bluuebunny/crossref_metadata_2025 huggingface dataset:
Secondary Water Recovery by Air Injection: 2. The Implicit Simultaneous Solution Method
Authors: Moridis George J. , Reddell Donald L.
Published: February 2004

The finite difference equations of air and water flow in air‐driven secondary water recovery define a multidimensional strongly nonlinear system with sharp pressure and saturation fronts, large differences in the magnitude of flow coefficients, physical and mathematical discontinuities, sudden flow reversals, and high injection rates. The implicit simultaneous solution (SS) method, which solves simultaneously for the unknown pressures and saturation changes, was the sole method capable of handling these problems. Instabilities were alleviated by introducing implicit flow coefficients, implicit capillary pressures, and implicit accumulation terms. The treatment of hysteresis was based on petroleum engineering models. The concept of two separate air‐water interfaces was introduced: (1) the “zero air saturatution interface,” which indicates the physical boundary of air discontinuity, and (2) the “zero capillary pressure interface,” defined as the upper boundary of a zero capillary pressure zone. A method for the numerical tracking of the two interfaces, necessary for the evaluation of the effectiveness of secondary water recovery, was also developed.
Stable Channel Cross Sections of Straight Sand Rivers
Authors: Ikeda Syunsuke , Izumi Norihiro
Published: February 2004

A mathematical model is presented for defining the size and cross section of self‐formed straight sand rivers in which sediments are actively transported everywhere as bedload and suspended load. A balance of lateral bedload and lateral diffusive transport of suspended sediment is imposed to maintain a stable channel cross section. Singular perturbation technique is employed to solve the sediment balance equation, from which a relation for stable depth is derived. A resistance formula for dune‐covered beds is used to obtain stable width. It is revealed theoretically that the channel center depth relative to sediment size is approximately proportional to S−0.8 for natural sand rivers, in which S is longitudinal slope. The analysis is found to agree reasonably well with available laboratory and field data.
A Semidiscrete Model for Water and Solute Movement in Tile‐Drained Soils: 2. Field Validation and Applications
Authors: Kamra S. K. , Singh Sita Ram , Rao K. V. G. K. , van Genuchten M. Th.
Published: February 2004

An exact‐in‐time two‐dimensional finite element model for simulating convective‐dispersive solute transport in a tile‐drained field is validated against observed data from a subsurface drainage experiment. The model is capable of predicting the long‐term effects of different irrigation and drainage practices on the salt distribution in an artificially drained soil‐aquifer system. The model was used to predict transient changes in the salinity of the soil, the shallow ground water table, and the drain effluent. Results are also presented on the effects of imposing alternative drain spacing‐depth combinations, initial groundwater salinities, solute distribution coefficients, and different types of layering of the aquifer, on the computed salinity distributions in the unsaturated zone, the groundwater, and the drain effluent.
Optimal Estimation and Scheduling in Aquifer Remediation With Incomplete Information
Authors: Lee Sang‐Il , Kitanidis Peter K.
Published: February 2004

This work presents new results on a method for optimal aquifer remediation when available information is limited. The methodology combines computer simulation models of solute transport and fate, descriptions of spatial variability, probabilistic analysis of uncertainty, and optimization. The objective is to find the most cost‐effective management policy for aquifer decontamination. Advantages of the method include the following: (1) it utilizes measurements in real time, (2) it simultaneously estimates aquifer parameters and makes decisions for remediation, and (3) it devises a more cost‐effective and reliable aquifer remediation strategy than deterministic optimization, specifically, the method known as deterministic feedback control. Subject to constraints and for a given reliability of meeting water quality standards, this method minimizes the expected value of the cost in the remaining periods. That is, because of incomplete information about the site the cost of a decontamination strategy is not known a priori. The objective is to minimize the cost weighted by the probability that it will be incurred. The optimal aquifer management policy is expressed as the sum of a deterministic and a stochastic control term. The former is obtained by solving a deterministic optimization problem through constrained differential dynamic programming, and the latter is obtained by a perturbation approximation to the stochastic optimal control problem. Extended Kalman filtering is incorporated into the optimization method to improve the accuracy of the estimated state and parametric variables using available measurements. A hypothetical contamination case with two‐dimensional unsteady flow and transport for a persistent solute is studied to illustrate the applicability of the methodology. The effectiveness in terms of cost and reliability of the proposed method is studied under various conditions and then compared with the cost and reliability of the deterministic feedback control method through Monte Carlo simulations. The proposed methodology is shown to be superior to deterministic feedback control.
Groundwater Flow and Solute Movement to Drain Laterals, Western San Joaquin Valley, California: 1. Geochemical Assessment
Authors: Deverel S. J. , Fio John L.
Published: February 2004

A study was undertaken to quantitatively evaluate the hydrologic processes affecting the chemical and isotopic composition of drain lateral water in a drained agricultural field in the western San Joaquin Valley, California. The results elucidate the process of mixing of deep and shallow groundwater (below and within 6 m from land surface) entering the drain laterals. The deep groundwater was subject to evapoconcentration prior to drainage system installation and has been displaced downward (to depths greater than 6 m) in the groundwater system. The proportions of deep and shallow groundwater entering the drain laterals was calculated from the end‐member oxygen 18 compositions determined in groundwater samples. The percentage of total drain lateral flow which is deep groundwater flow is about 30% for the shallow drain lateral (1.8 m below land surface) (drain lateral 1)) and 60% for the deep drain lateral (2.7 m below land surface (drain lateral 2)). During irrigation, the percentages of deep groundwater flow decrease to 0 and 30% for the shallow and deep drain laterals, respectively. Selenium concentrations in drain lateral waters decrease during irrigation but selenium loads increase. Total estimated annual loads were 1.1 and 5.4 kg of selenium for drain laterals 1 and 2, respectively. Substantial percentages of the annual load occurred during 8 days of irrigation, 23 and 9% for drain laterals 1 and 2, respectively.
Groundwater Flow and Solute Movement to Drain Laterals, Western San Joaquin Valley, California: 2. Quantitative Hydrologic Assessment
Authors: Fio John L. , Deverel S. J.
Published: February 2004

Groundwater flow modeling was used to quantitatively assess the hydrologic processes affecting ground water and solute movement to drain laterals. Modeling results were used to calculate the depth distribution of groundwater flowing into drain laterals at 1.8 m (drain lateral 1) and 2.7 m (drain lateral 2) below land surface. The simulations indicated that under nonirrigated conditions about 89% of the flow in drain lateral 2 was from groundwater originating from depths greater than 6 m below land surface. The deep groundwater has higher selenium concentrations than shallow groundwater. Simulation of irrigated conditions indicates that as recharge (deep percolation) increases, the proportional contribution of deep groundwater to drain lateral flow decreases. Groundwater flow paths and travel times estimated from the simulation results indicate that groundwater containing high concentrations of selenium (greater than 780 μg L−1) probably will continue to enter drain lateral 2 for decades.
Infiltration of a Liquid Front in an Unsaturated, Fractured Porous Medium
Authors: Nitao John J. , Buscheck Thomas A.
Published: February 2004

We consider liquid infiltrating by gravity flow into a system of parallel, regularly spaced fractures in an unsaturated porous medium. The position of the fracture liquid front as a function of time, under some simplifying assumptions, is shown to obey a nonlinear integrodifferential equation. Approximate analytic solutions are developed, showing that the movement of the liquid front exhibits three major flow periods: (1) at early time, the frontal position is determined by the fracture inlet boundary condition and the gravity‐driven flow behavior of the fracture with negligible influence by the matrix; (2) at intermediate time, matrix imbibition retards the frontal advance against the pull of gravity; (3) at late time, the matrix approaches saturation and the frontal velocity approaches a limiting value. A two‐dimensional numerical model is used to confirm the approximate solutions. Implications of the model for nuclear waste storage are discussed. The analysis is applicable not only to fractured rock but also to lateral infiltration into coarse‐grained sediments lying between layers of fine‐grained soil.
A Hidden Markov Model for Space‐Time Precipitation
Authors: Zucchini Walter , Guttorp Peter
Published: February 2004

A family of multivariate models for the occurrence/nonoccurrence of precipitation at N sites is constructed by assuming a different joint probability of events at the sites for each of a number of unobservable climate states. The climate process is assumed to follow a Markov chain. Simple formulae for first‐ and second‐order parameter functions are derived, and used to find starting values for a numerical maximization of the likelihood. The method is illustrated by applying it to data for one site in Washington and to data for a network in the Great Plains.
Exact Solutions for Water Infiltration With an Arbitrary Surface Flux or Nonlinear Solute Adsorption
Authors: Barry D. A. , Sander G. C.
Published: February 2004

Several authors have now used the Bäcklund transformation to linearize Richards' equation and so obtain analytical solutions for infiltration and redistribution processes for the linearizable class of diffusivities and hydraulic conductivities. After transformation a convection‐diffusion equation is obtained. To date, all the analytical results making use of the Bäcklund transform have been based on a specified, constant flux that is assumed to exist at the surface boundary. We generalize the previous work by removing this restriction and obtain a general solution for an arbitrary temporal variation in the surface flux. The solution contains a function that is specified by a Volterra integral equation. In practice, the Volterra equation must be evaluated numerically. This task is accomplished using a relatively straightforward algorithm. The analytical results for infiltration can be applied to the process of solute transport subject to a nonlinear adsorption isotherm since these two phenomena are equivalent under another mapping. Our new analytical results, therefore, also apply to this class of solute transport processes. The general form of the adsorption isotherm for which exact results can be obtained is derived. This isotherm appears capable of representing a relatively large family of physically relevant cases, although this topic remains open for future investigation.
Optimal Groundwater Management: 1. Simulated Annealing
Authors: Dougherty David E. , Marryott Robert A.
Published: February 2004

Simulated annealing is introduced and applied to the optimization of groundwater management problems cast in combinatorial form. This heuristic, probabilistic optimization method seeks minima in analogy with the annealing of solids and is effective on large‐scale problems. No continuity requirements are imposed on objective (cost) functions. Constraints may be added to the cost function via penalties, imposed by designation of the solution domain, or imbedded in submodels (e.g., mass balance in aquifer flow simulators) used to evaluate costs. The location of global optima may be theoretically guaranteed, but computational limitations lead to searches for nearly optimal solutions in practice. Like other optimization methods, most of the computational effort is expended in flow and transport simulators. Practical algorithmic guidance that leads to enormous computational savings and sometimes makes simulated annealing competitive with gradient‐type optimization methods is provided. The method is illustrated by example applications to idealized problems of groundwater flow and selection of remediation strategy, including optimization with multiple groundwater control technologies. They demonstrate the flexibility of the method and indicate its potential for solving groundwater management problems. The application of simulated annealing to water resources problems is new and its development is immature, so further performance improvements can be expected.
Scaling of the Richards Equation Under Invariant Flux Boundary Conditions
Authors: Kutilek M. , Zayani K. , Haverkamp R. , Parlance J. Y. , Vachaud G.
Published: February 2004

Richards' equation of the unsaturated flow has been scaled in an invariant form with regard to the variation of boundary conditions within a defined class of flow problems. Two classes of problems were examined: (1) vertical infiltration into a homogeneous soil with a constant surface boundary flux, and (2) vertical infiltration into a soil topped by a seal layer of negligible thickness and with a given positive pressure head above the seal layer. The solution of the problem when plotted as function of scaled variables is unchanged for any variation at the boundary, i.e., variation of the flux in the first class and variation of the seal in the second class.
Prediction Uncertainty in Seasonal Partial Duration Series
Authors: Rasmussen Peter Funder , Rosbjerg Dan
Published: February 2004

In order to obtain a good description of the exceedances in a partial duration series it is often necessary to divide the year into a number (2–4) of seasons. Hereby a stationary exceedance distribution can be maintained within each season. This type of seasonal models may, however, not be suitable for prediction purposes due to the large number of parameters required. In the particular case with exponentially distributed exceedances and Poissonian occurrence times the precision of the T year event estimator has been thoroughly examined considering both seasonal and nonseasonal models. The two‐seasonal probability density function of the T year event estimator has been deduced and used in the assessment of the precision of approximate moments. The nonseasonal approach covered both a total omission of seasonality by pooling data from different flood seasons and a discarding of nonsignificant season(s) before the analysis of extremes. Mean square error approximations (bias second order, variance first and second order) were employed as measures for prediction uncertainty. It was found that optimal estimates can usually be obtained with a nonseasonal approach.
A New Total Variation Diminishing Scheme for the Solution of Advective‐Dominant Solute Transport
Authors: Cox Ronald A. , Nishikawa Tracy
Published: February 2004

It is well known that the use of standard numerical techniques can lead to numerical oscillations in the solution of the advective‐dominant case of solute transport in groundwater systems. In this work a class of numerical schemes commonly employed in aeronautical engineering called total variation diminishing (TVD) schemes is investigated. A new, formally third‐order accurate, TVD algorithm is developed in one dimension for purely advective transport and applied to a variety of problems with large mesh Peclét numbers. The one‐dimensional approach is then extended to the two‐dimensional case. In both one and two dimensions the numerical results compare favorably with their respective analytic solutions.
Quantifying Dissolved Nitrogen Flux Through a Coastal Watershed
Authors: Weiskel Peter K. , Howes Brian L.
Published: February 2004

Available nitrogen loading models, commonly used to estimate subsurface fluxes of dissolved nitrogen to coastal waters, have not been quantitatively or systematically compared; nor have they generally been field‐verified at regional scales. We employed three published loading models, a site‐specific model based upon water use data, and both Darcian and non‐Darcian field approaches to obtain estimates of steady state, dissolved nitrogen flux through a permeable Massachusetts watershed. The two field approaches, based on independent data, yielded similar results. Results of the published loading models agreed closely with each other, but exceeded the mean of the field approaches (130 ± 12 mol N m−1 aquifer width yr−1) by 60%, on average. The Water Use loading model agreed closely with the field results (within 4%), largely because it did not require estimates of occupancy rate, which was found to be the major source of error to the published models. The observed, median concentration of total dissolved nitrogen (TDN) in groundwater increased from 1.9 to 313 μM during transport through the subbasin, confirming loading model predictions that >99% of the TDN flux is anthropogenic. In contrast to the watershed inputs, downgradient TDN was dominantly nitrate (98%), indicating near‐complete nitrification during transport. Significant transverse horizontal and vertical variations were found in the groundwater TDN distribution at scales of meters and tenths of meters, respectively, consistent with a large number of discrete nitrogen sources at the ground surface, and low transverse macrodispersivities in the aquifer. Loading models, if properly verified by field measurements at the stream tube scale, hold promise for characterizing the effects of land use on subsurface nitrogen flux through coastal watersheds.
Analytical Solutions for Solute Transport in Three‐Dimensional Semi‐infinite Porous Media
Authors: Leij Feike J. , Skaggs Todd H. , Van Genuchten Martinus Th.
Published: February 2004

This paper presents several analytical solutions for three‐dimensional solute transport in semi‐infinite porous media with unidirectional flow using first‐type (or concentration) and third‐type (or flux) boundary conditions at the inlet location of the medium. The solutions may be used for predicting solute concentrations in homogeneous media, verification of more comprehensive numerical models, and laboratory or field determination of solute transport parameters. The transport equation incorporates terms accounting for advection, dispersion, zero‐order production, and first‐order decay. General solutions were derived for an arbitrary initial distribution and solute input with the help of Laplace, Fourier, and Hankel transforms. Specific solutions are presented for rectangular and circular solute inflow regions, as well as for solutes initially present in the form of parallelepipedal or cylindrical regions of the medium. The solutions were mathematically verified against simplified analytical solutions. Examples of concentration profiles are presented for several solute transport parameters using both first‐ and third‐type boundary conditions. A mass balance constraint is defined based on a prescribed solute influx; the third‐type condition is shown to conserve mass whereas the first‐type condition was found to always overestimate resident solute concentrations in the medium.
A Note on Fractal Channel Networks
Authors: Marani Alessandro , Rigon Riccardo , Rinaldo Andrea
Published: February 2004

This paper studies the relation between the structure of river networks and the features of their geomorphologic hydrologic response. A mathematical formulation of connectivity of a drainage network is proposed to relate contributing areas and the network geometry. In view of the connectivity conjecture, Horton's bifurcation ratio RB tends, for high values of Strahler's order Ω of the basin, to the area ratio RA, and Horton's length ratio RL equals, in the limit, the single‐order contributing area ratio Ra. The relevance of these arguments is examined by reference to data from real basins. Well‐known empirical results from the geomorphological literature (Melton's law, Hack's relation, Moon's conjecture) are viewed as a consequence of connectivity. It is found that in Hortonian networks the time evolution of contributing areas exhibits a multifractal behavior generated by a multiplicative process of parameter 1/RB. The application of the method of the most probable distribution in view of connectivity contributes new inroads toward a general formulation of the geomorphologic unit hydrograph, in particular generalizing its width function formulation. A quantitative example of multifractal hydrologic response of idealized networks based on Peano's construct (for which RB = RA = 4, RL = 2) closes the paper.
Dispersion in Sub‐Representative Elementary Volume Fracture Networks: Percolation Theory and Random Walk Approaches
Authors: Berkowitz B. , Braester C.
Published: February 2004

A law for dispersion in fracture networks below the representative elementary volume (REV) is established by analyzing random walks in two‐dimensional fracture networks in conjunction with percolation theory. Irregular fracture networks near the percolation threshold were obtained by removing some of the fractures of a regular orthogonal network, consisting of fractures of equal length and different apertures, drawn randomly from a lognormal distribution. The random walk was directed by an exact solution of flow through the network, and Monte Carlo simulations were performed to track particles through the fracture system. The percolation theory analysis indicates a proportionality between the mean square displacement and time raised to the power 1.27, in excellent agreement with the simulations in the fracture networks, which indicate a proportionality with time raised to the power 1.3.
Water fluxes in oxisols: A comparison of approaches
Authors: Buttler I. W. , Riha S. J.
Published: February 2004

Two approaches to simulating soil water flow were evaluated: a capacity‐type water flow model combined with a plant water uptake model based on the concept of plant‐available water, and a numerical solution to the Richards equation combined with a potential‐driven water uptake model. Irrigation water was applied at rates ranging from 0.3 to 1.6 potential evapotranspiration to an Oxisol under fallow and planted to corn (Zea mays L.). Results indicate that a two‐parameter soil moisture release curve does not sufficiently describe these soils over the entire plant‐available water range. Field saturated water contents were generally only 70% of total porosity. The potential‐driven model better predicts profile water content distribution under fallow and cropped conditions than the capacity‐type approach (R2 = 0.80 and 0.83 versus R2 = 0.59 and 0.70). When integrated over the growing season, drainage, evaporation and transpiration rates were very similar for capacity‐type water movement and potential‐driven water movement over the range of irrigation treatments.
On the variability and use of the hydraulic conductivity alpha parameter in stochastic treatments of unsaturated flow
Authors: White I. , Sully M. J.
Published: February 2004

The quasi‐linear parameterization for unsaturated hydraulic conductivity K(Ψ) = Ks exp (αΨ), where K is hydraulic conductivity, Ψ is soil water matric potential, Ks is saturated hydraulic conductivity, and α is a porous material parameter, has been used in both stochastic and deterministic models of unsaturated water flow in porous materials. In the stochastic approach, Ks is assumed lognormally distributed, but α and the volumetric soil water capacity C = dθ/dΨ, with θ volumetric soil water content, are assumed normally distributed. We point out here that α and Ks are related to the same internal pore geometry of the soil. This interrelationship ensures that if Ks is lognormal, then α, and possibly C, will also be lognormal. Additionally, we present preliminary field results which indicate that α is better described by a lognormal than a normal distribution. The quasi‐linear parameterization can be expected to be correct only in some integral sense. Predictions of increases in the variability of hydraulic conductivity with decreasing Ψ may therefore be prejudiced by the use of the exponential form for K(Ψ). Tests of the sensitivity of stochastic model predictions to both the parameterizations adopted for K(Ψ) and the assumed distribution functions of parameters seem warranted. Reliable experimental evidence on field variability of K(Ψ) and Ψ(θ) at substantial negative values of Ψ are also needed.
Modeling water erosion due to overland flow using physical principles: 1. Sheet flow
Authors: Hairsine P. B. , Rose C. W.
Published: February 2004

A new model for erosion of plane soil surfaces by water is developed using physical principles. Raindrop impact and overland flow remove soil from the original cohesive soil. Once eroded soil enters overland flow, either as aggregates or primary particles, a significant proportion of it returns to the soil bed, forming a cohesionless deposited layer from which it can be removed again by the same erosion processes. The action of the eroding agents will be divided between eroding the unshielded original cohesive soil and reintroducing sediment from the deposited layer. The theory recognizes that the nature of the surface is modified by the erosion and deposition processes affecting it. Solutions of the governing differential equations describing sediment concentration are developed for two distinct equilibrium cases. The first case, when the deposited layer completely shields the original soil, appears to correspond with what has been previously called a “transport‐limited” situation. The second case occurs when such shielding is incomplete, and sediment concentration is affected by the cohesive strength of the soil. The resulting equations for sediment concentration at equilibrium are compared with existing equations. Firstly, the equation for the case where the soil is lacking cohesion is shown to be similar to the semiempirical equation of Yang (1973). Secondly, when the soil is cohesive the slope length relationships are shown to be in good agreement with the universal soil loss equation over a wide range of slope steepness.
An example of using Landsat and GOES data in a water budget model
Authors: Duchon Claude E. , Salisbury Jayne M. , Lee Williams T. H. , Nicks Arlin D.
Published: February 2004

Landsat and GOES satellite data are used in analyzing monthly water budgets on a 538‐km2 watershed in central Oklahoma for 1984–1985. The budget components examined are water yield, percolation loss, evapotranspiration and change in soil water content. The hydrologic model employed is SWRRB (Simulator for Water Resources in Rural Basins) developed by the Agricultural Research Service of the U.S. Department of Agriculture. Landsat imagery is used to subdivide the basin into land covers for model application. The land cover subareas are more homogeneous than subbasins with mixed vegetation and their use allows tracking of the unique contribution of each type of cover to the water budget. Daily insolation is determined from GOES imagery. A comparison of budget components based on pyranometer insolation versus unbiased GOES estimates shows a maximum difference less than 4% and 5 mm for any component of the annual and monthly budgets, respectively. Satellite‐derived temperatures are simulated by adding systematic and random errors to observed temperatures. A temperature bias of a few degrees greatly changes the growing season and monthly budgets of winter wheat.
Modeling solute transport influenced by multiprocess nonequilibrium and transformation reactions
Authors: Brusseau Mark L. , Jessup Ron E. , Rao P. Suresh C.
Published: February 2004

We present an advective‐dispersive solute transport model that explicitly accounts for multiple sources of nonequilibrium and transformation reactions during steady state flow in porous media. The multiprocess nonequilibrium with transformation (MPNET) model is formulated for cases where nonequilibrium, caused by a combination of transport‐related and sorption‐related processes, and abiotic/biotic transformations can be described as first‐order processes. The impact of the coupling of nonequilibrium and transformation reactions on solute transport is examined using selected illustrative examples. The performance of the model is evaluated by comparing predictions obtained with the model, where values for all model parameters are obtained independently, to a data set obtained from the literature. The prediction obtained with the MPNET model matched the data very well, much better than did the predictions obtained with the MPNET model assuming no degradation and with a model that does not account for rate‐limited sorption.
Bubble plume dynamics in a stratified medium and the implications for water quality amelioration in lakes
Authors: Schladow S. G.
Published: February 2004

The behavior of a bubble plume discharging vertically into a stably stratified water column is described using a simple one‐dimensional plume model. It is confirmed that the behavior can be described with just two dimensionless groupings, C and M, representative of the strength of the stratification and the discharge momentum. Depending on the values of these parameters, the plume can either extend the full depth of the water column or eject water at one or more internal detrainment points. The occurrence of these internal detrainment points can be described in terms of the relative magnitudes of the terms comprising the buoyancy conservation equation. Further, these internal detrainment points can be linked to both the mechanical efficiency and mixing effectiveness of bubble plumes. This is of importance when the bubble plume is being used to act as a destratification device in a lake. Generally, an integral number of internal detrainment points correspond to peak mechanical efficiencies. Maximum mixing effectiveness is favored by lower values of the stratification parameter C and higher values of the source strength parameter M.
Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface: 1. Numerical formulation
Authors: Falta Ronald W. , Pruess Karsten , Javandel Iraj , Witherspoon Paul A.
Published: February 2004

A multidimensional integral finite difference numerical simulator is developed for modeling the steam displacement of nonaqueous phase liquid (NAPL) contaminants in shallow subsurface systems. This code, named STMVOC, considers three flowing phases, gas, aqueous, and NAPL; and three mass components, air, water, and an organic chemical. Interphase mass transfer of the components between any of the phases is calculated by assuming local chemical equilibrium between the phases, and adsorption of the chemical to the soil is included. Heat transfer occurs due to conduction and multiphase convection and includes latent heat effects. A general equation of state is implemented in the code for calculating the thermophysical properties of the NAPL/chemical. This equation of state is primarily based on corresponding states methods of property estimation using a chemical's critical constants. The necessary constants are readily available for several hundred hazardous organic liquid chemicals. In part 2 (Falta et al., this issue), the code is used to simulate two one‐dimensional laboratory steam injection experiments and to examine the effect of NAPL properties on the steam displacement process.
The Laplace Transform Galerkin Technique for large‐scale simulation of mass transport in discretely fractured porous formations
Authors: Sudicky E. A. , McLaren R. G.
Published: February 2004

The ability to simulate contaminant migration in large‐scale porous formations containing a complex network of discrete fractures is limited by traditional modeling approaches. One primary reason is because of vastly different transport time scales in different regions due to rapid advection along the discrete fractures and slow but persistent diffusion in the porous matrix. In addition to time‐related complexities, standard numerical methods require a fine spatial discretization in the porous matrix to represent sharp concentration gradients at the interface between the fractures and the matrix. In order to circumvent these difficulties, the Laplace transform Galerkin method is extended for application to discretely fractured media with emphasis on large‐scale modeling capabilities. The technique avoids time stepping and permits the use of a relatively coarse grid without compromising accuracy because the Laplace domain solution is relatively smooth and devoid of discontinuities even in advection‐dominated problems. Further computational efficiency for large‐grid problems is achieved by employing a preconditioned, ORTHOMIN‐accelerated iterative solver. A unique feature of the method is that each of the several needed p space solutions are independent, thus making the scheme highly parallel. Other features include the accommodation of advective‐dispersive transport in the porous matrix and the straightforward inclusion of dual‐porosity theory to represent matrix diffusion in regions where microfractures exist below the modeling scale. An example problem involving contaminant transport through an aquitard into an underlying aquifer leads to the conclusion that deep, essentially undetectable fractures in clayey aquitards can greatly compromise the quality of groundwater in the impacted aquifer.
Spatial and temporal soil water estimation considering soil variability and evapotranspiration uncertainty
Authors: Or Dani , Hanks R. J.
Published: February 2004

Lack of accurate information stemming from soil variability and climatic uncertainty obstructs efficient irrigation management. State‐space models of soil water balance and potential evapotranspiration were used in the application of spatial‐temporal estimation methods to reduce uncertainty. Temporal soil water storage estimates and estimation errors were obtained by the Kalman filter (KF). Spatial estimates were obtained by the conditional multivariate normal method. These spatial and temporal estimates were combined by an additional KF step that considers spatial estimates as measurements. Time‐dependent soil water spatial covariance was approximated by assuming a constant correlation range and by using measurements variance to estimate the variogram “sill.” Simulation and field results indicate that soil water storage estimates by the proposed method agreed better with measurements than estimates based on either spatial or temporal information only. The proposed estimation scheme can be extended to other systems with a simple physical model and a known spatial structure where only a few field measurements are available.
Benefit transfer: Conceptual problems in estimating water quality benefits using existing studies
Authors: Desvousges William H. , Naughton Michael C. , Parsons George R.
Published: February 2004

The Environmental Protection Agency has used existing studies to estimate the benefits of environmental improvements associated with several regulatory proposals. The problems encountered in using existing studies to measure the benefits of water quality improvements are investigated in this paper. We propose criteria for selecting transfer studies and present a case study of a transfer. Our research indicates that although benefit transfer may offer promise, the fact that existing studies were not designed for transfer places severe limitations on the current effectiveness of transfer. Suggestions for future research are presented to address these limitations.
Benefits and costs of pulp and paper effluent controls under the Clean Water Act
Authors: Luken Ralph A. , Johnson F. Reed , Kibler Virginia
Published: February 2004

This study quantifies local improvements in environmental quality from controlling effluents in the pulp and paper industry. Although it is confined to a single industry, this study is the first effort to assess the actual net benefits of the Clean Water Act pollution control program. An assessment of water quality benefits requires linking regulatory policy, technical effects, and behavioral responses. Regulatory policies mandate specific controls that influence the quantity and nature of effluent discharges. We identify a subset of stream segments suitable for analysis, describe water quality simulations and control cost calculations under alternative regulatory scenarios, assign feasible water uses to each segment based on water quality, and determine probable upper bounds for the willingness of beneficiaries to pay. Because the act imposes uniform regulations that do not account for differences in compliance costs, existing stream quality, contributions of other effluent sources, and recreation potential, the relation between water quality benefits and costs varies widely across sites. This variation suggests that significant positive net benefits have probably been achieved in some cases, but we conclude that the costs of the Clean Water Act as a whole exceed likely benefits by a significant margin.
A continuous‐time inverse operator for groundwater and contaminant transport modeling: Model identifiability
Authors: Ginn Timothy R. , Cushman John H.
Published: February 2004

General identifiability conditions are derived for the model coefficients of the spatially discretized continuous‐time diffusion equation. These conditions in turn determine some sufficient and necessary conditions for the existence and uniqueness of the continuous‐time inverse operator described in a previous article. The identifiability conditions are in terms of the initial conditions and the flux vector containing boundary condition information and the eigenspace of the spatially discretized system. The derivation of these conditions gives some insight into the location of the solution of the inverse problem in terms of the direct operator under investigation in the space of the Laplace transform and limited insight into the stability of the solution near that location.
Gibbs' Distribution on drainage networks
Authors: Troutman Brent M. , Karlinger Michael R.
Published: February 2004

We propose a spatial stochastic model for drainage networks defined on a square lattice of points. The probability of a particular spanning tree s draining a given basin represented by a set of lattice points is proportional to exp [−βH(s)], where β is a parameter to be estimated and H(s) is defined to be the difference between total flow distance to the outlet through the drainage tree and total distance along shortest paths to the outlet. Thus H(s) is a global measure of sinuosity of the channels constituting the drainage tree. This probability distribution on trees is known as Gibbs' distribution and is well known in statistical mechanical contexts. The distribution with β = 0 (a uniform distribution) has been studied in a previous paper by the authors and was found to yield networks that are too sinuous. In this paper, β is allowed to be greater than zero, which produces more realistic networks that are not as sinuous. The question of spatial variability of β is addressed from an equilibrium point of view using ideas from statistical mechanics. To examine the question of spatial variability, the parameter β is defined in a Bayesian sense and allowed to vary randomly from basin to basin. In a case study we express β in terms of a log linear model with three independent variables: pixel size (grid spacing), drainage area, and average channel slope. We then estimate the parameters of this model with a set of 50 drainage trees obtained using digital elevation data for Willow Creek in Montana. Parameter estimates indicate that β tends to vary directly with slope and inversely with drainage area, which suggests heterogeneities within larger basins that are not adequately accounted for by Gibbs' distribution with a constant parameter value.
Conditional estimation of solute travel time in heterogeneous formations: Impact of transmissivity measurements
Authors: Rubin Yoram , Dagan Gedeon
Published: February 2004

Solute transport through heterogeneous formations is modeled by the travel time approach, i.e., the time τ it takes a solute particle to travel from the source to a control plane. Due to uncertainty τ is a random variable characterized by its cumulative probability density function G(τ). This function is used by regulatory agencies in pollution site assessment. The main aim of the present study is to examine the impact of data, namely measured transmissivities, upon G(τ) and reduction of uncertainty. This is achieved for two‐dimensional steady flow of average uniform head gradient by using a Lagrangian approach developed in the past (Dagan, 1982, 1984, 1989; Rubin, 1990, 1991). The impact of data is seen in conditioning on measured values and in estimation of parameters characterizing flow and formation properties. The approach is illustrated by a simulation based on synthetic data. The results show how uncertainty is reduced by increasing the density of measurements for a control plane sufficiently far from the source.
Dynamic optimal control for groundwater remediation with flexible management periods
Authors: Culver Teresa B. , Shoemaker Christine A.
Published: February 2004

A successive approximation linear quadratic regulator (SALQR) method with management periods is combined with a finite element groundwater flow and transport simulation model to determine optimal time‐varying groundwater pump‐and‐treat reclamation policies. Management periods are groups of simulation time steps during which the pumping policy remains constant. In an example problem, management periods reduced the total computational demand, as measured by the CPU time, by as much as 85% compared to the time needed for the SALQR solution without management periods. Conversely, the optimal costs increased as the number of times that the control can change is reduced. With two simulation periods per management period, the optimal cost increased by less than 1% compared to the optimal cost with no management periods, yet the computational work was reduced by a third. The optimal policies, including the number and locations of wells, changed significantly with the number of management periods. Complexity analysis revealed that the SALQR algorithm with management periods can significantly reduce the computational requirements for nonsteady optimization of groundwater reclamation and other management applications.
Power law distributions of discharge mass and energy in river basins
Authors: Rodríguez‐Iturbe I. , Ijjász‐Vásquez E. J. , Bras R. L. , Tarboton D. G.
Published: February 2004

River networks constitute dissipative systems with many spatial degrees of freedom. Previous work by Mandelbrot (1983) and Bak et al. (1987, 1988, 1990) suggests that such systems will follow power law distributions in their mass and energy characteristics. It is shown that this is the case for river networks where the exponent β in the distribution, P[X > x] ∝ x−β, is approximately equal to 0.45 and 0.90 for discharge and energy respectively in the case of several networks analyzed in North America when these variables are calculated for each individual link throughout the drainage network. An explanation of the values of β is offered based on the fractal structure of rivers and on principles of energy expenditure in river basins.
Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach: 2. Results
Authors: Dykaar Bruce B. , Kitanidis Peter K.
Published: February 2004

Using the numerical spectral method described in the companion paper (Dykaar and Kitanidis, this issue) the effective conductivity of a three‐dimensional, Isotropic, stationary, lognormally distributed hydraulic conductivity is computed. Six cases were investigated for variances in log conductivity ranging between 1 and 6. The results show that averaging volumes of at least 30 integral scales are required before the effective conductivity reaches its asymptotic value. The results support Matheron's (1967) hypothesis that Ke = KG exp (σY2/6), where Ke is the effective hydraulic conductivity, and KG and σY2 are the geometric mean and variance, respectively, of the hydraulic conductivity field. We also find that for a Gaussian covariance function, heterogeneities smaller than about 1.3 integral scales do not significantly contribute to the effective conductivity. In two dimensions, averaging volumes of more than 80 integral scales are required before the effective conductivity reaches the analytic infinite‐domain result of the geometric mean, while the effective conductivity is insensitive to heterogeneities less than 2 integral scales in size. The method is also applied to data from a shale and sandstone formation, and the results are compared with those from other methods.
A solute flux approach to transport in heterogeneous formations: 1. The general framework
Authors: Dagan G. , Cvetkovic V. , Shapiro A.
Published: February 2004

It is common to represent solute tranport in heterogeneous formations in terms of the resident concentration C(x, t), regarded as a random space function. The present study investigates the alternative representation by q, the solute mass flux at a point of a control plane normal to the mean flow. This representation is appropriate for many field applications in which the variable of interest is the mass of solute discharged through a control surface. A general framework to compute the statistical moments of q and of the associated total solute discharge Q and mass M is established. With x the direction of the mean flow, a solute particle is crossing the control plane at y = η, z = ζ and at the travel (arrival) time τ. The associated expected solute flux value is proportional to the joint probability density function (pdf) g1 of η, ζ and τ, whereas the variance of q is shown to depend on the joint pdf g2 of the same variables for two particles. In turn, the statistical moments of η, ζ and τ depend on those of the velocity components through a system of stochastic ordinary differential equations. For a steady velocity field and neglecting the effect of pore‐scale dispersion, a major simplification of the problem results in the independence of the random variables η, ζ and τ. As a consequence, the pdf of η and ζ can be derived independently of τ. A few approximate approaches to derive the statistical moments of η, ζ and τ are outlined. These methods will be explored in paper 2 in order to effectively derive the variances of the total solute discharge and mass, while paper 3 will deal with the nonlinear effect of the velocity variance upon the moments of η, ζ and τ