• Literature Pertaining to Water Quality and Quantity in Unsaturated Porous Media

      Tyagi, Avdhesh K. (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1972-05)
      Introduction: The movement of moisture and the simultaneous transfer of water and solutes in unsaturated porous media are problems of practical interest in ground water hydrology and soil physics. A large fraction of the water falling as rain on the land surfaces of the earth moves through unsaturated zone of soil during the subsequent processes of infiltration, drainage, evaporation, and absorption of soil -water by plant roots. A soil profile is characteristically nonuniform in its properties, nonisothermal, and may be nonrigid. Microorganisms and the roots of higher plants are a part of the system. This region is characterized by cylic fluctuation of water content as water is removed from the soil profile by evaportranspiration and replenished by recharge, irrigation, or rainfall. In unsaturated porous media the problem of movement and retention of water may be approached from (1) the molecular, (2) the microscopic, or (3) the macroscopic standpoint. In the molecular viewpoint theories of the mechanisms of flow and retention in terms of the behavior of water molecules are devised. At microscopic level a theory of flow treating the fluid in pores as a continuum and applying the principles of continuum mechanics to understand the detailed behavior of fluid within the pores is developed. The complicated pore geometry and consequent impossibility of specifying the boundary conditions on flow, preclude any practical progress by this appraoch. Since the behavior of individual molecules and the distributions of fluid velocity and pressure cannot be observed in porous media, a macroscopic theory of flow is needed. In the macroscopic approach, all variables are treated continuous functions of time and space. Velocity, pressure, and other variables are assumed as point functions. Thus, any theory of water transport to be useful must be developed to the point of describing the transfer of water on the macroscopic level. The coefficients of transport such as permeability and diffusivity can be defined microscopically. In many investigations which involve the transport of pesticides and fertilizes along with water , the simultaneous movement of water and solutes is of primary concern. These pollutants when mixed with water move in the unsaturated soil and finally join the region of saturated soil or water table, resulting in the contamination of fresh water existing below the water table. The scope of this report is to review the available literature, that may be categorized into two parts; one, the movement of water in unsaturated soil, and the other, the simultaneous movement of water and solutes in unsaturated soil. The papers, reviewed in this report, pertain to the theoretical study, laboratory study and field study on the two problems. At the end, an appendix appears which lists the references, categorizing the kind of study by various investigators.
    • A lower San Pedro river basin groundwater flow model

      Whittier, Jonathan Douglas; Maddock, Thomas, III; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2004)
      Water issues in the Lower San Pedro River basin in southeastern Arizona are becoming increasingly contentious as urban development, agriculture, and mining needs compete with the needs of the riparian habitat. To better understand the water demands in this basin, a new groundwater flow model has been created. First, the conceptual model was produced using various Geographic Information System (GIS) applications. A new method allocating digital precipitation data to the smaller drainages within the watershed was used to estimate mountain front recharge. Well data was gathered from both the United States Geological Survey (USGS) and Arizona Department of Water Resources (ADWR). Depth to bedrock was interpolated from an earlier gravity survey of the area. The current extent of riparian vegetation was determined by recent United States Forest Service aerial photography. GIS shapefiles were created depicting the data necessary for MODFLOW. Second, the numerical MODFLOW model was formed using GMS (Groundwater Modeling System), a graphical user interface for MODFLOW. GMS was used to create the grid, allocate the information from the shapefiles into MODFLOW input files, create the MODFLOW numerical model, and calibrate the model. The model results project potential impacts to the overall sustainability of groundwater within the basin. In the future, the model will be used as an administrative tool to assess alternative land management scenarios and their abilities to sustain or improve the riparian habitat along the San Pedro River.
    • Management Model for Electrical Power Production from a Hot-Water Geothermal Reservoir

      Maddock, Thomas, III; Mercer, James W.; Faust, Charles R.; Attanasi, Emil D.; University of Arizona; U.S. Geological Survey (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1979-11)
      A management model is developed that determines the optimum economic recoverability of a particular hot -water geothermal reservoir undergoing exploitation for electric power generation. The management model integrates a physical model of the reservoir that predicts the areas of pressure decline due to withdrawals, and pressure rise due to reinjection of spent fluid, with a model of a two -stage steam turbine power plant that determines the quantity of electricity generated for a rate of hot -water extraction. Capital costs, variable costs and annual fixed costs are obtained for the reservoir development, extraction and reinjection, the transmission system, and the power plant. Revenues are determined for electrical power production. Application of the management model to a simplified, yet realistic example reservoir demonstrates that the methodology developed in this report can be used for analyzing the management of an integrated geothermal reservoir-power plant system.

      Everett, Lorne G.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1972-09)
      The temporal and spatial changes in chemical and biological properties of Lake Mead have been investigated, thereby indicating the sources of water pollution and the time of highest pollution potential. Planktonic organisms have been shown to indicate the presence of water problems. Macro- and micro-nutrient analyses have shown that primary productivity is not inhibited by limiting concentrations. A mathematical model has been developed, tested with one set of independent data, and shown worthy of management utility. Although the model works very well for the Lake Mead area, the physical reality of the Multiple Linear Regression equation should be tested on independent data.

      Rogers, James Joseph, 1942-; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1971-06)
      This study explores the possible role of mathematical system theory in integrating existing ecological knowledge within the existing concepts of the structure of the biosphere. The objective of this integration is a theory of ecosystems which must include interactions. The basic unit of the biosphere is the biogeocoenose; similar to the ecosystem, but homogeneous with respect to topographic, microclimatic, vegetation, animal, pedalogical, hydrological and geochemical conditions. The role of the biogeocoenose in a theory of ecosystems based on system theory is discussed. The biogeocoenose may serve as the building block for modeling watersheds as ecosystems. The fundamentals of system theory are reviewed. As an example, an analysis and synthesis of the arid zone water balance follows. The water balance is resolved into twenty components which represent the water balance of (1) the canopy, (2) the mulch, (3) the soil surface, (4) the soil, and (5) the plant, including interactions. The twenty components were modeled as separate systems which were later coupled into one overall, complex, well defined ecosystem water balance system. The example illustrates the role of system theory in integrating ecological knowledge. Further discussion indicates the need for explicitly including plant behavior in the water balance model.
    • Model Choice in Multiobjective Decision Making in Water and Mineral Resource Systems

      Gershon, Mark Elliot; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1981-05)
      The problem of model choice in multiobjective decision making, that is, the selection of the appropriate multiobjective solution technique to solve an arbitrary multiobjective decision problem, is considered. Classifications of the available techniques are discussed, leading to the development of a set of 27 model choice criteria and an algorithm for model choice. This algorithm divides the criteria into four groups, oily one of which must be reevaluated for each decision problem encountered. Through the evaluation of the available multiobjective techniques with respect to each of the model choice criteria, the model choice problem is modeled as a multiobjective decision problem. Compromise programming is then used to select the appropriate technique for implementation. Two case studies are presented to demonstrate the use of this algorithm. The first is a river basin planning problem where a predefined set of alternatives is to be ranked with respect to a set of criteria, some of which cannot be quantified. The second is a coal blending problem modeled as a mathematical programming problem with two linear objective functions and a set of linear constraints. An appropriate multiobjective solution technique is selected for each of these case studies. In addition, an approach for the solution of dynamic multiobjective problems, one area where solution techniques are not available, is presented. This approach, known as dynamic compromise programming, essentially transforms a multiobjective dynamic programming problem into a classical dynamic programming problem of higher dimension. A dynamic programming problem, modeled in terms of three objectives, is used to demonstrate an application of this technique.

      Castano, Eugenio; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1976-06)
      The model choice problem in Hydrology is illustrated by means of the optimum levee design for flat rivers along a confluence reach. Special attention is given to the selection of a probability distribution for the joint flood stages. The optimality criterion used is the minimization of construction plus expected flood damage costs. The main assumption in the mathematical model is that the levee profile is uniquely determined as a function of the levee heights at the extremes of the reach; thus the problem is reduced to the determination of the optimum pair of extreme levee heights. The selection of a probability distribution of flood stages, from a set of distributions estimated from the partial duration series, is performed using either one of two selection procedures: likelihood of the Chi -square statistic and sample likelihoods. A composite distribution, taking into account the model uncertainty, is also derived. The methodology presented is applied to the remodeling of the levee on the west bank of the Zagyva River, in Hungary. A sensitivity analysis is performed, using the best ranking distributions according to the two model choice procedures. The composite distribution appears to offer a reasonable choice.
    • Modeling of Ground-Water Flow and Surface/Ground-Water Interaction for the San Pedro River Basin Part I Mexican Border to Fairbank, Arizona

      Vionnet, Leticia Beatriz; Maddock, Thomas, III; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1992)
      Many hydrologic basins in the southwest have seen their perennial streamflows turn to ephemeral, their riparian communities disappear or be jeopardized, and their aquifers suffer from severe overdrafts. Under -management of ground -water exploitation and of conjunctive use of surface and ground waters are the main reasons for these events.
    • MODRSP: a program to calculate drawdown, velocity, storage and capture response functions for multi-aquifer systems

      Maddock, Thomas, III; Lacher, Laurel J.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1991)
      MODRSP is program used for calculating drawdown, velocity, storage losses and capture response functions for multi - aquifer ground -water flow systems. Capture is defined as the sum of the increase in aquifer recharge and decrease in aquifer discharge as a result of an applied stress from pumping [Bredehoeft et al., 19821. The capture phenomena treated by MODRSP are stream- aquifer leakance, reduction of evapotranspiration losses, leakance from adjacent aquifers, flows to and from prescribed head boundaries and increases or decreases in natural recharge or discharge from head dependent boundaries. The response functions are independent of the magnitude of the stresses and are dependent on the type of partial differential equation, the boundary and initial conditions and the parameters thereof, and the spatial and temporal location of stresses. The aquifers modeled may have irregular -shaped areal boundaries and non -homogeneous transmissive and storage qualities. For regional aquifers, the stresses are generally pumpages from wells. The utility of response functions arises from their capacity to be embedded in management models. The management models consist of a mathematical expression of a criterion to measure preference, and sets of constraints which act to limit the preferred actions. The response functions are incorporated into constraints that couple the hydrologic system with the management system (Maddock, 1972). MODRSP is a modification of MODFLOW (McDonald and Harbaugh, 1984,1988). MODRSP uses many of the data input structures of MODFLOW, but there are major differences between the two programs. The differences are discussed in Chapters 4 and 5. An abbreviated theoretical development is presented in Chapter 2, a more complete theoretical development may be found in Maddock and Lacher (1991). The finite difference technique discussion presented in Chapter 3 is a synopsis of that covered more completely in McDonald and Harbaugh (1988). Subprogram organization is presented in Chapter 4 with the data requirements explained in Chapter 5. Chapter 6 contains three example applications of MODRSP.
    • MR2K: A program to calculate drawdown, velocity, storage and capture response functions

      Maddock, Thomas, III; Lacher, Laurel J.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2008)
      A program, MR2K, used for calculating drawdown, velocity, storage loss, and capture response functions for multi -aquifer groundwater flow systems was developed. Capture is defined as the sum of the increase in aquifer recharge and decrease in aquifer discharge as a result of an applied stress from groundwater pumping. The capture phenomena treated are stream-aquifer leakance, reduction of evapotranspiration losses, reduction of drain flows, flows to and from prescribed head boundaries, and increases or decreases in natural recharge or discharge from head-dependent boundaries. The response functions are independent of the magnitude of the pumping stresses, and are dependent on the type of partial differential equation, boundary and initial conditions and the parameters thereof, and the spatial and temporal locations of stresses. The aquifers modeled may have irregular- shaped boundaries and nonhomogeneous transmissive and storage qualities. The stresses are groundwater withdrawals from wells. The utility of response functions arises from their capacity to be embedded in management models such as decision support systems. The response functions are incorporated into the objective function or constraints that couple the hydrologic system with the management system. Three response -function examples are presented for a hypothetic basin.

      Ohte, Nobuhito; Bales, Roger C.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1994)
      The University of Arizona's Alpine Hydrochemical Model (AHM) is an integrated set of algorithms for water and chemical balances that describes hydrologic and chemical processes in a headwater catchment. We developed AHM for use both as a research tool and as a predictive model for estimating effects of natural and anthropogenic changes in climate or in atmospheric -pollutant loading on alpine watersheds. We initially applied AHM to Emerald Lake watershed in the southern Sierra Nevada, and estimated model parameters by trial and error using a single water year of data and process -level studies. Using the same parameters, AHM successfully reproduced stream chemistry and discharge for a second water year. We have extended that empirical analysis by doing a systematic analysis of parameter sensitivity and an automatic optimization of model parameters. In the sensitivity analysis, a large number of Monte -Carlo simulations done on the multi -dimensional function field were used to identify the sensitive parameters and to set an appropriate range for each parameter. These results were then used to reduce the computational load in the automatic optimization, which is based on the downhill simplex method in multiple dimensions; we estimate the global optimum parameter set according to the fluctuation of the sum of squared errors between observed and modeled stream discharge and chemistry. Sensitive physical and chemical parameters were identified, including those describing evapotranspiration, hydraulic conductivity and soil depth or porosity; and those describing mineral weathering, ion release from the snow - pack, ion exchange, soil CO2 and nitrogen reactions. The automatic optimization method succeeded in estimating a global optimum parameter set from a single water year of data that improved the fitting compared to the set from trial and error manipulation.
    • A multi-step automatic calibration scheme (MACS) for river forecasting models utilizing the national weather service river forecast system (NWSRFS)

      Sorooshian, Soroosh; Gupta, Hoshin; Hogue, Terri S.; Holz, Andrea; Braatz, Dean; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1999-10)
      Traditional model calibration by National Weather Service (NWS) River Forecast Center (RFC) hydrologists involves a laborious and time -consuming manual estimation of numerous parameters. The National Weather Service River Forecasting System (NWSRFS), a software system used by the RFCs for hydrologic forecasting, includes an automatic optimization program (OPT3) to aid in model calibration. The OPT3 program is not used operationally by the majority of RFC hydrologists who perform calibration studies. Lack of success with the traditional single - step, single-criterion automatic calibration approach has left hydrologists more comfortable employing a manual step-by-step process to estimate parameters. This study develops a Multistep Automatic Calibration Scheme (MACS), utilizing OPT3, for the river forecasting models used by the RFCs: the Sacramento Soil Moisture Accounting (SAC-SMA). and SNOW-17 models. Sixteen parameters are calibrated in three steps, replicating the progression of manual calibration steps used by NWS hydrologists. MACS is developed by minimizing different objective functions for different parameters in a step -wise manner. Model runs are compared using the MACS optimized parameters and the manually estimated parameters for six basins in the North Central River Forecast Center (NCRFC) forecast area. Results demonstrate that the parameters obtained via the MACS procedure generally yield better model performance than those obtained by manual calibration. The MACS methodology is a time-saving approach that can provide prompt model forecasts for NWS watersheds.
    • A multiobjective global optimization algorithm with application to calibration of hydrologic models

      Yapo, Patrice O.; Gupta, Hoshin Vijai; Sorooshian, Soroosh; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1997-02)
      This report presents a new multiple objective optimization algorithm that is capable of solving for the entire Pareto set in one single optimization run. The multi-objective complex evolution (MOCOM-UA) procedure is based on the following three concepts: (1) population, (2) rank-based selection, and (3) competitive evolution. In the MOCOM-UA algorithm, a population of candidate solutions is evolved in the feasible space to search for the Pareto set. Ranking of the population is accomplished through Pareto ranking, where all points are successively placed on different Pareto fronts. Competitive evolution consists of selecting subsets of points (including all worst points in the population) based on their ranks and moving the worst points toward the Pareto set using the newly developed multi-objective simplex (MOSIM) procedure. Test analysis on the MOCOM-UA algorithm is accomplished on mathematical problems of increasing complexity and based on a bi-criterion measure of performance. The two performance criteria are: (1) efficiency, as measured by the ability of the algorithm to converge quickly, and (2) effectiveness, as measured by the ability of the algorithm to locate the Pareto set. Comparison of the MOCOM-UA algorithm against three multi-objective genetic algorithms (MOGAs) favors the former. In a realistic application, the MOCOM-UA algorithm is used to calibrate the Soil Moisture Accounting model of the National Weather Service River Forecasting Systems (NWSRFS-SMA). Multi-objective calibration of this model is accomplished using two bi-criterion objective functions, namely the Daily Root Mean Square-Heteroscedastic Maximum Likelihood Estimator (DRMS-HMLE) and rising limb /falling limb (RISE/FALL) objective functions. These two multi-objective calibrations provide some interesting insights into the influence of different objectives in the location of final parameter values, as well as limitations in the structure of the NWSRFS-SMA model.
    • 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.

      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.

      Staker, Robert Dale, 1945-; 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.

      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.