Hydrology & Water Resources Technical Reports: Recent submissions
Now showing items 1-20 of 104
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Simulation of Groundwater Conditions in the Upper San Pedro Basin for the Evaluation of Alternative FuturesThe creation of the groundwater model of the Upper San Pedro Basin included two developmental phases: the creation of a conceptual and numerical model. The creation of the conceptual model was accomplished through the utilization of Geographic Information System (GIS) software, namely ArcView, used primarily to view and create point, line, and polygonal shapes. The creation of a numerical model was accomplished by the infusion of the conceptual model into a 3D finite difference grid used in MODFLOW groundwater software from the U.S. Geological Survey. MODFLOW computes the hydraulic head (water level) for each cell within the grid. The infusion of the two models (conceptual and numerical) was allowed through the use of Department of Defense Groundwater Modeling System (GMS) software. The time period for groundwater modeling began with predevelopment conditions, or "steady state." Steady state conditions were assumed to exist in 1940. The steady state was used as the initial condition for the subsequent transient analysis. The transient simulation applied historical and current information of pumping stresses to the system from 1940 to 1997. After modeling current conditions, Alternative Futures' scenarios were simulated by modifying current stresses and by adding new ones. The possible future impacts of to the hydrologic system were then evaluated.
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Evaluation of flood forecasting-response 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.
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MODRSP: a program to calculate drawdown, velocity, storage and capture response functions for multi-aquifer systemsMODRSP 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.
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Evaluation of flood forecasting-response systems IIsystem model and computational methodology have been developed which evaluate the worth of flood forecast - response systems in reducing the economic damage caused by floods. The efficiencies of the forecast system, the response system, and the overall system may be individually obtained and compared. In this report the case study of Milton, Pennsylvania, was extended and further case studies were performed including a large residential section of Victoria, Texas, and all the residences in Columbus, Mississippi. These locations show better forecast and response efficiencies than obtained for Milton, Pennsylvania. The difference is attributed to longer forecast lead times at Columbus and Victoria. Sensitivity analyses were run at all three locations. These show the effects of many system factors, such as the time required to produce, disseminate and respond to a forecast, on the efficiency of the system. The forecast efficiency improves significantly as these times are reduced. Further analysis of the response system based on human factors involved has led to the development of a simulation model of the process by which the floodplain dweller determines the appropriate response to a flood warning. Investigation of ways to extend the methodology to evaluate regions lacking the detailed data used for the case studies has indicated more problems than answers. Extrapolation based on overall system efficiency related to published regional and national flood damage estimates was used to provide an approximate value of the flood forecast - response system for two regions and for the nation.A listing of simplicities and approximations which make computations tractable but which may affect accuracy is given. Finally, an evaluation of the work accomplished for this project and suggestions for the constructive use of the flood forecast -response system model and computational procedures is given.
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Optimal Operation of Water-Supply SystemsThe 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.
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WORTH OF DATA USED IN DIGITAL-COMPUTER MODELS OF GROUND-WATER BASINSTwo digital- computer models of the ground -water reservoir of the Tucson basin, in south - central Arizona, were constructed to study errors in digital models and to evaluate the worth of additional basic data to models. The two models differ primarily in degree of detail -- the large -scale model consists of 1,890 nodes, at a 1/2 -mile spacing; and the small -scale model consists of 509 nodes, at a l -mile spacing. Potential errors in the Tucson basin models were classified as errors associated with computation, errors associated with mathematical assumptions, and errors in basic data: the model parameters of coefficient of storage and transmissivity, initial water levels, and discharge and recharge. The study focused on evaluating the worth of additional basic data to the small -scale model. A basic form of statistical decision theory was used to compute expected error in predicted water levels and expected worth of sample data (expected reduction in error) over the whole model associated with uncertainty in a model variable at one given node. Discrete frequency distributions with largely subjectively- determined parameters were used to characterize tested variables. Ninety -one variables at sixty - one different locations in the model were tested, using six separate error criteria. Of the tested variables, 67 were chosen because their expected errors were likely to be large and, for the purpose of comparison, 24 were chosen because their expected errors were not likely to be particularly large. Of the uncertain variables, discharge /recharge and transmissivity have the largest expected errors (averaging 155 and 115 feet, respectively, per 509 nodes for the criterion of absolute value of error) and expected sample worths (averaging 29 and 14 feet, respectively, per 509 nodes). In contrast, initial water level and storage coefficient have lesser values. Of the more certain variables, transmissivity and initial water level generally have the largest expected errors (a maximum of 73 per feet per 509 nodes) and expected sample worths (a maximum of 12 feet per 509 nodes); whereas storage coefficient and discharge/ recharge have smaller values. These results likely are not typical of those from many ground -water basins, and may apply only to the Tucson basin. The largest expected errors are associated with nodes at which values of discharge /recharge are large or at which prior estimates of transmissivity are very uncertain. Large expected sample worths are associated with variables which have large expected errors or which could be sampled with relatively little uncertainty. Results are similar for all six of the error criteria used. Tests were made of the sensitivity of the method to such simplifications and assumptions as the type of distribution function assumed for a variable, the values of the estimated standard deviations of the distributions, and the number and spacing of the elements of each distribution. The results are sensitive to all of the assumptions and therefore likely are correct only in order of magnitude. However, the ranking of the types of variables in terms of magnitude of expected error and expected sample worth is not sensitive to the assumptions, and thus the general conclusions on relative effects of errors in different variables likely are valid. Limited studies of error propagation indicated that errors in predicted water levels associated with extreme erroneous values of a variable commonly are less than 4 feet per node at a distance of 1 mile from the tested node. This suggests that in many cases, prediction errors associated with errors in basic data are not a major problem in digital modeling.
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A RANDOM-WALK SIMULATION MODEL OF ALLUVIAL-FAN DEPOSITIONA digital model based on a random walk was used in an experiment to determine how well such a model is able to simulate alluvial - fan deposition. The model is in three dimensions and is dynamic with respect to both time and space. Two principal stochastic events were employed, (1) a relative uplift of the mountain area that is the source of the fan sediments, and (2) a storm event of sufficient magnitude to result in the deposition of material on the fan. These two events are assumed to follow independent Poisson processes with exponentially distributed interoccurrence times. The pattern of deposition is determined by a random walk from the canyon mouth at the mountain front, and each depositional event is assumed to occur instantaneously. The direction that each step in the walk takes is determined probabilistically by the gradient in the direction of flow, the momentum of flow, and the boundary conditions stipulated in the model. The type of flow, whether a depositing debris or water flow, or eroding water flow, depends upon the thickness of erodible material in the source basin. Deposition is assumed to occur over the entire route of flow either as a bed tapered in the direction of flow or as a bed of uniform thickness. The particle -size distribution of the water -flow deposits is governed by the slope in the direction of flow. Erosion is considered negative deposition and results from the exponential decline in elevation of the main stream channel at the fan apex during periods of no uplift, or from water flows containing little basin sediment. Results from the computer runs were printed as geologic maps of the fan surface, and geologic sections through the deposits; these indicate that, at least qualitatively, a random -walk model provides a reasonable basis for simulating alluvial -fan deposition.
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WATER QUALITY IN THE LOWER COLORADO RIVER AND THE EFFECT OF RESERVOIRSComparison of the power spectra of TDS time series from different locations on the Lower Colorado River is useful in showing changes in salinity and for indicating physical factors influencing salinity. Similarities between the power spectra of the Lee Ferry and Grand Canyon tine series indicated that lateral inputs and evaporation are not greatly influencing the salinity cycle. The salinity change within this reach was approximated by a constant concentration change of 66.6 ppm. A similar model form was used for the Hoover Dam to Parker Dam reach. Dissimilarities between power spectra indicated that additional inputs are significant and must be accounted for in any model of such reaches. The model for Lake Mead required compensation for evaporation and for the inputs of the Virgin River and Las Vegas Wash. The modeled salinity increase between Parker Dam and Yuma contained a trend factor to allow for the effect of irrigation return flows and seepage. The crosscovariance function was used to approximate the time lag between data stations. Time series statistics, including coherence, response function spectra, and overall unit response, were used and are of utility in estimating salinity in a river system.
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HYDROLOGIC MODEL SELECTION IN A DECISION MAKING CONTEXTThe 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.
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AN INTERACTIVE ALGORITHM FOR MULTIOBJECTIVE DECISION MAKINGThis 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.
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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.
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SPATIAL VARIABILITY OF PRECIPITATION IN THE SAN DIMAS EXPERIMENTAL FOREST AND ITS EFFECT ON SIMULATED STREAMFLOWThe effect of altitude on individual storm precipitation in some of the San Dimas experimental watersheds is investigated. It is found that there is a well- defined increase of storm precipitation with altitude for storms greater than one inch. This increase is a linear function of storm depth. Using 41 storms of different magnitudes, a precipitation -altitude relationship is derived for a small area in the San Dimas Experimental Forest. The regionalization of this relationship and its transferability are tested by analyzing differences (errors) between computed and observed storm precipitation values in each case. In testing the regionalization of the precipitation- altitude relationship by computing mean areal storm precipitation over a larger area the standard error of estimate is around 11 percent. In transfering the same relationship the results are not as good and give a standard error of 16 percent. For individual points, however, the error is much higher. A rainfall- runoff model is used as a tool for evaluating the effect of precipitation errors, on simulated streamflow, in a watershed of 4.5 square miles. For annual flows, errors range between 3.4 and 12.3 percent while errors in simulated monthly flows are as high as 22 percent. It is also evident that there is a strong dependence of the error magnitude on the state (wet, dry, etc.) of the preceding year or months, whichever is applicable. An error propagation is observed as a result of consistently over -estimating the precipitation input to the model. This evaluation is more of a qualitative nature and the values of error given should be viewed in this sense.
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A STOCHASTIC APPROACH TO SPACE-TIME MODELING OF RAINFALLThis study gives a phenomenologically based stochastic model of space -time rainfall. Specifically, two random variables on the spatial rainfall, e.g. the cumulative rainfall within a season and the maximum cumulative rainfall per rainfall event within a season are considered. An approach is given to determine the cumulative distribution function (c.d.f.) of the cumulative rainfall per event, based on a particular random structure of space -time rainfall. Then the first two moments of the cumulative seasonal rainfall are derived based on a stochastic dependence between the cumulative rainfall per event and the number of rainfall events within a season. This stochastic dependence is important in the context of the spatial rainfall process. A theorem is then proved on the rate of convergence of the exact c.d.f. of the seasonal cumulative rainfall up to the ith year, i > 1, to its limiting c.d.f. Use of the limiting c.d.f. of the maximum cumulative rainfall per rainfall event up to the ith year within a season is given in the context of determination of the 'design rainfall'. Such information is useful in the design of hydraulic structures. Special mathematical applications of the general theory are developed from a combination of empirical and phenomenological based assumptions. A numerical application of this approach is demonstrated on the Atterbury watershed in the Southwestern United States.
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PLANKTONIC DYNAMICS AS AN INDICATOR OF WATER QUALITY IN LAKE MEADThe 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.
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A STOCHASTIC SEDIMENT YIELD MODEL FOR BAYESIAN DECISION ANALYSIS APPLIED TO MULTIPURPOSE RESERVOIR DESIGNThis thesis presents a methodology for obtaining the optimal design capacity for sediment yield in multipurpose reservoir design. A stochastic model is presented for the prediction of sediment yield in a semi -arid watershed based on rainfall data and watershed characteristics. Uncertainty stems from each of the random variables used in the model, namely, rainfall amount, storm duration, runoff, peak flow rate, and number of events per season. Using the stochastic sediment yield model for N- seasons, a Bayesian decision analysis is carried out for a dam site in southern Arizona. Extensive numerical analyses and simplifying assumptions are made to facilitate finding the optimal solution. The model has applications in the planning of reservoirs and dams where the effective lifetime of the facility may be evaluated in terms of storage capacity and of the effects of land management on the watershed. Experimental data from the Atterbury watershed are used to calibrate the model and to evaluate uncertainties associated with our knowledge of the parameters of the joint distribution of rainfall and storm duration used in calculating the sediment yield amount.
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MODEL UNCERTAINTY IN THE DESIGN OF A FLOOD PROTECTION LEVEEThe 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.
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ON THE THEORY AND MODELING OF DYNAMIC PROGRAMMING WITH APPLICATIONS IN RESERVOIR OPERATIONThis 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.
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APPLICATION OF A GROUND-WATER FLOW MODEL TO THE MESILLA BASIN, NEW MEXICO AND TEXASIt has been said that watersheds and aquifers ignore political boundaries. This phenomenon is often the reason for extensive regulation of surface -water and ground -water resources which are shared by two or more political entities. Regulation is often the result of years of litigation over who really owns the water, how much is owned, and how much is available for future use. Groundwater models are sometimes used as quantitative tools which aid in the decision making process regarding appropriation and regulation of these scarce, shared, water resources. The following few paragraphs detail the occurrences in the Lower Rio Grande Basin which led to the current ground -water modeling effort. New Mexico, Texas and Mexico have wrestled forever over the rights to the Lower Rio Grande and the aquifers of the Rio Grande Basin (Figure 1). As early as 1867, due to a flood event on the Rio Grande, Texas and Mexico were disputing the new border created by the migrating Rio Grande. During the 1890's, the users upstream from the Mesilla and El Paso Valleys were diverting and applying so much of the Rio Grande that the Mesilla and El Paso valley farmers litigated in order to apportion and guarantee the supply. In the recent past, disputes over who may use the ground -water resources of the region and the effect of surface- water uses on aquifer water levels resulted in litigation between El Paso, Texas, and New Mexico.
