bluuebunny/crossref_metadata_2025 huggingface dataset:
Two‐phase flow in heterogeneous porous media: 2. Model application
Authors: Kueper Bernard H. , Frind Emil O.
Published: February 2004

The migration of a dense, nonaqueous phase liquid through heterogeneous porous media is examined using numerical simulation. Laboratory measurements of capillary pressure‐saturation curves were performed on samples obtained from a sand aquifer and scaled to permeability to provide a data base of model input parameters. Numerical simulations incorporating 25,200 finite difference cells are carried out in a spatially correlated, random permeability field to illustrate the influence of fluid properties on the migration of a nonwetting liquid below the water table. The simulation results are characterized by spatial moments to reflect the relative degrees of lateral spreading exhibited by the migrating nonwetting body in the presence of lenses of differing permeability. In addition, numerical simulations were performed in a solution domain containing a single lens of lower permeability material in order to examine the local‐scale sensitivity to porous media and fluid properties. The results of the study show the migration of a nonwetting liquid to be extremely sensitive to subtle variations in the capillary properties of the porous medium and to be influenced strongly by the fluid physical properties.
Quasi‐steady vertical two‐phase flows in porous media
Authors: Weir Graham J. , Young Roger M.
Published: February 2004

Two‐phase flows in which the pressure profile is essentially constant are called quasi‐steady. One‐dimensional quasi‐steady flows have the remarkable property that volumetric flux is essentially independent of position and is a function of time alone. Such volumetric fluxes are (to within an additive constant) inversely proportional to the spatial mean value of flowing viscosity. Consequently, the evolution of such a system is controlled by global properties of viscosity. Vertical two‐phase quasi‐steady flows evolving from an initial steady flow to another final steady flow are analyzed, and the corresponding theory is matched to output from a numerical simulator. Good agreement between the theory and simulator is demonstrated for simple shocks and expansion waves.
Analytical solutions for unsteady multidimensional infiltration in heterogeneous soils
Authors: Protopapas Angelos L. , Bras Rafael L.
Published: February 2004

Appendix is available with entire article on microfiche. Order from American Geophysical Union, 2000 Florida Avenue, N.W., Washington, DC 20009. Document W91‐003; $2.50. Payment must accompany order.

The problem of unsteady multidimensional infiltration in heterogeneous soils is approached analytically. By assuming that the hydraulic conductivity is an exponential function of the soil matric potential and a linear function of the soil moisture, the governing flow equation is linearized for a special variation of the saturated hydraulic conductivity in space. By using integral transform methods, analytical solutions to the one‐ and two‐dimensional flow problem are derived and shown to be generalized versions of known results for homogeneous soils. The development aims at obtaining quantitative criteria for the validity of the one‐dimensional approximation, which is commonly used in hydrologic applications.
Numerical evaluation of iterative and noniterative methods for the solution of the nonlinear Richards equation
Authors: Paniconi Claudio , Aldama Alvaro A. , Wood Eric F.
Published: February 2004

Several noniterative procedures for solving the nonlinear Richards equation are introduced and compared to the conventional Newton and Picard iteration methods. Noniterative strategies for the numerical solution of transient, nonlinear equations arise from explicit or linear time discretizations, or they can be obtained by linearizing an implicit differencing scheme. We present two first order accurate linearization methods, a second order accurate two‐level “implicit factored” scheme, and a second order accurate three‐level “Lees” method. The accuracy and computational efficiency of these four schemes and of the Newton and Picard methods are evaluated for a series of test problems simulating one‐dimensional flow processes in unsaturated porous media. The results indicate that first order accurate schemes are inefficient compared to second order accurate methods; that second order accurate noniterative schemes can be quite competitive with the iterative Newton and Picard methods; and that the Newton scheme is no less efficient than the Picard method, and for strongly nonlinear problems can outperform the Picard scheme. The two second order accurate noniterative schemes appear to be attractive alternatives to the iterative methods, although there are concerns regarding the stability behavior of the three‐level scheme which need to be resolved. We conclude that of the four noniterative strategies presented, the implicit factored scheme is the most promising, and we suggest improved formulations of the method.
The steady distribution of moisture beneath a two‐dimensional surface source
Authors: Martinez M. J. , McTigue D. F.
Published: February 2004

The steady distribution of moisture beneath a two‐dimensional strip source is analyzed by applying the quasi‐linear approximation. The source is described by specifying either the moisture content or the infiltration rate. A water table is specified at some depthDbelow the surface, the depth varying from shallow to semi‐infinite. Numerical solutions are determined, via the boundary integral equation method, as a function of the material inverse sorptive length α, the width of the strip source 2L, and the depth to the water table. The moisture introduced at the source is broadly spread below the surface when αL≪ 1, for which absorption by capillary forces is dominant over gravity‐induced flow. Conversely, the distribution becomes fingerlike along the vertical when αL≫ 1, where gravity is dominant over absorption. For a source described by specifying the moisture content, the presence of a water table at finite depth influences the infiltration through the source when αDis less than about 4; infiltration rates obtained assuming the water table depth is semi‐infinite are of sufficient accuracy for greater values of αD. When the source is described by a specified infiltration flux, the maximum allowable value of this flux for which the material beneath the source remains unsaturated is determined as a function of nondimensional sorptive number and depth to the water table.
Numerical modeling of natural and enhanced denitrification processes in aquifers
Authors: Kinzelbach Wolfgang , Schäfer Wolfgang , Herzer Jörg
Published: February 2004

Nitrate modeling in the groundwater environment must incorporate microbial denitrification as the major process of nitrate elimination. A multispecies transport model is presented which describes the interaction of oxygen, nitrate, organic carbon, and bacteria. Three phases (mobile pore water, biophase, and aquifer material) are taken into account. The model is applied to a natural aquifer situation as well as to an in situ remediation case where nitrate is employed as an oxidant. In the natural aquifer it is shown that the release of organic carbon from the matrix is the controlling factor for denitrification. In the remediation case, on the other hand, the data suggest that diffusion limitation of the nutrient supply to the biophase controls bacterial growth.
Simulation of Moisture Deficits and Areal Interpolation by Universal Cokriging
Authors: Stein A. , Staritsky I. G. , Bouma J. , Van Eijnsbergen A. C. , Bregt A. K.
Published: February 2004

Simulation models for calculating moisture deficits for areas of land require interpolation procedures to arrive from point observations to area‐covering statements. We use both (1) calculate first, interpolate later (CI) procedures, which interpolate calculated model results for test locations, and (2) procedures which interpolate basic soil data toward test locations, followed by model calculations, interpolate first, calculate later (IC) procedures. In this study several CI and IC procedures which simulate moisture deficits are compared by means of a test set of 100 observations, yielding the mean standard error (MSE). CI procedures consistently produced lower MSE values than IC procedures. Parameters of the pseudocovariance function (PCF), which models the spatial structure of bivariate increments in universal cokriging, were estimated by means of the restricted maximum likelihood procedure. Compared to universal kriging, universal cokriging yielded comparable MSE values, but a lower mean variance of the prediction error. Best results in this study were obtained by pointwise simulation model calculations, followed by statistical interpolations.
Surface Climate and Streamflow Variability in the Western United States and Their Relationship to Large‐Scale Circulation Indices
Authors: Redmond Kelly T. , Koch Roy W.
Published: February 2004

A statistical analysis was undertaken to determine the nature and magnitude of the relationship of precipitation, temperature and streamflow in the western United States to large‐scale atmospheric circulation patterns. The Southern Oscillation Index (SOI) was used as an indicator of the El Niño/Southern Oscillation (ENSO) and the PNA index as an indicator of the Pacific//North America pattern. These indices were correlated with surface climate data and split sample analyses were conducted to determine climate response during the extreme phases of each index. October–March precipitation was shown to be most strongly correlated with SOI averaged over the July–November period. The analysis showed that there are two centers of opposite association with the SOI. During low values of the SOI (ENSO events) precipitation is low in the Pacific northwest and high in the desert southwest. Correlations between SOI and temperature were greatest in the Pacific northwest. The split sample analysis also revealed statistically significant differences in precipitation occurring during extremes of the SOI. The PNA pattern was related to precipitation and temperature over a concurrent time period. Especially strong associations were noted in the Pacific northwest for both precipitation and temperature. Streamflow showed associations with SOI similar to precipitation.
Reliability improvement for water distribution networks through increasing pipe size
Authors: Fujiwara Okitsugu , Tung Hoang Duong
Published: February 2004

A method of reliability improvement is proposed for water distribution networks. The ratio of expected maximum total water supplied to total water demanded is employed as a measure of reliability. A nonlinear maximum flow model is used to calculate the maximum supply of water under possible link failures and the reliability of the network. Reliability is improved by increasing pipe size. The pipe size increase is determined by considering the ratio of marginal reliability to marginal cost. The method gives a symmetric design when the network is symmetric.
Modeling the Nonequilibrium Transport of Linearly Interacting Solutes in Porous Media: A Review
Authors: Sardin M. , Schweich D. , Leij F. J. , van Genuchten M. Th.
Published: February 2004

The transport of linearly interacting solutes in porous media is investigated with the help of residence time distributions, transfer functions, methods of system dynamics, and time‐moment analyses. The classical one‐dimensional convection‐dispersion equation is extended to two‐region (mobile‐immobile water) transport by including diffusional mass transfer limitations characteristic of aggregated soils. The two‐region model is further revised by incorporating the effects of multiple retention sites (in parallel or in series), multiple porosity levels, and arbitrary but steady flow fields. It is shown that different physical situations can be represented by a relatively small number of transfer functions containing only two types of parameters: distribution coefficients to account for equilibrium properties and characteristic times reflecting kinetic processes. Relevant kinetic processes include convective transport, hydrodynamic dispersion, adsorption‐desorption, and physical or chemical mass transfer limitations. In most situations, theoretical breakthrough curves are found to be relatively insensitive to the mathematical structure of the transfer function, irrespective of the physical interpretation of the distribution coefficients and the characteristic times in the model. This means that alternative physical and chemical interpretations of model parameters can lead to nearly identical breakthrough curves. Certain transfer time distributions can lead to quite unusual shapes in the breakthrough curves; these curves strongly depend on the characteristic times and a few operational variables. Results of this study show that the transfer time distribution is an extremely useful tool for explaining some unexpected experimental results in the solute transport literature.
Influence of Matrix Diffusion and Exchange Reactions on Radiocarbon Ages in Fissured Carbonate Aquifers
Authors: Maloszewski Piotr , Zuber Andrzej
Published: February 2004

The parallel fissure model coupled with the equation of diffusion into the matrix and with exchange reaction equations has been used to derive a simple formula for estimating the influence of matrix porosity and reaction parameters on the determination of radiocarbon ages in fissured carbonate rocks. Examples of evidently too great radiocarbon ages in carbonate formations, which are not explainable by models for the initial 14C corrections, can easily be explained by this formula. Parameters obtained for a chalk formation from a known multitracer experiment combined with a pumping test suggest a possibility of 14C ages more than three orders of magnitude greater than the ages which would be observed if the radiocarbon transport took place only in the mobile water in the fissures. It is shown that contrary to the solute movement on a small scale and with a variable input, the large‐scale movement, characteristic for the 14C dating, does not necessarily require the knowledge of kinetic parameters, because they may be replaced by the distribution coefficient. Discordant tritium and 14C concentrations are commonly interpreted as a proof of mixing either in the aquifer or at the discharge site. For fissured carbonate formations, however, an alternative explanation is given by the derived model showing a considerable delay of 14C with respect to nonsorbable tracers.
Stable Isotopes of Oxygen and Natural and Fallout Radionuclides Used for Tracing Runoff During Snowmelt in an Arctic Watershed
Authors: Cooper L. W. , Olsen C. R. , Solomon D. K. , Larsen I. L. , Cook R. B. , Grebmeier J. M.
Published: February 2004

Stable isotopes of oxygen, and natural and fallout radionuclides, have been used, respectively, to identify water sources and to quantify watershed fluxes of precipitation‐borne solutes and particles that come in contact with tundra vegetation at Imnavait Creek, Alaska (68° 37′N, 149° 17′W). Oxygen 18/oxygen 16 ratios of water in the snowpack, stream, and unfrozen soil during the peak of snowmelt showed that less than ∼14% of streamwater was derived from sources other than snow. Within a month of snowmelt, 18O/16O ratios in the stream indicated that only negligible amounts of water derived from snow remained in the watershed, in contrast to the low degree of mixing between snow and underlying soil water, greater than 90% of the atmospherically derived 7Be (53‐day half‐life) that was deposited in the snowpack was adsorbed onto the surface 2–3 cm of frozen organic soils and vegetation. A slightly lower degree of absorption (∼2/3) on tundra was observed for atmospherically derived 35S (87‐day half‐life) released during snowmelt. These data indicate that atmospherically derived substances in the snowpack are often retained strongly by sorption or chemical interaction with vegetation and soil during snowmelt. This conclusion is also supported by the vegetation and soil inventories of 137Cs (30.2‐year half‐life), which are similar to values expected as a result of atmospheric deposition over the past 40 years.
Paradoxes and Realities in Unsaturated Flow Theory
Authors: Gray William G. , Hassanizadeh S. Majid
Published: February 2004

In currently applied theory of unsaturated flow, paradoxes exist concerning the equation of state for the water phase, the idea of a water phase at negative absolute pressure, the applicability of the hydrostatic pressure gradient at equilibrium, and the lack of explicit inclusion of interface effects in the problem formulation. The theory of unsaturated flow presented here eliminates those paradoxes and indicates that the hysteresis in capillary pressure and relative permeability may be accounted for by allowing these quantities to depend on interfacial area as well as saturation. The wettability potential is shown to be a thermodynamic function which is important in describing unsaturated flow processes. The momentum balance equation for the interface between the air and water phases also contributes to a systematic and tractable set of equations which describe unsaturated flow.
Groundwater Flow and Solute Transport in Fractured Lacustrine Clay Near Mexico City
Authors: Rudolph D. L. , Cherry J. A. , Farvolden R. N.
Published: February 2004

A network of piezometers was installed in a surficial lacustrine clay aquitard overlying a thin saline water aquifer of volcanoclastic origin at a study site near Mexico City in the Basin of Mexico. The aquifer is underlain by additional lacustrine sediments which in turn overlie a thick regional freshwater aquifer. The regional aquifer provides approximately 70% of the water supply for 20 million people in the Basin of Mexico. In the study area, major ions, oxygen 18, and deuterium in the pore water of the surficial aquitard exhibit large variations with depth. The nature of these variations suggests that the saline pore water is being displaced downward by infiltrating meteoric water. The infiltration has been induced by strong downward hydraulic gradients imposed two to three decades ago when heavy aquifer pumping of the thin saline water aquifer began. One‐dimensional analytical models representing solute transport in both fractured and unfractured porous media were used to simulate the geochemical profiles in the surficial aquitard. The fractured porous medium model, using a realistic mean hydraulic gradient and fracture spacing (1.5 m) and small but significant fracture aperture (30 μm) provide nearly an exact match to the field data. From this we infer that, because of vertical fractures, there is a much greater potential for downward leakage of water and contaminants through the Mexico City clay into underlying aquifers than has been previously thought.
The Second Las Cruces Trench Experiment: Experimental Results and Two‐Dimensional Flow Predictions
Authors: Hills R. G. , Wierenga P. J. , Hudson D. B. , Kirkland M. R.
Published: February 2004

As part of a comprehensive field study designed to provide data to test stochastic and deterministic models of water flow and contaminant transport in the vadose zone, several trench experiments were performed in the semiarid region of southern New Mexico. The first trench experiment is discussed by Wierenga et al. (this issue). During the second trench experiment, a 1.2 m wide by 12 m long area on the north side of and parallel to a 26.4 m long by 4.8 m wide by 6m deep trench was irrigated with water containing tracers using a carefully controlled drip irrigation system. The irrigated area was heavily instrumented with tensiometers and neutron probe access tubes to monitor water movement, and with suction samplers to monitor solute transport. Water containing tritium and bromide was. applied during the first 11.5 days of the study. Thereafter, water was applied without tracers for an additional 64 days. Both water movement and tracer movement were monitored in the subsoil during infiltration and redistribution. The experimental results indicate that water and bromide moved fairly uniformly during infiltration and the bromide moved ahead of the tritium due to anion exclusion during redistribution. Comparisons between measurements and predictions made with a two‐dimensional model show qualitative agreement for two of the three water content measurement planes. Model predictions of tritium and bromide transport were not as satisfactory. Measurements of both tritium and bromide show localized areas of high relative concentrations and a large downward motion of bromide relative to tritium during redistribution. While the simple deterministic model does show larger downward motions for bromide than for tritium during redistribution, it does not predict the high concentrations of solute observed during infiltration, nor can it predict the heterogeneous behavior observed for tritium during infiltration and for bromide during redistribution.
A Test of Equal Mobility in Fluvial Sediment Transport: Behavior of the Sand Fraction
Authors: Church M. , Wolcott J. F. , Fletcher W. K.
Published: February 2004

Mobile fine sediment was caught in six screened pit traps installed in the bed of a cobble gravel channel. Sample periods lasted from several hours to several days, so the trapped material represents a good integration of the range of sizes in traction up to a limit near 10 mm imposed by the screens. All the traps, distributed along a bar, caught similar amounts of material, of similar texture. The peak transport rate for the <2‐mm fraction, corresponding with the lower portion of the bimodal bed material, was about 3 × 10−4 kg s−1 m−1. Observations continued for 6 weeks, through the nival flood on the stream. There was a sensible threshold for motion of material of all sizes, but minor transport occurred below it. Material up to 210 μm in size, including conventionally classified “wash” material, moved with near equal mobility over the season, but there were departures in individual sample periods. “Equal mobility” of fine material appears at best to be a statistical phenomenon which holds for a limited range of grain sizes over a seasonal period.
Porous Media With Linearly Variable Hydraulic Properties
Authors: Vogel T. , Cislerova M. , Hopmans J. W.
Published: February 2004

The similar media concept is reformulated and extended to allow for analysis of unsaturated or saturated flow in a system of parallel nonhomogeneous one‐, two‐, or three‐dimensional soil profiles. The resulting invariance of Richards' equation for a set of soil profiles is valid for certain initial and boundary conditions only. Simple techniques are outlined and demonstrated by examples for direct identification of scaling factors based on measured soil hydraulic data, and indirect identification based on measured dynamic characteristics of a soil water system. Suggested applications of the discussed concept are (1) the classification of soils according to the shape of their reference hydraulic properties and (2) the description of time and space variability of soil water properties for numerical modeling purposes.
Water Flow Paths and the Spatial Distribution of Soils and Exchangeable Cations in an Acid Rain‐Impacted and a Pristine Catchment in Norway
Authors: Mulder Jan , Pijpers Marc , Christophersen Nils
Published: February 2004

The dynamic pattern of soil water transport is a major factor in determining the chemistry of streamwater. In the acidified Birkenes catchment (southernmost Norway) the streamwater chemistry is, to a first approximation, explained by mixing solutions from the forest floor, the B horizon and the deep peat, in various proportions depending on the hydrological conditions. Paradoxically, a direct physical contact between the forest floor and the B horizon on the one hand and the stream on the other is lacking, as the stream banks largely consist of peats. To investigate this paradox, soils and their levels of exchangeable cations were studied in a 100 m × 100 m grid. Results indicate that the exchange sites of the surface peat along the stream are significantly enriched in Al, probably due to return flow of Al‐rich B horizon water. This view is supported by the similarity of the solution chemistry in surface peats and B horizons. Exchangeable base cations dominate in the forest floor upslope. Forest floor solutions, an important component of streamwater during intensive storms, are depleted in Al and may bypass the A‐enriched surface peats via ephemeral flow channels. A parallel study in a pristine catchment in mid‐Norway shows a similar accumulation of Al in return flow areas. This indicates that acid deposition is not a prerequisite for elevated levels of exchangeable Al in the surface organic layers of return flow areas.
Coupled and partially coupled Eulerian‐Lagrangian Model of freshwater‐seawater mixing
Authors: Galeati G. , Gambolati G. , Neuman S. P.
Published: February 2004

The problem of density‐dependent transport of salt in unconfined coastal aquifers is solved numerically by means of an implicit Eulerian‐Lagrangian finite element formulation. Such a formulation leads to symmetric positive definite finite element matrices which are ideally suited for efficient solution by preconditioned conjugate gradient methods. Additional known advantages of the formulation are unconditional stability, reduced numerical dispersion and suitability for parallel computation. The method has been used to study the effect of dewatering on seawater intrusion within a vertical cross section through an aquifer in southern Italy, related to the construction of a thermoelectric power plant. To investigate the extent to which the dependence of fluid density on salt concentration affects the numerical solution, the flow and advection‐dispersion equations were solved in coupled (iterative), partially coupled (noniterative) and completely decoupled modes. Partial coupling was found to yield results very close to those obtained by full coupling but at great savings in computer time; the less rigorous decoupled approach led to results substantially different from those obtained through coupling and partial coupling. Effects of aquifer heterogeneity and the construction of a cutoff wall on seawater intrusion are discussed.
Effects of Soil Heterogeneity on Pesticide Leaching to Groundwater
Authors: van der Zee Sjoerd E. A. T. M. , Boesten Jos J. T. I.
Published: February 2004

Pesticide leaching was simulated numerically assuming Freundlich adsorption, first‐order transformation and passive plant uptake, taking transient flow, hydrodynamic dispersion, and depth as well as temperature dependence of (bio)chemical parameters into account. The dependency of the leached fraction on sorption and transformation parameters appeared to be in good general agreement with the model developed by Jury et al. (1987). We incorporated spatial variability of )bio)chemical parameters into the piston flow model and showed how spatial variability may be accounted for without having to resort to demanding Monte Carlo techniques. Such spatial variability affects the leached fraction significantly. The data requirement of the simple stochastic model is small and the versatility relatively high. For parameter values often not of prime practical interest for pesticide screening this model fails. Considering transport by convection and dispersion in the semi‐infinite domain, this spatial variability can be easily accounted for using parameter ranges for which our original analytical model for spatially variable piston transport failed. In this revised model, hydrodynamic dispersion, preferential flow, and spatial variability of transformation, sorption and soil thickness are dealt with in a similar fashion, while both correlation or the absence of correlation of parameters can be incorporated through an approximation of apparent residence time variance.
Probability Plot Goodness‐of‐Fit and Skewness Estimation Procedures for the Pearson Type 3 Distribution
Authors: Vogel Richard W. , McMartin Daniel E.
Published: February 2004

Uniform flood frequency guidelines in the United States currently recommend fitting a Pearson (P3) distribution to the logarithms of annual maximum flood flows. As a result, a plethora of procedures have been recommended for obtaining unbiased plotting positions and unbiased estimates of the skew coefficient and for inverting the cumulative distribution function of a P3 variate. These developments are precisely the ingredients required for the construction of P3 probability plots. Using Monte Carlo simulation, we develop a probability plot correlation coefficient (PPCC) hypothesis test for the P3 distribution. Power studies are performed to evaluate the ability of the test to discriminate among competing distributional alternatives and to enhance our understanding of why the P3 distribution often appears to provide such a good fit to observed flood flow data. A new estimator of the skew coefficient is presented which, unlike the biased and unbiased moment estimators, is unbounded and has significantly lower root mean square error than the moment estimators for highly skewed samples.
Analysis of subsurface flow and formation anisotropy in a fractured aquitard using transient water level data
Authors: Rophe B. , Berkowitz B. , Magaritz M. , Ronen D.
Published: February 2004

A new methodology is proposed to estimate the actual direction of water flow in a fractured aquitard. According to the conceptual model, the flow direction in a fractured aquitard is dictated by the azimuth of the fractures, since almost no flow occurs within the rock matrix, which possesses very low hydraulic conductivity. Thus, while ground water in reality continues to flow along the fractures, calculations based on water level data may incorrectly indicate changes in hydraulic gradients and azimuth of flow. The present methodology is based on simultaneous analysis of hydraulic gradients and flow direction, as calculated from equipotential surfaces. The approach was tested in a fractured chalky aquitard, and the calculated direction of principal fractures was found to be in good agreement with subsurface fracture data obtained from a tunnel excavated in the vicinity of the study area.
Rate‐limited mass transfer and transport of organic solutes in porous media that contain immobile immiscible organic liquid
Authors: Brusseau Mark L.
Published: February 2004

A general model is presented that simulates the effect of an immobile immiscible organic liquid, as well as rate‐limited solid phase sorption, on the transport of dissolved organic contaminants in heterogeneous porous media. Specific models are developed for four cases (1) immobile immiscible liquid that resides in nonadvective domains of a heterogeneous porous medium; (2) immobile immiscible liquid that resides in the advective domain; (3) homogeneous porous media wherein mass transfer within the immiscible liquid, as well as across the liquid‐water interface, is rate limited; (4) homogeneous porous media with a single resistance to liquid‐liquid mass transfer. The performance of the homogeneous‐based, single‐resistance model was evaluated by attempting to predict a break‐through curve reported in the literature. Based on the successful prediction of the data, where values for all parameters were obtained independent of the data being simulated, it appears that the conceptual basis of the model is valid. Through a series of simulations, the effect of the immiscible liquid on retention was shown to be great, even at relatively low levels of saturation. Release of solute from residual saturation located within regions of relatively low hydraulic conductivity can be significantly rate limited, even when mass transfer between immiscible liquid and water is rapid. This has ramifications concerning the efficacy of remediation systems based on imposed hydraulic gradients (e.g., pump‐and‐treat). The model should prove useful in further investigations of the effect of immobile immiscible organic liquids on the retention and transport of organic solutes in porous media.
Numerical analysis of solute migration through fractured clayey deposits into underlying aquifers
Authors: Harrison B. , Sudicky E. A. , Cherry J. A.
Published: February 2004

This study examines the degree to which vertically fractured clayey aquitards protect an underlying aquifer from near‐surface sources of contamination. Evidence from field studies indicates that many clayey aquitards previously assumed to be unfractured at depth have vertical fractures that actively transmit groundwater. Calculated groundwater velocities within these fractures can exceed several meters per day for apertures in the range of those reported to occur in clays. If this is the case, significant quantities of dissolved contaminants originating in near‐surface zones may move rapidly downward through the fracture network into underlying aquifers. A two‐dimensional Laplace transform Galerkin finite element model (Sudicky and McLaren, this issue) was used to assess the importance of idealized planar vertical fractures on flow and solute transport through a 15‐m‐thick aquitard and subsequent plume evolution within an underlying aquifer in which groundwater flows horizontally. Sensitivity analyses indicate that solute transport through the aquitard is strongly affected by downward flow in widely spaced deep fractures with apertures as small as 10 μm and that a plume of large lateral extent and significant concentration forms within the underlying aquifer in a few tens of years for apertures of the order of 20 μm or much sooner if the apertures are 50 μm. This finding suggests that small hydraulically active fractures that are very difficult to detect or identify within an otherwise protective clayey barrier may cause rapid and large‐scale contamination of groundwater beneath the barrier.
Benefit transfer studies: Myths, pragmatism, and idealism
Authors: Boyle Kevin J. , Bergstrom John C.
Published: February 2004

Benefit transfer has been an ongoing, practical analysis for years in legal proceedings and government policy analyses where timely benefit estimates are critically dependent on the use of existing data. Most benefit transfer studies to date have been conducted behind closed doors and have not been open to scholarly review, and no systematic research agenda has been established to determine whether benefit transfer estimates are valid for public policy analyses. In this paper we propose a systematic, conceptual foundation for conducting benefit transfer studies, and suggest a research agenda to identify conditions under which valid benefit transfer estimates can be derived. We conclude, however, that this research agenda must be accompanied by improved conduct and reporting of original valuation studies before benefit transfer can become a widely used tool in public policy analyses.
The evolution of a more rigorous approach to benefit transfer: Benefit function transfer
Authors: Loomis John B.
Published: February 2004

The desire for economic values of recreation for unstudied recreation resources dates back to the water resource development benefit‐cost analyses of the early 1960s. Rather than simply applying existing estimates of benefits per trip to the study site, a fairly rigorous approach was developed by a number of economists. This approach involves application of travel cost demand equations and contingent valuation benefit functions from existing sites to the new site. In this way the spatial market of the new site (i.e., its differing own price, substitute prices and population distribution) is accounted for in the new estimate of total recreation benefits. The assumptions of benefit transfer from recreation sites in one state to another state for the same recreation activity is empirically tested. The equality of demand coefficients for ocean sport salmon fishing in Oregon versus Washington and for freshwater steelhead fishing in Oregon versus Idaho is rejected. Thus transfer of either demand equations or average benefits per trip are likely to be in error. Using the Oregon steelhead equation, benefit transfers to rivers within the state are shown to be accurate to within 5–15%.
What happens near a quasi‐linear point source?
Authors: Philip J. R.
Published: February 2004

The quasi‐linear continuous point source has been central to many studies of multidimensional flow in unsaturated soil. Immediately next to the source, however, the water pressure Ψ is positive and indefinitely large, so the quasi‐linear flow equation (limited to Ψ ≤ 0) fails in principle. We investigate whether this is a serious problem in practice. Exact analysis would be complicated and difficult, since the problem is of mixed saturated‐unsaturated flow with an unknown free boundary between the two regions. When the source strength is not too large, the saturated region is close to spherical. A simple approximate analysis follows with exterior and interior flow velocities matched on the boundary. The correction, taking into account the saturated region, shifts the quasi‐linear source a small distance above the actual source location. In practical applications the correction is usually negligibly small. Physical reasons why the approximation works well and the correction is small are indicated. In addition, these physical reasons suggest that the scope of the quasi‐linear analysis is wider than supposed hitherto. The solution in potential theory for the eccentric point source needed for the study is given in the appendix.
Debris flow rheology: Experimental analysis of fine‐grained slurries
Authors: Major Jon J. , Pierson Thomas C.
Published: February 2004

The rheology of slurries consisting of ≤2‐mm sediment from a natural debris flow deposit was measured using a wide‐gap concentric‐cylinder viscometer. The influence of sediment concentration and size and distribution of grains on the bulk rheological behavior of the slurries was evaluated at concentrations ranging from 0.44 to 0.66. The slurries exhibit diverse rheological behavior. At shear rates above 5 s−1 the behavior approaches that of a Bingham material; below 5 s−1, sand exerts more influence and slurry behavior deviates from the Bingham idealization. Sand grain interactions dominate the mechanical behavior when sand concentration exceeds 0.2; transient fluctuations in measured torque, time‐dependent decay of torque, and hysteresis effects are observed. Grain rubbing, interlocking, and collision cause changes in packing density, particle distribution, grain orientation, and formation and destruction of grain clusters, which may explain the observed behavior. Yield strength and plastic viscosity exhibit order‐of‐magnitude variation when sediment concentration changes as little as 2–4%. Owing to these complexities, it is unlikely that debris flows can be characterized by a single rheological model.
A location modeling approach for groundwater monitoring network augmentation
Authors: Hudak Paul F. , Loaiciga Hugo A.
Published: February 2004

A heuristic approach based on facility location theory effectively augments groundwater quality monitoring configurations through the strategic siting of additional wells. The approach is an alternative to variance‐based schemes previously established for the augmentation problem. The method developed herein is practical in that it (1) is relatively easily understood, (2) is not difficult to implement and solve, and (3) does not require a large number of preexisting observation points. The approach has been applied to a case study involving a landfill‐contaminated buried valley aquifer in southwest Ohio. Configurations derived by the heuristic approach exhibit two key characteristics: (1) location of wells near areas of high estimated contaminant concentration and (2) interwell separation distances that facilitate areal plume coverage.
A linearized solution of the slope crest infiltration problem
Authors: Philip J. R.
Published: February 2004

It was found recently that the long‐slope ponded infiltration solution applies also to a wide range of nonplanar topographies. The long‐slope solution neglects any slope crest effect, and a careful analysis of this is needed. The present work reassesses the previous primitive estimate of the crest effect. We solve the problem of linearized infiltration into a symmetrical ridge with 45° slope angles. The integral matching of flow behavior gives results of ample accuracy for our purpose. The 45° slope is very steep in nature, but yields a simple product solution. We use this to calibrate the previous long‐slope criterion for arbitrary slope angle. The primary slope crest effect is increase of moisture content and decrease of capillary potential gradients near the crest. The affected region propagates downslope but its influence on infiltration dynamics tends to dissipate because the relative importance of capillarity diminishes as time increases. We find that the previous criterion for applicability of long‐slope infiltration dynamics was too conservative by a factor ranging from 2 at very small infiltration times to 100 at large times. The solution gives details of both downslope and inslope unsaturated flows. The ponded infiltration rate is least at the crest and increases downslope: This result is independent of linearization or slope angle.
Optimal maintenance‐related decision making for deteriorating water distribution systems: 1. Semi‐Markovian Model for a water main
Authors: Li Duan , Haimes Yacov Y.
Published: February 2004

An optimal maintenance‐related decision‐making problem is investigated in this paper for deteriorating water distribution systems. A semi‐Markovian model is developed to capture the dynamic evolution of the failure mode of a deteriorating main pipe, thus facilitating the determination of the optimal replacement/repair decision at various deteriorating stages. An example problem is solved to demonstrate the proposed methodology and to show the trade‐off between the system's availability and the expected maintenance cost.
Electrical resistivity tomography of vadose water movement
Authors: Daily William , Ramirez Abelardo , LaBrecque Douglas , Nitao John
Published: February 2004

Cross borehole electrical resistivity tomography (ERT) was used to image the resistivity distribution before and during two infiltration experiments. In both cases water was introduced into the vadose zone, and the change in resistivity associated with the plume of wetted soil was imaged as a function of time. The primary purpose of this work was to study the capabilities and limitations of ERT to image underground structure and ground water movement in the vadose zone. A secondary goal was to learn specifics of unsaturated flow in a complex geologic setting. Tomographs of electrical resistivity taken before infiltration image coarser, well‐drained soils (sands and gravels) as more resistive zones, whereas finer grained soils (silts and clays), which hold more water by capillarity, are imaged as more conductive. Images of changes in resistivity during infiltration show growth of the water infiltration plume with time that is consistent with known geology. In the ERT images we see the effects of capillary barriers and infer differences between capillary‐driven flow through fine sediments and gravity‐driven flow through very permeable sediments. Images are consistent with numerical flow simulations using hydrological parameter values consistent with soil types inferred from well logs. ERT can be a useful tool to monitor movement of circuitous moisture fronts in a heterogeneous field setting that would go undetected by borehole measurements.
A comparison of several evaporation equations
Authors: Crago Richard D. , Brutsaert Wilfried
Published: February 2004

Several well‐known evaporation equations were tested with daily data averaged over six stations in a 15×15 km region in Kansas. The equilibrium evaporation and advection‐aridity evaporation equations produced acceptable results, under the generally moist conditions encountered, with the former performing slightly better. Three methods tested also required soil moisture (SM) availability data. These were the Penman and equilibrium evaporation equations adjusted with SM‐dependent coefficients, and the Penman‐Monteith formulation with surface resistance. All three gave significantly better performances than the unadjusted equilibrium equation. In general, it appeared that the use of simple temporal (daily) and spatial averages may not be appropriate, especially under conditions of variable SM. The Penman, equilibrium, and advection‐aridity evaporation equations are linear combinations of the same two terms, with different coefficients. The optimal values of these coefficients, determined for various ranges of SM, were consistent with the underlying physical models.
Confidence limits and bias correction for estimating angles between directions with applications to paleomagnetism
Authors: Debiche M. G. , Watson G. S.
Published: February 2004

Many problems in the earth sciences, particularly in the use of paleomagnetic data in plate tectonics, require estimates of the angles between directions and confidence intervals for these angles. To give a set of interrelated simple methods, we approximate all estimated directions by appropriate concentrated Fisher distributions. In preliminary numerical experiments we verify previous results for the distribution of the means of samples drawn from Fisher distributions and study the distributions of six estimators of the Fisher concentration parameter κ. We selected Fisher's original estimator for κ, κ = (n ‐ 1)/(n ‐ R), for use in our subsequent simulations. We then study the bias in, and confidence intervals around, the estimator
of the angle between the means of samples drawn from two Fisher distributions (“Fisher means”). We find an approximate expression for the geometric bias in this angle, B(θ) = ‐tanθ + [tan2θ + θcrit2]1/2 where θcrit = [1/(R1κ1) + 1/(R2κ2)]1/2, and show that it works well for θ > 2θcrit. (When, for example, Rk = 250 for both samples, θcrit = 5.1°.) We then show that the bias‐corrected estimator of
, is normally distributed with mean equal to the true angle and variance
. Thus one can construct a 95% confidence interval for this angle with the formula
. We show by extensive simulation that coverage probabilities for this confidence interval are slightly conservative for θ > 2θcrit and good for θ > 3θcrit. We derive related results for angles between various combinations of fixed directions and Fisher means. We find that the estimator
of the angle between two great circles containing a known fixed direction and two different Fisher means is unbiased and normally distributed with variance
where the θi are the angular distances between the Fisher means and the known fixed direction. Thus the confidence interval on this rotation angle is
. We give examples of applying these techniques to paleomagnetic data analysis, especially for determining terrane motions. Our methods provide confidence intervals for poleward displacement. For rotation, simulation suggests that they provide results at least as accurate as previous methods [McWilliams, 1984; Demarest, 1983] over a wide range of relevant parameter values, while being simpler or more flexible. We apply these methods to estimating rates of apparent polar wander and point out an additional bias due to dating errors.