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AuthorsDepartment of Hydrology & Water Resources, The University of Arizona (96)Maddock, Thomas, III (21)Sorooshian, Soroosh (12)Yeh, T.-C. Jim (9)Baird, Kathryn J. (4)Gupta, Hoshin Vijai (4)Maddock, Thomas III (4)Neuman, Shlomo P. (4)Yeh, Tian-Chyi J. (4)Arizona Research Laboratory for Riparian Studies (3)View MoreTypesTechnical Report (101)

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COLLECTIVE ADJUSTMENT OF THE PARAMETERS OF THE MATHEMATICAL MODEL OF A LARGE AQUIFER

Lovell, Robert E. (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1971-06)

The 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.

EFFECTS OF RADAR-ESTIMATED PRECIPITATION UNCERTAINTY ON DIFFERENT RUNOFF-GENERATION MECHANISMS

Winchell, Michael; Gupta, Hoshin Vijai; Sorooshian, Soroosh (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1997)

Runoff 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 radar-based precipitation estimates. When uncalibrated or poorly calibrated radar products were used as input to a rainfall-runoff model, the resulting predicted runoff varied severely from the runoff generated using well-calibrated 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.

RESPONSE FUNCTIONS IN THE CRITICAL COMPARISON OF CONJUNCTIVE MANAGEMENT SYSTEMS IN TWO WESTERN STATES

Lacher, Laurel Jane,1964-; Maddock, Thomas, III; Lord, William B. (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1993-04)

Conjunctive management of surface and ground -water resources on state and local levels is a relatively new political phenomenon. This type of management has evolved, in part, in response to growing populations with ever -increasing, and often conflicting, water demands. In addition, a more sophisticated technical understanding of the physical link between groundwater and surface waters has led water managers to reconsider historical strategies for solving water supply problems. In light of growing demand and improved technology, some western states have begun the transition from crisis- oriented water management to one of long -term planning for population growth and environmental protection. This planning process requires that the constituents of a region define their water use goals and objectives so that various approaches to conjunctive management may be evaluated for their suitability to that particular physical and socio- political environment.

Effect Of Filtering On Autocorrelation, Flow, And Transport In Random Fractal Fields

Federico, Vittorio Di; Neuman, Shlomo P. (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1995-12)

" 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.

A COST-EFFECTIVENESS STUDY AND ANALYSIS OF MUNICIPAL REFUSE DISPOSAL SYSTEMS

Popovich, Michael Lee, 1944- (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1973-06)

The 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.

Hydrogeology in the United States 1780-1950

Davis, Stanley N.; Davis, Augusta G. (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2005-11)

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

Analysis of Borehole Infiltration Tests Above the Water Table

Stephens, Daniel Bruce; Neuman, Shlomo P. (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1980-03)

Constant 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.

Aquifer Modeling by Numerical Methods Applied to an Arizona Groundwater Basin

Fogg, Graham E.; Simpson, Eugene S.; Neuman, Shlomo P. (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1979-06)

FLUMP, 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.

Eutrophication: A Mathematical Model

Friedman, Joel Herbert (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1973-06)

Various 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.

EXPERIMENTAL INVESTIGATION OF SEEPAGE THROUGH HETEROGENEOUS POROUS MEDIA

Mathieu, James T., Jr.; Yeh, T.-C. Jim (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1988-10)

Five sand tank experiments were conducted to investigate the behavior of unsaturated flow in heterogeneous porous media and to test the recent stochastic theories of Yeh et al. (1985a, b. c) and Mantoglou et al. (1987a, b, c) on flow through unsaturated porous media. The hydraulic properties @(w) and K(0) of the medium and coarse sand used in the experiments were measured with various laboratory columns. Fourteen medium and coarse sands were alternately layered in the 2.38 m long x 1.12 m high x 0.1 m thick sand tank. Water was infiltrated from a point source for three of five experiments and from a channel source for two experiments. An array of 62 tensiometers were used to record the capillary tension head distribution during each experiment. The wetting front profiles for the first experiment show the stratified sand effects both the development and dissipation of preferential flow paths. The experimental results qualitatively support stochastic theory of saturation dependent anisotropy. Three of the five experiments agree with the stochastic result of Yeh et al. (1985a and b) that an increase in the variance of the capillary tension head (soil becomes drier) is proportional to an increase in the mean tension head.

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