical situations but it predicts the ensemble behavior of a system which can be quite different from reality. To obtain predictions at higher resolutions than the effective property approach, many heterogeneous approaches have also been developed. This paper presents an overview of the stochastic theories related to both equivalent homogeneous media and heterogeneous approaches, it highlights their applications, and it discusses some of their deficiencies.
    • A REVIEW OF THE SCALE PROBLEM AND APPLICATIONS OF STOCHASTIC METHODS TO DETERMINE GROUNDWATER TRAVEL TIME AND PATH

      Yeh, T.-C. Jim; Stephens, Daniel B.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1989)
      The groundwater travel time along the fastest path of likely radionuclide transport is a regulatory criterion used to assess the hydrogeologic quality of a high - level radioactive waste repository. Hydrologists and engineers are limited in their ability to define with confidence the fastest path, owing to the heterogeneous nature of geologic materials. Field measurements of hydraulic properties such as in test or observation wells, are inherently averages of properties at scales smaller than the scale of the field measurement. As a result of averaging, subscale information is lost and there is uncertainty in defining the fastest trajectory of groundwater. This scale problem is explained through a review of the continuum and REV concepts in groundwater hydrology. The application of hydrodynamic dispersion concepts is recommended as a means of incorporating the effect of subscale heterogeneity on the fastest groundwater travel time. Sources of uncertainties in predicting groundwater travel time are discussed in the report. The uncertainties are mainly attributed to the heterogeneous nature of geologic formations. The heterogeneity of geologic materials can, however, be characterized quantitatively using geostatistical methods. Important statistical parameters include mean and variance. as well as the spatial correlation structures of the hydrologic properties within the hydrogeologic system. These parameters may he obtained from limited data base. Stochastic methods, reviewed and explained in this report, can take advantage of the geostatistical characterization to predict large -scale groundwater flow and solute transport. Several examples from recent scientific literature are provided to illustrate the application of stochastic methods to the groundwater travel time analysis. Stochastic methods in subsurface hydrology have only recently been evaluated under field conditions for a few locations, and validation of the theories is incomplete, especially in unsaturated fractured rocks. Nevertheless, research efforts should continue to improve the state -of -the art. Geostatistics and stochastic methods will be valuable tools in addressing the groundwater travel time objective
    • A riparian evapotranspiration package

      Maddock, Thomas, III; Baird, Kathryn J.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2002-10)
      A new evapotranspiration package for the U.S. Geological Survey's groundwater -flow model, MODFLOW, is documented. The Riparian Evapotranspiration Package (RIP-ET), provides flexibility in simulating riparian and wetland evapotranspiration (ET) not provided by the MODFLOW-96 Evapotranspiration (EVT) Package, nor by the MODFLOW-2000 Segmented Function Evapotranspiration (ETS1) Package. This report describes how the package was conceptualized and provides input instructions, listings and explanations of the source code, and an example simulation. Traditional approaches to modeling ET processes assume a piecewise linear relationship between ET flux rate and hydraulic head. The Riparian ET Package replaces this traditional relationship with a segmented, nonlinear dimensionless curve that reflects the eco-physiology of riparian and wetland ecosystems. Evapotranspiration losses from these ecosystems are dependent not only on hydraulic head but on the plant types present. User-defined plant functional groups (PFGs) are used to elucidate the interactive processes of plant ET with groundwater conditions. Five generalized plant functional groups based on transpiration rates, plant rooting depth, and drought tolerance are presented: obligate wetland, shallow-rooted riparian, deep-rooted riparian, transitional riparian and bare ground/open water. Plant functional groups can be further divided into subgroups (PFSG) based on plant size and/or density. The Riparian ET Package allows for partial habitat coverage and mixtures of plant functional subgroups to be present in a single model cell. This requires a determination of fractional coverage for each of the plant functional subgroups present in a cell to simulate the mixture of coverage types and resulting ET. The fractional cover within a cell has three components: 1) fraction of active habitat, 2) fraction of plant functional subgroup in a cell, and 3) fraction of plant canopy area. The Riparian ET package determines the ET rate for each plant functional group in a cell, the total ET in the cell, and the total ET rate over the region of simulation.
    • A riparian evapotranspiration package for MODFLOW-2000 and MODFLOW-2005

      Maddock, Thomas, III; Baird, Kathryn J.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2008-03)
      A new version of an evapotranspiration package for the U.S. Geological Survey's groundwater -flow model, MODFLOW, is documented. The Riparian Evapotranspiration Package (RIP-ET) provides flexibility in simulating riparian and wetland evapotranspiration (ET) not provided by the MODFLOW -2000 and MODFLOW 2005 traditional Evapotranspiration (EVT) Package, nor by the MODFLOW-2000 Segmented Function Evapotranspiration (ETS1) Package. This report describes how the package was conceptualized and provides input instructions, listings and explanations of the source code, and an example simulation. Traditional approaches to modeling ET processes assume a piecewise linear relationship between ET flux rate and hydraulic head. The RIP-ET replaces this traditional relationship with a segmented, nonlinear dimensionless curve that reflects the eco-physiology of riparian and wetland ecosystems. Evapotranspiration losses from these ecosystems are dependent not only on hydraulic head but on the plant types present. User -defined plant functional groups (PFGs) are used to elucidate the interactive processes of plant ET with groundwater conditions. Five generalized plant functional groups based on transpiration rates, plant rooting depth, and water tolerance ranges are presented: obligate wetland, shallow-rooted riparian, deep- rooted riparian, transitional riparian and bare ground /open water. Plant functional groups can be further divided into subgroups (PFSG) based on plant size, density or other user defined field. The RIP -ET allows for partial habitat coverage and mixtures of plant functional subgroups to be present in a single model cell. Habitat areas are designated by polygons. A polygon can contain a mixture of PFSGs and bare ground, and is assigned a calculated land surface elevation. This process requires a determination of fractional coverage for each of the plant functional subgroups present in a polygon to simulate the mixture of coverage types and resulting ET. The fractional cover within a cell has two components: 1) the polygonal fraction of active habitat in a cell, and 2) fraction of plant flux area in a polygon. The RIP -ET determines the ET rate for each plant functional group in a cell, the total ET in the cell, and the total ET rate over the region of simulation.
    • Scale issues of heterogeneity in vadose zone hydrology and practical solutions

      Yeh, T.-C. Jim; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1996-08-03)
      Hydrological properties of the vadose zone often exhibit a high degree of spatial variability at various scales due to the heterogeneous nature of geological formations. For laboratory scale problems (i.e., small cores, soil columns, and sand boxes), variation in pore size, pore geometry, and tortuosity of pore channels are the major source of heterogeneity. They are called laboratory-scale heterogeneity. Microstratification, foliation, cracks, and roots are also some possible heterogeneities at this scale. As our observation scale increases to a field, stratification or layering in a geologic formation becomes the dominant heterogeneity, which is often classified as field-scale heterogeneity. At an even larger observation scale, the regional-scale heterogeneity represents the variation of geologic formations or facies. Variations among sedimentary basins are then categorized as the global-scale heterogeneity. Fundamental theories for flow and solute transport through porous media are essentially derived for the laboratory-scale heterogeneity. When we attempt to apply these theories to the vadose zone, comprising heterogeneities of many different scales, we encounter the scale problem. To resolve this problem two approaches have evolved in the past: the system approach and the physical approach. The former approach treats the vadose zone as a low pass filter and its governing principle is determined by the relationship between its input and output histories (e.g., Jury et al., 1986). The latter approach however relies on upscaling the laboratory-scale theories to the vadose zone. While the system approach has been widely used by soil scientists, it is often criticized for its empiricism and the lack of physical principles. Besides, it is known to be limited to nonpoint source problems or those related to the integrated behavior of a system (for example, the average concentration of nitrate in the irrigation return flow at irrigation drains or their breakthrough at the water table beneath an irrigation field). Since this approach requires the knowledge of input and output histories and model calibrations, flow and tracer experiments must be carried out at a given site prior to prediction. Further, a calibrated system model for the vadose zone at a given depth under a given condition is often found unsuitable for different depths and conditions (e.g., Butters et al., 1989; Butters and Jury, 1989; Roth et al., 1991). While such system approaches are practical tools for predicting water flow and pollutant transport through thin vadose zones to the water table or to irrigation drains at agricultural fields, their utility for general hydrogeological problems is limited. Hydrogeological problems involve vadose zones of tens and hundreds of meters in thickness. Input sources to these vadose zones are small compared with the scale of hydrogeological settings. Yet, groundwater hydrologists have to focus on the spatial and temporal evolution of flow and spread of solutes over the vadose zone and regional aquifers (Stephens, 1996). Because of these above- mentioned reasons, the following discussion will concentrate on the physical approach that has been widely used by groundwater hydrologists. Moreover, the discussion will present only the author's point of view about the scale issue and approaches to the heterogeneity in the vadose zone.
    • SIMULATION OF GROUND-WATER FLOW TO ASSESS THE EFFECTS OF PUMPING AND CANAL LINING ON THE HYDROLOGIC REGIME OF THE MESILLA BASIN: Dona Ana County, New Mexico & El Paso County, Texas

      Lang, Patrick T.; Maddock, Thomas, III; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1995-04)
      This study, which is to provide information to a settlement over the rights to water resources in the Mesilla Basin, uses a groundwater model to estimate how pumping in the basin affects the hydrologic regime.
    • Simulation of groundwater conditions in the Colorado River Delta, Mexico

      Feirstein, Eden Jael; Zamora, Francisco; Vionnet, Leticia Beatriz; Maddock, Thomas, III; Department of Hydrology & Water Resources, The University of Arizona; Sonoran Institute; Facultad de Ingeniería y Ciencias Hídricas (FICH) - Universidad Nacional del Litoral (UNL) (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2008-05)
      The Colorado River Delta (CRD) is a large sedimentary complex within a tectonically active structurally controlled basin. The CRD lies across the U.S.-Mexico international boundary and is traversed by the Colorado River on is way to the Gulf of California. Multidisciplinary research addressing the impact of the hydrologic change in the CRD has been increasing since the 1980's. To help expand the base of this knowledge, a groundwater model for the CRD within Mexico was developed. A conceptual model was constructed and transformed within the Department of Defense Groundwater Modeling Software (GMS) into a numerical model using the MODFLOW 2005 code made available by the U.S. Geological Survey. Model results indicates that large scale flood events on the Colorado River act as a recharge to the aquifer and show that the relationship between groundwater withdrawals and capture are evident on an seasonal scale. The model will form the parent basis for further Delta studies using the Local Grid Refinement (LRG), a methodology inherent to MODFLOW 2005.
    • Simulation of Groundwater Conditions in the Upper San Pedro Basin for the Evaluation of Alternative Futures

      Goode, Tomas Charles; Maddock, Thomas, III; Department of Hydrology & Water Resources, The University of Arizona; University of Arizona Research Laboratory for Riparian Studies (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2000)
      The creation of the groundwater model of the Upper San Pedro Basin included two developmental phases: the creation of a conceptual and numerical model. The creation of the conceptual model was accomplished through the utilization of Geographic Information System (GIS) software, namely ArcView, used primarily to view and create point, line, and polygonal shapes. The creation of a numerical model was accomplished by the infusion of the conceptual model into a 3D finite difference grid used in MODFLOW groundwater software from the U.S. Geological Survey. MODFLOW computes the hydraulic head (water level) for each cell within the grid. The infusion of the two models (conceptual and numerical) was allowed through the use of Department of Defense Groundwater Modeling System (GMS) software. The time period for groundwater modeling began with predevelopment conditions, or "steady state." Steady state conditions were assumed to exist in 1940. The steady state was used as the initial condition for the subsequent transient analysis. The transient simulation applied historical and current information of pumping stresses to the system from 1940 to 1997. After modeling current conditions, Alternative Futures' scenarios were simulated by modifying current stresses and by adding new ones. The possible future impacts of to the hydrologic system were then evaluated.