Browsing Hydrology & Water Resources Technical Reports by Publisher "Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ)"
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Advances in seasonal forecasting for water management in Arizona: a case study of the 199798 El NiñoThis 199798 El Niño provided a unique opportunity for climate information and forecasts to be utilized by water management agencies in the Southwestern U.S. While Arizona has experienced high streamflow associated with previous El Niño events, never before had an event of such magnitude been predicted with advance warning of several months. Likewise, the availability of information, including Internet sources and widespread media coverage, was higher than ever before. Insights about use of this information in operational water management decision processes are developed through a series of semi structured in depth interviews with key personnel from a broad array of agencies responsible for emergency management and water supply, with jurisdictions ranging from urban to rural and local to regional. The interviews investigate where information was acquired, how it was interpreted and how it was incorporated into specific decisions and actions. The interviews also investigate agency satisfaction with the products available to them, their operational decisions, and intentions to utilize forecast products in the future. Study findings lead to recommendations about how to more effectively provide intended users of forecasts with information required to enact mitigation measures and utilize opportunities that some climatic events present. The material presented in this report is primarily based on the Masters Thesis of Thomas Pagano.

Analysis of Borehole Infiltration Tests Above the Water TableConstant head borehole infiltration tests are widely used for the in situ evaluation of saturated hydraulic conductivities of unsaturated soils above the water table. The formulae employed in analyzing the results of such tests disregard the fact that some of the infiltrating water may flow under unsaturated conditions. Instead, these formulae are based on various approximations of the classical free surface theory which treats the flow region as if it were fully saturated and enclosed within a distinct envelope, the so called "free surface." A finite element model capable of solving free surface problems is used to examine the mathematical accuracy of the borehole infiltration formulae. The results show that in the hypothetical case where unsaturated flow does not exist, the approximate formulae are reasonably accurate within a practical range of borehole conditions. To see what happens under conditions closer to those actually encountered in the field, the effect of unsaturated flow on borehole infiltration is investigated by means of two different numerical models: A mixed explicit  implicit finite element model, and a mixed explicit implicit integrated finite difference model. Both of these models give nearly identical results; however, the integrated finite difference model is considerably faster than the finite element model. The relatively low computational efficiency of the finite element scheme is attributed to the large humber of operations required in order to reevaluate the conductivity (stiffness) matrix at each iteration in this highly nonlinear saturated unsaturated flow problem. The saturated unsaturated analysis demonstrates that the classical free surface approach provides a distorted picture of the flow pattern in the soil. Contrary to what one would expect on the basis of this theory, only a finite region of the soil in the immediate vicinity of the borehole is saturated, whereas a significant percentage of the flow takes place under unsaturated conditions. As a consequence of disregarding unsaturated flow, the available formulae may underestimate the saturated hydraulic conductivity of fine grained soils by a factor of two, three, or more. Our saturated unsaturated analysis leads to an improved design of borehole infiltration tests and a more accurate method for interpreting the results of such tests. The analysis also shows how one can predict the steady state rate of infiltration as well as the saturated hydraulic conductivity from data collected during the early transient period of the test.

Analysis of hydrologic data collected by the U.S. Bureau of Land Management 19871995 and recommendations for future monitoring programsThe purpose of this study was to establish a more efficient monitoring program for the San Pedro Riparian National Conservation Area (SPRNCA). This report analyzes data on stream flow measurements taken at nine locations on the San Pedro river and one location on the Babocomari river and ground water levels in eighteen wells collected by the BLM over the period from 1987 to 1995 and discusses possible causes for trends and anomalies in the data. The report also recommends future data collection and analytical efforts. All of the stream discharge data and some of the groundwater levels were collected at discrete and unsystematic intervals, and further, the streamflow measurements may not have been collected at the same location at each site. Surface water flow was measured by a Marsh McBirney flow meter.

An analysis of the effects of retiring irrigation pumpage in the San Pedro riparian national conservation area, Cochise county, ArizonaA seasonal groundwater model was developed to simulate fluxes and head distributions with periodic boundary conditions within the San Pedro Riparian National Conservation Area (SPRNCA) in southeastern Arizona. This model incorporated a seasonal approach for the period 19401995. Two years were used to simulate streamflow, 1990 and 1995. The model, as currently calibrated, does not accurately reproduce observed baseflow conditions in the San Pedro River and simulates an exaggerated effect of retiring irrigation within the SPRNCA. The model simulated increased baseflows while the observed baseflows declined at the USGS Charleston stream gage, though increases in baseflow contributions between Hereford Bridge and Lewis Springs have been reported. The original (Corell, et al., 1996) model and the seasonal transient model suffer from over estimation of discharge from the floodplain aquifer to the San Pedro river, as well as errors in the seasonal transient model's simulation of riparian ET, and seasonal variations in stream conductance. These problems precluded the seasonal transient model from replicating the observed baseflows in the San Pedro river at the Charleston bridge, however, the results of the simulation are thought to be qualitatively indicative of changes in the flow system resulting from the retirement of irrigated agriculture in the San Pedro Riparian National Conservation Area. Possible sources for this problem include replacement of irrigation stresses by the expansion of cones of depression more distant from the river, overestimation of mountain front recharge, poor baseflow estimates and evapotransipration calculations from the stream gages at Charleston and Palominas, and the effects of a recently discovered silt clay body that may dampen the speed of the rivers response to changes in stress. Additional efforts to re calibrate the model, taking these areas into account, should provide better simulated baseflow values of the observed data.

An Analysis of the Water Quality Problems of the Safford Valley, ArizonaA marked change in ground water quality in the Safford Valley of Graham County, Arizona, averaging approximately +0.129 x 103 mhos electrical conductivity per year and +35 parts per million chloride per year, has been documented between 1940 and 1972 with data from ten long term sample wells. A chloride change map constructed between these two years shows a general increase of 200 to 400 ppm chloride. The 1972 iso chemical maps show areas of up to 1600 ppm chloride and 8.0 x 103 mhos electrical conductivity, which is extremely saline and considered threshold level for agricultural waters. The Safford Valley, a structural trough with approximately east west orientation, averages 12 miles in width and 30 miles in length in the study area. Bounded by typical basin and range province mountains on the northeast and southwest, the valley contains a perennial stream flowing toward the west. A bi aquifer system constitutes the ground water reservoir of the area with a deep, artesian aquifer of several thousand feet thickness overlaid by a water table aquifer averaging 400 feet in thickness and with the water table rarely over fifty feet from the surface on the eastern end of the valley, deepening to over 5000 feet at the western end. This bedrock alluvium interface is the lower vertical constraint for the artesian system, thus the thickness of this aquifer increases downstream (to the west). The basin fill consists of a basal conglomerate overlaid by lacustrine evaporite beds, the aquifer cap beds, and recent alluvial material. The artesian aquifer is shown to be up to ten times as saline as the water table aquifer, and appears to increase in temperature and salinity in a downstream direction (corresponding to increasing thicknesses of lacustrine beds included in the extent of this aquifer). The decrement in the water quality of the surficial aquifer seems to be attributable to four major mechanisms. An increase in salinity may be expected from leakage of saline water from the artesian aquifer. Suck leakage would be stimulated by pumping caused reduction of confining pressure, and by the puncture of the cap beds by deep wells. Water reaching the aquifer from natural recharge may contribute salts to the system. Such recharging water, if passed through soluble beds, could contribute to the salt content of the aquifer. Lateral movement of water through similar deposits may be a contribution, and the concentration and infiltration of agricultural water could also add to aquifer salinity. Ground water applied to the land surface is concentrated by evaporation and dissolves salts in the unsaturated zone as it re enters the water table aquifer. Iso salinity and salinity change maps show the quality situation of the water table aquifer to be broken up into three major sections. From the eastern limit of the study area to Safford, the quality is relatively high and stable. From Safford to Pima there appears a uniform increase of low magnitude but continued decrement. Beyond Pima the area exhibits extremely irregular salinity conditions with marked increases and high salinity gradients. The salinity pattern corresponds to the extent of the underlying artesian aquifer but may be influenced to an unknown extent by the down gradient transport of salts. The 1972 iso chemical maps show chevrons of high quality water protruding into the aquifer at points corresponding to the locations of washes. Such wash bottoms are the principal zones of recharge in arid regions. Recharge from the Gila River is of extremely high quality relative to the salinity of the aquifer. There appear no configurations of iso chemical lines which are attributable to internal movement through saline deposits. The hydraulic gradient of the water table aquifer is relatively constant and follows the gradient of the land surface. Concentration of irrigation water by evaporation and subsequent leaching while in conveyance to the water table seems to increase the salinity of this percolating water by approximately three fold. The magnitude of this increase at any one point in space and time is a function of the volume of water applied to the land surface, the amount of evaporation, the initial chemical composition of the water, the chemical characteristics of the unsaturated zone through which it penetrates, and the transmission properties of the aquifer. The salinity increase seems significant but the extent of the contribution to the salinity of the aquifer is dependent on the amount of infiltration to the aquifer. This amount is currently undetermined, but is probably a sizable volume  especially from pre irrigation applications. A sociologic investigation based on responses from a detailed questionnaire  interview program of 41 farmers (25 percent of the farming population), indicated that there is an awareness of the high salinity of ground water being used for irrigation but relatively little concern about the rate of increase of that salinity. The farmers seem reluctant to leave the area and are willing to take somewhat greater economic losses than expected. Since the farmers of the area are principally Mormon, there may be a tie to this historically Mormon region which is stronger than usual. The economic analysis of the Safford Valley based on the modeling of a "Representative Farm" analog indicates that cotton will remain economical to produce on the basis of the projected salinity trends and ceteris paribus conditions, for a significant time beyond limits of prediction. The analysis indicates that the optimum saltresistant crops for the area are being cultivated, and that of these, alfalfa, the least tolerant, will cease to be productive in large areas of the valley by 1990. The entire valley will not be able to economically produce alfalfa by 2040, but will remain in production since it is a necessary crop for cotton and the cotton profits should be sufficient to cover the alfalfa losses. Pumping is the only element in the operation of the social, physical and economic systems by which salinity change could be influenced significantly. The area east of Safford is the optimal pumping region while that west of Pima is the worst. The employment of surface water should be maximized, and salt oriented field methods should be employed. Although agriculture does not seem in danger in predictable time, these practices would increase yield (or slow the decrease) and postpone the day when farming will no longer by profitable in the Safford Valley of Graham County, Arizona.

APPLICATION OF A GROUNDWATER 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.

APPLICATION OF BORON ISOTOPE RATIOS FOR IDENTIFYING NITRATE CONTAMINATION SOURCES IN THE GROUNDWATER OF AVRA VALLEY, ARIZONAThe stable isotopes of the conservative element boron, 11B and 1°B, have been employed as co migrating isotopic tracers to determine the origin of nitrate observed in groundwater from a large capacity (2500 gpm) irrigation well in the Avra Valley of southeastern Arizona. The isotopic ratios of the conservative element, boron, provided an identifying signature for various nitrate rich source waters. Additional chemical parameters were also examined to corroborate the isotopic indications. Findings of this investigation indicate that most of the nitrate observed in groundwater from well CMID 18 at the beginning of the 1993 irrigation season was due to municipal wastewater contamination. As the irrigation season progressed, an increasing proportion of nitrate was contributed by irrigation return flow from neighboring agricultural fields.

Application of snow distribution models within the laguna Negra basin, ChileSpectral linear unmixing and binary regression trees were used to estimate the distribution of snow within the Laguna Negra basin in Chile. Spectral linear unmixing was performed for multiband Landsat 5 images for the determination of subpixel snow fractions. We were interested in determining the number of bands needed for an adequate distribution of SCA. Results showed that for winter scenes (scenes with greater than 90% snow cover and portions of the basin covered by shadows) linear spectral unmixing can be used to model SCA using at least four bands with a rock, a snow and a shaded snow endmember, but that five bands, using two rock endmembers, a snow and a shaded rock endmember, are needed for the fall scenes (scenes with less than 10% snow cover and portions of the basin covered by shadows). The spring scenes (scenes with 50 percent and higher snow cover and no shadows) showed plausible results with three bands, but the need for a second rock endmember in the fall scenes suggest 4 bands may give a more accurate result. A binary regression tree model was used to determine distributed SWE at peak accumulation in the Echaurren basin, a sub basin of Laguna Negra. Regression trees grown from field snow survey data did an excellent job at explaining the variation of SWE in two of the three surveys examined when resubstitution was used to evaluate the model, but did a poor job in all cases when cross validation was used. However, cross validation may over estimate the errors associated with the model. Basinwide SWE maps resulting from the application of the regression trees formed plausible structures. Normalized snow distribution was sufficiently different between years such that a "typical" SWE map could not be developed. Nonetheless, there were identifiable patterns that did occur in the SWE distributions from different years that gave insight into the factors affecting SWE in the basin. Such factors include a strong dependance on radiation in the lower portion of Echaurren for two of the years, and the presence of heavy SWE regions near cliffs. Insights such as these provided useful information on how the type of data and method of collection might be improved. The large SWE values near cliffs, for instance, suggest that use of an avalanche map might improve the modeled SWE distribution. The dependance of SWE on radiation in the lower basin suggest the SWE data should be obtained over the entire range of radiation values in the lower basin.

Aquifer Modeling by Numerical Methods Applied to an Arizona Groundwater BasinFLUMP, a recently developed mixed explicit implicit finite element program, was calibrated against a data base obtained from a portion of the Tucson Basin aquifer, Arizona, and represents its first application to a real world problem. Two previous models for the same region were constructed (an electric analog and a finite difference model) in which calibration was based on prescribed flux boundary conditions along stream courses and mountain fronts. These fluxes are not directly measured and estimates are subject to large uncertainties. In contrast, boundary conditions used in the calibration of FLUMP were prescribed hydraulic heads obtained from direct measurement. At prescribed head boundaries FLUMP computed time  varying fluxes representing subsurface lateral flow and recharge along streams. FLUMP correctly calculated fluctuations in recharge along the Santa Cruz River due to fluctuations in storm runoff and sewage effluent release rates. FLUMP also provided valuable insight into distributions of recharge, discharge, and subsurface flow in the study area.Properties of FLUMP were compared with those of two other programs in current use: ISOQUAD, a finite element program developed by Pinder and Frind (1972), and a finite difference program developed by the U.S. Geological Survey (Trescott, et al., 1976). It appears that FLUMP can handle a larger class of problems than the other two programs, including those in which the boundary conditions and aquifer parameters vary arbitrarily with time and /or head. FLUMP also has the ability to solve explicitly when accuracy requires small time steps, the ability to solve explicitely in certain parts of the flow region while solving implicitly in other parts, flexibility in mesh design and numbering of nodes, computation of internal as well as external fluxes, and global as well as local mass balance checks at each time step.

Basin Scale and Runoff Model ComplexityDistributed RainfallRunoff models are gaining widespread acceptance; yet, a fundamental issue that must be addressed by all users of these models is definition of an acceptable level of watershed discretization (geometric model complexity). The level of geometric model complexity is a function of basin and climatic scales as well as the availability of input and verification data. Equilibrium discharge storage is employed to develop a quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance. Equilibrium storage ratios are used to define the transition from overland to channel dominated flow response. The methodology is tested on four subcatchments in the USDA ARS Walnut Gulch Experimental Watershed in Southeastern Arizona. The catchments cover a range of basins scales of over three orders of magnitude. This enabled a unique assessment of watershed response behavior as a function of basin scale. High quality, distributed, rainfall runoff data was used to verify the model (KINEROSR). Excellent calibration and verification results provided confidence in subsequent model interpretations regarding watershed response behavior. An average elementary channel support area of roughly 15% of the total basin area is shown to provide a watershed discretization level that maintains model performance for basins ranging in size from 1.5 to 631 hectares. Detailed examination of infiltration, including the role and impacts of incorporating small scale infiltration variability in a distribution sense, into KINEROSR, over a range of soils and climatic scales was also addressed. The impacts of infiltration and channel losses on runoff response increase with increasing watershed scale as the relative influence of storms is diminished in a semiarid environment such as Walnut Gulch. In this semiarid environment, characterized by ephemeral streams, watershed runoff response does not become more linear with increasing watershed scale but appears to become more nonlinear.

BAYES RISK ANALYSIS OF REGIONAL REGRESSION ESTIMATES OF FLOODSThis thesis defines a methodology for the evaluation of the worth of streamflow data using a Bayes risk approach. Using regional streamflow data in a regression analysis, the Bayes risk can be computed by considering the probability of the error in using the regionalized estimates of bridge or culvert design parameters. Cost curves for over and underestimation of the design parameter can be generated based on the error of the estimate. The Bayes risk can then be computed by integrating the probability of estimation error over the cost curves. The methodology may then be used to analyze the regional data collection effort by considering the worth of data for a record site relative to the other sites contributing to the regression equations. The methodology is illustrated by using a set of actual streamflow data from Missouri. The cost curves for over and underestimation of the streamflow design parameter for bridges and culverts are hypothesized so that the Bayes risk might be computed and the results of the analysis discussed. The results are discussed by demonstrating small sample bias that is introduced into the estimate of the design parameter for the construction of bridges and culverts. The conclusions are that the small sample bias in the estimation of large floods can be substantial and that the Bayes risk methodology can evaluate the relative worth of data when the data are used in regionalization.

BAYESIAN DECISION ANALYSIS OF A STATISTICAL RAINFALL/RUNOFF RELATIONThe first purpose of this thesis is to provide a framework for the inclusion of data from a secondary source in Bayesian decision analysis as an aid in decision making under uncertainty. A second purpose is to show that the Bayesian procedures can be implemented on a computer to obtain accurate results at little expense in computing time. The state variables of a bridge design example problem are the unknown parameters of the probability distribution of the primary data. The primary source is the annual peak flow data for the stream being spanned. Information pertinent to the choice of bridge design is contained in rainfall data from gauges on the watershed but the distribution of this secondary data cannot be directly expressed in terms of the state variables. This study shows that a linear regression equation relating the primary and secondary data provides a means of using secondary data for finding the Bayes risk and expected opportunity loss associated with any particular bridge design and single new rainfall observation. The numerical results for the example problem indicate that the information gained from the rainfall data reduces the Bayes risk and expected opportunity loss and allows for a more economical structural design. Furthermore, the careful choice of the numerical methods employed reduces the computation time for these quantities to a level acceptable to any budget.

CALIBRATION AND VALIDATION OF AQUIFER MODELSThe main aim of this study is to develop a suitable method for the calibration and validation of mathematical models of large and complex aquifer systems. Since the calibration procedure depends on the nature of the model to be calibrated and since many kinds of models are used for groundwater, the question of model choice is broached first. Various aquifer models are critically reviewed and a table to compare them as to their capabilities and limitations is set up. The need for a general calibration method for models in which the flow is represented by partial differential equations is identified from this table. The calibration problem is formulated in the general mathematical framework as the inverse problem. Five types of inverse problems that exist in modeling aquifers by partial differential equations are identified. These are, to determine (1) parameters, (2) initial conditions, (3) boundary conditions, (4) inputs, and (5) a mixture of the above. Various methods to solve these inverse problems are reviewed, including those from fields other than hydrology. A new direct method to solve the inverse problem (DIMSIP) is then developed. Basically, this method consists of transforming the partial differential equations of flow to algebraic equations by substituting in them the values of the various derivatives of the dependent variable (which may be hydraulic pressure, chemical concentration or temperature). The parameters are then obtained by formulating the problem in a nonlinear optimization framework. The method of sequential unconstrained minimization is used. Spline functions are used to evaluate the derivatives of the dependent variable. Splines are functions defined by piecewise polynomial arcs in such a way that derivatives up to and including the order one less than the degree of polynomials used are continuous everywhere. The natural cubic splines used in this study have the additional property of minimum curvature which is analogous to minimum energy surface. These and the derivative preserving properties of splines make them an excellent tool for approximating the dependent variable surfaces in groundwater flow problems. Applications of the method to both a test situation as well as to real world data are given. It is shown that the method evaluates the parameters, boundary conditions and inputs; that is, solves inverse problem type V. General conditions of heterogeneity and anisotropy can be evaluated. However, the method is not applicable to steady flows and has the limitation that flow models in which the parameters are functions of the dependent variable cannot be calibrated. In addition, at least one of the parameters has to be preassigned a value. A discussion of uncertainties in calibration procedures is given. The related problems of model validation and sampling of aquifers are also discussed.

CALIBRATION OF RAINFALLRUNOFF MODELS USING GRADIENTBASED ALGORITHMS AND ANALYTIC DERIVATIVESIn the past, derivativebased optimization algorithms have not frequently been used to calibrate conceptual rainfall riff (CRR) models, partially due to difficulties associated with obtaining the required derivatives. This research applies a recently developed technique of analytically computing derivatives of a CRR model to a complex, widely used CRR model. The resulting least squares response surface was found to contain numerous discontinuities in the surface and derivatives. However, the surface and its derivatives were found to be everywhere finite, permitting the use of derivative based optimization algorithms. Finite difference numeric derivatives were computed and found to be virtually identical to analytic derivatives. A comparison was made between gradient (Newton Raphsoz) and direct (pattern search) optimization algorithms. The pattern search algorithm was found to be more robust. The lower robustness of the NewtonRaphsoi algorithm was thought to be due to discontinuities and a rough texture of the response surface.

Characterization of aquifer heterogeneity using transient hydraulic tomographyHydraulic tomography is a cost effective technique for characterizing the heterogeneity of hydraulic parameters in the subsurface. During hydraulic tomography surveys, a large number of hydraulic heads (i.e., aquifer responses) are collected from a series of pumping or injection tests in an aquifer. These responses are then used to interpret the spatial distribution of hydraulic parameters of the aquifer using inverse modeling. In this study, we developed an efficient sequential successive linear estimator (SSLE) for interpreting data from transient hydraulic tomography to estimate threedimensional hydraulic conductivity and specific storage fields of aquifers. We first explored this estimator for transient hydraulic tomography in a hypothetical onedimensional aquifer. Results show that during a pumping test, transient heads are highly correlated with specific storage at early time but with hydraulic conductivity at late time. Therefore, reliable estimates of both hydraulic conductivity and specific storage must exploit the head data at both early and late times. Our study also shows that the transient heads are highly correlated over time, implying only infrequent head measurements are needed during the estimation. Applying this sampling strategy to a well posed problem, we show that our SSLE can produce accurate estimates of both hydraulic conductivity and specific storage fields. The benefit of hydraulic tomography for ill posed problems is then demonstrated. Finally, to affirm the robustness of our SSLE approach, we apply the SSLE approach to transient hydraulic tomography in a hypothetical two dimensional aquifer with nonstationary hydraulic properties, as well as a hypothetical threedimensional heterogeneous aquifer.

COLLECTIVE ADJUSTMENT OF THE PARAMETERS OF THE MATHEMATICAL MODEL OF A LARGE AQUIFERThe problem of evaluating the parameters of the mathematical model of an unconfined aquifer is examined with a view toward development of automated or computer aided methods. A formulation is presented in which subjective confidence ranges for each of the model parameters are quantified and entered into an objective function as linear penalty functions. Parameters are then adjusted by a procedure which seeks to reduce the model error to acceptable limits. A digital computer model of the Tucson basin aquifer is adapted and used to illustrate the concepts and demonstrate the method.

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?