bluuebunny/crossref_metadata_2025 huggingface dataset:
Optimal control of nonlinear groundwater hydraulics using differential dynamic programming
Authors: Jones LaDon , Willis Robert , Yeh William W.‐G.
Published: February 2008

Optimal groundwater management models are based on the hydraulic equations of the aquifer system. These equations relate the state variables of the groundwater system, the head, and the decision variables that control the magnitude, location, and timing of pumping, or artificial recharge. For the unconfined aquifer these management models are large‐scale, nonlinear programming problems. A differential dynamic programming (DDP) algorithm is used for unsteady, nonlinear, groundwater management problems. Due to the stagewise decomposition of DDP, the dimensionality problems associated with embedding the hydraulic equations as constraints in the management model are significantly reduced. In addition, DDP shows a linear growth in computing effort with respect to the number of stages or planning periods, and quadratic convergence. Several example problems illustrate the application of DDP to the optimal control of nonlinear groundwater hydraulics.
Flow processes in a curved alluvial channel
Authors: Odgaard A. Jacob , Bergs Mary A.
Published: February 2008

Dynamic features of the flow in a 180° constant‐radius, recirculating laboratory channel are studied. The width‐depth ratio and radius‐width ratio of the channel are 16 and 5.4, respectively, and the sediment is sand with median grain diameter and geometric standard deviation of 0.3 mm and 1.45, respectively. The particle densimetric Froude number is 6.5. Individual components of the momentum equation are measured, and their relative effect on the momentum balance is evaluated. It is found that flow accelerations, notably downstream acceleration of the downstream and cross‐stream velocity components, induced as a result of change in channel curvature at the entrance to the bend have a significant effect on the flow processes in this bend. The cross‐stream velocity gradients are relatively insignificant. The curvature change affects the flow and bed topography in a manner similar to that in which a driving force affects an underdamped oscillating system. The findings are used for an evaluation of available bend flow models.
Multicomponent exchange and subsurface solute transport: Characteristics, coherence, and the Riemann Problem
Authors: Charbeneau Randall J.
Published: February 2008

When water of one chemical composition is displaced by water of another, there is a change in composition at any point within the flow system which may occur more or less rapidly, depending on both the hydraulics and chemistry of the system. For many applications it is possible to decouple the hydraulic and chemical analyses, and later combine them for prediction of effluent compositions from well fields or concentration histories at observation wells. When an advection‐reaction model is used, the displacement problem is described mathematically as a Riemann problem. In this paper the Riemann problem is solved for the ternary exchange system using the method of characteristics. The pattern of composition changes is found to follow the right eigenvector paths in composition space, and the eigenvalues provide composition‐dependent retardation functions. The hydraulics is treated fairly generally and allows one to consider steady uniform or nonuniform flow fields or stochastic flow models. Both laboratory and field applictions are presented.
The fluid mechanics of fracture and other junctions
Authors: Philip J. R.
Published: February 2008

In connection with solute transfer in fracture networks, Hull and Koslow (1986) proposed proportional routing of streamlines through discontinuous fracture junctions (in which inlet and outlet branches alternate). We apply fluid mechanics to the problem and show that the errors of proportional routing may be unacceptably large when the two inlet discharges and the two outlet discharges both differ greatly in magnitude. In extreme cases one inlet flow is wholly excluded from one of the two outlets, and proportional routing is maximally incorrect. Solutions are established for arbitrary discharge patterns through four‐way coplanar junctions: exact solutions for Laplace flows (Hele‐Shaw flows and Darcy flows (fractures filled with porous material)) and approximate solutions for Stokes flows. The Laplace solutions apply also to a range of transport processes.
Geochemistry of groundwater in tertiary and cretaceous sediments of the southeastern Coastal Plain in eastern Georgia, South Carolina, and southeastern North Carolina
Authors: Lee Roger W. , Strickland Donald J.
Published: February 2008

Geochemical samples of groundwater taken along hydrologic flow paths in eastern Georgia, South Carolina, and southeastern North Carolina, from noncalcareous sand aquifers, largely of Cretaceous age, are dominated by sodium and bicarbonate ions. Calcareous sand aquifers, largely of Tertiary age, contain water whose chemistry is dominated by calcium and bicarbonate ions, but may evolve downgradient to sodium and bicarbonate dominance. Water chemistry in both types of aquifer evolves to sodium chloride dominance as a result of fresh water mixing with subsurface brines or seawater present in the deeper downgradient parts of the aquifers. Principal aqueous chemical reactions appear to occur in five reaction zones in the aquifers and include feldspar hydrolysis to kaolinite, calcite dissolution, calcium‐for‐sodium cation exchange, and neoformation of sodium smectite in the downgradient parts of the aquifers. Redox reactions produce dissolved iron concentrations greater than 1 mg/L near the recharge areas. Organic matter in the aquifers is oxidized to CO2 by iron reduction and sulfate reduction processes. Production of CO2 by a methanogenic process may also occur. Geochemical mass‐transfer models simulating the observed chemistry in western Alabama and eastern Mississippi have been extended to account for higher concentrations of sodium and bicarbonate observed in the South Carolina part of the aquifers.
Variability of yield of an irrigated crop and its causes: 3. Numerical simulation and field results
Authors: Dagan Gedeon , Bresler Eshel
Published: February 2008

The prediction of yield variability of an irrigated crop, as influenced by the uncertainty of soil, plant, and boundary conditions parameters, and an investigation through numerical simulation, using the probability theory apparatus, are tested against field data. Among the large number (19) of parameters, six which have a significant impact on yield variability have been singled out. These include two plant parameters with an average relative contribution of 23%, three soil hydraulic parameters with a relative impact of 47%, and one irrigation boundary condition parameter, related to the nonuniformity of water application, with 30% average contribution upon yield variability. An additional set of results is related to the yield coefficient of variation. Its range was simulated to be generally between 0.3 and 1, with an average of approximately 0.6. A similar range, but with a somewhat lower average was measured in the field. The detection of the parameters of large impact, obtained by both simulation and field validation, give an indication of weak links which require further investigation, and for which collection of field data is important.
The extent of snowpack influence on water chemistry in a North Cascades Lake
Authors: Loranger Thomas J. , Brakke David F.
Published: February 2008

Integrated snowpack samples and lakewater samples were collected from a low‐alkalinity watershed in the North Cascades in 1984 and 1985 and analyzed for inorganic chemical parameters. Mean concentrations of NO3− and SO4−2 from North Cascades snowpack were near 4.5 and 5.5 μeq L−1, respectively. Mean pH was 5.2–5.3. During melting, anion levels in the snowpack decreased and pH increased. By July, mean NO3− and SO4−2 concentrations were 0.32 and 1.73 μeq L−1, respectively, and mean pH was 5.48. Acid neutralizing capacity at the lake outlet during snowmelt was diluted to 50% of April premelt values. During snowmelt runoff there was no apparent neutralization of bicarbonate by strong acids. By comparing lakewater NO3− concentrations to snowpack concentrations, over 75% of the NO3− in the lake could be attributed to a snowpack source. An estimated 30% of the SO4−2 in the lake was derived from the snowpack.
Effective discharge for suspended sediment transport in streams of the Saskatchewan River Basin
Authors: Ashmore P. E. , Day T. J.
Published: February 2008

Effective discharge for suspended sediment load was determined for 21 sites in the Saskatchewan River basin at which sediment records range from 5 to 29 years in length. The drainage areas for these streams ranges from 10 to over 300,000 km2. The sediment discharge histograms have a variety of forms ranging from the classic unimodal form in which the peak occurs at discharges with a duration of 1–3% to those in which the effective discharge is the extreme event of record and cases in which a single effective discharge is difficult to define. The percentage duration of the effective‐discharge ranges from less than 0.1% to over 15%, a greater range than previously has been reported. There is an obvious tendency for the percentage duration of the effective discharge to increase with drainage area and hence downstream through the drainage system.
Dispersion in heterogeneous porous media: 1. Local volume averaging and large‐scale averaging
Authors: Plumb O. A. , Whitaker S.
Published: February 2008

The problem of diffusion and dispersion in porous media is considered in the absence of either adsorption or chemical reaction. For this situation, local volume averaging has been used to obtain both a convection‐dispersion equation and a method of closure that provides for a direct theoretical prediction of the dispersion tensor. This approach is associated with three length scales, lβ, the pore diameter, ro, the radius of the averaging volume, and L the macroscopic length scale, and makes use of a representative unit cell to determine the dispersion tensor. Previous work suggests that extremely complex unit cells must be used to capture the observed dispersion phenomena, and complex unit cells naturally introduce another length scale, i.e., the length scale associated with the local heterogeneities. To deal with this problem, we propose the use of large‐scale averaging to account for the influence of the local heterogeneities. This leads to a large‐scale convection‐dispersion equation that contains additional terms involving time derivatives which arise as a result of the presence of heterogeneities and which do not appear in the conventional local volume average convection‐dispersion equation. The first new term contains the second derivative with respect to time and is likely to be unimportant for time scales appropriate for groundwater transport processes; however, it may be important for small‐scale laboratory experiments. The second new term contains a mixed space‐time derivative which may be important for many cases of practical interest. A closure scheme is presented that allows for the theoretical determination of all the coefficients that appear in the large‐scale convective‐convection‐dispersion equation.
Multiple reflection and attenuation of time domain reflectometry pulses: Theoretical considerations for applications to soil and water
Authors: Yanuka M. , Topp G. C. , Zegelin S. , Zebchuk W. D.
Published: February 2008

The application of time domain reflectometry (TDR) to determine soil water content, using only the time axis of a TDR trace, has been widely investigated. Other interpretations from the TDR trace, such as the determination of electrical conductivity, make use of the amplitude or reflection coefficient values. These latter interpretations must take account of multiple reflections in the media. A multiple‐reflection algorithm is developed which takes account of primary reflection first, then provides for inclusion of higher‐order reflections as well. The algorithm is formulated to generate the TDR trace from a sequence of known dielectrics. The inverse case is analyzed where the dielectric constant of the layered medium is calculated from a measured TDR trace. The model allows for both conductive and nonconductive dielectrics. Experiments showed that the model is a reasonably good qualitative representation of the layered nonconductive media with a wide range of dielectric constants. There is insufficient information in a TDR trace to solve the conductive cases except for a single layer. From KCl solutions at two concentrations the experiments showed that instantaneous reflection and transmission are inadequate assumptions for conductive systems. This indicates the need for caution when applying the model to conductive media such as soils, especially where soil water content is not uniform.
An optimization model for screening multipurpose reservoir systems
Authors: Lall Upmanu , Miller Craig W.
Published: February 2008

An optimization model is presented for selecting among and sizing potential reservoirs on a river basin. The provision of water to meet municipal and industrial, irrigation, and hydropower demands, as well as recreation and flood control at each candidate reservoir site are considered. A compact, nonlinear optimization formulation for the reservoir sizing problem is derived by decomposing the problem into simulation and optimization components. Reservoir storage capacities needed are determined using a modified sequent peak algorithm to simulate monthly reservoir operation. Simulation is also employed to determine optimal sizes for hydropower generators at each site. Similarly, average annual flood control and recreation benefits are determined through simulation. An optimization scheme that considers annual yields for each purpose with specified reliabilities and conservation and flood storage as decision variables is used to integrate these simulations into an optimal screening algorithm. Significant savings in computational and memory requirements over other formulations are offered at the expense of nonlinear functional forms. Applications of the model developed with data from sites on the Lower Bear River are presented.
A distributed parameter approach for evaluating the accuracy of groundwater model predictions: 2. Application to groundwater flow
Authors: McLaughlin Dennis , Wood Eric F.
Published: February 2008

The distributed parameter theory presented by McLaughlin and Wood (this issue) is used to evaluate the accuracy of a groundwater flow model. The special case investigated assumes that the model's prediction errors are due primarily to data limitations. In this case, approximate prediction error moments (mean and covariance) are obtained by solving two sets of coupled partial differential equations which have the same basic structure as the original flow equation. Solutions can be obtained with spectral, Green's function, or numerical techniques, depending on the assumptions made. Two examples are solved using a finite element approach. The first (two‐dimensional) example confirms steady state infinite domain results obtained with spectral methods. The second (three‐dimensional) example investigates the influence of spatial variability, sampling strategy, and suboptimal estimation on model prediction accuracy.
Extension of the Fujita Solution to air and water movement in soils
Authors: Sander G. C. , Parlance J.‐Y. , Hogarth W. L.
Published: February 2008

For specific soil properties the fundamental solution of Fujita (1952b) is extended to include the effect of air movement on horizontal absorption. This exact solution is then used to determine the accuracy and range of applicability of two approximations to the sorptivity with air effects previously presented by Parlange et al. (1982) and Sander and Parlange (1984). The optimal sorptivity of Parlange et al. has very good accuracy while the surface water content θs is near saturation but decreases in accuracy as θs decreases. The approximate sorptivity of Sander and Parlange, however, proves to be extremely accurate for all θs with a maximum error of only 0.5%. Sander and Parlange additionally give an approximation to the water profile which is also shown by comparison with the exact solution to have a maximum error of only 0.5%. The aim of this paper is primarily of a theoretical nature in that we use the exact solution to check the accuracy of the approximate solutions as stated above. Alternatively, the solution may be used for checking the accuracy of numerical models.
Twin Lake Tracer Tests: Setting, methodology, and hydraulic conductivity distribution
Authors: Killey R. W. D. , Moltyaner G. L.
Published: February 2008

Following evaluation of three potential sites, a fluvial sand aquifer with high (0.7–1.6 m d−1) linear average groundwater flow velocities was instrumented with a fully penetrating injection well and 82 monitoring installations over a 40‐m flow path length. Two natural gradient tracer migration experiments have employed pulse injections of a nonreactive radioisotope (131I) in a study of hydraulic conductivity structure and dispersive characteristics of the flow system. The use of a gamma‐emitting radionuclide in these experiments allowed measurement of tracer distribution by scanning fully penetrating boreholes with a scintillation detector. This technique provided many advantages in data collection over conventional tracers, including unprecedented resolution of the vertical distribution of tracer, measurements without pumping and the attendant concerns for flow system perturbation, and minimal manpower for sample analysis. Tracer breakthroughs at monitors along the axis of flow revealed the presence of heterogeneities in aquifer hydraulic conductivity at two scales. Over the 40‐m path length, six regions with hydraulic conductivities substantially different from adjacent strata were identified. Thicknesses of these regions varied from 0.2 to more than 3 m; their lateral extents (in the direction of groundwater flow) ranged from 15 m to more than 40 m. Smaller strata, with an average thickness of 0.34 m and lengths of less than 10 m, were detected within all six of the hydraulic conductivity regions, but there was no evidence of increases in local dispersivity with increased transport distance as a result of these variations. The six hydraulic conductivity regions do, however, have measurable effects on whole‐aquifer dispersion. Stratification characteristics of the tested aquifer, believed to have been deposited in a sandy braided river, are consistent with those observed in similar modern environments. Estimation of the magnitude and spatial structure of hydraulic conductivity variations in aquifers of concern would be greatly aided by studies of the stratification characteristics in well‐exposed modern or lithified sedimentary analogues.
Recession characteristics of groundwater outflow and base flow from mountainous watersheds
Authors: Zecharias Yemane B. , Brutsaert Wilfried
Published: February 2008

The relationship between base flow recession characteristics in steep watersheds and geomorphologic and soil parameters is investigated. The formulation for the groundwater outflow was obtained by means of a hydraulic approach applied to a simple conceptual model for a hillslope. Long‐term flow data of 19 representative basins in the Allegheny Mountain section of the Appalachian Plateaus were analyzed on the basis of this formulation. Results showed that the reaction factor, which is a time scale of base flow recession, is dependent on the mean land slope, the drainage density, and the ratio (K/f) of the hydraulic conductivity and the drainable porosity. On account mainly of the nonuniform distribution of the physical characteristics within a basin, the reaction factor for a given watershed is somewhat variable with time, but the adoption of a constant value is useful to represent average conditions for a recession period. Analysis of the (K/f) dependency showed that macropores and other structural features may greatly affect the watershed base flow. Evaporation from groundwater appears to constitute only a minor portion of overall basin evaporation.
On the Dagan Model of solute transport in groundwater: Application to the Borden Site
Authors: Barry D. A. , Coves J. , Sposito Garrison
Published: February 2008

In the first part of this study, Sposito and Barry (1987) derived an ensemble‐mean convection‐dispersion equation (CDE) for tracer solute transport subject to a random velocity field. It was shown that the model dispersion coefficients originally presented by Dagan (1984) could be derived from the general expression for the dispersion coefficients in this mean CDE. Under the assumption of ergodicity, the Dagan model is used in this paper to predict chloride and bromide concentrations in the well‐documented Borden aquifer experiment reported by Roberts and Mackay (1986). Because of a possible influence on the solute from the upper aquifer boundary, it was appropriate to apply the two‐dimensional form of the model. A number of steps was necessary to reduce the three‐dimensional raw data to a two‐dimensional form, the main ones being integration over the vertical axis and the use of a gridding algorithm to form a two‐dimensional solute concentration surface. Incomplete sampling of the solute plume during the early sampling sessions, as well as the assumptions made with respect to the data analysis, produce a rather large degree of uncertainty in the specification of the initial solute plume. These factors hinder a thorough experimental evaluation of the Dagan model. Data from some of the later sampling sessions were more complete, however, and the model predictions appeared to agree well with the field concentration data, especially in the preasymptotic region for the longitudinal dispersion coefficient.
Determination of fluid flow properties from the response of water levels in wells to atmospheric loading
Authors: Rojstaczer Stuart
Published: February 2008

The water level in a well that taps a partially confined aquifer is often sensitive to atmospheric loading. The magnitude and character of this response is partly governed by the well radius, the lateral hydraulic diffusivity of the aquifer, the thickness and vertical pneumatic diffusivity of the unsaturated zone, and the thickness and vertical hydraulic diffusivity of the saturated zone overlying the aquifer. These key elements can be combined into five dimensionless parameters that partly govern the phase and attenuation of the response. In many cases, the response of a well to atmospheric loading can be broken up into a high‐, intermediate‐, and low‐frequency response. The high‐frequency response is governed largely by the well radius and lateral diffusivity of the aquifer. The intermediate‐frequency response is governed by the loading efficiency of the aquifer. The low‐frequency response is governed by the vertical pneumatic diffusivity and thickness of the unsaturated zone and the vertical hydraulic diffusivity and thickness of the saturated material above the aquifer. Cross‐spectral estimation is used to fit the response to atmospheric loading of three water wells to the theoretical curves in order to yield estimates of three of the key dimensionless parameters. These estimates then are used to make estimates or place bounds on the vertical pneumatic diffusivity of the unsaturated zone, the lateral permeability of the aquifer, and the composite vertical hydraulic diffusivity of the overlying saturated materials.
Two‐dimensional steady state unsaturated water flow in heterogeneous soils with autocorrelated soil hydraulic properties
Authors: Hopmans J. W. , Schukking H. , Torfs P. J. J. F.
Published: February 2008

The stochastic nature of soil water pressure head and vertical and horizontal flux density under two‐dimensional unsaturated steady state flow conditions was examined by using a Monte Carlo technique. Random autocorrelated scale factors were generated by a first‐order nearest neighbor model and were used to describe a stationary random field of hydraulic conductivity functions. Scale factor values were assumed to vary only in the horizontal direction, perpendicular to the mean flow. The water flow equation was numerically solved for steady state infiltration and transpiration in a two‐dimensional domain, of which the lower boundary was described by a groundwater level. Differences in results between a saturated and unsaturated soil water system were most likely caused by the direction in which the hydraulic properties are randomly autocorrelated and differences in the applied boundary conditions. In contrast to earlier findings with respect to the saturated system, the variability in fluxes for the unsaturated system decreased with an increase in the autocorrelation length, and the variation in soil water pressure head for one‐ and two‐dimensional systems tended to be equal with increasing autocorrelation lengths. When considering a two‐layer system it was found that the variability in the lateral flow component at the layer boundary was severely increased as compared to the single‐layer simulations.
Fast multireservoir multiperiod linear programing models
Authors: Kuczera George
Published: February 2008

Multireservoir, multiperiod linear programing models are typically computationally very expensive. Some of these models can be formulated as network linear programs (NLPs), for which computer codes about 100 times faster than general linear programing codes are available. A NLP formulation is presented for determining water assignments in a multireservoir system over some time horizon. It provides for demand zone shortfalls due to drought or transfer limitations, instream flow requirements, which can be violated during droughts, and seasonal reservoir target volumes. It also allows the trade‐off between reliability and demand shortfall severity to be explored. A case study illustrates computational performance. A NLP was formulated for a three‐reservoir, two‐demand zone water supply system modeled over 324 periods. It was solved in 26 CPU seconds on a VAX 8550 computer. Finally, it is shown that a NLP can be formulated to find the required minimum capacity of one reservoir in a multireservoir system so that system demand is just meet over some planning period.
Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers
Authors: Valocchi Albert J.
Published: February 2008

Spatial moment analysis is used in this paper to study the asymptotic, long‐time behavior of the depth‐averaged solute plume for transport in a perfectly stratified aquifer. The solute is assumed to adsorb onto the aquifer solids according to a first‐order reversible kinetic rate law; steady, unidirectional, horizontal flow is assumed with arbitrary vertical variation in pore water velocity, dispersion coefficients, and adsorption reaction parameters. We derive general formulas to calculate the effective dispersion coefficient governing the transport of the depth‐averaged plume. The results demonstrate that overall longitudinal spreading of the plume results from three distinct factors: local Darcy scale longitudinal dispersion, vertical variations in the pore water velocity and retardation factor, and adsorption kinetics. For the example of a two‐layer aquifer, a simple nonequilibrium index is derived which shows that deviations from local equilibrium diminish as the degree of heterogeneity of the retarded pore water velocity increases. It is also demonstrated that enhanced plume spreading can be caused by negative correlation between the vertically varying pore water velocity and retardation factor in addition to slow adsorption kinetics. Thus great caution is warranted in interpreting the results of field scale reactive tracer experiments.
Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, leakance, and recharge
Authors: Gómez‐Hernández J. Jaime , Gorelick Steven M.
Published: February 2008

A stochastic simulation approach was used to inspect the influence of spatial variability in aquifer and recharge properties on effective (averaged) groundwater model parameters. A two‐dimensional unconfined aquifer model was set up for an area similar to that near Livermore, California. Monte Carlo simulations were generated for different sets of spatial correlation structures assuming stationarity and an exponential semivariogram. For each Monte Carlo realization, groundwater flow was simulated, and estimates of the means and standard deviations of the hydraulic head were obtained. Nine different cases were studied involving different correlation lengths of hydraulic conductivity, conditional simulations, parameter zonation, and spatial recharge distributions. Results indicate that there is no single uniform value of the hydraulic conductivity that reproduces the expected head values. Spatial averaging to obtain effective values was based on the p norm (power norm) which ranges from 1 for the arithmetic mean to −1 for the harmonic mean, with 0 representing the geometric mean. For the unconditional case the −0.4 p norm seems to best reproduce the expected values. The −0.2 p norm gave the best result for the conditional simulation case. If the geometric mean were used instead, the heads would deviate from the expected heads by about 2 m near the wells. Some value between the arithmetic and the geometric means of riverbed leakance will give results close to the expected head values. The arithmetic mean of aerially distributed recharge produced results with small deviations from the expected head values. These particular results may only apply to this modeled system, as the pumping pattern and magnitudes exhibited strong influences on zones of maximum head deviation. The implication of this work is that if an effective hydraulic conductivity is used in a simulation model, it must be selected for a particular set of wells and pumping rates. In an aquifer with significant pumping centers the best effective value for a two‐dimensional unconfined flow model is most likely between the geometric and harmonic mean. If the wells are turned off, the effective hydraulic conductivity for that flow model reverts to the geometric mean.
Solution of the flow at a corner problem with a stagnation zone
Authors: Boast Charles W. , Baveye Philippe
Published: February 2008

Laboratory one‐dimensional flow experiments in soil columns have long given mixed indications as to whether there are deviations from Darcian proportionality at low hydraulic gradients. Recently, evidence for the existence of “stagnant” zones was obtained by Desaulniers et al. (1986) in natural systems, where measured chemical parameters were found inconsistent with predictions based on measured gradients and hydraulic conductivities, and an assumption of Darcy behavior. These data could lead one to speculate that deviations from Darcy behavior may be of practical consequence, even for situations where the deviation does not appreciably decrease the total flux through a flow system, and even though soil column flow experiments have been ambiguous on the question of non‐Darcy behavior. If a deviation from Darcy's equation is such that the flux density is zero for any hydraulic gradient less than a “threshold gradient,” then for particular flow regimes there will be flow in some portion of a porous medium and no flow in another, referred to here as a “stagnation zone.” The location of a “stagnation boundary,” separating a flow zone and a stagnation zone, is unknown a priori in a boundary value problem statement. The determination of the stagnation boundary is part of the problem solution (just as is the determination of the water table position in an unconfined groundwater flow problem). The principles governing stagnation boundaries are elucidated; a method is described for determining the location of the stagnation boundary for a porous medium with “jump‐to‐proportionality” threshold gradient behavior, and the method is used to solve the “flow at a corner” boundary value problem. The solution is compared to that of the analogous classical problem, in which strict adherence to Darcy's equation is assumed.
Contaminant transport in a single fracture: Periodic boundary and flow conditions
Authors: Lowell Robert P.
Published: February 2008

The effects of time‐periodic inlet contaminant concentration and groundwater flow velocity on contaminant transport in a single, planar fracture, imbedded in a relatively impermeable rock matrix, are investigated. The calculations show that the contaminant propagates as a damped traveling wave into the matrix and along the fracture. If longitudinal dispersion is neglected, penetration of the wave into the matrix and fracture depends upon the input frequency σ as σ−½. Under uniform flow conditions, a daily oscillation penetrates into the matrix and fracture approximately 1 cm and 1 m, respectively. An annual oscillation penetrates approximately 10 cm and tens of meters for the matrix and fracture, respectively. These results depend upon physical properties of the rock matrix and fracture, and upon the flow velocity. Because longitudinal dispersion acts to further damp the amplitude of the traveling waves, these results give maximum penetration distances for the waves. If the flow velocity also has a small, time‐periodic component, the downstream contaminant oscillations are virtually unchanged unless the inlet condition and flow have the same frequency. In this case, a dc transport of contaminant transport occurs that may have an amplitude as large as one‐half of the magnitude of the velocity oscillation. These results indicate that in the absence of resonance, negligible error occurs in treating contaminant transport using mean inlet and flow conditions rather than more realistic time‐varying ones. Observations of oscillations, however, can be used to provide useful information on rock and fracture transport properties such as D′ and D.
An analytical model of contaminant transport from diffuse sources in saturated porous media
Authors: Dillon P. J.
Published: February 2008

An analytical two‐dimensional model of solute transport along a vertical cross section of an aquifer is described. The model extends analytical methods to two‐dimensional dispersive solute transport in a two‐dimensional flow field which until now has been the exclusive province of numerical models. This avoids the very significant problems of numerical instability and numerical dispersion facing the application of numerical transport models at a regional scale. Furthermore, the model is simple and very fast. A novel feature is the segregation of longitudinal and transverse transport components. The model is intended for preliminary evaluation of groundwater quality on a regional scale in areas subject to diffuse sources of contamination. It gives vertical resolution of contaminant concentrations through the aquifer thickness. Results compare favorably with finite element model results for a case involving a strip source of contaminants. It has been useful in predicting the impact of diffuse source nitrate contamination on groundwater quality in the Lower South East of South Australia.
Methods for determining transverse dispersion coefficients of porous media in laboratory column experiments
Authors: Robbins Gary A.
Published: February 2008

Continuous point source and instantaneous finite source methods are presented for determining the transverse dispersion coefficient of saturated porous media in laboratory column experiments. The methods entail injecting a conservative tracer from an injector embedded in a porous medium, monitoring concentration variations with time within the column upgradient from where the tracer impinges on the column wall, and extracting longitudinal and transverse dispersion coefficient values from relative concentration‐time data using three‐dimensional advection‐dispersion formulations. The methods were tested in a column packed with glass beads for comparison with reported flow tank tests. The transverse dispersion coefficient values calculated using column test data agree closely with flow tank results. The methods presented offer new approaches for investigating dispersion phenomena in porous media and especially offer the potential for determining the transverse as well as the longitudinal dispersion coefficient of undisturbed core samples.
A modified method of characteristics technique and mixed finite elements method for simulation of groundwater solute transport
Authors: Chiang C. Y. , Wheeler M. F. , Bedient P. B.
Published: February 2008

A comprehensive groundwater solute transport simulator is developed based on the modified method of characteristics (MMOC) combined with the Galerkin finite element method for the transport equation and the mixed finite element (MFE) method for the groundwater flow equation. The preconditioned conjugate gradient algorithm is used to solve the two large sparse algebraic system of equations arising from the MMOC and MFE discretizations. The MMOC takes time steps in the direction of flow, along the characteristics of the velocity field of the total fluid. The physical diffusion and dispersion terms are treated by a standard finite element scheme. The crucial aspect of the MMOC technique is that it looks backward in time, along an approximate flow path, instead of forward in time as in many method of characteristics or moving mesh techniques. The MFE procedure involves solving for both the hydraulic head and the specific discharge simultaneously. One order of convergence is gained by the MFE method, as compared with other standard finite element methods, and therefore more accurate velocity fields are simulated. The overall advantages of the MMOC‐MFE method include minimum numerical oscillation or grid orientation problems under steep concentration gradient simulations, and material balance errors are greatly reduced due to a very accurate velocity simulation by the MFE method. In addition, much larger time steps with Courant number well in excess of 1, as compared with the standard Galerkin finite element method, can be taken on a fixed spatial grid system without significant loss of accuracy.
Modeling of two‐dimensional overland flow
Authors: Zhang Weihua , Cundy Terrance W.
Published: February 2008

A two‐dimensional hydrodynamic and numerical model for overland flow is developed in this paper. The model allows spatial variations in hillslope physical characteristics, including surface roughness, infiltration, and microtopography. The accuracy of the model is tested by comparison with characteristic‐based solutions and experimental data. The results of these tests indicate that the model is accurate and has good stability and convergence properties. The application of the model to two‐dimensional overland flow on hillslopes is demonstrated by applying it to surfaces with spatially variable roughness, infiltration, and microtopography. These simulations show that microtopography is the dominant factor causing spatial variation in overland flow depth, velocity, and direction.
Multiobjective sampling design for parameter estimation and model discrimination in groundwater solute transport
Authors: Knopman Debra S. , Voss Clifford I.
Published: February 2008

Sampling design for site characterization studies of solute transport in porous media is formulated as a multiobjective problem. Optimal design of a sampling network is a sequential process in which the next phase of sampling is designed on the basis of all available physical knowledge of the system. Three objectives are considered: model discrimination, parameter estimation, and cost minimization. For the first two objectives, physically based measures of the value of information obtained from a set of observations are specified. In model discrimination, value of information of an observation point is measured in terms of the difference in solute concentration predicted by hypothesized models of transport. Points of greatest difference in predictions can contribute the most information to the discriminatory power of a sampling design. Sensitivity of solute concentration to a change in a parameter contributes information on the relative variance of a parameter estimate. Inclusion of points in a sampling design with high sensitivities to parameters tends to reduce variance in parameter estimates. Cost minimization accounts for both the capital cost of well installation and the operating costs of collection and analysis of field samples. Sensitivities, discrimination information, and well installation and sampling costs are used to form coefficients in the multiobjective problem in which the decision variables are binary (zero/one), each corresponding to the selection of an observation point in time and space. The solution to the multiobjective problem is a noninferior set of designs. To gain insight into effective design strategies, a one‐dimensional solute transport problem is hypothesized. Then, an approximation of the noninferior set is found by enumerating 120 designs and evaluating objective functions for each of the designs. Trade‐offs between pairs of objectives are demonstrated among the models. The value of an objective function for a given design is shown to correspond to the ability of a design to actually meet an objective.
An interpretation of the difference between aperture estimates derived from hydraulic and tracer tests in a single fracture
Authors: Silliman S. E.
Published: February 2008

Recent field efforts involving testing of single fractures indicate that hydraulic and tracer tests provide different estimates of fracture aperture. It is argued that this behavior is a result of the averaging involved in the use of the cubic law for these tests. This argument leads to the following predictions for slow flow through variable aperture fields: (1) For flow parallel to aperture channeling the aperture estimate from a tracer test will be greater than the estimate from a hydraulic test, (2) for flow perpendicular to aperture channeling the tracer test provides the smaller estimate, and (3) for flow in isotropic aperture fields the tracer test again provides the smaller aperture estimate. Lognormally distributed aperture fields are used to demonstrate the magnitude of aperture variability which may be observed under three flow geometries. It is noted that the maximum difference between aperture estimates occurs when the variance of the aperture distribution is large, a result which is consistent with other studies of random aperture fields. Finally, it is suggested that the relative variation of the aperture estimates may provide a means whereby the orientation of anisotropy or channeling may be identified.
Stochastic analysis of field measured unsaturated hydraulic conductivity
Authors: Ünlü K. , Kavvas M. L. , Nielsen D. R.
Published: February 2008

Unsaturated hydraulic conductivity K values as a function of soil‐water pressure head h were measured in the soil at 75 cm depth at 70 different sites separated from one another by a distance of l m along a horizontal transect. K field was viewed as a random function of spatial location x. Field data were analyzed (1) to examine the isotropy and stationarity of K, (2) to check the ergodicity of K in the mean and covariance functions, and (3) to characterize the distribution properties of K by estimating the higher‐order correlations, that is, third and fourth cumulants. The mean functions were estimated by averaging over h and x. The covariance function was studied to investigate its spatial origin dependency. Logs and square roots of K were used for estimating the third and fourth cumulants. Results showed that spatial covariance functions are anisotropic and both lag and origin dependent, that is, spatially nonhomogeneous. Because the stationarity (statistical homogeneity) of K is scale dependent, which was indicated by the identification of locally stationary covariance regions, the ergodic properties of K are also scale dependent at smaller spatial scales. Results related to the distribution characteristics of K indicated that although ln K is marginally Gaussian distributed, in the context of spatial stochastic processes the random field of ln K is not Gaussian because the third and fourth cumulants of the field are still significantly different from zero and have the same order of magnitude as the first and second cumulants. The square root transformation, however, resulted in a random field that is approximately Gaussian although marginal distributions of
remained skewed. Analyses of ln K and
indicated that better transformations which would result in both marginal and joint Gaussian behavior for the random field of K are needed.
Contaminant accumulation during transport through porous media
Authors: Gruber Joachim
Published: February 2008

When a soil, rock, or sediment is exposed to changes of its chemical environment, that is, by infiltration of water, the new chemical composition propagates as a wave through the medium. Adsorbed contaminants may desorb behind the front of this remobilizing wave. If the velocity of the front is intermediate between the contaminant velocities upstream and downstream of the front, the remobilized contaminant accumulates at the front. The behavior of adsorbates on oxides under these circumstances is discussed. The analysis suggests that contaminant adsorption isotherms are insufficient to characterize the potential hazard associated with a contaminated soil or sediment. The additional data needed are the velocities of the possible remobilizing waves.
Sampling stochastic dynamic programming applied to reservoir operation
Authors: Kelman Jerson , Stedinger Jery R. , Cooper Lisa A. , Hsu Eric , Yuan Sun‐Quan
Published: February 2008

Most models for reservoir operation optimization have employed either deterministic optimization or stochastic dynamic programming algorithms. This paper develops sampling stochastic dynamic programming (SSDP), a technique that captures the complex temporal and spatial structure of the streamflow process by using a large number of sample streamflow sequences. The best inflow forecast can be included as a hydrologic state variable to improve the reservoir operating policy. A case study using the hydroelectric system on the North Fork of the Feather River in California illustrates the SSDP approach and its performance.
Multivariate geostatistical approach to space‐time data analysis
Authors: Rouhani Shahrokh , Wackernagel Hans
Published: February 2008

A large number of hydrological phenomena may be regarded as realizations of space‐time random functions. Most available hydrological data sets exhibit time‐rich/space‐poor characteristics, as well as, some form of temporal periodicity and spatial non‐stationarity. To better understand the space‐time structure of such hydrological variables, the observed values at each measurement site are considered as separate, but correlated time series. Moreover, it is assumed that the time series are realizations of a mixture of random functions, each associated with a different temporal scale, represented by a particular basic variogram. To preserve the observed temporal periodicities, the experimental direct and cross variograms are modelled as linear combinations of a number of hole function variograms. In a further step, the principal component analysis is used to determine groupings of measurement stations at different temporal scales. The proposed procedure is then applied to monthly piezometric data in a basin south of Paris, France. The temporal scales are determined to be the 12‐month seasonal and the 12‐year climatic cycles. At each temporal scale different spatial groupings are observed which are attributed to the contrast between the nearly steady state climatic variations versus the almost transient seasonal fluctuations.