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Deciding to RechargePublic water policy decision making tends to be too complex and dynamic to be described fully by traditional, rational models. Information intended to improve decisions often is rendered ineffective by a failure to understand the process. An alternative, holistic description of how such decisions actually are made is presented here and illustrated with a case study. The role of information in the process is highlighted. Development of a Regional Recharge Plan for Tucson, Arizona is analyzed as the case study. The description of how decisions are made is based on an image of public water policy decision making as 1) a structured, nested network of individuals and groups with connections to their environment through their senses, mediated by their knowledge; and 2) a nonlinear process in which decisions feed back to affect the preferences and intentions of the people involved, the structure of their interactions, and the environment in which they operate. The analytical components of this image are 1) the decision makers, 2) the relevant features of their environment, 3) the structure of their interactions, and 4) the products or outputs of their deliberations. Policy decisions analyzed by these components, in contrast to the traditional analysis, disclose a new set of relationships and suggest a new view of the uses of information. In context of information use, perhaps the most important output of the decision process is a shared interpretation of the policy issue. This interpretation sets the boundaries of the issue and the nature of issuerelevant information. Participants are unlikely to attend to information incompatible with the shared interpretation. Information is effective when used to shape the issue interpretation, fill specific gaps identified as issuerelevant during the process, rationalize choices, and reshape the issue interpretation as the issue environment evolves.

Decision Making Under Uncertainty in Systems HydrologyDesign of engineering projects involve a certain amount of uncertainty. How should design decisions be taken in face of the uncertainty? What is the most efficient way of handling the data? Decision theory can provide useful answers to these questions. The literature review shows that decision theory is a fairly well developed decision method, with almost no application in hydrology. The steps of decision theoretic analysis are given. They are augmented by the concept of expected expected opportunity loss, which is developed as a means of measuring the expected value of additional data before they are received. The method is applied to the design of bridge piers and flood levees for Rillito Creek, Pima County, Arizona. Uncertainty in both the mean and the variance of the logarithms of the peak flows of Rillito Creek is taken into account. Also shown are decision theoretic methods for: 1) handling secondary data, such as obtained from a regression relation, 2) evaluating the effect of the use of non  sufficient statistics, 3) considering alternate models and 4) regionalizing data.It is concluded that decision theory provides a rational structure for making design decisions and for the associated data collection and handling problems.

DESIGN OF WATER RESOURCES SYSTEMS IN DEVELOPING COUNTRIES: THE LOWER MEKONG BASINThis study focuses on the design of water resources systems in developing nations with particular reference to the development of water resources in the Lower Mekong Basin (Khmer Republic, Laos, Thailand, and Republic of South Viet Nam). The determination of the "best" system in terms of social goals reflecting the economic and social environment of the Mekong countries is the main issue of this dissertation. The imperfection of the usual technique for planning water resources systems, namely, cost benefit analysis, leads to the use of the standardized cost effectiveness methodology. To illustrate how the design is accomplished, two distinctly different structural alternatives of possible development in the Lower Mekong Basin are defined. The design process starts from the statements of goals or objectives of water resources development, which are then mapped onto specifications sets in which social needs are represented. Next, the capabilities of alternative systems are determined through simulation in which three 50 year sequences of synthetic streamflow are generated by a first order autoregressive scheme. The two alternatives are then compared using both quantitative and qualitative criteria. To illustrate how a decision in selecting an alternative system could be reached, ranking of criteria by order of preference is demonstrated. With the choice of either a fixed cost or fixed effectiveness approach, the decision to select the best alternative system could be made. At this point, the use of a weighting technique, which is a common fallacy of systems analysis, will be automatically eliminated. The study emphasizes that a systematic design procedure of water resources systems is provided by the standardized cost effectiveness approach, which possesses several advantages. The approach will suggest and help identify the system closest to meeting the desired economic and social goals of the developing countries in the Lower Mekong Basin. In this connection, the approach will help governments in the preparation of programming and budgeting of capital for further investigations and investments. It is believed that the approach will eliminate unnecessary expenses in projects that are planned on an individual basis or by methods used at present. Further, the approach provides an appropriate mechanism for generating essential information in the decision process. Both quantifiable and non quantifiable criteria are fully considered. The choice of a fixed cost or fixed effectiveness approach will determine the trade off between these criteria. The study recognizes that research to determine appropriate hydrologic models for monthly streamfiow generation for tributary projects in the Basin is necessary. This leads to another important area of research which is to find the appropriate number of monthly sequences of streamflow to be generated in relation to number of states and decision variables. Research on the design of computer experiments is necessary to improve simulation as a tool to estimate the quantitative effects of a given project.

DEVELOPMENT AND VALIDATION OF A NEW MAXIMUM LIKELIHOOD CRITERION SUITABLE FOR DATA COLLECTED AT UNEQUAL TIME INTERVALSA new Maximum Likelihood Criterion (MLE) suitable for data which are recorded at unequal time intervals and contain autocorrelated errors is developed. Validation of the new MLE criterion has been carried out both on a simple two  parameter reservoir model using synthetical data and on a more complicated hillslope model using real data from the Pukeiti Catchment in New Zealand. Comparison between the new MLE criterion and the Simple Least Squares (SLS) criterion reveals the superiority of the former over the latter. Comparison made between the new MLE and the MLE for autocorrelated case proposed by Sorooshian in 1978 has shown that both criteria would yield results with no practical difference if equal time interval data were used. However, the new MLE can work on variable time interval data which provide more information than equal time interval data, and therefore produces better visual results in hydrologic simulations.

A Distributed Surface Temperature and Energy Balance Model of a SemiArid WatershedA simple model of surface and sub surface soil temperature was developed at the watershed scale ( 100 km2) in a semi arid rangeland environment. The model consisted of a linear combination of air temperature and net radiation and assumed: 1) topography controls the spatial distribution of net radiation, 2) near surface air temperature and incoming solar radiation are relatively homogeneous at the watershed scale and are available from ground stations and 3) soil moisture dominates transient soil thermal property variability. Multiplicative constants were defined to account for clear sky diffuse radiation, soil thermal inertia, an initially fixed ratio between soil heat flux and net radiation and exponential attenuation of solar radiation through a partial canopy. The surface temperature can optionally be adjusted for temperature and emissivity differences between mixed hare soil and vegetation canopies. Model development stressed physical simplicity and commonly available spatial and temporal data sets. Slowly varying surface characteristics, such as albedo, vegetation density and topography were derived from a series of Landsat TM images and a 7.5" USGS digital elevation model at a spatial resolution of 30 m. Diurnally variable atmospheric parameters were derived from a pair of ground meteorological stations using 30 60 min averages. One site was used to drive the model, the other served as a control to estimate model error. Data collected as part of the Monsoon '90 and WG '92 field experiments over the ARS Walnut Gulch Experimental. Watershed in SE Arizona were used to validate and test the model. Point, transect and spatially distributed values of modeled surface temperature were compared with synchronous ground, aircraft and satellite thermal measurements. There was little difference between ground and aircraft measurements of surface reflectance and temperature which makes aircraft transects the preferred method to "ground truth" satellite observations. Mid morning modeled surface temperatures were within 2° C of observed values at all but satellite scales, where atmospheric water vapor corrections complicate the determination of accurate temperatures. The utility of satellite thermal measurements and models to study various ground phenomena (eg. soil thermal inertia and surface energy balance) were investigated. Soil moisture anomalies were detectable, but were more likely associated with average near surface soil moisture levels than individual storm footprints.

DPRCI /GAUSS A Program to Calculate Reservoir Yield Curves Using a Dynamic Programming Reservoir Operation AlgorithmThis report presents a computer program which will calculate reservoir yield curves for reservoir operation policy based on optimization accomplished using a. dynamic programming algorithm. After discussion of the dynamic programming and Gauss elimination algorithms, the input requirements, execution procedures, source code presentation, sample output, and references are presented. The programs run in a relatively short time on an 80286 personal computer. They are written in FORTRAN7.7 and compiled using the LAHEY F776 compiler.

Dynamic Management of a Surface and Groundwater System on Both Sides of the Lower Yellow RiverThis paper analyzes the management problem of the conjunctive use of surface and ground water in an irrigation system on both sides of the Lower Yellow River. For this purpose, a stochastic dynamic programming model is developed. In the model, the statistical characteristics of seasonal rainfall within 2 years are considered; groundwater level control is also emphasized in order to prevent soil salinity and waterlogging. Through computer calculations, optimal operation policies are obtained for efficient conjunctive use of surface and groundwater. These policies take into account the interactions between pumping groundwater by farmers, canal diversions by irrigation system managers, and the physical response of the stream aquifer system, and minimize the total operation costs. In this paper, we take an irrigation district, the People's Victory Canal System, as an example to illustrate the development and solution of the model. At the same time, the effects of system parameters, including surface irrigation efficiency and rainfall recharge coefficient, on the optimal policies or total operation costs, are discussed. The analytical results in this example indicate that the variation in optimal operation costs caused by the proportion of rainfall infiltrated is small, but the effect of surface irrigation efficiency on the costs is significant. Hence, the surface irrigation efficiency must be increased as much as possible. Then, efficient conjunctive use of surface and groundwater can be attained with the optimal policies.

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

EFFECTS OF RADARESTIMATED PRECIPITATION UNCERTAINTY ON DIFFERENT RUNOFFGENERATION MECHANISMSRunoff 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 radarbased precipitation estimates. When uncalibrated or poorly calibrated radar products were used as input to a rainfallrunoff model, the resulting predicted runoff varied severely from the runoff generated using wellcalibrated 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.

Effluent recharge to the Upper Santa Cruz River floodplain aquifer, Santa Cruz county, ArizonaThe City of Nogales, Arizona, is in the Santa Cruz Active Management Area and is subject to the assured water supply and conservation mandates of the 1980, Groundwater Management Act (State of Arizona, 1980). The primary water supply for both Nogales Arizona, and Nogales, Sonora, (commonly referred to as Ambos Nogales) is groundwater pumped from the shallow alluvial aquifers which underlie the Upper Santa Cruz River in Arizona and Mexico, and its tributaries (principally Nogales Wash and Potrero Creek). Nogales, Sonora also obtains water from the Los Alisos Basin, which is south of the Santa Cruz Basin in Mexico (Carruth, 1995). The NIWTP provides wastewater treatment for Ambos Nogales, and discharges treated wastewater to the Upper Santa Cruz River near the confluence with Nogales Wash and Sonoita Creek. The discharge of effluent creates an intermittent stream from the NIWTP outfall for approximately 13 river miles to Tubac, Arizona. The conservation mandates of the 1980, Groundwater Management Act (State of Arizona, 1980) require the City of Nogales, Arizona to prove the existence of a 100year water supply as a condition for future growth. The Act also allows Nogales, Arizona to receive recharge credits for the portion of effluent that recharges the aquifer underlying the Santa Cruz River. The recharge credits will be used by the City of Nogales as partial proof of a 100year water supply (Carruth, 1995).

THE ESTIMATION AND SCALING OF LANDSURFACE FLUXES OF LATENT AND SENSIBLEHEAT WITH REMOTELY SENSED DATA OVER A GRASSLAND SITEThe overall topic of the research described in this dissertation was the partitioning of available energy at the Earth's surface into sensible and latent heat flux, with an emphasis on the development of techniques which utilize remotely sensed data. One of the major objectives was to investigate the modification of existing techniques, developed over agricultural surfaces, to "natural" ecosystems (i.e., non agricultural vegetation types with variable and incomplete canopy cover). Ground based measurements of surface fluxes, vegetation cover, and surface and root zone soil moisture from the First ISLSCP (International Land Surface Climatology Program) Field Experiment (FIFE) were used to examine the factors controlling the partitioning of energy at ground stations with contrasting surface characteristics. Utilizing helicopter based and satellite based data acquired directly over ground based flux stations at the FINE experimental area, relatively simple algorithms were developed for estimating the soil heat flux and sensible heat flux from remotely sensed data. The root mean square error (RMSE) between the sensible heat flux computed with the remotely sensed data and the sensible heat flux measured at the ground stations was 33 Wm 2. These algorithms were then applied on a pixel by pixel basis to data from a Landsat TM (Thematic Mapper) scene acquired over the FIFE site on August 15, 1987 to produce spatially distributed surface energy balance components for the FIFE site. A methodology for quantifying the effect of spatial scaling on parameters derived from remotely sensed data was presented. As an example of the utility of this approach, NDVI values for the 1,IFE experimental area were computed with input data of variable spatial resolution. The differences in the values of NDVI computed at different spatial resolutions were accurately predicted by an equation which quantified those differences in terms of variability in input observations.

Estimation of effective unsaturated hydraulic conductivity tensor using spatial moments of observed moisture plumeKnowledge of unsaturated zone hydraulic properties is critical for many environmental and engineering applications. Various stochastic methods have been developed during the past two decades to estimate the effective unsaturated hydraulic properties. Independent of these stochastic methods, we develop in this paper a practical approach to estimate the threedimensional (3 D) effective unsaturated hydraulic conductivity tensor using spatial moments of 3D snapshots of a moisture plume under transient flow conditions. approach hydraulic hydraulic Application of the new to a field site in southeastern Washington State yields an effective unsaturated conductivity tensor that exhibits moisture dependent anisotropy. The effective conductivities compare well with laboratory measured unsaturated hydraulic conductivity data from small core samples; they also reproduce the general behavior of the observed moisture plume at the site. We also define a moisture diffusivity length concept which we use in conjunction with estimated correlation scales of the geological media at the field site to explain deviations between the observed and simulated plumes based on the derived effective hydraulic properties.

Eutrophication: A Mathematical ModelVarious approaches to modeling phytoplanktonzooplankton nutrient interactions have been investigated. A stochastic birth death model was developed to describe changes in phytoplankton and zooplankton population levels at a given point. Tuie stochastic birth death model was combined with a deterministic mass balance of limiting nutrient concentration to form an over all system theoretic model that enables one to use Monte Carlo simulation to study the problem of eutrophication. A comparison made between this modeling approach and the standard differential equation approach suggested that further investigation was desirable, particularly in the area of model calibration.

Evaluation of flood forecastingresponse systemsThe value of a forecast system in preventing urban property damage depends on the accuracy of the forecasts, the time at which they are received, the response by the floodplain dweller and the êfficacy of that response. A systems model of the overall flood forecast response system is developed. Evaluation of the system is accomplished by a decision theoretic methodology. A case study is done for Milton, Pennsylvania, which evaluates the present system and potential changes to it. It is concluded that the sequential nature of the forecast sequence must be considered in modeling the flood forecast response system if a meaningful evaluation of the economic value of the system is to be obtained. Methodology for obtaining the parameterization of the model from the available data is given. Computer programs have been written to handle a good portion of the calculations. While more work is needed on obtaining accurate parameterization of certain parts of the model, such as the actual response to forecasts; use of the procedures and programs as they now stand produces reasonable evaluations.

Evaluation of flood forecastingresponse systems IIsystem model and computational methodology have been developed which evaluate the worth of flood forecast  response systems in reducing the economic damage caused by floods. The efficiencies of the forecast system, the response system, and the overall system may be individually obtained and compared. In this report the case study of Milton, Pennsylvania, was extended and further case studies were performed including a large residential section of Victoria, Texas, and all the residences in Columbus, Mississippi. These locations show better forecast and response efficiencies than obtained for Milton, Pennsylvania. The difference is attributed to longer forecast lead times at Columbus and Victoria. Sensitivity analyses were run at all three locations. These show the effects of many system factors, such as the time required to produce, disseminate and respond to a forecast, on the efficiency of the system. The forecast efficiency improves significantly as these times are reduced. Further analysis of the response system based on human factors involved has led to the development of a simulation model of the process by which the floodplain dweller determines the appropriate response to a flood warning. Investigation of ways to extend the methodology to evaluate regions lacking the detailed data used for the case studies has indicated more problems than answers. Extrapolation based on overall system efficiency related to published regional and national flood damage estimates was used to provide an approximate value of the flood forecast  response system for two regions and for the nation.A listing of simplicities and approximations which make computations tractable but which may affect accuracy is given. Finally, an evaluation of the work accomplished for this project and suggestions for the constructive use of the flood forecast response system model and computational procedures is given.

An evaluation of hydrologic and riparian resources in Saguaro National Park, Tucson, ArizonaWithin Saguaro National Park only Rincon Mountain District contains significant riparian areas. The geologic framework of the Tanque Verde Ridge and Rincon Valley exerts strong control on the hydrology of these riparian systems. Pantano fault constitutes a line of hydrogeologic separation between the occurrence and utilization of groundwater in the Rincon Valley and the main Tucson basin. No known, comparable fault isolates the upper Tanque Verde Creek alluvium from downstream pumping effects. However, east of the confluence with Agua Caliente Wash, the highly permeable alluvial materials are much thinner, and serve to dampen such downstream effects. Therefore, the ground water reservoirs supporting the riparian areas within Rincon Mountain District are not directly connected to the Tucson basin aquifer. In what is described herein as upper basin areas, high gradient tributary streams to Tanque Verde Creek and Rincon Creek have discontinuous bodies of shallow alluvium interspersed with bedrock channel. Alluvium has accumulated behind small faults or resistant bedrock ledges and contains shallow ground water basins that support small pockets of riparian or xeroriparian vegetation. The ground water in these small basins is sustained by seeps or springs, and by runoff from precipitation and is not likely to be connected to a regional ground water system. In what we have characterized as middle basin areas, the stream gradients are less than 25m/km. In these low gradient reaches, the alluvial floodplain sediments are continuous, though not thick, as ledges of more resistant bedrock formations appear in the stream channel. These low gradient reaches contain larger volumes of ground water than the high gradient basins and support more robust riparian vegetation. The ground water in the low gradient reaches is believed to be connected to the regional ground water system. Such a low gradient reach exists in a tributary to Tanque Verde Creek about 1.4 km east of Wentworth Road and extends about 1.6 km into the Park. A similar low gradient reach occurs along Rincon Creek in the Expansion Area, and at the mouths of Chiminea and Madrona Creeks.

Evaluation of national weather service ensemble streamflow predictions (ESP) for the Colorado river basinThe National Weather Service (NWS) developed the Ensemble Streamflow Prediction (ESP) system to generate probabilistic water supply forecasts that consist of an ensemble of streamflow traces (scenarios) conditioned on the initial states of the basin. Uncertainty information available from ESP may be more useful to riskbased decision makers than what is currently provided by linear regression forecasts. Because the use of ESP has been limited to date, there are few operational forecasts available for verification. Therefore, it was necessary to generate simulated operational ESP forecasts to test the forecasting procedure's potential to enhance current forecasting techniques. Simulated historical forecasts were generated for 14 forecast points in the Colorado River basin. The median and best forecast traces were analyzed as representations of ESP deterministic forecasts. General scalar statistics were used to evaluate these traces. The probability information contained in the entire ensemble was analyzed using probabilistic and conditional verification methods. It was found that the information contained in the median trace is limited and that choosing one trace is not the optimal use of ESP forecast information. ESP provides a probabilistic forecast that performs better than a probabilistic forecast based on climatology. In addition, ESP can provide accurate information about the magnitude of future streamflow discharge even at lead times of up to seven months. With shorter lead times (23 months), the forecasts become more informative and accurate.

EXPERIMENTAL INVESTIGATION OF SEEPAGE THROUGH HETEROGENEOUS POROUS MEDIAFive 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.

Flow model for the Bingham cienega area, San Pedro river basin, Arizona: a management and restoration toolA finite element groundwater flow model was used to support a hydrologic assessment for a study area in the Lower San Pedro River Basin which contains the Bingham Cienega. Consolidated sedimentary rocks associated with an extension of the Catalina Core Complex truncate the floodplain aquifer system in the study area. The elevated water table produced by this "hardrock" results in spring discharge at the cienega and a locally gaining reach of the San Pedro River. The steady state model suggests that recharge (and discharge) components for the floodplain aquifer sum to 3.10 cfs. Mountain front recharge, underflow, and stream leakage are the primary recharge mechanisms, while stream leakage, evapotranspiration, spring flow, and underflow out are sources for groundwater discharge. A steady oscillatory model was used to account for seasonal periodicity in the system's boundary conditions. Monthly variation in the evapotranspiration rate was offset primarily by storage changes in the aquifer. Due to a lack of measured hydrologic data within the study area, results from the model simulations are only preliminary. Model development and the subsequent sensitivity analyses have provided insight into what type of data needs to be collected. Head measurements are most needed in the area just downstream from Bingham Cienega. The mountain front recharge and evapotranspiration rates are shown to be highly sensitive parameters in the model; improved estimation of these values would be helpful. Spring discharge would be a valuable calibration tool if it could be accurately measured. A more extensive record of stream baseflow in the San Pedro River should be established. After more hydrologic data is collected, the model could be recalibrated so as to better represent the system. Eventually, this tool may be used in direct support of management and/or restoration decisions.

A Geostatistical Inverse Method for Variably Saturated Flow in the Vadose ZoneA geostatistical inverse technique utilizing both primary and secondary information is developed to estimate conditional means of unsaturated hydraulic conductivity parameters (saturated hydraulic conductivity and pore size distribution parameters) in the vadose zone. Measurements of saturated hydraulic conductivity and pore size distribution parameters are considered as the primary information, while measurements of steady state flow processes (soil water pressure head and degree of saturation) are regarded as the secondary information. This inverse approach relies on the classical linear predictor (cokriging) theory and takes the advantage of the spatial cross correlation between soil water pressure head, degree of saturation, saturated hydraulic conductivity, and pore size distribution parameter. Using an approximate perturbation solution for steady, variably saturated flow under general boundary conditions, the cross covariances between the primary and secondary information are derived. The approximate solution is formulated based on a first order Taylor series expansion of a discretized finite element equation. The sensitivity matrix in the solution is evaluated by an adjoint state sensitivity approach for flow in heterogeneous media under variably saturated conditions. Through several numerical examples, the inverse model demonstrates its ability to improve the estimates of the spatial distribution of saturated hydraulic conductivity and pore size distribution parameters using the secondary information.