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THE QUANTITATIVE FEATURES OF CHINA'S WATER RESOURCES: AN OVERVIEW(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 198302)China has a long history of hydrological development. According to Chinese legends, famous projects of flood water diversion were developed by the Great Yu as early as the year two thousand B.C. The earliest hydrological record appeared in 256 B.C., when Mr. Lipin and his son constructed the Dujiangyan irrigation system in the upper reach of the Mingjiang River in Sichuan Province. At Baopingkao, the water intake point of the Dujiangyan irrigation system, a water staff gage was carved on a stone for the measurement of water levels. Although hydrological studies in China started early, hydrology and water resources as modern sciences have been developed only in the last several decades, particularly rapidly in the last 30 years. For instance, the number of hydrological stations has increased 45 times, from about 350 to more than 16,000. Of these, about 3300 stations also take flow velocity measurements. The average density of the hydrological stations is about one per 530 km2 and that of discharge measurement stations about one in 3,000 km2. These stations are highly concentrated in eastern China. The longest records of precipitation are maintained in the large cities in eastern China, including Beijing, Shanghai and Tianjing. Beijing has 140 years of precipitation records. The Hankao hydrological station on the Changjiang (Yangtze) River has the longest discharge record spanning 117 years (1865 1982).

Rainfall estimation from satellite infrared imagery using artificial neural networks(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1997)Infrared (IR) imagery collected by geostationary satellites provides useful information about the dirunal evolution of cloud systems. These IR images can be analyzed to indicate the location of clouds as well as the pattern of cloud top temperatures (Tbs). During the past several decades, a number of different approaches for estimation of rainfall rate (RR) from Tb have been explored and concluded that the TbRR relationship is (1) highly nonlinear, and (2) seasonally and regionally dependent. Therefore, to properly model the relationship, the model must be able to: (1) detect and identify a nonlinear mapping of the TbRR relationship; (2) Incorporate information about various cloud properties extracted from IR image; (3) Use feedback obtained from RR observations to adaptively adjust to seasonal and regional variations; and (4) Effectively and efficiently process large amounts of satellite image data in real time. In this study, a kind of artificial neural network (ANN), called Modified Counter Propagation Network (MCPN), that incorporates these features, has been developed. The model was calibrated using the data around the Japanese Islands provided by the Global Precipitation Climatology Project (GPCP) First Algorithm Intercomparison Project (AIPI). Validation results over the Japanese Islands and Florida peninsula show that by providing limited groundtruth observation, the MCPN model is effective in monthly and hourly rainfall estimation. Comparison of results from MCPN model and GOES Precipitation Index (GPI) approach is also provided in the study.

RAINFALLRUNOFF MODELING OF FLASH FLOODS IN SEMIARID WATERSHEDS(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 199206)Flash floods caused by localized thunderstorms are a natural hazard of the semi arid Southwest, and many communities have responded by installing ALERT flood forecasting systems. This study explored a rainfall runoff modeling approach thought to be appropriate for forecasting in such watersheds. The kinematic model KINEROS was evaluated because it is a distributed model developed specifically for desert regions, and can be applied to basins without historic data. This study examined the accuracy of KINEROS under data constraints that are typical of semi arid ALERT watersheds. The model was validated at the 150 km2, semi arid Walnut Gulch experimental watershed. Under the conditions examined, KINEROS provided poor simulations of runoff volume and peak flow, but good simulations of time to peak. For peak flows, the standard error of estimate was nearly 100% of the observed mean. Surprisingly, when model parameters were based only on measurable watershed properties, simulated peak flows were as accurate as when parameters were calibrated on some historic data. The accuracy of KINEROS was compared to that of the SCS model. When calibrated, a distributed SCS model with a simple channel loss component was as accurate as KINEROS. Reasons for poor simulations were investigated by examining a) rainfall sampling errors, b) model sensitivity and dynamics, and c) trends in simulation accuracy. The cause of poor simulations was divided between rainfall sampling errors and other problems. It was found that when raingage densities are on the order of 1/20 km2, rainfall sampling errors preclude the consistent and reliable simulation of runoff from localized thunderstorms. Even when rainfall errors were minimized, accuracy of simulations were still poor. Good results, however, have been obtained with KINEROS on small watersheds; the problem is not KINEROS itself but its application at larger scales. The study also examined the hydrology of thunderstorm generated floods at Walnut Gulch. The space time dynamics of rainfall and runoff were characterized and found to be of fundamental importance. Hillslope infiltration was found to exert a dominant control on runoff, although flow hydraulics, channel losses, and initial soil moisture are also important. Watershed response was found to be nonlinear.

A RANDOMWALK SIMULATION MODEL OF ALLUVIALFAN DEPOSITION(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 197206)A 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.

RESPONSE FUNCTIONS IN THE CRITICAL COMPARISON OF CONJUNCTIVE MANAGEMENT SYSTEMS IN TWO WESTERN STATES(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 199304)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.

REVIEW OF MODELING OF WATER FLOW AND SOLUTE TRANSPORT IN THE VADOSE ZONE: Stochastic Approaches(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 19941110)Hydrologic properties of the vadose zone are heterogeneous at many different scales. An accurate prediction of water flow and solute transport in the vadose zone requires detailed information about spatial distributions of the properties. Collecting such detailed spatial distribution of hydrologic properties of geological formations is a formidable task. As a result, hydrologic modelers face a difficult challenge: to make the best prediction with little information. During the past few decades many approaches and theories based on stochastic concepts have been developed in an attempt to overcome this difficulty. These stochastic approaches and theories provide ways not only to predict flow and transport processes in large scale, heterogeneous vadose zones, but also to assess uncertainties in our predictions. One widely investigated stochastic approach involves the use of effective flow and transport properties. The effective property approach essentially represents a generalization of the well known equivalent homogeneous media approach discussed in most hydrology textbooks (e.g., using the arithmetic mean conductivity and harmonic mean conductivity for flow parallel to and normal to stratification, respectively, in layered media). This approach is a valuable tool in many practical situations but it predicts the ensemble behavior of a system which can be quite different from reality. To obtain predictions at higher resolutions than the effective property approach, many heterogeneous approaches have also been developed. This paper presents an overview of the stochastic theories related to both equivalent homogeneous media and heterogeneous approaches, it highlights their applications, and it discusses some of their deficiencies.

A REVIEW OF THE SCALE PROBLEM AND APPLICATIONS OF STOCHASTIC METHODS TO DETERMINE GROUNDWATER TRAVEL TIME AND PATH(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1989)The groundwater travel time along the fastest path of likely radionuclide transport is a regulatory criterion used to assess the hydrogeologic quality of a high  level radioactive waste repository. Hydrologists and engineers are limited in their ability to define with confidence the fastest path, owing to the heterogeneous nature of geologic materials. Field measurements of hydraulic properties such as in test or observation wells, are inherently averages of properties at scales smaller than the scale of the field measurement. As a result of averaging, subscale information is lost and there is uncertainty in defining the fastest trajectory of groundwater. This scale problem is explained through a review of the continuum and REV concepts in groundwater hydrology. The application of hydrodynamic dispersion concepts is recommended as a means of incorporating the effect of subscale heterogeneity on the fastest groundwater travel time. Sources of uncertainties in predicting groundwater travel time are discussed in the report. The uncertainties are mainly attributed to the heterogeneous nature of geologic formations. The heterogeneity of geologic materials can, however, be characterized quantitatively using geostatistical methods. Important statistical parameters include mean and variance. as well as the spatial correlation structures of the hydrologic properties within the hydrogeologic system. These parameters may he obtained from limited data base. Stochastic methods, reviewed and explained in this report, can take advantage of the geostatistical characterization to predict large scale groundwater flow and solute transport. Several examples from recent scientific literature are provided to illustrate the application of stochastic methods to the groundwater travel time analysis. Stochastic methods in subsurface hydrology have only recently been evaluated under field conditions for a few locations, and validation of the theories is incomplete, especially in unsaturated fractured rocks. Nevertheless, research efforts should continue to improve the state of the art. Geostatistics and stochastic methods will be valuable tools in addressing the groundwater travel time objective

A riparian evapotranspiration package(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 200210)A new evapotranspiration package for the U.S. Geological Survey's groundwater flow model, MODFLOW, is documented. The Riparian Evapotranspiration Package (RIPET), provides flexibility in simulating riparian and wetland evapotranspiration (ET) not provided by the MODFLOW96 Evapotranspiration (EVT) Package, nor by the MODFLOW2000 Segmented Function Evapotranspiration (ETS1) Package. This report describes how the package was conceptualized and provides input instructions, listings and explanations of the source code, and an example simulation. Traditional approaches to modeling ET processes assume a piecewise linear relationship between ET flux rate and hydraulic head. The Riparian ET Package replaces this traditional relationship with a segmented, nonlinear dimensionless curve that reflects the ecophysiology of riparian and wetland ecosystems. Evapotranspiration losses from these ecosystems are dependent not only on hydraulic head but on the plant types present. Userdefined plant functional groups (PFGs) are used to elucidate the interactive processes of plant ET with groundwater conditions. Five generalized plant functional groups based on transpiration rates, plant rooting depth, and drought tolerance are presented: obligate wetland, shallowrooted riparian, deeprooted riparian, transitional riparian and bare ground/open water. Plant functional groups can be further divided into subgroups (PFSG) based on plant size and/or density. The Riparian ET Package allows for partial habitat coverage and mixtures of plant functional subgroups to be present in a single model cell. This requires a determination of fractional coverage for each of the plant functional subgroups present in a cell to simulate the mixture of coverage types and resulting ET. The fractional cover within a cell has three components: 1) fraction of active habitat, 2) fraction of plant functional subgroup in a cell, and 3) fraction of plant canopy area. The Riparian ET package determines the ET rate for each plant functional group in a cell, the total ET in the cell, and the total ET rate over the region of simulation.

A riparian evapotranspiration package for MODFLOW2000 and MODFLOW2005(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 200803)A new version of an evapotranspiration package for the U.S. Geological Survey's groundwater flow model, MODFLOW, is documented. The Riparian Evapotranspiration Package (RIPET) provides flexibility in simulating riparian and wetland evapotranspiration (ET) not provided by the MODFLOW 2000 and MODFLOW 2005 traditional Evapotranspiration (EVT) Package, nor by the MODFLOW2000 Segmented Function Evapotranspiration (ETS1) Package. This report describes how the package was conceptualized and provides input instructions, listings and explanations of the source code, and an example simulation. Traditional approaches to modeling ET processes assume a piecewise linear relationship between ET flux rate and hydraulic head. The RIPET replaces this traditional relationship with a segmented, nonlinear dimensionless curve that reflects the ecophysiology of riparian and wetland ecosystems. Evapotranspiration losses from these ecosystems are dependent not only on hydraulic head but on the plant types present. User defined plant functional groups (PFGs) are used to elucidate the interactive processes of plant ET with groundwater conditions. Five generalized plant functional groups based on transpiration rates, plant rooting depth, and water tolerance ranges are presented: obligate wetland, shallowrooted riparian, deep rooted riparian, transitional riparian and bare ground /open water. Plant functional groups can be further divided into subgroups (PFSG) based on plant size, density or other user defined field. The RIP ET allows for partial habitat coverage and mixtures of plant functional subgroups to be present in a single model cell. Habitat areas are designated by polygons. A polygon can contain a mixture of PFSGs and bare ground, and is assigned a calculated land surface elevation. This process requires a determination of fractional coverage for each of the plant functional subgroups present in a polygon to simulate the mixture of coverage types and resulting ET. The fractional cover within a cell has two components: 1) the polygonal fraction of active habitat in a cell, and 2) fraction of plant flux area in a polygon. The RIP ET determines the ET rate for each plant functional group in a cell, the total ET in the cell, and the total ET rate over the region of simulation.

Scale issues of heterogeneity in vadose zone hydrology and practical solutions(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 19960803)Hydrological 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, Texas(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 199504)This 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, Mexico(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 200805)The 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 Futures(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2000)The 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 Texas(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 19990930)A 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 STREAMFLOW(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 197206)The 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 experiment(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 200410)A 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 CONDITIONS(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 19950908)A 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 RAINFALL(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 197306)This 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 zone(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 200203)Inverse 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 DESIGN(Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 197507)This 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.