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Scale issues of heterogeneity in vadose zone hydrology and practical solutionsHydrological properties of the vadose zone often exhibit a high degree of spatial variability at various scales due to the heterogeneous nature of geological formations. For laboratory scale problems (i.e., small cores, soil columns, and sand boxes), variation in pore size, pore geometry, and tortuosity of pore channels are the major source of heterogeneity. They are called laboratoryscale heterogeneity. Microstratification, foliation, cracks, and roots are also some possible heterogeneities at this scale. As our observation scale increases to a field, stratification or layering in a geologic formation becomes the dominant heterogeneity, which is often classified as fieldscale heterogeneity. At an even larger observation scale, the regionalscale heterogeneity represents the variation of geologic formations or facies. Variations among sedimentary basins are then categorized as the globalscale heterogeneity. Fundamental theories for flow and solute transport through porous media are essentially derived for the laboratoryscale heterogeneity. When we attempt to apply these theories to the vadose zone, comprising heterogeneities of many different scales, we encounter the scale problem. To resolve this problem two approaches have evolved in the past: the system approach and the physical approach. The former approach treats the vadose zone as a low pass filter and its governing principle is determined by the relationship between its input and output histories (e.g., Jury et al., 1986). The latter approach however relies on upscaling the laboratoryscale theories to the vadose zone. While the system approach has been widely used by soil scientists, it is often criticized for its empiricism and the lack of physical principles. Besides, it is known to be limited to nonpoint source problems or those related to the integrated behavior of a system (for example, the average concentration of nitrate in the irrigation return flow at irrigation drains or their breakthrough at the water table beneath an irrigation field). Since this approach requires the knowledge of input and output histories and model calibrations, flow and tracer experiments must be carried out at a given site prior to prediction. Further, a calibrated system model for the vadose zone at a given depth under a given condition is often found unsuitable for different depths and conditions (e.g., Butters et al., 1989; Butters and Jury, 1989; Roth et al., 1991). While such system approaches are practical tools for predicting water flow and pollutant transport through thin vadose zones to the water table or to irrigation drains at agricultural fields, their utility for general hydrogeological problems is limited. Hydrogeological problems involve vadose zones of tens and hundreds of meters in thickness. Input sources to these vadose zones are small compared with the scale of hydrogeological settings. Yet, groundwater hydrologists have to focus on the spatial and temporal evolution of flow and spread of solutes over the vadose zone and regional aquifers (Stephens, 1996). Because of these above mentioned reasons, the following discussion will concentrate on the physical approach that has been widely used by groundwater hydrologists. Moreover, the discussion will present only the author's point of view about the scale issue and approaches to the heterogeneity in the vadose zone.

SIMULATION OF GROUNDWATER FLOW TO ASSESS THE EFFECTS OF PUMPING AND CANAL LINING ON THE HYDROLOGIC REGIME OF THE MESILLA BASIN: Dona Ana County, New Mexico & El Paso County, TexasThis study, which is to provide information to a settlement over the rights to water resources in the Mesilla Basin, uses a groundwater model to estimate how pumping in the basin affects the hydrologic regime.

Simulation of groundwater conditions in the Colorado River Delta, MexicoThe Colorado River Delta (CRD) is a large sedimentary complex within a tectonically active structurally controlled basin. The CRD lies across the U.S.Mexico international boundary and is traversed by the Colorado River on is way to the Gulf of California. Multidisciplinary research addressing the impact of the hydrologic change in the CRD has been increasing since the 1980's. To help expand the base of this knowledge, a groundwater model for the CRD within Mexico was developed. A conceptual model was constructed and transformed within the Department of Defense Groundwater Modeling Software (GMS) into a numerical model using the MODFLOW 2005 code made available by the U.S. Geological Survey. Model results indicates that large scale flood events on the Colorado River act as a recharge to the aquifer and show that the relationship between groundwater withdrawals and capture are evident on an seasonal scale. The model will form the parent basis for further Delta studies using the Local Grid Refinement (LRG), a methodology inherent to MODFLOW 2005.

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.

Simulation Of Groundwater Flow In The Rincon Valley Area And Mesilla Basin, New Mexico And TexasA groundwater flow model was constructed for the Rincon Valley area and Mesilla Basin. The system is dominated by the complex interaction of the Rio Grande, canals, laterals, and drains with groundwater pumping. The primary purpose of the model was to aid the New Mexico Texas Water Commission in assessing options for water resources development in the Lower Rio Grand Basin from Caballo Reservoir in New Mexico to El Paso, Texas. One such assessment was to evaluate the effect of secondary irrigation releases from Caballo Reservoir on the water budget. In addition, the model will eventually be linked to a surface water model (BESTSM) being utilized by the New Mexico Texas Water Commission to evaluate water supply alternatives for El Paso, Texas. Stress periods were specified on a seasonal basis, a primary irrigation season from March through October and a secondary irrigation season from November through February. Analysis of model output indicates that groundwater pumping decreases Rio Grande flows, secondary irrigation season releases do not alter the water budget significantly, and that recharge and discharge from aquifer storage are strongly related to the season.

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.

Stochastic analysis of moisture plume dynamics of a field injection experimentA vadose zone field injection experiment was conducted in the summer of 2000 at theHanford Site, Washington. The unique moisture content database is used to identify the lithology at the field site and to interpret, visualize, and quantify the spatio temporal evolution of the three dimensional (3 D) moisture plume created by the injection experiment. We conducted a hierarchical geostatistical analysis to examine the large scale geologic structure for the entire field site, and then investigate small scale features within different layers. Afterward, variogram analysis is applied to the O field measured for seven different days during the injection experiment. Temporal variations of sills and ranges are related to the observed moisture plume dynamics. A visualization of the 3 D moisture plume evolution illustrates effects of media heterogeneity. Statistics of changes in moisture content as a function of distance reveals large variance near the wetting front and the coefficient of variation increases with decreasing mean.These findings support the gradient and mean dependent variability in the moisture content distribution as reported by existing stochastic theories. Spatial moment analysis is also conducted to quantify the rate and direction of movement of the plume mass center and its spatial spreading. The ratio of horizontal to vertical spreading at varying moisture contents suggests moisture dependent anisotropy in effective unsaturated hydraulic conductivity, confirming existing stochastic theories. However, the principal directions of the spatial moments are found to vary as the moisture plume evolves through local heterogeneity, a feature that has not been recognized in the theories.

STOCHASTIC ANALYSIS OF WATER FLOW IN HETEROGENEOUS UNSATURATED SOILS UNDER TRANSIENT CONDITIONSA numerical model for the analysis of uncertainty propagation in flow through unsaturated soils is developed. This model is based on the first order Taylor series expansion of the discretized Richards' equation, for one dimensional flow. Soil hydrologic properties, the saturated hydraulic conductivity and the pore size distribution, are assumed to be stochastic processes in space. The surface boundary conditions are considered to be deterministic variable in time or stochastic time series. The purpose of this model is to examine the effect of uncertainty in boundary conditions and heterogeneity on the pressure head and flux variance profiles at various times.

A STOCHASTIC APPROACH TO SPACETIME 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.

Stochastic fusion of information for characterizing and monitoring the vadose zoneInverse problems for vadose zone hydrological processes are often being perceived as ill  posed and intractable. Consequently, solutions to inverse problems are often subject to skepticism. In this paper, using examples, we elucidate difficulties associated with inverse problems and the prerequisites for such problems to be well posed so that a unique solution exists. We subsequently explain the need of a stochastic conceptualization of the inverse problem and, in turn, the conditional effective parameter concept. This concept aims to resolve the ill posed nature of inverse problems for the vadose zone, for which generally only sparse data are available. Next, the development of inverse methods for the vadose zone, based on a conditional effective parameter concept, is explored, including cokriging, the use of a successive linear estimator, and a sequential estimator. Their applications to the vadose zone inverse problems are subsequently examined, which include hydraulic /pneumatic and electrical resistivity tomography surveys, and hydraulic conductivity estimation using observed pressure heads, concentrations, and arrival times. Finally, a stochastic information fusion technology is presented that assimilates information from unsaturated hydraulic tomography and electrical resistivity tomography. This technology offers great promise to effectively characterize heterogeneity, to monitor processes in the vadose zone, and to quantify uncertainty associated with vadose zone characterization and monitoring.

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.

STREAMAQUIFER INTERACTION MODELING IN LOWER CIENEGA CREEK BASIN, ARIZONA USING FINITE ELEMENTSOnly a few areas in the deserts of the southwestern United States possess perennial streamflows. Cienega Creek near Tucson, Arizona is one of them (Figurel). Because of ground water punping, some of these streams are in jeopardy of becoming ephemeral. The variability of surface water supply in the southwestern United States is very important because of its effects on riparian systems. Declines in water table and ground water storage (over  exploitation of pumping wells) pose major concern as land subsidence and earth fissures, and produce stream and vegetation losses through ground and surface water interactions. This report examines the Lower Cienega Creek Basin (LCCB) and the potential impact of nearby commercial development on the perennial stream. This area was chosen because it contains a natural preserve and a perennial stream. Perennial water flow and shallow water levels along the creek support various riparian species which shelter many types of insects and wildlife. The stream contained several species of fish including the endangered Gila Topminnow before they were extinct from this creek. This natural preserve, near the basin's exit, is one of the few desert places in the U.S. supporting a suitable habitat for animals, birds, and fishes because of its lush vegetation. An important riparian indicator for water table levels are cottonwood trees. These trees require shallow water to survive. As water levels decline, the cottonwoods produce less leaves. These cottonwoods could limit their existence by ceasing reproduction. Ultimately, a detrimental impact will be noticed in the surrounding ecosystem.

A SUPERIOR TRAINING STRATEGY FOR THREELAYER FEEDFORWARD ARTIFICIAL NEURAL NETWORKSA new algorithm is proposed for the identification of threelayer feedforward artificial neural networks. The algorithm, entitled LLSSIM, partitions the weight space into two major groups: the input hidden and hidden output weights. The input hidden weights are trained using a multi start SIMPLEX algorithm and the hidden output weights are identified using a conditional linear least square estimation approach. Architectural design is accomplished by progressive addition of nodes to the hidden layer. The LLSSIM approach provides globally superior weight estimates with fewer function evaluations than the conventional back propagation (BPA) and adaptive back propagation (ABPA) strategies. Monte carlo testing on the XOR problem, two function approximation problems, and a rainfall runoff modeling problem show LLSSIM to be more effective, efficient and stable than BPA and ABPA.

Traditional Aquifer Tests: Comparing Apples to Oranges?Traditional analysis of aquifer tests uses the observed hydrograph at one well caused by pumping at another well for estimating transmissivity and storage coefficient of an aquifer. The analysis relies on Theis' or Jacob's approximate solution, which assumes aquifer homogeneity. Aquifers are inherently heterogeneous at different scales. If the observation well taps into a low permeability zone while the pumping well is located in a high permeable zone, the resulting situation contradicts the homogeneity assumption embedded in the traditional analysis. As a result, a practical but important question we ask: What do we derive from the traditional analysis? Using numerical experiments in synthetic aquifers, we answer this question. Results of the experiments indicate that the effective transmissivity, Teff , and storage coefficient, Seff , values vary with time, as well as the principal directions of the transmissivity, but both values approach their geometric means of the aquifer at large times. Analysis of the estimated transmissivity (T) and storage coefficient (S ) using well hydrographs from a single observation well shows that at early times, both the estimated T and S values vary with time. At late times, both estimates approach local averages near the observation well. The T value approaches but does not equal Teff , representing an average value over a broad area in the vicinity of the observation well while the S value converges to the value dominated by the storage coefficient near the observation wells (i.e., its average area is much smaller than that of the t value).

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.

WATERBUD: A SPREADSHEETBASED MODEL OF THE WATER BUDGET AND WATER MANAGEMENT SYSTEMS OF THE UPPER SAN PEDRO RIVER BASIN, ARIZONAThis report describes the development and application of a spreadsheet based model of the water budget and water management systems of the Upper San Pedro River Basin in southeastern Arizona. The model has been given the name, WATERBUD.

WORTH OF DATA USED IN DIGITALCOMPUTER MODELS OF GROUNDWATER 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.