• Hydrogeology in the United States 1780-1950

      Davis, Stanley N.; Davis, Augusta G.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2005-11)
      Most modern textbooks that deal with subsurface water, or hydrogeology, include a brief summary of the historical development of the science. In our book, we have expanded on this general theme without introducing the more technical aspects of the topic. We have, however, emphasized two important points that are commonly overlooked. First, most of the fundamental contributions made during the 1800's were not American but were primarily European. Second, 1885 was the date of the first ground -water publication of the United States Geological Survey, but it did not mark the birth of hydrogeology in the United States. Some American contributions were made about 80 years earlier. The authors are grateful for the assistance of many individuals. T. N. Narasimhan, M. P. Anderson, F. M. Phillips, D. B. Stephens, J. V. Brahana, C. W. Fetter, D. Deming, and D. I. Siegel were given the initial version of our book and provided numerous useful comments.

      Lovell, Robert Edmund,1921-; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1975-06)
      The problem of selecting appropriate mathematical models for use in studying hydrological phenomena has created a situation in which the choice of suitable models by hydrologic practitioners has become exceedingly complex. The extensive comments in the literature indicate that neither the traditional system of technical journals nor the more modern computer -based retrieval schemes have really solved the problem. Further examination shows that similar problems have arisen in many fields, hence a well organized attack on the specific problem of hydrologic model choice can have a more general application. The present problem is identified as a requirement to codify and make accessible to users information in a more directly user oriented format. The problem of model choice arises at several levels, ranging from decision on what fundamental structure to use, to choice of parameters, and on to model calibration and validation. This paper is focused on a scheme to aid in model structure choice. The essential ingredients of model structure choice, and indeed of many choice processes, are extracted and embedded in a generalized set theoretic mathematical notational framework in order to give some insight into the nature of the problem. Within this framework the specialized features of the model choice problem are analyzed, and a specialized model is developed for assisting in model choice and all problems similarly situated. These considerations lead to the development of a finite vector of objective statements with codified responses prepared by a panel of qualified researchers who are willing and able to construct the essential information in a user oriented format. It is required that the panel not only couch their information in objective oriented terms but that they also generate value judgments for the individual components. In this way, those using the system can take advantage of the expert opinions embedded in the model while, at the same time, tailoring the choice to meet their own specific needs and aspirations. This results in what is defined as a mathematical CHOICEMODEL. The implementation of a system for interactive computation of the CHOICEMODEL is described in detail, and the associated computer programs are presented in appendices. A detailed instruction manual is given, and the implementation of the method is illustrated by an easily understood model of the ingredients of the problem of selecting an 8 -track stereo tape deck for home use. The plan is outlined whereby hydrologic choice models can be developed within the CHOICEMODEL system by a selected panel of expert EVALUATORs.
    • Hydrologic resource assessment of upper Sabino Creek basin, Pima county, Arizona

      Peters, Christopher J.; Bales, Roger C.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2001-01)
      A hydrologic resource assessment was performed for upper Sabino Creek basin, using data from a variety of local, state, and Federal agencies and organizations. Hydrologic fluxes were identified and quantified in order to create a monthly water budget. Snowmelt and rainfall are the major inputs to the watershed. Evapotranspiration accounts for the greatest loss of water. Human consumption and streamflow, while important for regulatory and aesthetic reasons, are relatively minor components of the water budget. Evapotranspiration, precipitation, and groundwater recharge / soil moisture account for the greatest fluxes of water in the basin. Precipitation is the most variable hydrologic process in the study area. Over a 47-year period, the greatest amount of water moving through the system in any one month was 6,300 acre-feet in October of 1983. The month with the lowest movement of water was December 1996, with 400 acre-feet. A comparison of Sabino Creek data with the El Niño Southern Oscillation phenomenon shows a strong correlation with precipitation and streamflow in upper Sabino Creek basin.

      Harshman, Celina Anne; Maddock, Thomas III; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1993)
      Riparian forests, which support rich biological diversity in the North American southwest, have experienced a sharp decline in the last century. The extent of this decline has been estimated to range from 70% to 95% across the southwest (Johnson and Haight, 1984). The principal components of riparian forests which sustain a broad spectrum of species and describe the overall health of a system are cottonwoods (sp. Populus) and willows (sp. Salix). The importance of cottonwoods is aptly described by Rood et al (1993): "....these trees provide the foundation of the riparian forest ecosystem in semi -arid areas of western North America. Unlike wetter areas to the east and west, a loss of cottonwoods in these riparian areas is not compensated through enrichment from other tree species. If the cottonwoods die, the entire forest ecosystem collapses." Cottonwood and willow species are adversely affected by anthropogenic influences ranging most prominently from the introduction of regulated flows via dams to agricultural clearing, water diversions, livestock grazing, and domestic settlement. These influences effectively alter the system hydrology that the forests rely upon. As the widespread destruction of these forests and the associated irreparable damage to endangered species habitat has come into clear view in the past decade, research efforts have focused upon identifying the ecological needs of riparian systems. The potential of modifying such systems to soften the human impact upon them, in effect presenting further alterations on a hydrologic system to return it to its natural regime, is another component of the research on riparian systems. The Bill Williams River riparian corridor, near Parker, Arizona (Figure 1.1), contains the last extensive native riparian habitat along the lower Colorado River (BWC Technical Committee, 1993). This unique resource was established as the Bill Williams River Management Unit, Havasu National Wildlife Refuge in 1941 and covers 6105 acres along the lower 12 miles of the Bill Williams River (Rivers West, 1990). The Bill Williams Unit is currently managed by the U.S. Fish and Wildlife Service of the U.S. Department of Interior. The U.S. Fish and Wildlife Service also funded this research effort. The lush vegetation corresponding to the wetland conditions along the valley floor sharply contrast with the Sonoran desert landscape of the upper valley walls creating a magnificent picture. The Management Unit terminates at Lake Havasu, which forms the confluence of the Bill Williams and Colorado Rivers. The system provides habitat for a wide variety of species, many of which are endangered or state- listed species, including habitat for neotropical migratory birds. This habitat has undergone serious degeneration during the past quarter century. The recruitment of cottonwood and willow trees has been fatally interrupted by anthropogenic encroachment in the form of the construction of Alamo Dam in 1969 at the head of the Bill Williams River and commercial development along the River.
    • Improving the Reliability of Compartmental Models: Case of Conceptual Hydrologic Rainfall-Runoff Models

      Sorooshian, Soroosh; Gupta, Vijai Kumar; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1986-08)

      Wolford, Ross A.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1992-12)
      Seasonally snow covered alpine areas play a larger role in the hydrologic cycle than their area would indicate. Their ecosystems may be sensitive indicators of climatic and atmospheric change. Assessing the hydrologic and bio- geochemical responses of these areas to changes in inputs of water, chemicals and energy should be based on a detailed understanding of watershed processes. This dissertation discusses the development and testing of a model capable of predicting watershed hydrologic and hydrochemical responses to these changes. The model computes integrated water and chemical balances for watersheds with unlimited numbers of terrestrial, stream, and lake subunits, each of which may have a unique, variable snow -covered area. Model capabilities include 1) tracking of chemical inputs from precipitation, dry deposition, snowmelt, mineral weathering, basefiow or flows from areas external to the modeled watershed, and user -defined sources and sinks, 2) tracking water and chemical movements in the canopy, snowpack, soil litter, multiple soil layers, streamflow, between terrestrial subunits (surface and subsurface movement), and within lakes (2 layers), 3) chemical speciation, including free and total soluble species, precipitates, exchange complexes, and acid -neutralizing capacity, 4) nitrogen reactions, 5) a snowmelt optimization procedure capable of exactly matching observed watershed outflows, and 6) modeling riparian areas. Two years of data were available for fitting and comparing observed and modeled output. To the extent possible, model parameters are set based on physical or chemical measurements, leaving only a few fitted parameters. The effects of snowmelt rate, rate of chemical elution from the snowpack, nitrogen reactions, mineral weathering, and flow routing on modeled outputs are examined.

      Monarchi, David Edward, 1944-; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1972-06)
      This research develops an algorithm for solving a class of multiple objective decision problems. These problems are characterized by continuous policy variables, nonlinear constraints, and nonlinear criterion functions. Our underlying philosophy is that of the Gestalt psychologists-- we cannot separate the problem and its solution from the environment in which the problem is placed. The decision maker is necessarily a part of this environment, thus implying that he, as an individual, must be part of the solution of the problem. Another central assumption in this research is that there is not an "optimal" answer to the problem, only "satisfactory" solutions. The reasons for this are based partly on the insensitivities of the body to minute changes and to the insensitivity of our preferences within certain ranges of acceptance. In addition, we assure that the individual is capable of solving decision situations involving a maximum of about 10 goals and that he operates upon them in some sort of serial manner as he searches for a satisfactory alternative. The serial manner is a reflection of his current ranking of the goals. Based on these assumptions we have developed a cyclical interactive algorithm in which the decision maker guides a search mechanism in attempting to find a satisfactory alternative. Each cycle in the search consists of an optimization phase and an evaluation phase, after which the decision maker can define a new direction of search or terminate the algorithm. The optimization phase is based on a linearization technique which has been quite effective in terms of the problems we have attempted to solve. It is capable of solving general nonlinear programming problems with a large number of nonlinear constraints. Although the constraint set must be convex in order to guarantee the location of a global optimum, we can use the method on concave sets recognizing that we may find only a local optimum. An extensive synthetic case study of a water pollution decision problem with 6 conflicting goals is provided to demonstrate the feasibility of the algorithm. Finally, the limitations of the research are discussed. We tentatively conclude that we have developed a method applicable to our research problem and that the method can be applied to "real world" decision situations.
    • An interdisciplinary analysis of the water quality problems of the Safford Valley, Arizona

      Muller, Anthony B.; Battaile, John F.; Bond, Leslie A.; Kukuck, Margret C.; Lamson, Philip W.; Leonard, Guy J.; Zimbler, Linda; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1972-09)
    • Investigation of the national weather service soil moisture accounting models for flood prediction in the northeast floods of january 1996

      Hogue, Terri S.; Sorooshian, Soroosh; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1999-10)
      Extensive flooding occurred throughout the northeastern United States during January of 1996. The flood event cost the lives of 33 people and over a billion dollars in flood damage. Following the `Blizzard of `96 ", a warm front moved into the Mid-Atlantic region bringing extensive rainfall and causing significant melting and flooding to occur. Flood forecasting is a vital part of the National Weather Service (NWS) hydrologic responsibilities. Currently, the NWS River Forecast Centers use either the Antecedent Precipitation Index (API) or the Sacramento Soil -Moisture Accounting Model (SAC-SMA). This study evaluates the API and SAC -SMA models for their effectiveness in flood forecasting during this rain -on -snow event. The SAC -SMA, in conjunction with the SNOW-17 model, is calibrated for five basins in the Mid -Atlantic region using the Shuffled Complex Evolution (SCE-UA) automatic algorithm developed at the University of Arizona. Nash-Sutcliffe forecasting efficiencies (Ef) for the calibration period range from 0.79 to 0.87, with verification values from 0.42 to 0.95. Flood simulations were performed on the five basins using the API and calibrated SAC-SMA model. The SAC-SMA model does a better job of estimating observed flood discharge on three of the five study basins, while two of the basins experience flood simulation problems with both models. Study results indicate the SAC-SMA has the potential for better flood forecasting during complex rain-on-snow events such as during the January 1996 floods in the Northeast.
    • Investigations into the availability of additional water supplies and water storage areas for the Santa Cruz active management area, Arizona

      Pranschke, Stephanie; Mac Nish, Robert D.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2002)
      The desert climate of Southern Arizona coupled with the overdraft of its groundwater resources, led to the passing of the 1980, Groundwater Management Act. The Act mandates the creation of management plans in designated areas of heavy overdraft. Of the four initial Active Management Areas (AMAs, three had management plans that were designed to secure sustainable yield of the aquifer by 2025. In 1994, the Arizona legislature created a fifth AMA by designating the southern part of the Tucson AMA as the Santa Cruz AMA (SCAMA). The purpose for this subdivision was to facilitate the bi- national negotiations for coordinated water resource management in this internationally shared basin. Additionally, the SCAMA is to coordinate the management of surface water and groundwater rights for public health, safety and welfare. A.R.S. § 45-411.04. The legislature also assigned the SCAMA the management goals of maintaining safe -yield conditions and preventing long -term declines in local water table levels. A.R.S. § 45- 562(C) (ADWR, 1999). This study is a result of a grant award from the 1999 Augmentation and Conservation Assistance Program in an attempt to investigate the availability of additional water supplies and water storage areas within the SCAMA.
    • Investigations of stream-aquifer interactions using a coupled surface-water and ground-water flow model

      Vionnet, Leticia Beatriz; Maddock, Thomas, III; Goodrich, David C.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1997-01)
      A finite element numerical model is developed for the modeling of coupled surface-water flow and ground-water flow. The mathematical treatment of subsurface flows follows the confined aquifer theory or the classical Dupuit approximation for unconfined aquifers whereas surface-water flows are treated with the kinematic wave approximation for open channel flow. A detailed discussion of the standard approaches to represent the coupling term is provided. In this work, a mathematical expression similar to Ohm's law is used to simulate the interacting term between the two major hydrological components. Contrary to the standard approach, the coupling term is incorporated through a boundary flux integral that arises naturally in the weak form of the governing equations rather than through a source term. It is found that in some cases, a branch cut needs to be introduced along the internal boundary representing the stream in order to define a simply connected domain, which is an essential requirement in the derivation of the weak form of the ground-water flow equation. The fast time scale characteristic of surface-water flows and the slow time scale characteristic of ground-water flows are clearly established, leading to the definition of three dimensionless parameters, namely, a Peclet number that inherits the disparity between both time scales, a flow number that relates the pumping rate and the streamflow, and a Biot number that relates the conductance at the river-aquifer interface to the aquifer conductance. The model, implemented in the Bill Williams River Basin, reproduces the observed streamflow patterns and the ground-water flow patterns. Fairly good results are obtained using multiple time steps in the simulation process.
    • An Iterative Geostatistical Inverse Method For Steady-Flow In The Vadose Zone

      Zhang, Jinqi; Yeh, T.-C. Jim; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1996-02-01)
      An iterative stochastic inverse technique utilizing both primary and secondary information is developed to estimate conditional means of unsaturated hydraulic conductivity parameters (saturated hydraulic conductivity and pore -size distribution parameters) in the vadose zone. Measurements of saturated hydraulic conductivity and pore -size distribution parameter are considered as the primary information, while measurements of steady -state flow processes (soil -water pressure head and degree of saturation) are regarded as the secondary information. This inverse approach is similar to the classical geostatistical approach, which utilizing a linear estimator that depends on the cross- covariance and covariance functions of unsaturated hydraulic conductivity parameters and flow processes. The linear estimator is, however, improved successively by solving the governing flow equation and by updating the residual covariance and cross- covariance functions, in an iterative manner. Using an approximate perturbation solution for steady, variably saturated flow under general boundary conditions, the covariances of secondary information and the cross -covariance between the primary and secondary information are derived. The approximate solution is formulated based on a first -order Taylor series expansion of a discretized finite element equation. The sensitivity matrices in the solution are evaluated by an adjoint state sensitivity approach for flow in heterogeneous media under variably saturated conditions. As a result, the nonlinear relationships between unsaturated hydraulic conductivity parameters and flow processes are incorporated in the estimation. Through some numerical examples, the iterative inverse model demonstrates its ability to improve the estimates of the spatial distribution of saturated hydraulic conductivity and pore -size distribution parameters compared to the classical geostatistical inverse approach. In addition, the inconsistency problem existing in classical geostatistical inverse approach is alleviated. The estimated fields of unsaturated hydraulic conductivity parameters and flow fields not only retain their observed values at sample locations, but satisfy the governing flow equation as well.

      Yeh, T.-C. Jim; Jin, Minghui; Hanna, Samuel; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1995-08-29)
      An iterative stochastic approach is developed to estimate transmissivity and head distributions in heterogeneous aquifers. This approach is similar to the classical cokriging technique and it uses a linear estimator that depends on the covariances of transmissivity and hydraulic head and their cross -covariance. The linear estimator is, however, improved successively by solving the governing flow equation and by updating the covariances and cross -covariance function of transmissivity and hydraulic head fields in an iterative manner. As a result, the nonlinear relationship between transmissivity and head is incorporated in the estimation and the estimated fields are approximate conditional means. The ability of the iterative approach is tested with some deterministic and stochastic inverse problems. The results show that the estimated transmissivity and hydraulic head fields have smaller mean square errors than those obtained by classical cokriging even in the aquifer with variance of transmissivity up to 3.
    • 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.