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COLLECTIVE UTILITY IN THE MANAGEMENT OF NATURAL RESOURCES: A SYSTEMS APPROACHThe main purpose of this report is to develop an economic theory, along the lines of the Bergson Samuelson social welfare theory, to regulate the utilization of natural resources in the long term interest of a political economic group of individuals and firms. The theory, called Collective Utility, qualifies as a "systems approach" because of its inherent flexibility, generality, and comprehensiveness. Collective Utility is a function of individual satisfactions and firm revenues, which are, in general, contingent upon the actions of other individuals and /or firms. Such interactions are called externalities. It is the contention of this report that efficient management of natural resources will follow from efficient control of externalities. A taxation  subsidy structure is suggested as an efficient control and the complete mathematics of determining and implementing such a structure are provided. Finally, the idea of externalities is integrated within the framework of Collective Utility to form an optimal policy for the utilization of natural resources using the techniques of calculus of variations.

COLORADO RIVER TRIPS WITHIN THE GRAND CANYON NATIONAL PARK AND MONUMENT: A SOCIOECONOMIC ANALYSISThe recreational use of the Colorado River within the Grand Canyon National Park and National Monument increased on the order of 60 to 70 per cent during each year of the interval 1967 to 1970. Consequently, the U. S. National Park Service instituted user limits to protect and preserve the area commencing with the 1971 season. This limit was established with limited data on the users of the river or about their perceptions of the trip experience. A need existed to collect and analyze this type of data, and to suggest possible management alternatives. This study used a mailed questionnaire to a random sample of past participants in order to collect basic socioeconomic data. The analysis was based on a 65% response rate, and consisted of individual question tabulation and multivariate data cluster analysis. The data show background characteristics of the participants, reasons for taking the trip, reactions to the experience, perceptions of problems associated with the trips, reactions to crowded conditions, and needs for regulatory policy concerning user intensities.

CONFUSION WHERE GROUND AND SURFACE WATERS MEET: GILA RIVER GENERAL ADJUDICATION, ARIZONA AND THE SEARCH FOR SUBFLOWArizona is presently in the midst of a general adjudication for the Gila River system  the watershed which comprises the southern two thirds of the state. The purpose of the adjudication is to prioritize all water claims in the river system: both state established and federally reserved rights. Arizona adheres to a bifurcated (or divided) system of water law which only recognizes a component of ground water  called subflow  to be appropriable. Wells which pump nonappropriable water  called tributary flow  are not to be included in the adjudication. The problem is that federal laws do not recognize this artificial bifurcation. The challenge lies in identifying a subflow zone which satisfies the hydrologic fiction of existing state precedents and the hydrologic reality of federal statutes. At the core of the problem lies the fate of Arizona's perennial stream water and the fulfillment of federally reserved tribal water rights. Thus, larger questions loom: can Arizona law reconcile its glutinous past with a water scarce future, will the adjudication ever reach a finality, and even if it does, will it be a finality that all sides can live with?

A CONTINUOUS REVIEW INVENTORY MODEL FOR IRRIGATION WATER APPLICATIONThis thesis is concerned with the problem of determining an optimal irrigation policy, that is, an optimal quantity and frequency of irrigation water application. The purpose is to present a solution to this problem using a continuous review model of an inventory system. Initially, the functions of the plant water soil system are discussed. This is followed by a review of several existing methods for maximizing crop yield or profit by determining an optimal irrigation policy. Next, the inventory problem is briefly examined. An analogy is drawn between the farmer's problem of determining an optimal irrigation policy and the businessman's problem of determining an optimal ordering policy. Subsequently, a continuous review model of the irrigation system is developed and an example of its use is given.

A COSTEFFECTIVENESS STUDY AND ANALYSIS OF MUNICIPAL REFUSE DISPOSAL SYSTEMSThe comparison of alternative systems of disposing efficiently and effectively of four to five pounds of solid waste per person per day in the United States urban communities is undertaken by using Kazanowski's standardized cost effectiveness methodology. The economic criteria for studying this problem are often limited to cost or marketable measures; in contrast, use of a cost effectiveness approach allows the inclusion of non quantifiable measures of effectiveness such as public acceptance, politics, health risks, environmental considerations, and soil benefits. Data from a case study in Tucson, Arizona, is used to illustrate the problem.

COUPLING STOCHASTIC AND DETERMINISTIC HYDROLOGIC MODELS FOR DECISIONMAKINGMany planning decisions related to the land phase of the hydrologic cycle involve uncertainty due to stochasticity of rainfall inputs and uncertainty in state and knowledge of hydrologic processes. Consideration of this uncertainty in planning requires quantification in the form of probability distributions. Needed probability distributions, for many cases, must be obtained by transforming distributions of rainfall input and hydrologic state through deterministic models of hydrologic processes. Probability generating functions are used to derive a recursive technique that provides the necessary probability transformation for situations where the hydrologic output of interest is the cumulative effect of a random number of stochastic inputs. The derived recursive technique is observed to be quite accurate from a comparison of probability distributions obtained independently by the recursive technique and an exact analytic method for a simple problem that can be solved with the analytic method. The assumption of Poisson occurrence of rainfall events, which is inherent in derivation of the recursive technique, is examined and found reasonable for practical application. Application of the derived technique is demonstrated with two important hydrology related problems. It is first demonstrated for computing probability distributions of annual direct runoff from a watershed, using the USDA Soil Conservation Service (SCS direct runoff model and stochastic models for rainfall event depth and watershed state. The technique is also demonstrated for obtaining probability distributions of annual sediment yield. For this demonstration, thedeterministic transform model consists of a parametric event based sediment yield model and the SCS models for direct runoff volume and peak flow rate. The stochastic rainfall model consists of a marginal Weibull distribution for rainfall event duration and a conditional log normal distribution for rainfall event depth, given duration. The stochastic state model is the same as used for the direct runoff application. Probability distributions obtained with the recursive technique for both the direct runoff and sediment yield demonstration examples appear to be reasonable when compared to available data. It is, therefore, concluded that the recursive technique, derived from probability generating functions, is a feasible transform method that can be useful for coupling stochastic models of rainfall input and state to deterministic models of hydrologic processes to obtain probability distributions of outputs where these outputs are cumulative effects of random numbers of stochastic inputs.

Deciding to RechargePublic water policy decision making tends to be too complex and dynamic to be described fully by traditional, rational models. Information intended to improve decisions often is rendered ineffective by a failure to understand the process. An alternative, holistic description of how such decisions actually are made is presented here and illustrated with a case study. The role of information in the process is highlighted. Development of a Regional Recharge Plan for Tucson, Arizona is analyzed as the case study. The description of how decisions are made is based on an image of public water policy decision making as 1) a structured, nested network of individuals and groups with connections to their environment through their senses, mediated by their knowledge; and 2) a nonlinear process in which decisions feed back to affect the preferences and intentions of the people involved, the structure of their interactions, and the environment in which they operate. The analytical components of this image are 1) the decision makers, 2) the relevant features of their environment, 3) the structure of their interactions, and 4) the products or outputs of their deliberations. Policy decisions analyzed by these components, in contrast to the traditional analysis, disclose a new set of relationships and suggest a new view of the uses of information. In context of information use, perhaps the most important output of the decision process is a shared interpretation of the policy issue. This interpretation sets the boundaries of the issue and the nature of issuerelevant information. Participants are unlikely to attend to information incompatible with the shared interpretation. Information is effective when used to shape the issue interpretation, fill specific gaps identified as issuerelevant during the process, rationalize choices, and reshape the issue interpretation as the issue environment evolves.

Decision Making Under Uncertainty in Systems HydrologyDesign of engineering projects involve a certain amount of uncertainty. How should design decisions be taken in face of the uncertainty? What is the most efficient way of handling the data? Decision theory can provide useful answers to these questions. The literature review shows that decision theory is a fairly well developed decision method, with almost no application in hydrology. The steps of decision theoretic analysis are given. They are augmented by the concept of expected expected opportunity loss, which is developed as a means of measuring the expected value of additional data before they are received. The method is applied to the design of bridge piers and flood levees for Rillito Creek, Pima County, Arizona. Uncertainty in both the mean and the variance of the logarithms of the peak flows of Rillito Creek is taken into account. Also shown are decision theoretic methods for: 1) handling secondary data, such as obtained from a regression relation, 2) evaluating the effect of the use of non  sufficient statistics, 3) considering alternate models and 4) regionalizing data.It is concluded that decision theory provides a rational structure for making design decisions and for the associated data collection and handling problems.

DESIGN OF WATER RESOURCES SYSTEMS IN DEVELOPING COUNTRIES: THE LOWER MEKONG BASINThis study focuses on the design of water resources systems in developing nations with particular reference to the development of water resources in the Lower Mekong Basin (Khmer Republic, Laos, Thailand, and Republic of South Viet Nam). The determination of the "best" system in terms of social goals reflecting the economic and social environment of the Mekong countries is the main issue of this dissertation. The imperfection of the usual technique for planning water resources systems, namely, cost benefit analysis, leads to the use of the standardized cost effectiveness methodology. To illustrate how the design is accomplished, two distinctly different structural alternatives of possible development in the Lower Mekong Basin are defined. The design process starts from the statements of goals or objectives of water resources development, which are then mapped onto specifications sets in which social needs are represented. Next, the capabilities of alternative systems are determined through simulation in which three 50 year sequences of synthetic streamflow are generated by a first order autoregressive scheme. The two alternatives are then compared using both quantitative and qualitative criteria. To illustrate how a decision in selecting an alternative system could be reached, ranking of criteria by order of preference is demonstrated. With the choice of either a fixed cost or fixed effectiveness approach, the decision to select the best alternative system could be made. At this point, the use of a weighting technique, which is a common fallacy of systems analysis, will be automatically eliminated. The study emphasizes that a systematic design procedure of water resources systems is provided by the standardized cost effectiveness approach, which possesses several advantages. The approach will suggest and help identify the system closest to meeting the desired economic and social goals of the developing countries in the Lower Mekong Basin. In this connection, the approach will help governments in the preparation of programming and budgeting of capital for further investigations and investments. It is believed that the approach will eliminate unnecessary expenses in projects that are planned on an individual basis or by methods used at present. Further, the approach provides an appropriate mechanism for generating essential information in the decision process. Both quantifiable and non quantifiable criteria are fully considered. The choice of a fixed cost or fixed effectiveness approach will determine the trade off between these criteria. The study recognizes that research to determine appropriate hydrologic models for monthly streamfiow generation for tributary projects in the Basin is necessary. This leads to another important area of research which is to find the appropriate number of monthly sequences of streamflow to be generated in relation to number of states and decision variables. Research on the design of computer experiments is necessary to improve simulation as a tool to estimate the quantitative effects of a given project.

DEVELOPMENT AND VALIDATION OF A NEW MAXIMUM LIKELIHOOD CRITERION SUITABLE FOR DATA COLLECTED AT UNEQUAL TIME INTERVALSA new Maximum Likelihood Criterion (MLE) suitable for data which are recorded at unequal time intervals and contain autocorrelated errors is developed. Validation of the new MLE criterion has been carried out both on a simple two  parameter reservoir model using synthetical data and on a more complicated hillslope model using real data from the Pukeiti Catchment in New Zealand. Comparison between the new MLE criterion and the Simple Least Squares (SLS) criterion reveals the superiority of the former over the latter. Comparison made between the new MLE and the MLE for autocorrelated case proposed by Sorooshian in 1978 has shown that both criteria would yield results with no practical difference if equal time interval data were used. However, the new MLE can work on variable time interval data which provide more information than equal time interval data, and therefore produces better visual results in hydrologic simulations.

A Distributed Surface Temperature and Energy Balance Model of a SemiArid WatershedA simple model of surface and sub surface soil temperature was developed at the watershed scale ( 100 km2) in a semi arid rangeland environment. The model consisted of a linear combination of air temperature and net radiation and assumed: 1) topography controls the spatial distribution of net radiation, 2) near surface air temperature and incoming solar radiation are relatively homogeneous at the watershed scale and are available from ground stations and 3) soil moisture dominates transient soil thermal property variability. Multiplicative constants were defined to account for clear sky diffuse radiation, soil thermal inertia, an initially fixed ratio between soil heat flux and net radiation and exponential attenuation of solar radiation through a partial canopy. The surface temperature can optionally be adjusted for temperature and emissivity differences between mixed hare soil and vegetation canopies. Model development stressed physical simplicity and commonly available spatial and temporal data sets. Slowly varying surface characteristics, such as albedo, vegetation density and topography were derived from a series of Landsat TM images and a 7.5" USGS digital elevation model at a spatial resolution of 30 m. Diurnally variable atmospheric parameters were derived from a pair of ground meteorological stations using 30 60 min averages. One site was used to drive the model, the other served as a control to estimate model error. Data collected as part of the Monsoon '90 and WG '92 field experiments over the ARS Walnut Gulch Experimental. Watershed in SE Arizona were used to validate and test the model. Point, transect and spatially distributed values of modeled surface temperature were compared with synchronous ground, aircraft and satellite thermal measurements. There was little difference between ground and aircraft measurements of surface reflectance and temperature which makes aircraft transects the preferred method to "ground truth" satellite observations. Mid morning modeled surface temperatures were within 2° C of observed values at all but satellite scales, where atmospheric water vapor corrections complicate the determination of accurate temperatures. The utility of satellite thermal measurements and models to study various ground phenomena (eg. soil thermal inertia and surface energy balance) were investigated. Soil moisture anomalies were detectable, but were more likely associated with average near surface soil moisture levels than individual storm footprints.

DPRCI /GAUSS A Program to Calculate Reservoir Yield Curves Using a Dynamic Programming Reservoir Operation AlgorithmThis report presents a computer program which will calculate reservoir yield curves for reservoir operation policy based on optimization accomplished using a. dynamic programming algorithm. After discussion of the dynamic programming and Gauss elimination algorithms, the input requirements, execution procedures, source code presentation, sample output, and references are presented. The programs run in a relatively short time on an 80286 personal computer. They are written in FORTRAN7.7 and compiled using the LAHEY F776 compiler.

Dynamic Management of a Surface and Groundwater System on Both Sides of the Lower Yellow RiverThis paper analyzes the management problem of the conjunctive use of surface and ground water in an irrigation system on both sides of the Lower Yellow River. For this purpose, a stochastic dynamic programming model is developed. In the model, the statistical characteristics of seasonal rainfall within 2 years are considered; groundwater level control is also emphasized in order to prevent soil salinity and waterlogging. Through computer calculations, optimal operation policies are obtained for efficient conjunctive use of surface and groundwater. These policies take into account the interactions between pumping groundwater by farmers, canal diversions by irrigation system managers, and the physical response of the stream aquifer system, and minimize the total operation costs. In this paper, we take an irrigation district, the People's Victory Canal System, as an example to illustrate the development and solution of the model. At the same time, the effects of system parameters, including surface irrigation efficiency and rainfall recharge coefficient, on the optimal policies or total operation costs, are discussed. The analytical results in this example indicate that the variation in optimal operation costs caused by the proportion of rainfall infiltrated is small, but the effect of surface irrigation efficiency on the costs is significant. Hence, the surface irrigation efficiency must be increased as much as possible. Then, efficient conjunctive use of surface and groundwater can be attained with the optimal policies.

Effect Of Filtering On Autocorrelation, Flow, And Transport In Random Fractal Fields" Fractal" concepts have become the focus of much interest in the earth sciences during the last fifteen years. The term "fractal" is especially appealing from a semantic point of view in that Mandelbrot [ 1983] derived it from the Latin "fractus ", describing the appearance of a broken stone. In this report, we focus on issues of flow and contaminant transport in porous media. Here, fractal concepts have been widely associated with attempts to explain scale effects such as the apparent growth of effective longitudinal dispersion with the scale of observation. However, a much broader range of topics has been explored in the literature on fractals, which can be roughly divided into two broad categories. The first category concerns a fractal description of medium geometry, over a given range of scales [Adler, 1992]. Within this category, the fractal geometry is considered to be either deterministic (self similar) or random (statistically self similar, or self affine) [Voss 1985]. The second category views medium physical properties (porosity, log conductivity) as random fields, most commonly with statistical self similarity of second order moments such as structure function ( variogram) or autocovariance. In this report, we focus on random fractal fields. We start with an introduction in Chapter 1 of isotropic random fractal fields and the scaling properties of corresponding power law variogram and spectral densities in one, two, and three dimensions. We then derive new expressions for autocovariance functions corresponding to truncated power law spectral densities; demonstrate that the power law variogram and associated power spectra can be constructed as weighted integrals of exponential autocovariance functions and their spectra, representing an infinite hierarchy of unconelated homogeneous isotropic fields (modes); and analyze the effect of filtering out (truncating) high and low frequency modes from this hierarchy in the realand spectral domains. In Chapter 2, we derive first order results relative to early preasymptotic, and late time asymptotic, transport in media characterized by a truncated log conductivity power law spectral density. In Chapter 3, we return to the multiscale log conductivity fields constructed in Chapter 1; present some general results for early preasymptotic and late time asymptotic transport; and obtain complete first order results for flow and transport, at preasymptotic and asymptotic stages, in two dimensions. In Chapter 4, we explore the multiscale behavior of conductivity from an aquifer in Mobile, Alabama, using different methods of data reduction. In Chapter 5, we summarize our main conclusions.

EFFECTS OF RADARESTIMATED PRECIPITATION UNCERTAINTY ON DIFFERENT RUNOFFGENERATION MECHANISMSRunoff generation has been shown to be very sensitive to precipitation input. With the use of precipitation estimates from weather radar, errors are introduced from both the transformation from reflectivity to precipitation rate and the spatial and temporal aggregation of the radar product. Currently, a significant degree of uncertainty exists in the accuracy of radarbased precipitation estimates. When uncalibrated or poorly calibrated radar products were used as input to a rainfallrunoff model, the resulting predicted runoff varied severely from the runoff generated using wellcalibrated radar products. Another source of uncertainty, errors in the precipitation system structure due to aggregation in time and space, has also been shown to affect runoff generation. This study focuses on separating the primary runoff generating mechanisms  infiltration excess and saturation excess  to assess their responses to variable precipitation inputs individually. For the case of saturation excess runoff, there was minimal sensitivity due to temporal aggregation of the precipitation; however, there was considerable sensitivity to spatial aggregation. For the case of infiltration excess runoff, temporal and spatial aggregation of the precipitation significantly reduced the amount of runoff produced. The magnitudes of these runoff reductions varied between storms and showed a high degree of dependence on storm characteristics, particularly the maximum precipitation intensity.

Effluent recharge to the Upper Santa Cruz River floodplain aquifer, Santa Cruz county, ArizonaThe City of Nogales, Arizona, is in the Santa Cruz Active Management Area and is subject to the assured water supply and conservation mandates of the 1980, Groundwater Management Act (State of Arizona, 1980). The primary water supply for both Nogales Arizona, and Nogales, Sonora, (commonly referred to as Ambos Nogales) is groundwater pumped from the shallow alluvial aquifers which underlie the Upper Santa Cruz River in Arizona and Mexico, and its tributaries (principally Nogales Wash and Potrero Creek). Nogales, Sonora also obtains water from the Los Alisos Basin, which is south of the Santa Cruz Basin in Mexico (Carruth, 1995). The NIWTP provides wastewater treatment for Ambos Nogales, and discharges treated wastewater to the Upper Santa Cruz River near the confluence with Nogales Wash and Sonoita Creek. The discharge of effluent creates an intermittent stream from the NIWTP outfall for approximately 13 river miles to Tubac, Arizona. The conservation mandates of the 1980, Groundwater Management Act (State of Arizona, 1980) require the City of Nogales, Arizona to prove the existence of a 100year water supply as a condition for future growth. The Act also allows Nogales, Arizona to receive recharge credits for the portion of effluent that recharges the aquifer underlying the Santa Cruz River. The recharge credits will be used by the City of Nogales as partial proof of a 100year water supply (Carruth, 1995).

THE ESTIMATION AND SCALING OF LANDSURFACE FLUXES OF LATENT AND SENSIBLEHEAT WITH REMOTELY SENSED DATA OVER A GRASSLAND SITEThe overall topic of the research described in this dissertation was the partitioning of available energy at the Earth's surface into sensible and latent heat flux, with an emphasis on the development of techniques which utilize remotely sensed data. One of the major objectives was to investigate the modification of existing techniques, developed over agricultural surfaces, to "natural" ecosystems (i.e., non agricultural vegetation types with variable and incomplete canopy cover). Ground based measurements of surface fluxes, vegetation cover, and surface and root zone soil moisture from the First ISLSCP (International Land Surface Climatology Program) Field Experiment (FIFE) were used to examine the factors controlling the partitioning of energy at ground stations with contrasting surface characteristics. Utilizing helicopter based and satellite based data acquired directly over ground based flux stations at the FINE experimental area, relatively simple algorithms were developed for estimating the soil heat flux and sensible heat flux from remotely sensed data. The root mean square error (RMSE) between the sensible heat flux computed with the remotely sensed data and the sensible heat flux measured at the ground stations was 33 Wm 2. These algorithms were then applied on a pixel by pixel basis to data from a Landsat TM (Thematic Mapper) scene acquired over the FIFE site on August 15, 1987 to produce spatially distributed surface energy balance components for the FIFE site. A methodology for quantifying the effect of spatial scaling on parameters derived from remotely sensed data was presented. As an example of the utility of this approach, NDVI values for the 1,IFE experimental area were computed with input data of variable spatial resolution. The differences in the values of NDVI computed at different spatial resolutions were accurately predicted by an equation which quantified those differences in terms of variability in input observations.

Estimation of effective unsaturated hydraulic conductivity tensor using spatial moments of observed moisture plumeKnowledge of unsaturated zone hydraulic properties is critical for many environmental and engineering applications. Various stochastic methods have been developed during the past two decades to estimate the effective unsaturated hydraulic properties. Independent of these stochastic methods, we develop in this paper a practical approach to estimate the threedimensional (3 D) effective unsaturated hydraulic conductivity tensor using spatial moments of 3D snapshots of a moisture plume under transient flow conditions. approach hydraulic hydraulic Application of the new to a field site in southeastern Washington State yields an effective unsaturated conductivity tensor that exhibits moisture dependent anisotropy. The effective conductivities compare well with laboratory measured unsaturated hydraulic conductivity data from small core samples; they also reproduce the general behavior of the observed moisture plume at the site. We also define a moisture diffusivity length concept which we use in conjunction with estimated correlation scales of the geological media at the field site to explain deviations between the observed and simulated plumes based on the derived effective hydraulic properties.

Eutrophication: A Mathematical ModelVarious approaches to modeling phytoplanktonzooplankton nutrient interactions have been investigated. A stochastic birth death model was developed to describe changes in phytoplankton and zooplankton population levels at a given point. Tuie stochastic birth death model was combined with a deterministic mass balance of limiting nutrient concentration to form an over all system theoretic model that enables one to use Monte Carlo simulation to study the problem of eutrophication. A comparison made between this modeling approach and the standard differential equation approach suggested that further investigation was desirable, particularly in the area of model calibration.

Evaluation of flood forecastingresponse systemsThe value of a forecast system in preventing urban property damage depends on the accuracy of the forecasts, the time at which they are received, the response by the floodplain dweller and the êfficacy of that response. A systems model of the overall flood forecast response system is developed. Evaluation of the system is accomplished by a decision theoretic methodology. A case study is done for Milton, Pennsylvania, which evaluates the present system and potential changes to it. It is concluded that the sequential nature of the forecast sequence must be considered in modeling the flood forecast response system if a meaningful evaluation of the economic value of the system is to be obtained. Methodology for obtaining the parameterization of the model from the available data is given. Computer programs have been written to handle a good portion of the calculations. While more work is needed on obtaining accurate parameterization of certain parts of the model, such as the actual response to forecasts; use of the procedures and programs as they now stand produces reasonable evaluations.