bluuebunny/crossref_metadata_2025 huggingface dataset:
The Relative Importance of Compressibility and Partial Saturation in Unconfined Groundwater Flow
Authors: Brutsaert Wilfried , El‐Kadi Aly I.
Published: February 2008

The flow of water in an unconfined aquifer is viewed within the framework of the Biot theory as extended for two‐fluid flow and for conditions of a vertical displacement with constant load. Order of magnitude inspection and an objective criterion, obtained from similitude considerations, are dealt with to estimate the relative importance of the compressibility of aquifer matrix and water and that of partial saturation. Finally, these are used to reconcile some apparently contradictory findings of past studies.
Economics of Timing Storm Drainage Improvements
Authors: Cochrane Harold C. , Huszar Paul C.
Published: February 2008

An important component of optimizing storm drainage improvements is the timing of their implementation. Both the number and the value of structures protected by a drainage project may increase with time, thus increasing the benefits of delaying the project. Delaying the project, however, also may entail costs of greater expected losses and rising construction expenditures. The issue of timing is also confused by inflation. The optimum time to construct a drainage project depends upon the initial value of the structures at risk, the construction costs of the project, and the rates of growth in these two values. Growth rates are properly computed in real terms so as not to be confused with inflation. The optimum time maximizes the difference between the changing present values of the benefits and costs of the project. In general, projects in urbanizing areas may be optimally delayed. Projects in mature, developed areas are not likely candidates for delay.
Nonsteady three‐phase immiscible fluid distribution in porous media
Authors: Eckberg David K. , Sunada Daniel K.
Published: February 2008

An experimental investigation was conducted to evaluate the three‐phase fluid distribution caused by a petroleum spill in an unconfined aquifer. The experiment consisted of introducing oil at the top of a vertical column of soil containing water and measuring the oil and water contents at various elevations and times. The static fluid distribution was then compared to the calculated distribution based on two‐phase capillary pressure versus saturation data obtained by a separate laboratory experiment. It was concluded that the water saturation at static equilibrium can be estimated satisfactorily by assuming it is a function of the capillary pressure between oil and water.
Modeling Sediment Detention Ponds Using Reactor Theory and Advection‐Diffusion Concepts
Authors: Wilson Bruce N. , Barfield Billy J.
Published: February 2008

An algorithm is presented to model the sedimentation process in detention ponds. This algorithm is based on a mass balance for an infinitesimal layer that couples reactor theory concepts with advection‐diffusion processes. Reactor theory concepts are used to (1) determine residence time of sediment particles and to (2) mix influent sediment with previously stored flow. Advection‐diffusion processes are used to model the (1) settling characteristics of sediment and the (2) vertical diffusion of sediment due to turbulence. Predicted results of the model are compared to those observed on two pilot scale ponds for a total of 12 runs. The average percent error between predicted and observed trap efficiency was 5.2%. Overall, the observed sedimentology values were predicted with reasonable accuracy.
A Two‐Phase Numerical Model for Prediction of Infiltration: Applications to a Semi‐Infinite Soil Column
Authors: Morel‐Seytoux Hubert J. , Billica Judith A.
Published: February 2008

A numerical algorithm for prediction of infiltration and water content profiles evolution in a soil column is presented. The algorithm is derived from the two‐phase flow theory for water and air. However, the governing equations reduce to the usual one‐phase flow equations by setting a parameter to a zero value. The model can shift back and forth from the one‐phase to the two‐phase mode within the course of a simulation as demanded by the situation. The need for the two‐phase approach is demonstrated for a couple of illustrative situations both with a semi‐infinite lower boundary condition, that is, for a case when the two‐phase approach might appear a priori least needed. It is shown that it is indeed needed even for a semi‐infinite soil column when mobile air cannot be confined. Rather amazingly the two‐phase computer runs cost less than the corresponding one‐phase runs. It is shown that the two‐phase algorithm is naturally more stable than the one‐phase algorithm when the water contents are high in a portion of the column. Thus the two‐phase approach is not only more realistic, but it is even less expensive whenever it is needed.
Comparison of Gaussian Conditional Mean and Kriging Estimation in the Geostatistical Solution of the Inverse Problem
Authors: Hoeksema Robert J. , Kitanidis Peter K.
Published: February 2008

Two separate applications of the geostatistical solution to the inverse problem in groundwater modeling are presented. Both applications estimate the transmissivity field for a two‐dimensional model of a confined aquifer under steady flow conditions. The estimates are based on point observations of transmissivity and hydraulic head and also on a model of the aquifer which includes prescribed head boundaries, leakage, and steady state pumping. The model used to describe the spatial variability of the log‐transmissivity describes large‐scale fluctuations through a linear mean or drift intermediate and small‐scale fluctuations through a two‐parameter covariance function. The first application presented estimates the log‐transmissivities using Gaussian conditional mean estimation. The second application uses an extended form of cokriging. The two methods are compared and their relative merits discussed. The extended cokriging application is applied to the Jordan Aquifer of Iowa. A comparison is also made between the conditional mean application and an analytical approach.
Monitoring Changes in Total and Unfrozen Water Content in Seasonally Frozen Soil Using Time Domain Reflectometry and Neutron Moderation Techniques
Authors: Hayhoe H. N. , Bailey W. G.
Published: February 2008

This paper presents the results of a study utilizing time domain reflectometry and the neturon moderation technique to monitor changes in total water content and unfrozen water content during fall, winter, and spring on a sandy loam site which was maintained snow free to maximize seasonal frost penetration. Soil temperatures were recorded continuously, and meteorological conditions were observed at a nearby climatological station. The procedure of combining the neutron probe and time domain reflectometry employed here showed good potential for augmenting the limited data on soil moisture redistribution in freezing soils under natural conditions. The data indicated the importance of obtaining a representative spatial average of water content measured with time domain reflectometry in order to obtain a good correspondence with neutron probe observations.
Approximations of Temporal Rainfall From a Multidimensional Model
Authors: Valdes Juan B. , Rodriguez‐Iturbe Ignacio , Gupta Vijay K.
Published: February 2008

The feasibility of representing the temporal structure of a multidimensional rainfall process with simpler stochastic models and a study of the effect of parameter robustness on the time scale is investigated here via performing controlled numerical experiments. A multidimensional representation for precipitation, given in the theory recently proposed by E. Waymire et al. (1984), is used for simulating rainfall in space and time. The model produces moving storms with realistic mesoscale meteorological features, e.g., clustering, birth and death of cells, cell intensity attenuation in time and space, etc. Two‐year traces of rainfall intensities at fixed gage stations were generated at intervals of 0.1 hours for three climates. These traces are then aggregated at different time scales ranging from 1 to 24 hours. First‐ and second‐order statistics are evaluated from the above series at each aggregation level and they are used for estimating the parameters of three one‐dimensional models of temporal rainfall at a point: (1) Poisson model with independent marks, (2) rectangular pulses with independent intensity and duration, and (3) Neyman‐Scott with independent marks. Only at very high levels of aggregation the compound Poisson model was able to reproduce the statistical structure of the simulated traces. The rectangular pulses model was found to have parameters which vary significantly with the time scale of aggregation and moreover, it leads to large distortions in the mean depth and duration of storm events. The Neyman‐Scott scheme proved to be the most stable model throughout the different time scales and it also reproduced quite well the average storm characteristics at the event level. None of these three models was able to reproduce in a satisfactory manner the simulated extreme value distribution of the multidimensional model.
Stochastic Soil Moisture Estimation and Forecasting for Irrigated Fields
Authors: Aboitiz Martin , Labadie John W. , Heermann Dale F.
Published: February 2008

A methodology is developed for estimating and forecasting soil water depletion and crop evapotranspiration, with explicit consideration of modeling errors and stochastic inputs. The water balance of an irrigated field and a time series model for reference crop evapotranspiration are formulated in state‐space form, with soil moisture depletion and reference evapotranspiration as state variables. The Kalman filter is used to generate estimates and forecasts of the state variables, together with statistical information on their associated errors. Model calibration and validity tests are performed with two independent data sets from locations in Colorado. Each set includes several years of reference crop evapotranspiration data calculated from climatological observations, one season of soil moisture measurements, and concurrent irrigation applications. The estimates, forecasts, and error covariance information provided by the model can allow irrigation decisions to be made with explicit consideration of the inherent risks of crop damage or failure under limitations in water, energy, labor, and capital.
An Approach for Frequency Analysis of Multiyear Drought Durations
Authors: Lee Kil Seong , Sadeghipour Jamshid , Dracup John A.
Published: February 2008

A practical approach is developed for frequency analysis of multiyear drought durations of annual streamflow series. The proposed approach utilizes a technique which smooths the frequency‐curve irregularity of drought durations and, therefore, reduces the statistical uncertainties associated with sample‐size limitations. Several hazard‐function models are examined with regard to their ability to represent the duration‐dependent termination rate of a drought data set. The logistic model with an exponential correction for short durations is considered to have sufficient flexibility for describing most portions of the termination‐rate function. The parameters of the logistic model are identified using a piecewise linear regression for the linearized termination probability curve. Once the form of the hazard model is specified arid its parameters are estimated, the probability distribution and exceedance probability of drought durations can be determined from their corresponding relationships with the hazard model. The historic droughts of Feather River, California, are used to demonstrate the methodology. Results indicate that the observed nine‐year drought of Feather River has a return period of 360 years.
Stochastic Analysis of Three‐Dimensional Flow in a Bounded Domain
Authors: Naff R. L. , Vecchia A. V.
Published: February 2008

A commonly accepted first‐order approximation of the equation for steady state flow in a fully saturated spatially random medium has the form of Poisson's equation. This form allows for the advantageous use of Green's functions to solve for the random output (hydraulic heads) in terms of a convolution over the random input (the logarithm of hydraulic conductivity). A solution for steady state three‐ dimensional flow in an aquifer bounded above and below is presented; consideration of these boundaries is made possible by use of Green's functions to solve Poisson's equation. Within the bounded domain the medium hydraulic conductivity is assumed to be a second‐order stationary random process as represented by a simple three‐dimensional covariance function. Upper and lower boundaries are taken to be no‐flow boundaries; the mean flow vector lies entirely in the horizontal dimensions. The resulting hydraulic head covariance function exhibits nonstationary effects resulting from the imposition of boundary conditions. Comparisons are made with existing infinite domain solutions.
Predicting pH, Alkalinity, and Total Acidity in Stream Water During Episodic Events
Authors: Lynch James A. , Hanna C. Mark , Corbett Edward S.
Published: February 2008

Acid precipitation was found to significantly influence the chemistry of a small headwater stream in central Pennsylvania. Stream discharge during 18 storms was sampled and analyzed for pH, bicarbonate alkalinity, and titratable acidity levels. The precipitation events varied considerably in their amounts, durations, and intensities and also produced highly variable hydrologic responses from the watershed. Stream pH and alkalinity levels were found to react inversely to stream discharge during storm flow periods, with their lowest levels occurring almost simultaneously with peak flow. In comparison, storm flow acidity was directly related to the discharge rate, with the peaks nearly coinciding. Models predicting the fluctuations in storm flow pH, alkalinity, and total acidity were developed. These models, which explained 88, 91, and 80% of the variations in stream pH, alkalinity, and acidity, respectively, used as their independent variables such hydrometeorological parameters as antecedent flow rate, time to peak, peak flow rate, quick flow volume, and storm precipitation amounts. These results suggest strongly that the hydrologic response of a watershed has potential application as an index of stream sensitivity to changes in pH, alkalinity, and acidity during acid precipitation/snowmelt events.
Production Function for Cotton With Dated Irrigation Quantities and Qualities
Authors: Dinar Ariel , Knapp Keith C. , Rhoades James D.
Published: February 2008

A dynamic crop‐water production function model is estimated for cotton. Evapotranspiration (ET) depends on soil moisture and soil salinity which in turn depend on irrigation volumes and qualities. Crop yield is a function of ET. A maximum likelihood approach is developed for estimating the ET function when moisture and ET observations are not available on a daily basis. The estimated ET function varies by crop growth stage and generally shows decreasing ET as soil water potential decreases. Soil salinities following irrigation are explained quite well using a piston flow model of salt transport. Several yield‐ET relations are estimated. The model can be used for predicting crop yield, ending soil salinity and soil moisture levels, and drainage volumes and qualities, given irrigation timing, quantity and quality of applied water, and initial levels of soil salinity and soil moisture.
On tide‐induced lagrangian residual current and residual transport: 1. Lagrangian residual current
Authors: Feng Shizuo , Cheng Ralph T. , Pangen Xi
Published: February 2008

Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long‐term transport processes. It has been pointed out by previous studies that it is more relevant to use a Lagrangian mean velocity than an Eulerian mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two‐dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the Lagrangian and Eulerian residual currents. When k is small, the first‐order Lagrangian residual is shown to be the sum of the Eulerian residual current and the Stokes drift. The Lagrangian residual drift velocity or the second‐order Lagrangian residual current has been shown to be dependent on the phase of tidal current. The Lagrangian drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first‐order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the Lagrangian residual current.
Transport of dissolved hydrocarbons influenced by oxygen‐limited biodegradation: 1. Theoretical development
Authors: Borden Robert C. , Bedient Philip B.
Published: February 2008

Many hydrocarbons and related organic contaminants are rapidly degradable in the presence of oxygen. Unfortunately, exchange of oxygen with subsurface contaminant plumes is often slow. In this paper, equations are developed for simulating the simultaneous growth, decay, and transport of microorganisms, as well as the transport and removal of hydrocarbon and oxygen. These equations are solved by conventional numerical techniques to study the impact of microbial kinetics, horizontal mixing, adsorption, and vertical exchange with the unsaturated zone on biodegradation. In the region near the hydrocarbon source, any available oxygen will be rapidly consumed. In the body of the hydrocarbon plume, oxygen transport will be rate limiting and the consumption of oxygen and hydrocarbon can be approximated as an instantaneous reaction. The major sources of oxygen to the plume appear to be transverse mixing, advective fluxes when adsorption is significant and vertical exchange with the unsturated zone. In a companion paper (R. C. Borden et al., this issue), hydrocarbon transport is simulated at a hazardous waste site where oxygen‐limited biodegradation is known to occur.
Measurements of large streamwise vortices in an open‐channel flow
Authors: Gulliver John S. , Halverson Martin J.
Published: February 2008

The moving‐bed flume, where the cross‐sectional mean velocity is zero, has proven to be useful for visualization of coherent structures in the flow, especially streamwise vortices with a size scale equal to the depth. The temporal mean of these streamwise vortices is turbulence driven secondary motion. Hydrogen bubbles illuminated by a plane of laser light are used to visualize and measure these vortices. Flow visualization at the zero mean velocity point provides a unique view of the streamwise vortices without the interference of the mean flow velocity.
Error analysis of conventional discrete and gradient dynamic programming
Authors: Kitanidis Peter K. , Foufoula‐Georgiou Efi
Published: February 2008

An asymptotic error analysis of the conventional discrete dynamic programming (DDP) method is presented, and upper bounds of the error in the control policy (i.e., the difference of the estimated and true optimal control) at each operation period are computed. This error is shown to be of the order of the state discretization interval (ΔS), a result with significant implications in the optimization of multistate systems where the “curse of dimensionality” restricts the number of states to a relatively small number. The error in the optimal cost varies with ΔS2. The analysis provides useful insights into the effects of state discretization on calculated control and cost functions, the comparability of results from different discretizations, and criteria about the required number of nodes. In an effort to reduce the discretization error in the case of smooth cost functions, a new discrete dynamic programming method, termed gradient dynamic programming (GDP), is proposed. GDP uses a piecewise Hermite interpolation of the cost‐to‐go function, at each stage, which preserves the values of the cost‐to‐go function and of its first derivatives at the discretization nodes. The error in the control policy is shown to be of the order of (ΔS)3 and the error in the cost to vary with ΔS4. Thus as ΔS decreases, GDP converges to the true optimum much more rapidly than DDP. Another major advantage of the new methodology is that it facilitates the use of Newton‐type iterative methods in the solution of the nonlinear optimization problems at each stage. The linear convergence of DDP and the superlinear convergence of GDP are illustrated in an example.
Surface geometry and stomatal conductance effects on evaporation from aquatic macrophytes
Authors: Anderson Michael G. , Idso Sherwood B.
Published: February 2008

Evaporative water loss rates of several floating and emergent aquatic macrophytes were studied over a 4‐year period through comparison of daily evaporative water losses from similar‐sized vegetated (E) and open water (E0) surfaces. Two species with planate floating leaves (water fern and water lily) yielded E/E0 values of 0.90 for one and four growing seasons, respectively, and displayed stomatal regulation of potential evaporation. Water hyacinths grown in ponds with different diameters exhibited E/E0 ratios which decreased with increasing pond diameter for both short (0.06–0.36 m) and tall (0.63–0.81 m) plants, producing high linear correlations with amount of peripheral vegetative surface area. The latter relationships suggested an E/E0 value less than unity for a relatively extensive canopy of short water hyacinths and a value of the order of 1.4 for a tall canopy possessing similar two‐dimensional surface area characteristics. The latter results were also demonstrated in a separate study utilizing polyurethane foam to insulate the peripheral exposure of tall water hyacinth canopies from advective energy. Finally, simultaneous stomatal conductance and daily E/E0 measurements on cattail and water hyacinth canopies with identical tank diameters indicated that although the mean stomatal conductance of the peripheral exposure of the cattail canopy was 72% less than that of the water hyacinth canopy, its total evaporative water loss was nearly equivalent, due to its greater height. Reducing the surface area of the peripheral cattail exposure by the fractional amount suggested by the stomatal conductance measurements harmonized its surface geometry‐evaporation relationship with that of the water hyacinth canopy and once again demonstrated the reality of stomatal control of potential evaporation.
Analytical solutions for radial dispersion with cauchy boundary at injection well
Authors: Chen Chia‐Shyun
Published: February 2008

In dealing with solute transport from an injection well into an aquifer a macroscopic boundary condition of the Cauchy type (the third type) can be formulated at the well‐aquifer interface if the mass balance principle is invoked. This Cauchy boundary condition includes effects of radial advection and longitudinal dispersion as molecular diffusion is neglected in the problem. Analytical solutions related to a continuous and a pulse injection are determined for the radial dispersion problem concerning such a Cauchy boundary condition. These solutions give resident concentrations in the radial flow system. Results of the continuous injection solution and of that related to a Dirichlet boundary condition (the first type) are different for short injection periods but converged for long injection periods. The deviation caused by using two different boundary conditions is further studied with appropriate asymptotic solutions valid only for short injection periods. It is found that significant concentration gradients may exist across the well‐aquifer interface for short injection periods. Under this condition, neglect of the local dispersion process at the well‐aquifer interface (as assumed in the Dirichlet boundary condition)amounts to forcing more solute mass into the aquifer. As injection is prolonged, the concentration gradient across the interface decreases as the associated local aquifer concentration is increased to the injected concentration level. For relatively long injection periods a local concentration equilibrium at the well‐aquifer interface is reached and thereafter advection dominates the local transport. The Dirichlet boundary condition is a special case neglecting local dispersion at the well bore to the Cauchy boundary condition. For the radial dispersion equation, solutions regarding a Dirichlet boundary condition do not give the flux concentrations due to the nonconstant groundwater velocity. Nevertheless, solutions of flux concentrations for a continuous and a pulse injection are acquired here by applying the flux concentration transformation to appropriate solutions regarding the Cauchy boundary condition.
Groundwater flow to a well in a layered porous medium: 2. Nonsteady multiple‐aquifer flow
Authors: Maas C.
Published: February 2008

The generalized integral transform method employed in part 1 is extended to solve the problem of nonsteady flow to a well in a layered porous medium. Distinction is made between aquifers, with mainly horizontal flow, and aquitards, with vertical flow. Elastic storage is taken into account in both aquifers and aquitards. The number of layers is arbitrary. The formula obtained serves as a theoretical check on an approximate solution to the same problem that was obtained earlier.
Improved algorithms for reservoir capacity calculation incorporating storage‐dependent losses and reliability norm
Authors: Lele Sharad M.
Published: February 2008

Two algorithms that improve upon the sequent‐peak procedure for reservoir capacity calculation are presented. The first incorporates storage‐dependent losses (like evaporation losses) exactly as the standard linear programming formulation does. The second extends the first so as to enable designing with less than maximum reliability even when allowable shortfall in any failure year is also specified. Together, the algorithms provide a more accurate, flexible and yet fast method of calculating the storage capacity requirement in preliminary screening and optimization models.
On hydrologic similarity: 2. A scaled model of storm runoff production
Authors: Sivapalan M. , Beven Keith , Wood Eric F.
Published: February 2008

The paper describes a simple physically based conceptual model of runoff production based on catchment topography and the spatial variablity of rainfall and soil properties. Both infiltration excess (Horton type) and saturation excess (Dunne type) runoff production mechanisms are considered. The effect of topography is modeled using the In (α/tan β)‐topographic index method of Beven and Kirkby (1979). The effects of the spatial variability of soil properties and rainfall on areal average infiltration rates are handled using a quasi‐analytical approach. The interaction between the two mechanisms of runoff production and the effect of a finite water table on the infiltration excess mechanism are explicitly considered. The model equations are cast in a dimensionless form to clarify the interrelationships involved in hydrological responses and to identify measures of similarity between different heterogeneous catchments. The dimensionless formulation has led to the identification of five similarity parameters and three dimensionless variables representing initial conditions and storm characteristics. Finally, a number of experiments were performed to study the sensitivity of the runoff production response to some of these similarity parameters.
Sample volume effects on solute transport predictions
Authors: Parker J. C. , Albrecht K. A.
Published: February 2008

Saturated hydraulic conductivities Ks and solute dispersivites under saturated flow conditions λ were determined in the laboratory on cores of three different volumes (92, 471, and 1770 mL) taken at two depths in different soil layers along closely spaced parallel transects. Variances of In Ks decreased and mean λ increased with increasing core volume reflecting greater within‐core and lower between‐core velocity variations for larger cores. Mean Ks values were significantly lower for the smallest core size suggesting structural disturbance. To investigate effects of sample volume on reduced time field scale transport predictions, Monte Carlo simulations were carried out. From multinormal joint probability distributions of In Ks and In λ for the two layers, mean breakthrough curves were generated for each soil layer separately and as a two‐layer system using a vertical stream tube approach with transverse mixing ignored. To evaluate effects of uncertainty in parameter estimates due to the finite sample number, a second level of Monte Carlo analysis was performed assuming normally distributed, independent errors in the estimated means and covariances of parameters for the two layers. Differences between break‐through curves predicted for each core size were relatively small and within 95% error bounds for the means.
Time to ponding: Comparison of analytic, quasi‐analytic, and approximate predictions
Authors: Broadbridge P. , White I.
Published: February 2008

An analytic expression for time to ponding is introduced using the nonlinear model of Broadbridge and White (1987). The hydraulic properties of this model can encompass properties ranging from those of a highly nonlinear Green‐Ampt‐like soil to those satisfying the weakly nonlinear Burgers' equation. Because of its versatility, this analytic solution is used as a benchmark against which extant analytic, quasi‐analytic, and approximate expressions are compared. Time to ponding is parameterized here in terms of the readily measured field properties, sorptivity and hydraulic conductivity. In the limit of Green‐Ampt‐like properties the analytic solution reduces exactly to the Parlange and Smith (1976) approximation. A similar functional dependence of time to ponding on rainfall rate is found from quasi‐analytic approximations. Based on this, a modified approximation is suggested which should give time to ponding for most soils to within ±10%. Some existing approximations are found to have unacceptable deviations from the analytic solution, and their continued use appears unwarranted. Finally, we address the field problem of predicting time to ponding at any antecedent water content, given sorptivity measured at only one initial water content.
The common property aquifer as a differential game
Authors: Negri Donald H.
Published: February 2008

Open‐loop and feedback equilibria are compared using a common property aquifer model. Open‐loop solutions correspond to assuming that participants commit themselves in the initial period to pumping rates in all future periods. Feedback solutions represent a more realistic assumption as farm operators adopt pumping strategies that depend on the reserve stock of water. Comparing the two equilibrium concepts reveals two sources of dynamic inefficiency in the common property aquifer: a pumping cost externality and a “strategic externality” that arises from the competition among users to capture the groundwater reserves. The qualitative results show that the open‐loop solution captures only the pumping cost externality. The feedback solution captures both externalities and exacerbates the over‐ exploitation of the commons compared to the open‐loop solution. Moreover, the dynamic inefficiency resulting from both externalities increases in the number of independent landowners with access to the aquifer.
Solute and water movement in unsaturated soils
Authors: Barnes C. J.
Published: February 2008

Chromatographic theory of competitive solute movement through porous, reactive soils with nonlinear adsorption isotherms is extended to conditions of unsteady flow in the unsaturated zone under gravity. By treating water content as an extra solute component, equations governing coupled movement of solute and water through reactive soils under gravity are shown to be a special case of those governing competitive solute movement, leading to a quantitative description of the coupled movement of the water and solute fronts through a soil column. When one solution displaces another at a different concentration and water potential in a reactive soil, the solute and water front splits up into two distinct subfronts, separated by a region in which both concentration and potential are constant. Each subfront is characterized by a region in which water content and concentration vary in a predetermined manner, according to certain functions (characteristics), one of which must remain constant over each subfront. Only in certain simple cases will solute concentration and water content vary independently of each other. The case when the hydraulic conductivity depends on solute concentration is explicitly considered.
Multidimensional steady infiltration to a water table
Authors: Philip J. R.
Published: February 2008

We address the question of the applicability of the body of solutions for quasi‐linear multidimensional steady infiltration with perfect drainage to cases with a water table (or, by inference, a sloping impermeable base) at a finite depth beneath the water supply source. The exact solutions for steady quasi‐linear point and line sources over a water table are our point of departure. With their aid we construct approximate solutions to the general problem of three‐dimensional axisymmetric and two‐dimensional steady infiltration from finite water supply sources at fixed moisture potential to a water table at finite depth. We take as illustrative solutions disc‐ and strip‐shaped water supply sources. When the depth from the source to the water table (or the base) is of order 4 sorptive lengths, perfect drainage solutions yield discharge estimates of ample accuracy. When the depth is less, our approximate analysis gives, in favorable cases, the requisite correction. In less favorable cases it gives the order of magnitude of the correction. The study is facilitated by a method of exponentially weighted images, applicable to the quasi‐linear flow equation.
Extended linear quadratic Gaussian control: Further extensions
Authors: Georgakakos Aristidis P.
Published: February 2008

The extended linear quadratic Gaussian (ELQG) control method (Georgakakos and Marks, 1987) is a stochastic control algorithm for the optimal operation of multiobjective reservoirs. Mathematically, this method optimizes a general functional of a stochastic system in state‐space form with upper and lower release constraints and probabilistic storage bounds. ELQG is a sequential algorithm which accounts for stochastic effects by preserving the first two statistical moments of the system's inputs and storages. In this paper, the method is first extended to handle nongaussian features which frequently characterize reservoir inputs. Second, ELQG's efficiency with respect to reliability storage constraints is discussed, and a new barrier function method is researched. These modifications are tested in case studies with the Savannah river system.
Derivation of conditions describing transport across zones of reduced dynamics within multiphase systems
Authors: Hassanizadeh S. Majid , Gray William G.
Published: February 2008

Equations for describing flow and transport in multiphase systems can be derived within the context of averaging theory. In some subsurface systems, the balance equations must be three dimensional in one portion of a domain of interest but need be only one or two dimensional in other regions (e.g., across clay lenses or within fractures). Conditions linking the dynamic processes among the different regions are typically obtained heuristically. Here a general framework is presented within which the needed conditions may be derived systematically. Particular conditions for mass, momentum, chemical species, and heat transfer are illustrated between main porous media domains and both a permeable fracture and a semipermeable layer.
Inferences about the mean from censored water quality data
Authors: El‐Shaarawi A. H.
Published: February 2008

Several methods which are commonly used for making inferences about the levels of many metals and organic contaminants in ambient waters from type I censored data are critically evaluated, and their applications are illustrated using the concentrations of polychlorinated biphenyls in water samples from the Niagara River. Difficulties encountered in the application of all the methods, except the method of maximum likelihood, include ignoring the information available about the analytical detection limit and the unavailability of the standard errors for these estimates. Under the assumption that the distribution of the data is lognormal, the log regression method is modified to produce estimates of the censored values which use the detection limit information, and the properties of the maximum likelihood estimates for the lognormal mean are derived. Furthermore, an approximate confidence interval for the lognormal mean is given, and its use for estimating the load to and from the Niagara River is illustrated. The above methods along with a modification to the method of maximum likelihood are evaluated using Monte Carlo simulation.
Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers: 2. Impervious boundary
Authors: Rubin Yoram , Dagan Gedeon
Published: February 2008

The spatial variability of the head H in a two‐dimensional flow in the vicinity of an impervious boundary is investigated. This study is a continuation of a previous one (Rubin and Dagan, 1988) which dealt with the influence of a given head boundary. By representing H and the log transmissivity Y as space random function and by solving the flow equation, first‐order, closed form, analytical expressions for the head variogram and the head‐log transmissivity Y covariance are developed. These expressions offer the means to evaluate the influence of the boundary on the joint Y, H random field. The assumption of unbounded domain is examined, and it is found to be a good approximation at distances larger than three log transmissivity integral scales from the boundary. By using conditional probabilities, a simple method to estimate the statistical moments close to the boundary is presented. It requires the knowledge of the moments of Y and H in the unbounded domain only. The method is compared with the exact analytical solution, showing favorable results.
Modeling one‐dimensional infiltration into very dry soils: 1. Model development and evaluation
Authors: Hills R. G. , Porro I. , Hudson D. B. , Wierenga P. J.
Published: February 2008

With the increasing economic growth in the arid regions of the West, and with the growing need for waste disposal and storage, the ability to efficiently model water flow and pollutant transport through unsaturated soils is becoming more important. One of the more difficult water flow problems to model, from a numerical point of view, is infiltration into very dry soils. The presence of very steep pressure gradients combined with the large field scales leads to algorithms that are very CPU intensive. Here we develop a water content based algorithm that is suitable for modeling one‐dimensional unsaturated water flow into layered soils. We show that this algorithm is a numerical approximation of a general form of Richards equation. We compare the computational efficiency of this algorithm with that of two pressure head based finite difference water flow algorithms for several test problems. We find that the mass balance errors for the noniterative water content formulation are of the order of machine round off error for most applications. We also find that for soils with fairly wet initial conditions (h ≈ −100 cm H2O) the water content formulation requires approximately the same CPU time as the faster of the two pressure head formulations. For very dry soils (h=−1000 to −50,000 cm H2O) the CPU time required for the water content formulation is not a function of the initial water content of the soil, whereas the CPU time required for the pressure head formulation strongly increases with decreasing initial water content. Because of this lack of sensitivity to initial conditions, the water content based algorithm is from 1 to 3 orders of magnitude faster than the pressure head based algorithms when applied to infiltration into very dry soils. The water content algorithm is not suitable for combined saturated‐unsaturated or near‐saturated flow that may be present because of local heterogeneities in the soil. In addition, the water content algorithm cannot handle positive pressure upper boundary conditions such as those associated with ponded surface water.
Radon in groundwater: A tool to assess infiltration from surface waters to aquifers
Authors: Hoehn E. , Von Gunten H. R.
Published: February 2008

We measured the concentrations of natural 222Rn (half‐life 3.8 days) in groundwater at three sites in Switzerland; here groundwater is recharged mainly by river water. Upon infiltration and movement in the ground, the radon concentration in the water increases by more than two orders of magnitude to reach a steady state. This increase was found at two of the three sites. At the site of main interest, we used the ingrowth of radon between the river and nearby observation wells to estimate groundwater residence times of up to about four half lives. We assumed that the ingrowth of radon can be described by the growth law of radioactivity, that the progenitors of radon (226Ra, 238U) are homogeneously distributed in the aquifer, and that the freshly infiltrated water is not mixed significantly with older groundwater. A linear regression through the data at the site of main interest yielded an average flow velocity of 4.6 m −1, which confirms earlier tracer observations. Radon accumulates to higher concentrations, when the top soil layer is frozen or exhibits a high moisture content. During these conditions the radon data cannot be used for dating purposes.
Modeling soil seal as a nonuniform layer
Authors: Mualem Y. , Assouline S.
Published: February 2008

A quantitative conceptual model of soil sealing is proposed, based on the assumption that the compaction of the upper soil layer by raindrops and the “washed in” material result in a nonuniform change in bulk density, which can be approximated by an exponential function. The change in density causes in turn variations in soil properties, such as porosity, water retention, and hydraulic conductivity. Empirical functions are suggested to simulate the pattern by which these properties vary as dependent upon the density change. The model was calibrated using data of two experimental studies related to crust properties of three different soils: sandy loam, loam (loess), and clay loam. The model reproduced quite well the observed features of the experimental sealing characteristics. Seals developed in two different flow systems subjected to simulated rain were analyzed: (1) seal developed under saturated conditions over a shallow soil bed and (2) seal developed under unsaturated flow conditions. The proposed model highlights some soil parameters that are quite important and should be observed in soil sealing investigations. It also presents a basis for quantitative analysis of the soil sealing phenomenon in terms of measurable physical parameters.
An isotopic investigation of groundwater in the Central San Juan Basin, New Mexico: Carbon 14 dating as a basis for numerical flow modeling
Authors: Phillips Fred M. , Tansey Michael K. , Peeters Leslie A. , Cheng Songlin , Long Austin
Published: February 2008

Carbon 14 dating of groundwater can be used to help determine the transmissivity distributions of aquifers. This method may offer significant advantages, in certain respects, over traditional aquifer pumping test techniques. We have applied 14C dating to a hydraulic analysis of a multilayer aquifer system in the central San Juan Basin of New Mexico. After corrections for geochemical evolution of the solutes, the influence of dispersive processes on the 14C distribution was investigated. A model incorporating stochastic dispersion theory indicated that macroscopic dispersion exerted only a small influence on the measured 14C activities. The 14C‐derived transmis sivity distribution was used to construct a numerical flow model which was applied to an analysis of interaquifer leakage. The model showed that even though vertical flow between aquifers was significant, in this case it did not cause the 14C distribution to differ significantly from that predicted by a simple piston flow model. Carbon 14 can be used as a basis for detailed hydraulic evaluations of groundwater flow in areas where traditional well hydraulics methods are not practical.
Hydrostratigraphic interpretation using indicator geostatistics
Authors: Johnson Nicholas M. , Dreiss Shirley J.
Published: February 2008

In this paper we describe an approach that uses indicator geostatistics to interpret qualitative borehole logs and compute experimental variograms for complex alluvial sediments. Borehole descriptions are first transformed into binary indicator values based on inferred relative permeability from the borehole descriptions. The resulting indicator data can then be used to compute variograms and construct three‐dimensional variogram models. The ranges of computed indicator variograms for a groundwater contamination site in Santa Clara Valley, California, are very sensitive to the orientation of the search plane. These variograms are consistent with known stratigraphie features and describe the spatial structure of deposits from different depositional environments. Indicator kriging weighs all the available data on the basis of a three‐dimensional, anisotropic variogram model and provides an estimate of uncertainty in the hydrostratigraphic correlation. Kriged indicator values represent probabilities that sediments at a specific location fall into one of two indicator categories. The location of the 0.5 indicator contour is approximately the boundary between high‐ and low‐permeability sediments that might be constructed in a geologic cross section.