bluuebunny/crossref_metadata_2025 huggingface dataset:
Graben inversion in nature and experiments
Authors: Brun Jean‐Pierre , Nalpas Thierry
Published: February 2004

The inversion of crustal‐scale basement grabens is studied here through laboratory experiments on small‐scale models and available oil industry seismic lines from the southern North Sea. Two basic configurations are considered. First, both the basement and the sedimentary cover are brittle, and inversion does not involve any potential décollement between them. Second, the basement and sedimentary cover are separated by a weak ductile layer (e.g., salt), which can allow décollement of the cover during both extension and later compression and inversion. The second configuration is more complicated and can lead to a large variety of geological structures. Laboratory experiments were carried out on brittle‐ductile models built with sand to represent brittle layers (basement and sedimentary cover) and silicone putty to simulate the décollement layer between basement and cover. A mechanically based classification of inversion structures is proposed. The effects of some crucial parameters are investigated, including obliquity between the direction of shortening and normal faults, as well as strength profiles, and the presence or absence of salt diapirs. The experimental investigation leads to the following conclusions: (1) the inversion of the graben by reactivation of normal faults implies that the angle between the direction of compression and the graben is less than 45°, (2) if there is a superficial décollement (e.g., basement‐cover interface), inversion initiates low dipping thrust faults in the cover, localized at graben borders, (3) salt diapirs or salt walls localized along the graben borders in the cover are preferential sites for the development of thrust faults, and (4) when the cover is decoupled from the basement by a décollement layer, inversion induced deformation in the cover which is partitioned between thrust faults along the graben borders and strike‐slip faults within the graben trending oblique to the graben borders. Experimental results are compared with field examples, in particular from the southern North Sea.
Analytical Solution for One‐Dimensional Drainage: Water Stored in a Fixed Depth
Authors: Parkin Gary W. , Warrick Arthur W. , Elrick David E. , Kachanoski R. Gary
Published: February 2004

We present a quasi‐analytical solution for drainage of water from a fixed depth of soil near the surface of a deeply wetted profile. The solution is an application of a previously published nonlinear constant rate rainfall infiltration solution and includes capillary and gravity effects. The solution is sensitive to its three hydrologic parameters (including a macroscopic capillary length and the saturated hydraulic conductivity) and is numerically stable for a wide range of parameter values. We develop an analytical form of the hydraulic gradient and flux density of water during drainage at any depth and time using the same drainage solution. The duration of unit hydraulic gradient is strongly dependent on the soil's hydrologic parameters. Generalized forms of the water storage, water content, and flux density given here can show the effects of an infinite combination of parameter values in single plots of each dimensionless form.
Comparison of Time Domain Reflectometry Performance Factors for Several Dielectric Geometries: Theory and Experiments
Authors: Maheshwarla S. V. , Venkatasubramanian R. , Boehm Robert F.
Published: February 2004

We propose three nontraditional dielectric geometries and present an experimental and theoretical analysis and comparison of time domain reflectometry (TDR) performances for them. The traditional geometry (the probes inserted in material of essentially infinite extent) is compared to three nontraditional geometries where the probes are affixed outside of a core sample, inside of a bore, or flat on the surface of a semi‐infinite solid. Our derivation relates the velocity of electromagnetic wave propagation to the complex permittivities and permeabilities of the media and the geometry for the three nontraditional configurations. Experimental results for air, styrofoam, dry sand, wet sand of varying water content, nylon, dry wood, and ferromagnetic steel are obtained for the three proposed configurations and are in fair agreement with the literature within the experimental uncertainties. Through experiments and theoretical analysis, the TDR performance is found to be the same within the experimental uncertainties for the three nontraditional geometries. The proposed geometries yield slightly lower sensitivities compared to the traditional geometry. Advantages and disadvantages of the geometries compared to the traditional geometry are also discussed.
In Situ Method for Estimating Subsurface Unsaturated Hydraulic Conductivity
Authors: Shani Uri , Or Dani
Published: February 2004

A method for the estimation of subsurface unsaturated hydraulic conductivity in situ was developed and field tested. The new method is based on Philip's (1992) approximation of water flow from a small subsurface cavity. Measurements of water pressure within the cavity (P) and associated discharge (Q) are used to infer the soil's saturated hydraulic conductivity (Ks) and capillary length (α). A probe for conducting the measurements was designed and field tested, and a measurement protocol was established. Comparisons were made with existing surface‐based methods by exposing the soil surface at the depth of the subsurface measurement. The method provided estimates of the soil parameters that were in close agreement with those obtained using surface‐based in situ methods.
A New Method for the Identification of Distributed Transmissivities
Authors: Giudici Mauro , Morossi Giorgio , Parravicini Guido , Ponzini Giansilvio
Published: February 2004

For two‐dimensional groundwater flow in an isotropic confined aquifer, it has been shown elsewhere that two independent steady state sets of data, i.e., piezometric heads and source terms corresponding to different steady state flow conditions, and the value of transmissivity at one point suffice to determine transmissivity uniquely in a connected domain. The data are independent if the hydraulic gradients are not parallel anywhere over the domain. Here transmissivity is numerically determined by integration of suitably approximated functions of the data along polygonal lines connecting the nodes of a lattice; integration starts from the node where transmissivity is given. The choice of the integration path is based on the results of the stability analysis and allows us to minimize the effects of the approximations on the data. Since the approximated solution is computed along internode segments, the internode transmissivities are immediately calculated without introducing arbitrary averages of the node transmissivities. The internode transmissivities are the quantities necessary to set up a management model within a conservative finite differences scheme. The applicability of this technique to real cases is tested with two synthetic examples. The first one was set up by ourselves, whereas the second one has been taken from the literature. The internode transmissivities identified with our procedure are compared with the synthetic reference ones. The ultimate check is performed of evaluating new head fields on the basis of the identified and reference internode transmissivities. The fit is good. The relative error for the identified internode transmissivities is very low when error‐free data are used, and it varies by an amount approximately constant over the entire aquifer when an error on the initial value of transmissivity is introduced. The errors on the piezometric heads bear more relevance, but nonetheless, the affected results are still good.
Estimating 14C Groundwater Ages in a Methanogenic Aquifer
Authors: Aravena Ramon , Wassenaar Leonard I. , Plummer L. Niel
Published: February 2004

This paper addresses the problem of 14C age dating of groundwaters in a confined regional aquifer affected by methanogenesis. Increasing CH4 concentrations along the groundwater flow system and 13C and 14C isotopic data for dissolved inorganic carbon, dissolved organic carbon, and CH4 clearly show the effect of methanogenesis on groundwater chemistry. Inverse reaction path modeling using NETPATH indicates the predominant geochemical reactions controlling the chemical evolution of groundwater in the aquifer are incongruent dissolution of dolomite, ion exchange, methanogenesis, and oxidation of sedimentary organic matter. Modeling of groundwater 14C ages using NETPATH indicates that a significant part of groundwater in the Alliston aquifer is less than 13,000 years old; however, older groundwater in the range of 15,000–23,000 years is also present in the aquifer. This paper demonstrates that 14C ages calculated using NETPATH, incorporating the effects of methanogenesis on the carbon pools, provide reasonable groundwater ages that were not possible by other isotopic methods.
Predicting Velocity Frequency Distributions in Stream Reaches
Authors: Lamouroux Nicolas , Souchon Yves , Herouin Eric
Published: February 2004

The quantification of management impacts on fish populations requires a reliable estimation of the local hydraulic habitat variability. In the case of complex natural flows, deterministic hydraulic models are expensive and not adapted to the description of local velocities. Statistical descriptions of the velocity distribution as a function of easily obtained input variables are therefore an attractive alternative. Existing velocity data on several French stream segments with intermediate‐to large‐scale roughness were analyzed statistically to define a shape parameter of the point velocity frequency distributions. Dimensional analysis was used to model this shape parameter, and thereby the velocity distributions, as a function of simple average descriptors of stream reaches (discharge, mean roughness, mean depth, and mean width). Such predictive models of the physical habitat availability for fish in the probability domain can provide stream managers with cost‐effective decision tools.
Transient Hydrogeological Controls on the Chemistry of a Seepage Lake
Authors: Krabbenhoft David P. , Webster Katherine E.
Published: February 2004

A solute mass balance method was used to estimate groundwater inflow and outflow rates for Nevins Lake, Michigan, a seepage lake in the upper peninsula that historically has shown extremely variable water chemistry compared with most other seepage lakes. A 4‐year study (1989–1992) of the hydrology and geochemistry of Nevins Lake and its contiguous groundwater system revealed that changes in the mass of dissolved solutes are the result of annual hydraulic gradient reversals. A pronounced acidification of Nevins Lake from 1986 to 1988 was likely caused by drought‐induced diminished groundwater inflow rates. In this study, dissolved calcium (the major cation in water of Nevins Lake, groundwater, and precipitation) was used for estimating mass flow rates. During the 1989–1992 period, Nevins Lake showed a reproducible annual cycle in calcium mass. Immediately following spring snowmelt and the resulting hydraulic gradient reversal, the mass of dissolved calcium in the lake increases rapidly, and then it decreases steadily throughout the summer and early fall, at which time the lake becomes hydraulically mounded and receives no groundwater inflow. Groundwater flow rates estimated by the solute mass balance method are sensitive to assumed solute concentrations in discharging groundwater. Pore water samples from the lake bed are shown to be more representative of water discharging to the lake than are samples from piezometers near the lake shore, but spatial and temporal variability in pore water chemistry must be considered. Stable isotope analyses (18O and 2H) of lake water, groundwater, and pore water samples show that water discharging to Nevins Lake in the spring is entirely recycled lake water, and no groundwater derived from terrestrial recharge reaches the lake. The conceptual model formulated during this study linking lake chemistry and the contiguous groundwater system and general groundwater flow patterns surrounding highly transient lake systems are likely transferable to other similar systems.
Modeling Transient Water and Solute Transport in a Biporous Soil
Authors: Zurmühl Torsten , Durner Wolfgang
Published: February 2004

In this study we investigate numerical simulations of one‐dimensional water flow and solute transport in a soil with a nonuniform pore‐size distribution. Water transport was modeled by treating the soil as one domain by applying Richards equation, while using alternatively a unimodal and a bimodal model for the hydraulic properties. The retention curves were fitted to a set of measured data; the relative conductivity functions were estimated by Mualem's (1976) model. Contrary to the unimodal case, the bimodal conductivity curve shows a steep decrease in water content θ near saturation. Simulated water regimes under transient boundary conditions differed strongly for the two cases. The use of the bimodal functions yielded a preferential flow characteristic which was not obtained using unimodal functions. For both hydraulic regimes we modeled solute transport comparing four different variants of the convection‐dispersion equation. For the classical one‐region model we found that the breakthrough curve of an ideal tracer was not affected by the dynamics of the water flow. For the two‐region approach, where the water‐filled pore domain is divided into a mobile region θm and an immobile region θim, three different conceptual treatments of θm under transient conditions were investigated. For the case where θim was kept constant, the different hydraulic regimes again caused only minor differences in solute transport. The same was true for the alternative case where the ratio θm/θ was kept constant. However, for the third case, where θm was treated as a dynamic variable which changes with the actual water content in a way that depends on the shape of the hydraulic conductivity function, the transport simulation based on the bimodal hydraulic model reflected enhanced preferential transport at high‐infiltration rates.
Non‐Fickian Ionic Diffusion Across High‐Concentration Gradients
Authors: Carey Anne E. , Wheatcraft Stephen W. , Glass Robert J. , O'Rourke John P.
Published: February 2004

A non‐Fickian physico‐chemical model for electrolyte transport in high‐ionic strength systems is developed and tested with laboratory experiments with copper sulfate as an example electrolyte. The new model is based on irreversible thermodynamics and uses measured mutual diffusion coefficients, varying with concentration. Compared to a traditional Fickian model, the new model predicts less diffusion and asymmetric diffusion profiles. Laboratory experiments show diffusion rates even smaller than those predicted by our non‐Fickian model, suggesting that there are additional, unaccounted for processes retarding diffusion. Ionic diffusion rates may be a limiting factor in transporting salts whose effect on fluid density will in turn significantly affect the flow regime. These findings have important implications for understanding and predicting solute transport in geologic settings where dense, saline solutions occur.
Noninvasive Soil Water Content Measurement Using Electromagnetic Induction
Authors: Sheets Keith R. , Hendrickx Jan M. H.
Published: February 2004

The feasibility of soil water content measurement using electromagnetic induction was investigated in an arid region of southern New Mexico. Soil water measurements were taken monthly with a neutron probe at 65 equally spaced stations along a 1950‐m transect. At the same time, noninvasive electrical conductivity measurements of the soil were taken with a Geonics EM‐31 ground conductivity meter. Using 16 months of measurements, we found a linear relationship exists between bulk soil electrical conductivity and total soil water content in the top 1.5 m of the profile. A simple linear regression model was developed to describe the relationship between soil water content and bulk soil electrical conductivity. The spatial and temporal accuracy of the regression model is addressed as well as the total number of neutron access tubes needed to accurately calibrate the model. By comparison with the neutron scattering method the electromagnetic induction method is quite accurate for the prediction of water content changes over time. The speed and ease of use combined with the accuracy of the measurements make the ground conductivity meter a valuable tool for rapid, noninvasive soil water measurements.
The Great Salt Lake: A Barometer of Low‐Frequency Climatic Variability
Authors: Lall Upmanu , Mann Michael
Published: February 2004

Low‐frequency (interannual or longer period) climatic variability is of interest because of its significance for the understanding and prediction of protracted climatic anomalies. Closed basin lakes are sensitive to long‐term climatic fluctuations and integrate out high‐frequency variability. It is thus natural to examine the records of such lakes to better understand long‐term climate dynamics. Here we use singular spectral analysis and multitaper spectral analysis to analyze the time series of Great Salt Lake (GSL) monthly volume change from 1848 to 1992 and monthly precipitation, temperature, and streamflow for nearby stations with 74 or more years of data. This analysis reveals high fractional variance in 15–18, 10–12, 3–7 and 2‐year frequency bands, which seems to be consistent across time series. The putative decadal and interdecadal signals appear to be related to large‐scale climate signals. The interannual signals are consistent with El Nino Southern Oscillation and quasi‐biennial variability. Prospects for improved prediction of the GSL volume and of protracted wet/dry periods in the western United States are discussed.
Parametric Studies on the Advancing Interface in Coastal Aquifers Due to Linear Variation of the Freshwater Level
Authors: Mahesha A.
Published: February 2004

The transient motion of the freshwater‐seawater interface in coastal aquifers due to a constant lowering of freshwater levels at inland locations is simulated using a sharp‐interface, finite‐element model. The performance of the numerical model is compared with a Hele‐Shaw model. The numerical model is then used to perform parametric studies on an advancing interface that considers hypothetical cases over a wider range of possible conditions. The advancement of the interface was found to be dependent on the rate, location, and period of freshwater level variations. A seaward moving freshwater divide is formed by the lowering of the freshwater level. When the advancing interface crosses the seaward moving divide, aggressive intrusion is likely because of the reversed freshwater gradient existing landward of the divide. A safe zone for the freshwater extraction can be determined based on the movement of the interface and the freshwater divide.
Saline groundwater in Mono Basin, California: 1. Distribution
Authors: Rogers David B. , Dreiss Shirley J.
Published: February 2004

Mono Lake, California is a perennial, closed‐basin saline lake. Up to 2 km of sediments have accumulated below the lake, and a well log shows that saline groundwater of concentration > 18,000 ppm extends to the bottom of the basin fill. We investigated the groundwater system with the variable‐density flow and solute transport code SUTRA to determine if the basin's recharge and inferred groundwater salinity are consistent with observational data. Steady state model predictions of the position and shape of the interface separating saline from fresh groundwater are consistent with the salinity profile derived from the spontaneous‐potential (SP) log of a geothermal well on the lake's shoreline. We also inferred the basin‐wide saline groundwater distribution and concentration from experiments with a steady state model of the entire basin groundwater system. Hydrologic variations around the lake determine the position of the saline‐fresh groundwater interface: Higher recharge rates characteristic of the Sierra Nevada shoreline push the interface far beneath the lake. The interface probably lies below the shoreline around much of the rest of the lake. On the low‐recharge northeastern shoreline the interface top may lie outside the lake edge. This positions the saline groundwater discharge zone just below the playa surface and contributes to development of salt flats on the recently exposed former lake bed. Simulations suggest that the basin fill permeability may not have significant anisotropy, possibly owing to extensive faulting which increases vertical permeability. For an anisotropic basin fill, the resultant increased channeling of recharge beneath the lake readily overcomes the opposing force of the saline groundwater density, and it is flushed out of the basin sediments. A simple permeability representation of the basin lithology, with low permeability below the lake and an anisotropic transition to higher permeability outside the lake, reasonably represents the well and spring water salinity observations.
A validation of a Dupuit‐Forchheimer Formulation for flow with variable density
Authors: Strack Otto D. L. , Bakker Mark
Published: February 2004

Comparisons are made between Dupuit‐Forchheimer solutions and solutions to the differential equation governing flow with variable density. The solutions apply to flow in the vertical plane in aquifers confined by two horizontal impervious boundaries. The comparisons serve as a validation of the Dupuit‐Forchheimer formulation presented by Strack [this issue].
A Dupuit‐Forchheimer Model for three‐dimensional flow with variable density
Authors: Strack Otto D. L.
Published: February 2004

A mathematical framework is presented for three‐dimensional shallow groundwater flow with variable density. The formulation is based on the Dupuit‐Forchheimer assumption. The problem is posed in terms of a discharge potential that satisfies the same differential equation as the discharge potentials for single‐density flow. The freshwater head, defined as the pressure divided by the unit weight of fresh water plus the elevation head, may be computed as a function of position in three dimensions from the potential and a known density distribution. The density distribution may be approximated using the multiquadrics interpolator. It is explained how the change in density may be computed as a function of time. Discontinuities in the aquifer properties cause a jump in the normal component of flow for flow fields computed with the Dupuit‐Forchheimer approximation. An interpretation of this jump is given by comparison with an exact formulation, which makes it possible to obtain the approximate streamlines as they cross discontinuities.
Recovering the History of a Groundwater Contaminant Plume: Method of Quasi‐Reversibility
Authors: Skaggs Todd H. , Kabala Z. J.
Published: February 2004

The method of quasi‐reversibility (QR) (Lattes and Lions, 1969) has been used previously to solve the diffusion equation with reversed time. We develop a quasi‐reversible solution to a convection‐dispersion equation by solving the QR diffusion operator in a moving coordinate system. The solution procedure is applied to the problem of recovering the history of a groundwater contaminant plume from observations of its present conditions. This approach to the plume history problem is potentially superior to the Tikhonov regularization approach used by Skaggs and Kabala (1994) because it is easier to implement and readily allows for space‐ and time‐dependent transport parameters. However, our results for a few example problems suggest that the QR procedure is less accurate than the regularization technique. Thus the easy implementation and improved generality of the QR procedure come at the expense of accuracy; this trade‐off will have to be weighed if the QR technique is to be used.
A geomorphologic and hydrologic evaluation of an extraordinary flood discharge estimate: Bronco Creek, Arizona
Authors: House P. Kyle , Pearthree Philip A.
Published: February 2004

The Bronco Creek, Arizona flood of August 19, 1971, was an extraordinary and rare flash flood. The published peak discharge estimate of 2080 m3 s−1 makes it virtually the world's largest known rainfall‐generated flood to come from a 50‐km2 basin. Previous workers have suggested that the peak discharge was overestimated based on its unlikely hydrological and hydraulic implications. In this study we reevaluate the Bronco Creek flood discharge by modeling peak discharges using relict high‐water marks in bedrock canyon reaches near the mouths of the three major subbasins of the watershed. The new estimated peak discharge of 750 to 850 m3 s−1 is based on summing the subbasin estimates and correcting for omitted drainage area. Qualitative and quantitative analyses of site‐specific and regional hydrological, meteorological, and geomorphological information support a lower peak discharge. We assessed preflood and postflood channel characteristics at the site of the original estimate using historical aerial photographs. Our analysis indicates that much of the discrepancy between the estimates may be explained by significant morphologic changes in the channel caused by the flood. The original estimate was made in a wide, high‐gradient alluvial channel where the flood changed the channel pattern from braided with vegetated bars to straight, wide, and devoid of vegetation. It is also likely that net vertical scour occurred in the channel. Although our new estimate is much lower than the original estimate, it is consistent with the dominant trend in regional flood magnitude‐drainage area relationships. By integrating hydraulic modeling of peak discharges in stable channel reaches with assessment of ancillary hydrological, meteorological, and geomorphological information, this study presents a viable approach to assessing the accuracy of extreme flood estimates in general. It also highlights potential uncertainties in estimating extreme flood discharges in steep, alluvial channels.
A three‐Region Analytical Model of Solute Leaching in a Soil with a Water‐Repellent Top Layer
Authors: de Rooij Gerrit H.
Published: February 2004

When water enters a water‐repellent topsoil, fingers develop and a large part of the soil is bypassed. Therefore fingering is expected to accelerate solute leaching to the groundwater. In soils with a groundwater‐affected wettable sublayer, fingering yields a flow pattern consisting of three regions. In the top few centimeters, water flow converges toward the finger top. In the finger, water moves vertically downward. In the wettable subsoil the flow diverges due to matric forces. Analytical steady state solutions are presented for each of these regions. The resulting model provides the breakthrough curve of a pulse of an inert solute and reveals the influence of each region. Calculations showed that the enhancement of leaching caused by fingers could be largely undone by a thick (0.75 m) wettable subsoil. A very thin (0.05 m) wettable subsoil had a much smaller effect. This illustrates the need for accurate field estimates of finger depth.
Chemical evolution of shallow groundwater along the northeast shore of Mono Lake, California
Authors: Connell Tracy L. , Dreiss Shirley J.
Published: February 2004

We attempted to quantitatively discriminate between hypothesized sources and geochemical processes responsible for the chemical evolution of shallow groundwater along the northeast shore of Mono Lake, an alkaline saline lake located in a hydrologically closed basin in east central California. Shallow groundwater samples from 17 sites perpendicular and 11 sites parallel to the lakeshore were analyzed for major ions. The shallow groundwater contains remnant solutes from higher lake stands, which are transported toward the lake by lateral flow and surface runoff. The flow system appears to be segregated into two different regions: a concentrated, highly saline groundwater underlying much of the northeast shore and pockets of more localized lower‐salinity groundwater. The saturation state of the groundwater with respect to certain minerals was determined, and simulations for both evaporative concentration of inflow and mixing of lake water with inflow coupled with mineral precipitation were performed. Solute trends in the shallow groundwater result primarily from the degree of mixing with historical lake water; however, evaporative concentration and redissolution cycles along with various chemical fractionation mechanisms including Ca, Mg, and Na carbonate precipitation, sulfate reduction, ion exchange, and potentially Mg silicate formation are also important controls.
Effective Hydraulic Conductivity of Bounded, Strongly Heterogeneous Porous Media
Authors: Paleologos Evangelos K. , Neuman Shlomo P. , Tartakovsky Daniel
Published: February 2004

We develop analytical expressions for the effective hydraulic conductivity Ke of a three‐dimensional, heterogeneous porous medium in the presence of randomly prescribed head and flux boundaries. The log hydraulic conductivity Y forms a Gaussian, statistically homogeneous and anisotropic random field with an exponential autocovariance. By effective hydraulic conductivity of a finite volume in such a field, we mean the ensemble mean (expected value) of all random equivalent conductivities that one could associate with a similar volume under uniform mean flow. We start by deriving a first‐order approximation of an exact expression developed in 1993 by Neuman and Orr. We then generalize this to strongly heterogeneous media by invoking the Landau‐Lifshitz conjecture. Upon evaluating our expressions, we find that Ke decreases rapidly from the arithmetic mean KA toward an asymptotic value as distance between the prescribed head boundaries increases from zero to about eight integral scales of Y. The more heterogeneous is the medium, the larger is Ke relative to its asymptote at any given separation distance. Our theory compares well with published results of spatially power‐averaged expressions and with a first‐order expression developed intuitively by Kitanidis in 1990.
An evaluation of nonlinearity in spatial second moments of ensemble mean concentration in heterogeneous porous media
Authors: Zhang You‐Kuan , Chi John A.
Published: February 2004

The integrodifferential equation for the spatial second moments X of the ensemble mean concentration in a heterogeneous aquifer is nonlinear due to statistical dependence of the particle displacement on X. This nonlinear equation is either linearized or quasi‐linearized in previous studies to derive the linear and quasi‐linear theories of time‐dependent macrodispersion in aquifers. In this study a fully nonlinear analysis is carried out by solving the integrodifferential equation for X numerically and iteratively. The effects of the variance of log hydraulic conductivities σY2, the local Péclet number Pe, and the anisotropic ratio e are then investigated. Results show that in both statistically isotropic and anisotropic media, as compared with the linear theories, the effect of nonlinearity in X is to reduce the spatial longitudinal variance, X11, and enhance the transverse spreading of a solute plume except in isotropic media with σY2 ≤ 1, where the linear theories may underestimate the longitudinal spreading of a solute. It is also shown that the effect of local dispersion on X11 can be neglected when Pe ≥ 10 but on the transverse macrodispersion, this effect is significant for Pe as large as 100. Nevertheless, the effect of Pe on macrodispersion is secondary as compared with the effect of nonlinearity in X. Application of the nonlinear results shows good fits to the observed spatial variances of tracer concentration in the Borden experiment and excellent agreement with the simulated variances from recent Monte Carlo simulations.
Effective stress principle for saturated fractured porous media
Authors: Tuncay Kagan , Corapcioglu M. Yavuz
Published: February 2004

An effective stress principle for saturated fractured porous media is proposed based on the double‐porosity representation. Both the solid grains and the fractured porous medium are assumed to be linearly elastic materials. The derivation employs volume averaging technique to obtain macroscopic scale expressions. Two parameters, the bulk modulus of the fractured medium and bulk modulus of the porous matrix, are introduced in the formulation. The final expression reduces to the one obtained by Biot and Willis [1957], Skempton [1960], Nur and Byeerle [1971], and Verruijt [1984] when the volume fraction of the fractures vanishes, that is, for a nonfractured porous medium.
Development of the Fokker‐Planck Equation and its solutions for modeling transport of conservative and reactive solutes in physically heterogeneous media
Authors: Su Ninghu
Published: February 2004

When a scale‐dependent fractal dispersivity is introduced in the convective‐dispersive equation of transport in subsurface flow, the Fokker‐Planck equation (FPE), also known as the second diffusion equation, is derived. Similarity solutions of the one‐dimensional FPE, subject to a Dirac delta function input, are also presented. The similarity solution is shown to function as a kernel in the convolution integral to yield an output on a real timescale. The input function is derived by a procedure known as the inverse problem with the aid of Laplace transform. The FPE and its solutions contain a fractal dimensionDand cutoff limit ϵ, two shape parameters β and γ in the FPE, and other parameters that appear in Darcy's law. A two‐dimensional FPE and its solutions have been presented elsewhere. It is reasoned that the scale‐dependent dispersion in unsaturated flow is also an issue for investigation.
Head and Velocity Covariances Under Quasi‐Steady State flow and their Effects on Advective Transport
Authors: Zhang Dongxiao , Neuman Shlomo P.
Published: February 2004

Most stochastic models of solute transport assume flow to be at steady state. However, even locally uniform gradients tend to show seasonal fluctuations in magnitude and direction. Such transients affect the prediction of flow and plume migration and spread. The question is how and to what extent. We address this question by developing low‐order approximations for autocovariances and cross covariances of velocity, head, and log hydraulic conductivity under quasi‐steady state flow, then using a first‐order Lagrangian approach to examine their effect on advective transport. Our results show that whereas periodic temporal fluctuations in the magnitude of the mean velocity may either enhance or reduce dispersion, similar fluctuations in its direction always cause longitudinal dispersion to decrease and transverse dispersion to increase.
Multiphase Approach to the Numerical Solution of a Sharp Interface Saltwater Intrusion Problem
Authors: Huyakorn P. S. , Wu Y. S. , Park N. S.
Published: February 2004

A sharp interface numerical model is developed to simulate saltwater intrusion in multilayered coastal aquifer systems. The model takes into account the flow dynamics of salt water and fresh water assuming a sharp interface between the two liquids. In contrast to previous two‐fluid flow models which were formulated using the hydraulic heads of fresh water and salt water as the dependent variables, the present model employs a mixed formulation having one fluid potential and a pseudosaturation as the dual dependent variables. Conversion of the usual sharp interface flow equations for each aquifer to an equivalent set of two‐phase flow equations leads to the definitions of pseudosaturation, capillary pressure, and constitutive relations. The desired governing equations are then obtained by connecting neighboring aquifers via vertical leakage. The proposed formulation is based on a Galerkin finite element discretization. The numerical solution incorporates upstream weighting and nonlinear algorithms with several enhanced features, including rigorous treatment of aquitard leakage and well conditions, and a robust Newton‐Raphson procedure with automatic time stepping. The present sharp interface numerical model is verified using three test problems involving unconfined, confined, and multilayered aquifer systems and consideration of steady state and transient flow situations. Comparisons of numerical and analytical solutions indicate that the numerical schemes are efficient and accurate in tracking the location, lateral movement, and upconing of the freshwater‐saltwater interface.
A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems
Authors: Gambolati Giuseppe , Teatini Pietro
Published: February 2004

A new quasi three‐dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss‐Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.
An Integrated Model for Optimal Reservoir Operation for Irrigation of Multiple Crops
Authors: Vedula S. , Kumar D. Nagesh
Published: February 2004

An integrated model is developed, based on seasonal inputs of reservoir inflow and rainfall in the irrigated area, to determine the optimal reservoir release policies and irrigation allocations to multiple crops. The model is conceptually made up of two modules. Module 1 is an intraseasonal allocation model to maximize the sum of relative yields of all crops, for a given state of the system, using linear programming (LP). The module takes into account reservoir storage continuity, soil moisture balance, and crop root growth with time. Module 2 is a seasonal allocation model to derive the steady state reservoir operating policy using stochastic dynamic programming (SDP). Reservoir storage, seasonal inflow, and seasonal rainfall are the state variables in the SDP. The objective in SDP is to maximize the expected sum of relative yields of all crops in a year. The results of module 1 and the transition probabilities of seasonal inflow and rainfall form the input for module 2. The use of seasonal inputs coupled with the LP‐SDP solution strategy in the present formulation facilitates in relaxing the limitations of an earlier study, while affecting additional improvements. The model is applied to an existing reservoir in Karnataka State, India.
Exact Solution for Contaminant Transport with Kinetic Langmuir Sorption
Authors: Manoranjan Valipuram S. , Stauffer Thomas B.
Published: February 2004

We study a contaminant transport model with Langmuir sorption under nonequilibrium conditions and show that the aqueous phase concentration profile can be obtained exactly in the form of a traveling wave front. The methodology of finding the exact solution is outlined, and an illustrative example is presented.
An Effect of Seiche on Groundwater Seepage Rate into Lake Biwa, Japan
Authors: Taniguchi Makoto , Fukuo Yoshiaki
Published: February 2004

Numerical analyses of seiche and continuous measurements of water level and groundwater seepage rates into Lake Biwa, Japan, were made to evaluate interactions between surface and subsurface waters. An automatic seepage meter was used to obtain continuous groundwater seepage rates. Analyses of the fluctuations of seepage rate and water level in the lake were done using the fast Fourier transform method. The finite element method was used for analysis of the seiche in the lake. Dominant periods of fluctuations of the groundwater seepage rate into Lake Biwa agree well with those of fluctuations of water levels in the lake. The dominant fluctuations of the groundwater seepage rate are caused by the seiche in Lake Biwa.
Uncertainty of Estimates of Monthly Areal Rainfall for Temporally Sparse Remote Observations
Authors: Steiner Matthias
Published: February 2004

The uncertainty of monthly areal mean rainfall estimates, caused by a finite sampling time resolution, is investigated making extensive use of data collected by tipping‐bucket rain gauge networks at Darwin, Australia, and Melbourne, Florida. Using a subsampling methodology, the uncertainty is studied for complete area‐covering observations occurring at regular time intervals. The analysis indicates that the sampling uncertainty is constrained by the rainfall depth, the sampling frequency, and the domain size. Taking into account that a rain gauge network does not truly reflect the sampling uncertainty one would encounter using complete area‐covering observations, such as provided by radar or satellite, a rule of thumb is established for estimating the average sampling uncertainty as a function of the above factors. The estimated root mean square error E, expressed as a percentage of the monthly rainfall amount Rs, is found to be inversely proportional to the rain amount and the domain size A but proportional to the sampling time interval δT and can be approximated by E = 8.5 × 103 × Rs−0.6A−0.5ΔT. Within this framework the various results reported in the literature from studies based on using other data and different spatial scales are found to be consistent with our results and among each other. The scaling of our results to timescales other than a month is indicated.
Nonlinear Dynamics of the Great Salt Lake: Nonparametric Short‐Term Forecasting
Authors: Lall Upmanu , Sangoyomi Taiye , Abarbanel Henry D. I.
Published: February 2004

Variations in the volume of closed basin lakes, such as the Great Salt Lake, are often driven by large‐scale, persistent climatic fluctuations. There is growing evidence of structure in the recurrence patterns of such fluctuations, their relation to physical mechanisms, and their manifestation in hydrologic time series. Classical, linear methods for time series analysis and forecasting may be inappropriate for modeling such processes. Here we consider the time series of interest as the outcome of a finite‐dimensional, nonlinear dynamical system and use nonparametric regression to recover the nonlinear, autoregressive “skeleton” of the underlying dynamics. The resulting model can be used for short‐term forecasting, as well as for exploring other properties of the system. The utility of the approach is demonstrated with synthetic periodic data and data from low dimensional, chaotic, dynamical systems. An application to the 1847–1992 Great Salt Lake biweekly volume time series is also reported.
Stochastic Optimization of Multi Reservoir Systems Using a Heuristic Algorithm: Case Study From India
Authors: Ponnambalam Kumaraswamy , Adams Barry J.
Published: February 2004

A general algorithm developed for stochastic optimization of multireservoir systems is used to determine optimal operational policies for five of the major reservoirs of the Parambikulam‐Aliyar irrigation and power project in India. A closed‐loop suboptimal policy was determined for the stochastic inflow, deterministic demand problem, subject to storage and cumulative release constraints imposed by an interstate water‐sharing agreement. The closed‐loop policies were further used to determine optimal rule curves for the major reservoirs. A comparison of the simulated optimal policies and the past performance of the project demonstrates the utility of the derived policies determined with the proposed algorithm.
Higher‐Order Effects on Flow and Transport in Randomly Heterogeneous Porous Media
Authors: Hsu Kuo‐Chin , Zhang Dongxiao , Neuman Shlomo P.
Published: February 2004

A higher‐order theory is presented for steady state, mean uniform saturated flow and nonreactive solute transport in a random, statistically homogeneous natural log hydraulic conductivity field Y. General integral expressions are derived for the spatial covariance of fluid velocity to second order in the variance σ2 of Y in two and three dimensions. Integrals involving first‐order (in σ) fluctuations in hydraulic head are evaluated analytically for a statistically isotropic two‐dimensional Y field with an exponential autocovariance. Integrals involving higher‐order head fluctuations are evaluated numerically for this same field. Complete second‐order results are presented graphically for σ2=1 and σ2=2. They show that terms involving higher‐order head fluctuations are as important as those involving lower‐order ones. The velocity variance is larger when approximated to second than to first order in σ2. Discrepancies between second‐ and first‐order approximations of the velocity autocovariance diminish rapidly with separation distance and are very small beyond two integral scales. Transport requires approximation at two levels: the flow level at which velocity statistics are related to those of Y, and the advection level at which macrodispersivities are related to velocity fluctuations. Our results show that a second‐order flow correction affects transport to a greater extent than does a second‐order correction to advection. Asymptotically, the second‐order transverse macrodispersivity tends to zero as does its first‐order counterpart. An approximation of advection alone based on Corrsin's conjecture, coupled with either a first‐ or a second‐order flow approximation, leads to a transverse macrodispersivity which is significantly larger than that obtained by standard perturbation and tends to a nonzero asymptote. Published Monte Carlo results yield macrodispersivities that lie significantly below those predicted by first‐ and second‐order theories. Considering that Monte Carlo simulations often suffer from sampling and computational errors, that standard perturbation approximations are theoretically valid only for σ2 < 1, and that Corrsin's conjecture represents the leading term in a renormalization group perturbation which contains contributions from an infinite number of high‐order terms, we find it difficult to tell which of these approximations is closest to representing transport in strongly heterogeneous media with σ2 ≥ 1.