bluuebunny/crossref_metadata_2025 huggingface dataset:
An alternative view on the origin of chemical and isotopic patterns in groundwater from the Milk River Aquifer, Canada
Authors: Hendry M. J. , Schwartz F. W.
Published: February 2008

The Milk River artesian aquifer underlies 15,000 km2 of southern Alberta, Canada. It consists of thin (30–75 m thick) sandstone and is confined above by the Pakowki shale (typically 120 m thick) and below by the Colorado shale. The aquifer subcrops in southern Alberta and northern Montana. Groundwater movement is to the north, west, and east from the outcrop area (dominant recharge area). Cl− and I− concentrations increase in the direction of flow from less than 0.05 and 0.001 mmol/L, respectively, near the recharge area to more than 140 and 0.15 mmol/L at the northern edge of the aquifer. Similarly, waters become more enriched in oxygen 18 and deuterium from less than −21.0 and −167‰ near the recharge area to values approaching −8.0 and −70.0‰ in the north. Isotope values in the recharge area plot on the global meteoric water line and indicate that the recharge waters are isotopically unaltered meteoric waters. Downgradient from the recharge area the data deviate from the meteoric water line (slope of 6.3 instead of 8.0). Three mechanisms have been advanced to explain the origin of the chemical and isotopic patterns: the introduction of connate formation water through the Colorado shale and subsequent mixing with infiltrating meteoric water; a finite source of meteoric recharge mixing with more saline water in the aquifer; and chemical and isotopic enrichment due to ion filtration. Hydraulic conductivity and hydraulic head data, Cl− concentrations of drill cuttings and isotopic values from groundwater from the Colorado shale provide arguments for reevaluating these ideas. An alternative mechanism, based on diffusion between saline, isotopically enriched water in the Colorado shale and fresher, isotopically depleted water in the aquifer, is tested using an analytical mass transport model. Although uncertainty exists in the model parameters, results showed that the patterns in Cl−, I−, δ18O, and δ2H in the aquifer can be explained by aquitard diffusion. Further, aquitard diffusion must be considered when using chlorine 36 dating methods in aquifer‐aquitard systems such as the Milk River aquifer.
Estimating residential price elasticity of demand for water: A contingent valuation approach
Authors: Thomas John F. , Syme Geoffrey J.
Published: February 2008

Residential households in Perth, Western Australia have access to privately extracted groundwater as well as a public mains water supply, which has been charged through a two‐part block tariff. A contingent valuation approach is developed to estimate price elasticity of demand for public supply. Results are compared with those of a multivariate time series analysis. Validation tests for the contingent approach are proposed, based on a comparison of predicted behaviors following hypothesised price changes with relevant independent data. Properly conducted, the contingent approach appears to be reliable, applicable where the available data do not favor regression analysis, and a fruitful source of information about social, technical, and behavioral responses to change in the price of water.
Using exogenous variables in testing for monotonic trends in hydrologic time series
Authors: Alley William M.
Published: February 2008

One approach that has been used in performing a nonparametric test for monotonic trend in a hydrologic time series consists of a two‐stage analysis. First, a regression equation is estimated for the variable being tested as a function of an exogenous variable. A nonparametric trend test such as the Kendall test is then performed on the residuals from the equation. By analogy to stagewise regression and through Monte Carlo experiments, it is demonstrated that this approach will tend to underestimate the magnitude of the trend and to result in some loss in power as a result of ignoring the interaction between the exogenous variable and time. An alternative approach, referred to as the adjusted variable Kendall test, is demonstrated to generally have increased statistical power and to provide more reliable estimates of the trend slope. In addition, the utility of including an exogenous variable in a trend test is examined under selected conditions.
A second‐order kinetic approach for modeling solute retention and transport in soils
Authors: Selim H. M. , Amacher M. C.
Published: February 2008

We present a second‐order kinetic approach for the description of solute retention during transport in soils. The basis for this approach is that it accounts for the sites on the soil matrix which are accessible for retention of the reactive solutes in solution. This approach was incorporated with the fully kinetic two‐site model where the difference between the characteristics of the two types of sites is based on the rate of kinetic retention reactions. We also assume that the retention mechanisms are site‐specific, e.g., the sorbed phase on type 1 sites may be characteristically different in their energy of reaction and/or the solute species from that on type 2 sites. The second‐order two‐site (SOTS) model was capable of describing the kinetic retention behavior of Cr(VI) batch data for Olivier, Windsor, and Cecil soils. Using independently measured parameters, the SOTS model was successful in predicting experimental Cr breakthrough curves (BTC's). The proposed second‐order approach was also extended to the diffusion controlled mobile‐immobile or two‐region (SOMIM) model. The use of estimated parameters (e.g., the mobile water fraction and mass transfer coefficients) for the SOMIM model did not provide improved predictions of Cr BTC's in comparison to the SOTS model. The failure of the mobile‐immobile model was attributed to the lack of nonequilibrium conditions for the two regions in these soils.
An approach to estimating hydraulic conductivity spatial correlation scales using geological characteristics
Authors: Phillips Fred M. , Wilson John L.
Published: February 2008

The estimation of hydraulic conductivity and other correlation scales by traditional geostatistical methods requires a large number of field measurements at appropriate horizontal and vertical spacings. In order to extend the application of stochastic subsurface hydrology analysis to situations where such data are limited we propose an approach to correlation scale estimation that incorporates geological mapping. Regions of the formation with hydraulic conductivity values above (or below) some specified cutoff value are mapped and their dimensions are related to the correlation scale, by means of threshold‐crossing theory.
A field study on turbidity currents initiated from spring runoffs
Authors: Chikita Kazuhisa
Published: February 2008

The hydrodynamics of turbidity currents from spring runoffs of an influent river is examined by measuring velocity, water temperature, and concentration of suspended sediment in a reservoir. Crosssectional measurement of turbidity currents, made from a bridge, shows the effect of centrifugal force on the downstream movement. This is due to considerable meandering of the old river channel. The turbidity currents, initiated at high sediment concentration of 1,700 mg/L, were bifurcated into an underflow and some interflows in the downstream reach, because of the relatively dense bottom water of the reservoir. The “lower layer” of turbidity currents exhibits a log linear relationship between dimensionless velocity and height under a hydraulically smooth condition. The velocity distribution in the upper and lower layers could be explained by overall Richardson number. Two drag coefficients, related with shear stresses at bottom bed and interface, generally decrease with increasing densimetric Froude number, but are independent of Reynolds number. The conditions of sediment deposition and erosion by turbidity currents can be explained by using the “extended Shields diagram.”
estimation of spatial covariance structures by adjoint state maximum likelihood cross validation: 1. Theory
Authors: Samper F. Javier , Neuman Shlomo P.
Published: February 2008

This series of three papers describes a cross‐validation method to estimate the spatial covariance structure of intrinsic or nonintrinsic random functions from point or spatially averaged data that may be corrupted by noise. Any number of relevant parameters, including nugget effect, can be estimated. The theory, described in this paper, is based on a maximum likelihood approach which treats the cross‐validation errors as Gaussian. Various a posteriori statistical tests are used to verify this hypothesis and to show that in many cases, correlation between these errors is weak. The log likelihood criterion is optimized through a combination of conjugate gradient algorithms. An adjoint state theory is used to efficiently calculate the gradient of the estimation criterion, optimize the step size downgradient, and compute a lower bound for the covariance matrix of the estimation errors. Issues related to the identifiability, stability, and uniqueness of the resulting adjoint state maximum likelihood cross‐validation (ASMLCV) method are discussed. This paper also describes the manner in which ASMLCV allows one to use model structure identification criteria to select the best covariance model among a given set of alternatives. Practical aspects of ASMLCV and its application to synthetic data are presented in paper 2 (Samper and Neuman, this issue (a)). Applications to real hydrogeological data (transmissivities and groundwater levels) have been presented elsewhere, while hydrochemical and isotopic data are analyzed by ASMLCV in paper 3 (Samper and Neuman, this issue (b)).
Cokriging model for estimation of water table elevation
Authors: Hoeksema R. J. , Clapp R. B. , Thomas A. L. , Hunley A. E. , Farrow N. D. , Dearstone K. C.
Published: February 2008

In geological settings where the water table is a subdued replica of the ground surface, cokriging can be used to estimate the water table elevation at unsampled locations on the basis of values of water table elevation and ground surface elevation measured at wells and at points along flowing streams. The ground surface elevation at the estimation point must also be determined. In the proposed method, separate models are generated for the spatial variability of the water table and ground surface elevation and for the dependence between these variables. After the models have been validated, cokriging or minimum variance unbiased estimation is used to obtain the estimated water table elevations and their estimation variances. For the Pits and Trenches area near Oak Ridge National Laboratory, water table estimations along a linear section, both with and without the inclusion of ground surface elevation as a statistical predictor, illustrate the advantages of the cokriging model.
Assessing the validity of the channel model of fracture aperture under field conditions
Authors: Shapiro Allen M. , Nicholas James R.
Published: February 2008

In recent investigations of fluid and solute movement in discrete fractures, spatial heterogeneity of the fracture aperture has been conceptualized as a series of noninterconnecting constant aperture flow paths, or channels. Two methods of estimating the distribution of the aperture sizes are presented using information from a single‐hole pumping test and a radially converging tracer test. The first method uses the transmissivity of the fracture and mean arrival time of the tracer, while the second method uses the mean and variance of the solute arrival time. If the fracture can be conceptualized as a series of nonintersecting flow paths of constant aperture, the two methods should yield identical estimates for the parameters of the distribution. The validity of the channel model can be assessed by comparing the parameters of the distribution that are estimated by the two methods. This technique was demonstrated using hydraulic and tracer tests conducted in a discrete, areally extensive, horizontal fracture in the Silurian dolomite in the northeastern Illinois. A lognormal and a truncated gamma distribution were used to describe the distribution of constant aperture flow paths. The lognormal distribution could not reproduce the abrupt rising limb and maximum rate of mass arrival that characterized the tracer tests. The gamma distribution more accurately predicted the shape of the breakthrough curves; however, the two methods of estimating the parameters of the distribution provided significantly different estimates of the variances of the aperture sizes. The mean aperture as estimated by the two methods was similar. The difference in the variance of the aperture as estimated by the two methods indicates that alternative conceptual models of aperture heterogeneity are required to more accurately describe both fluid and solute movement in this field situation.
Flood frequency analysis with regional and historical information
Authors: Jin Minghui , Stedinger Jery R.
Published: February 2008

This paper develops generalized maximum likelihood estimators which efficiently employ both at‐site historical information and systematic flood records with a regional index flood distribution. Monte Carlo experiments document the performance of these estimators in heterogeneous and homogeneous regions, with different historical record lengths, and with various perception thresholds. When carefully employed with stationary flood records and appropriate and robust statistical procedures, historical information is shown to be valuable at those sites where it is available, as well as in the estimation of the regional index flood distribution.
Wetting front instability: 2. Experimental determination of relationships between system parameters and two‐dimensional unstable flow field behavior in initially dry porous media
Authors: Glass R. J. , Steenhuis T. S. , Parlange J‐Y.
Published: February 2008

This paper describes and interprets experimental studies of wetting front instability guided by the dimensional analysis presented in paper 1 (R.J. Glass et al., this issue). When a wetting front passes from a fine‐textured layer of initially dry sand into an underlying coarse layer, the front breaks into fingers. A specially developed vertical slablike chamber and associated techniques were developed for the study of such fingering. The flow rate through the system is systematically varied by using different mean grain size separates for the upper layer (the same coarse separate being used for the bottom layer). Relationships between finger width, propagation velocity, moisture content, and flow rate through individual fingers are experimentally determined and related to the properties of the bottom layer and the flow rate through the system. The results are different than those found in a previous experimental study which used different techniques for sample preparation. Results obtained here agree with a formulation derived earlier by J‐Y. Parlange and D.E. Hill (1976) through linear stability analysis.
Effect of uneven snow cover on airborne snow water equivalent estimates obtained by measuring terrestrial gamma radiation
Authors: Carroll Steven S. , Carroll Thomas R.
Published: February 2008

Estimates of snow water equivalent derived from measurements of the attenuation of terrestrial gamma radiation are systematically biased downward if variability in the snow water equivalent exists in the snowpack. The degree of underestimation is a function of both the shape and the variance of the distribution. The effects of these two factors on the estimate of snow water equivalent are examined for three assumed distributions (discrete, normal, and uniform) over a wide range of variances. The downward bias that results in each of the examined distributions can be corrected if the variance in the snow water equivalent is known. Examples of the application of the methodology are provided for flight lines located in the plains of western Canada and in the mountainous region of Colorado. The methodology presented can aid National Weather Service hydrologists in improving river and flood forecasts, water supply forecasts, and spring flood outlooks for large areas of the United States and Canada.
Groundwater travel time uncertainty analysis using sensitivity derivatives
Authors: La Venue Marsh , Andrews Robert W. , RamaRao Banda S.
Published: February 2008

The evaluation of a Hydrogeologic system requires the definition of a system performance measure. Groundwater travel time is a key performance measure used in the performance assessment of a potential site for the storage of high‐level radioactive waste. Two approaches commonly used to quantify the uncertainty in a given prediction of a performance measure are the first‐order second‐moment (FOSM) approach and the stochastic approach. The FOSM approach predicts the mean and variance of the performance measure based on the mean and variance of the system parameters (e.g., permeability, porosity) and the sensitivity of the performance measure with respect to the system parameters. The sensitivity of the performance measure is directly determined by calculating its first derivative with respect to selected system parameters. The uncertainty of the performance measure is then calculated by multiplying the performance measure sensitivity to the uncertainty of the system parameters. The FOSM approach has been employed to determine the uncertainty of the predicted groundwater travel time performance measure at the proposed high‐level waste (HLW) repository site that had been undergoing detailed investigation in Deaf Smith County, Texas. The results are compared to a similar study using the stochastic approach. In the stochastic technique, the uncertainty is determined by sampling the probability distribution function (PDF) of the uncertain, independent parameters and directly calculating the PDF of the dependent parameter (or performance measure) by conducting multiple simulations. Although the approaches use different techniques to evaluate groundwater travel time uncertainty, the results from both are remarkably similar in this application. The FOSM approach is also used to predict changes in the mean groundwater travel time for selected changes in permeability values within the model. It is demonstrated that for changes in permeability of one half standard deviations or less, additional simulations are not required in order to reasonably predict the change in the groundwater travel time using FOSM. However, for perturbations of approximately 1 standard deviation, FOSM does not provide a reasonable prediction of the change in groundwater travel time. These results indicate the stochastic approach should be used when the variance or uncertainty of the Hydrogeologic parameters is high because of the limitations on the perturbation of these parameters in the FOSM approach.
A new analysis procedure for determining aquifer properties from slug test data
Authors: Peres Alvaro M. M. , Onur Mustafa , Reynolds Albert C.
Published: February 2008

A new method for determining hydraulic properties from slug test well data in a confined aquifer is presented. The new procedure is based on an exact equation which converts measured slug test head data to equivalent head data that would be obtained due to a constant discharge of a well with well bore storage and skin effects. A related procedure yields equivalent head derivative data (time rate of change of head) that would be obtained for the classical constant discharge with well bore storage and skin problem without applying numerical differentiation. After the constant discharge head data and its derivative data are generated by our procedure, these converted data can be analyzed by using existing well bore storage and skin type curves for the appropriate aquifer/well model. Therefore slug test type curves are no longer needed. For cases in which the relative change in the water level is not significant during the slug test, most of the converted data will fall on the unit slope line of the conventional well bore storage and skin type curves and it will be difficult to obtain a unique type curve match of converted head data. For such cases, it is shown that a discharge normalization procedure can be applied to improve the reliability of the analysis. A field case illustrating the reliability of the new method is presented.
Small perturbations solution for steady but nonuniform infiltration
Authors: Wallach Rony , Zaslavsky Dan , Israeli Moshe
Published: February 2008

The small perturbations method is applied to a two‐dimensional flow problem due to a steady but nonuniform infiltration into the soil and a given head at the lower boundary. The perturbation solution is compared to an analytic solution for periodic distributions of the infiltration. Good accuracy is obtained by only two terms of the expansion. The first term is simply the vertical flow with no lateral terms. In the second term the horizontal flow divergence depends parametrically only on the horizontal distribution and the zero‐order approximation, i.e., the vertical flow. For deep lower boundaries the naive perturbation expansion leads to some secular terms that made the convergence poorer. The uniform asymptotic expansion is then used and shown to give an improved accuracy in one term only. The perturbation method is extended to nonperiodic distribution, in fact, any distribution. It may be used for two‐ and three‐dimensional problems that evade any analytic solutions. One has to solve numerically or analytically only one dimensional and ordinary linear equations for any number of approximations. The problem is singular in that it accepts at this stage only impermeable vertical boundaries or symmetrical lines. However, this covers a very important class of practical problems.
Implementation of the three‐dimensional turning bands random field generator
Authors: Tompson Andrew F. B. , Ababou Rachid , Gelhar Lynn W.
Published: February 2008

Numerical techniques to generate replicates of spatially correlated random fields are often used to synthesize sets of highly variable physical quantities in stochastic models of naturally heterogeneous systems. Within the realm of hydrologic research, for example, such tools are widely used to develop hypothetical rainfall distributions, hydraulic conductivity fields, fracture set properties, and other surface or subsurface flow parameters. The turning bands method is one such algorithm which generates two‐ and three‐dimensional fields by combining values found from a series of one‐dimensional simulations along lines radiating outward from a coordinate origin. Previous work with two‐dimensional algorithms indicates that radial lines evenly spaced about the unit circle lead to enhanced convergence properties. The same can be said for the three‐dimensional models, but it is more difficult to choose an arbitrary number of evenly spaced lines about the unit sphere. The current investigation shows that the use of larger numbers of randomly oriented lines (100) can enhance the performance of the three‐dimensional algorithm. This improved performance is needed to effectively simulate problems characterized by full three dimensionality and/or anisotropy in either Monte Carlo or single‐realization applications. Use of a large number of lines will also reduce the presence of a distortion effect manifested as linelike patterns in the field. Increased computational costs can be reduced by employing a fast Fourier transform technique to generate the line processes.
A multiscale study of the permeability of a thick clayey till
Authors: Keller C. Kent , Van Der Kamp Garth , Cherry John A.
Published: February 2008

We describe and evaluate two previously undocumented methods of bulk permeability (K) determination and compare results obtained with results of conventional smaller‐scale tests on the same thick clayey till deposit. Analysis of the downward propagation of seasonal water table fluctuations yielded bulk K of approximately 10−10 m s−1, in close agreement with results of laboratory consolidation and permeameter tests, slug tests, and distribution of vertical hydraulic gradient with depth in the deposit. This agreement suggests that for such materials, high‐gradient tests conducted at small scales of distance and time can provide reasonable estimates of bulk K. The results also imply groundwater residence times in the till of thousands of years. The flow pattern observed near a large excavation in the till was consistent with the initial recoveries of piezometers installed in much smaller boreholes, assuming perturbation of hydraulic head in the formation due to borehole excavation. Time scales of these perturbations, which prevent interpretation of measured hydraulic head using conventional well hydraulic methods, varied from months to tens of years.
A stochastic analysis of the influence of soil and climatic variability on the estimate of pesticide groundwater pollution potential
Authors: Jury William A. , Gruber Joachim
Published: February 2008

Soil and climatic variability contribute in an unknown manner to the leaching of pesticides below the surface soil zone where degradation occurs at maximum levels. In this paper we couple the climatic variability model of Eagleson (1978) to the soil variability transport model of Jury (1982) to produce a probability density distribution of residual mass fraction (RMF) remaining after leaching below the surface degradation zone. Estimates of the RMF distribution are shown to be much more sensitive to soil variability than climatic variability, except when the residence time of the chemical is shorter than one year. When soil variability dominates climatic variability, the applied water distribution may be replaced by a constant average water application rate without serious error. Simulations of leaching are run with 10 pesticides in two climates and in two representative soil types with a range of soil variability. Variability in soil or climate act to produce a nonnegligible probability of survival of a small value of residual mass even for relatively immobile compounds which are predicted to degrade completely by a simple model which neglects variability. However, the simpler model may still be useful for screening pesticides for groundwater pollution potential if somewhat larger residual masses of a given compound are tolerated. Monte Carlo simulations of the RMF distribution agreed well with model predictions over a wide range of pesticide properties.
Kinetically influenced terms for solute transport affected by heterogeneous and homogeneous classical reactions
Authors: Bahr Jean M.
Published: February 2008

Simulation of transport affected by heterogeneous or homogeneous reversible reactions requires a choice between local equilibrium‐based and kinetics‐based models. The error associated with the use of equilibrium‐based models is equivalent to the error of neglecting certain mathematical terms in the governing kinetics‐based transport equations. Identification and evaluation of these kinetically influenced terms can therefore aid in the development of criteria for applicability of local equilibrium‐ based transport models. This paper extends a four‐step derivation procedure, previously presented for cases of transport affected by surface reactions, to transport problems involving homogeneous reactions (solution phase complex formation or oxidation‐reduction) and/or precipitation‐dissolution reactions. Derivations for these classes of reactions are used to illustrate the manner in which mathematical differences between reaction classes are reflected in the mathematical derivation procedures required to identify kinetically influenced terms. Simulation results for a case of transport affected by a single solution phase complexation reaction and for a case of transport affected by a precipitation‐dissolution reaction are used to demonstrate the nature of departures from equilibrium‐controlled transport as well as the use of kinetically influenced terms in determining criteria for the applicability of the local equilibrium assumption. A final derivation for a multireaction problem demonstrates the application of the generalized procedure to a case of transport affected by reactions of several classes.
Stochastic modeling of macrodispersion in heterogeneous porous media
Authors: Rubin Yoram
Published: February 2008

A method for the prediction of dispersion processes of inert solutes occurring in heterogeneous porous media, is presented. Its main features are as follows: (1) The velocity field is assumed to be a space random function. Its moments are expressed through the physical parameters of the log transmissivity and head random fields by linearizing the flow equation. The random velocity, being a linear function of the head and log transmissivity, which are assumed to be jointly multivariate normal (MVN), is thus also MVN. Its pdf is completely defined by its first two moments. (2) The statistics of the dispersion process are obtained by the particle‐tracking method through Monte Carlo simulations which are based on Gaussian conditioning. The method is applied to the Borden natural gradient tracer test (Freyberg, 1986), showing favorable results.
Simulation of biodegradable organic contaminants in groundwater: 1. Numerical formulation in principal directions
Authors: MacQuarrie K. T. B. , Sudicky E. A. , Frind E. O.
Published: February 2008

Groundwater contamination by organic chemicals is of concern because of the widespread use of these compounds and because even low concentrations may be very harmful. Dissolved organic contaminants are affected by advection, dispersion, sorption, and biological transformations in groundwater systems; however, biological degradation by indigeneous bacterial populations is the only mechanism whereby contaminant mass can be naturally removed from an aquifer. The purpose of this study is to develop a physically and biochemically based numerical solution for the transport of biodegradable organic solutes with emphasis on an efficient numerical approach. A dual‐Monod relationship, combined with the advection‐dispersion equation, is used to represent the biological and physical processes affecting the organic solute, electron acceptor, and microbial population. The three resulting differential equations are nonlinearly coupled through the Monod decay terms. By employing an iterative principal direction finite‐element technique, efficiency is achieved by decoupling each of the two‐dimensional transport equations into a series of one‐dimensional equations. This decoupling should easily allow for extension of the model to three dimensions. An iterative solution is adopted because a purely sequential technique was observed to greatly underestimate the dissolved mass of an organic plume. Comparison of numerical results with the results of a laboratory column experiment shows that the model equations adequately describe the behavior of toluene, dissolved oxygen, and the bacterial population, without considering solute diffusion through stagnant fluid layers or biofilms. In a two‐dimensional shallow aquifer setting an organic plume experiences mass loss, spreading controlled by the availability of dissolved oxygen, and skewing in the direction of groundwater flow. These features would be lost if the interactions between the organic contaminant, electron acceptor, and microbial population were ignored in the mathematical formulation of the problem.
Some general results on the seepage exclusion problem
Authors: Philip J. R.
Published: February 2008

Asymptotic roof boundary layer solutions are obtained for the quasilinear seepage exclusion problem for ellipsoidal cavities of arbitrary aspect ratio χ and arbitrary horizontal axial index k. The maximum dimensionless potential at the cavity wall, υmax, is given (χ > 0) by the equation υmax(σ, χ, k) ∼ 2σ + f0(χ, k) + f1(χ, k)/σ + f2(χ, k)/σ2 + …, where σ = ½ακ−1/2 (α, sorptive number; κ, apical curvature) and the fn are polynomials in χ−2 and k−2 of degree (n + 1). There is thus a hierarchy in importance of the geometrical parameters determining υmax. σ is dominant, χ is next in importance, and the effect of k is relatively minor. The above equation includes as special cases previous results for circular, elliptic, and parabolic cylinders and for spheres, spheroids, and paraboloids. For elliptic discs (χ = 0), υmax(σ1, k) ∼ 4σ12 + f0(k) + f1(k)/σ12 + f2(k)/σ14 + ⋯, where σ1 = ½α−1γ (γ, characteristic horizontal length) and the fn are polynomials in k−2 of degree (n + 1). This equation includes as special cases previous results for strips and circular discs. The various results are relevant also to cavities with ellipsoidal and flat elliptic roofs but otherwise of arbitrary (though not too irregular) configuration. The corresponding nonlinear analysis is straightforward.
Water flow paths and hydrochemical controls in the Birkenes Catchment as inferred from a rainstorm high in seasalts
Authors: Mulder Jan , Christophersen Nils , Hauhs Michael , Vogt Rolf D. , Andersen Sjur , Andersen Dag O.
Published: February 2008

At Birkenes, a small forested catchment with acidic soils in southernmost Norway, acid rain has resulted in high stream water H+, Al, and SO4 concentrations. Recent studies have revealed the complexity of the Al chemistry in Birkenes stream water, as inorganic Al is not regulated by one single solubility control. It has been hypothesized that this is due to the dynamic nature of water flow paths and the different Al solubilities in surface soils and subsoils. In this study we tested the flow path hypothesis as well as cation solubility controls, using soil solution lysimetry, before and after a storm event, exceptionally high in sea salts. Results indicate that considerable lateral flow through the organic surface layers to the stream did occur during rainstorms on nearly water‐saturated soils. In the organic surface horizons, Al concentrations were reduced and controlled by cation exchange, whereas in the mineral B horizons, Al was more soluble and close to equilibrium with gibbsite (pKs = −9.0 at 10°C).
A heuristic closed‐loop controller for water distribution in complex irrigation systems
Authors: Hiessl Harald , Plate Erich J.
Published: February 2008

The paper deals with the problem of finding an optimal, closed‐loop control strategy for water distribution among crops grown in an irrigation system. The proposed approach yields a strategy that allows the utilization of prior “soft” information. The control strategy is then optimized using a mixed simulation‐optimization method. The results which are illustrated by a Saudi Arabian case study show that it is possible to improve the crops' annual yields, both in terms of their expected value as well as in terms of their temporal distribution over the planning horizon.
Rainfall‐runoff relations derived from the probability theory of storage
Authors: Hosking J. R. M. , Clarke Robin T.
Published: February 2008

Using a simplified representation of how a river basin stores precipitation, generates runoff, and loses water through evapotranspiration, we derive probabilistic relationships between precipitation, soil moisture deficit, and generated runoff. The “distribution function model” is used to describe the soil moisture storage capacity of the basin: storage capacity, per unit of basin surface area, is regarded as a spatially variable quantity described by a density function. By routing the generated runoff through what is essentially a linear reservoir with stochastic inputs and outputs, we show how the median discharge can be calculated which corresponds to a rainfall input of some specified return periodTtime intervals. The return period for basin discharge can, with certain assumptions, also be calculated, thereby yielding probability statements relating theT‐period rainfall to its resultant discharge.
Estimating erosion risk on forest lands using improved methods of discriminant analysis
Authors: Lewis Jack , Rice Raymond M.
Published: February 2008

A population of 638 timber harvest areas in northwestern California was sampled for data related to the occurrence of critical amounts of erosion (>153 m3within 0.81 ha). Separate analyses were done for forest roads and logged areas. Linear discriminant functions were computed in each analysis to contrast site conditions at critical plots with randomly selected controls. Bootstrapping was used extensively in the development and testing of the equations, in estimating prediction bias, and in placing confidence limits around parameters and posterior probabilities. The resulting three‐variable equations had classification accuracy, corrected for prediction bias, of 77.7% for road plots and 69.2% for logged area plots. The use of linear discriminant functions facilitates the explicit consideration of erosion risk when planning land‐disturbing activities.
Three‐dimensional statistical moment analysis of the Stanford/Waterloo Borden tracer data
Authors: Barry D. A. , Sposito Garrison
Published: February 2008

We estimate the mass, mean position vector, and covariance tensor of the bromide plume investigated at the Borden site (Ontario, Canada) by researchers from Stanford University and the University of Waterloo. A number of interpretive steps was necessary to compute these plume moments. First, the spatially scattered data were interpolated onto a regular grid, with the interpolator selected on the basis of a cross‐validation criterion. The moment estimates then could be calculated readily, although it was recognized that the interpolation procedure can lead to bias in the moment estimates. For this reason, reduced‐bias, jackknifed estimates of the moments, as well as confidence intervals for these estimates, were derived. The total plume variance also was estimated with the jackknife method. The latter results were compared with the prediction of a recent stochastic model developed by Dagan (1988). When this model was applied in a completely predictive mode, a remarkably good estimate of the total plume variance resulted.
Approximation of confidence limits on sample semivariograms from single realizations of spatially correlated random fields
Authors: Shafer J. M. , Varljen M. D.
Published: February 2008

A fundamental requirement for geostatistical analyses of spatially correlated environmental data is the estimation of the sample semivariogram to characterize spatial correlation. Selecting an underlying theoretical semivariogram based on the sample semivariogram is an extremely important and difficult task that is subject to a great deal of uncertainty. Current standard practice does not involve consideration of the confidence associated with semivariogram estimates, largely because classical statistical theory does not provide the capability to construct confidence limits from single realizations of correlated data, and multiple realizations of environmental fields are not found in nature. The jackknife method is a nonparametric statistical technique for parameter estimation that may be used to estimate the semivariogram. When used in connection with standard confidence procedures, it allows for the calculation of closely approximate confidence limits on the semivariogram from single realizations of spatially correlated data. The accuracy and validity of this technique was verified using a Monte Carlo simulation approach which enabled confidence limits about the semivariogram estimate to be calculated from many synthetically generated realizations of a random field with a known correlation structure. The synthetically derived confidence limits were then compared to jackknife estimates from single realizations with favorable results. Finally, the methodology for applying the jackknife method to a real‐world problem and an example of the utility of semivariogram confidence limits were demonstrated by constructing confidence limits on seasonal sample variograms of nitrate‐nitrogen concentrations in shallow groundwater in an approximately 12‐mi2(∼30 km2) region in northern Illinois. In this application, the confidence limits on sample semivariograms from different time periods were used to evaluate the significance of temporal change in spatial correlation. This capability is quite important as it can indicate when a spatially optimized monitoring network would need to be reevaluated and thus lead to more robust monitoring strategies.
Stream functions and equivalent freshwater heads for modeling regional flow of variable‐density groundwater: 2. Application and implications for modeling strategy
Authors: Senger Rainer K. , Fogg Graham E.
Published: February 2008

Stream functions and equivalent freshwater heads are used to simulate steady state flow of variable‐density groundwater in a regional, cross‐sectional flow model through the Palo Duro Basin, Texas, where fluid densities vary between 1.0 and 1.15 g/cm3. Centroid‐consistent velocities computed from the stream function solution allow a more precise interpretation of local flow patterns in cross‐sectional models than those from the head solution. Effects of significant fluid density variation on the regional groundwater flow pattern are studied by comparing simulation results that incorporate spatially varying, time‐invariant densities with those that assume uniform density. Modeling shows that the regional groundwater flow pattern in the Palo Duro Basin is not significantly affected by variations in fluid densities, indicating that the topographically driven flow component dominates buoyancy forces associated with dense brines. An exception is near the eastern boundary where high fluid densities cause stronger downward flow. However, simulated equivalent freshwater heads in the variable‐density model differ significantly from simulated heads in the freshwater density model, which is important for model calibration. In addition to the well‐known problems of hydraulic parameter and boundary condition uncertainties, modeling strategies for regional flow systems require consideration of uncertainties associated with fluid density and evaluation of equivalent freshwater head data.
A physically based model for predicting solute transfer from soil solution to rainfall‐induced runoff water
Authors: Wallach Rony , van Genuchten Martinus Th.
Published: February 2008

A model was developed to predict the field outlet concentration Hydrograph for chemicals released into overland runoff induced by continuous rainfall on a sloping soil. The model accounts for convective‐dispersive solute transport in the soil and also considers rate‐limited mass transfer through a laminar boundary layer at the soil surface/runoff water interface. Solutes are assumed to be subject to linear equilibrium sorption onto the solid phase of the soil. Concentration hydrographs for rainfall‐induced runoff were derived by treating the runoff zone as a well‐mixed reactor characterized by an appropriate residence time distribution. The model was used to predict experimental data obtained by Ahuja and Lehman (1983) for runoff from soil boxes with permeable bottoms. Good agreement was obtained between predicted and measured outflow concentrations for relatively low infiltration rates, provided relatively large dispersion coefficients were used in the calculations. Solute concentrations in the soil were also predicted well. Results for relatively high infiltration rates were less accurate, perhaps in part because of an incorrect assumption in the model that the infiltration rate remained constant in time and space during the runoff experiments.
Fate of Aldicarb in the unsaturated zone beneath a citrus grove
Authors: Hornsby A. G. , Rao P. S. C. , Jones R. L.
Published: February 2008

A field study was conducted in a 1.6‐ha citrus grove located in central Florida to evaluate transport and transformations of the nematicide aldicarb and its two metabolites (aldicarb sulfoxide and aldicarb sulfone) in the unsaturated zone over a 218‐day period during 1984. Bromide leaching was also monitored to provide a tracer of water movement in this well‐drained, deep, sandy soil. Aldicarb and bromide were applied in 3‐m wide treatment bands located midway between tree rows (7.62 m apart) and incorporated into the top 5 cm of soil by disking. This application method resulted in extreme variability in solute concentrations across and within the treatment bands, which persisted at all depths even as the pesticide and bromide leached during the study period. Aldicarb, its metabolites (sulfoxide and sulfone), and bromide leached readily through the soil and moved past the 7.92 m depth by the last sampling date (218 days). Aldicarb dissipated rapidly (half‐life ≤2 weeks), yielding aldicarb sulfoxide and aldicarb sulfone. Both of these compounds also dissipated but at a rate slower than that for aldicarb. The dissipation of total carbamate residues under field conditions was characterized by a half‐life of about 69 days, which was in agreement with laboratory‐derived values. On the basis of the findings of this study, recommendations are made on the protocols for designing and conducting field studies in order to characterize pesticide behavior in the crop root zone.
Gas migration in discrete fracture networks
Authors: Thunvik Roger , Braester Carol
Published: February 2008

A mathematical model is presented for the upward pulsating gas‐water displacement, from a gas source at a constant production rate or pressure at the bottom boundary to a constant pressure boundary at the top boundary. The study shows a complicated flow phenomenon caused by the unequal advance of the gas in fractures of different permeability or different inclinations. The results show that the gas breakthrough at the surface is governed by the high permeability fractures. At a constant rate of gas production the breakthrough is associated with a gas pressure drop at the bottom gas boundary. As a result, downward back flow takes place until the gas pressure builds up and reinitiates the upward displacement. It is concluded that calculations with average properties of the fracture permeability, for example, using the continuum approach, will underestimate the breakthrough time of the gas at the surface. Under constant pressure boundary conditions at the top of the cavern the average permeability will overestimate the amount of gas carried out by the fracture network. Under constant flow rate boundary conditions at the top of the cavern (i.e., bottom of the flow domain), calculations with average fracture permeability will overestimate the pressure in the cavern. The problem is of practical interest for low‐level radioactive waste repositories located in hard rock below the sea bottom.
Estimating groundwater exchange with lakes: 1. The stable isotope mass balance method
Authors: Krabbenhoft David P. , Bowser Carl J. , Anderson Mary P. , Valley John W.
Published: February 2008

Groundwater inflow and outflow contributions to the hydrologic budget of lakes can be determined using a stable isotope (18O/16O) mass balance method. The stable isotope method provides a way of integrating the spatial and temporal complexities of the flow field around a lake, thereby offering an appealing alternative to the traditional time and labor intensive methods using seepage meters and an extensive piezometer network. In this paper the method is applied to a lake in northern Wisconsin, demonstrating that it can be successfully applied to lakes in the upper midwest where thousands of similar lakes exist. Inflow and outflow rates calculated for the Wisconsin lake using the isotope mass balance method are 29 and 54 cm/yr, respectively, which compare well to estimates, derived independently using a three‐dimensional groundwater flow and solute transport model, of 20 and 50 cm/yr. Such a favorable comparison lends confidence to the use of the stable isotope method to estimate groundwater exchange with lakes. In addition, utilization of stable isotopes in studies of groundwater‐lake systems lends insight into mixing processes occurring in the unsaturated zone and in the aquifer surrounding the lake and verifies assumed flow paths based on head measurements in piezometers.