bluuebunny/crossref_metadata_2025 huggingface dataset:
Behavior of sensitivities in the one‐dimensional advection‐dispersion equation: Implications for parameter estimation and sampling design
Authors: Knopman Debra S. , Voss Clifford I.
Published: February 2008

The spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media. Physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one‐dimensional form of the advection‐dispersion equation. When parameters are estimated in regression models of one‐dimensional transport, the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates. Several principles account for the observed influence of sensitivities on parameter uncertainty. (1) Information about a physical parameter may be most accurately gained at points in space and time with a high sensitivity to the parameter. (2) As the distance of observation points from the upstream boundary increases, maximum sensitivity to velocity during passage of the solute front increases and the consequent estimate of velocity tends to have lower variance. (3) The frequency of sampling must be “in phase” with the S shape of the dispersion sensitivity curve to yield the most information on dispersion. (4) The sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity. (5) The assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities. (6) If variance in random error in observations is large, trends in sensitivities of observation points may be obscured by noise and thus have limited value in predicting variance in parameter estimates among designs. (7) Designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters. (8) The time and space interval over which an observation point is sensitive to a given parameter depends on the actual values of the parameters in the underlying physical system.
Field‐scale evaluation of infiltration parameters from soil texture for hydrologic analysis
Authors: Springer Everett P. , Cundy Terrance W.
Published: February 2008

Recent interest in predicting soil hydraulic properties from simple physical properties such as texture has major implications in the parameterization of physically based models of surface runoff. This study was undertaken to (1) compare, on a field scale, soil hydraulic parameters predicted from texture to those derived from field measurements and (2) compare simulated overland flow response using these two parameter sets. The parameters for the Green‐Ampt infiltration equation were obtained from field measurements and using texture‐based predictors for two agricultural fields, which were mapped as single soil units. Results of the analyses were that (1) the mean and variance of the field‐based parameters were not preserved by the texture‐based estimates, (2) spatial and cross correlations between parameters were induced by the texture‐based estimation procedures, (3) the overland flow simulations using texture‐based parameters were significantly different than those from field‐based parameters, and (4) simulations using field‐measured hydraulic conductivities and texture‐based storage parameters were very close to simulations using only field‐based parameters.
Channel model of flow through fractured media
Authors: Tsang Y. W. , Tsang C. F.
Published: February 2008

On the basis of a review of recent theoretical and experimental studies of flow through fractured rocks, we have studied the fluid flow and solute transport in a tight fractured medium in terms of flow through channels of variable aperture. The channels are characterized by an aperture density distribution and a spatial correlation length. Aperture profiles along the channels are statistically generated and compared to laboratory measurements of fracture surfaces. Calculated tracer transport between two points in the fractured media is by way of a number of such channels. Tracer breakthrough curves display features that correspond well with recent data by Moreno et al., which lends support to the validity of our model. Calculated pressure profiles along the channels suggest possible measurements that may be useful in identifying the geometrical characteristics of the channels. Finally, predictions were made for tracer breakthrough curves in the case of single fractures under various degrees of normal stress. These suggest possible laboratory experiments which may be performed to validate this conceptual model.
Simulation of contaminant transport in three dimensions: 2. Dimensionality effects
Authors: Burnett R. D. , Frind E. O.
Published: February 2008

The alternating direction Galerkin technique developed in the first paper of this series is applied to the simulation of field‐scale contaminant transport scenarios in two and three dimensions, and dimensionality effects are examined. In the case of vertical‐plane simulation, the dimensionality effect, which becomes noticeable at a transverse dispersivity of only 1 cm, can result in significant overestimation of plume length. In the case of vertically averaged horizontal plane simulation, the apparent length of a plume defined in terms of vertical averages will be much less than that of the equivalent plume defined in terms of peak concentrations. Only the three‐dimensional simulation is capable of producing the actual concentration values that drive local processes such as chemical reactions. The cost of the three‐dimensional simulations, while substantially greater than that of the two‐dimensional simulations, is shown to be reasonable.
A capillarity correction for free surface flow of groundwater
Authors: Parlange J.‐Y. , Brutsaert Wilfried
Published: February 2008

The Boussinesq equation describes aquifer movement when capillarity effects are unimportant. A simple correction term to the equation is proposed here to take those effects into account. The correction can be quite significant for relatively short times. Comparison with experimental observations for a sudden drawdown shows that the present theory greatly improves the Boussinesq equation.
The statistical structure and filter characteristics of tritium fluctuations in fractured basalt
Authors: Duffy Christopher J. , Harrison Jack
Published: February 2008

The statistical structure and spectral‐covariance characteristics of tritium fluctuations are examined from injection of low‐level radioactive waste in a fractured basalt aquifer. The tritium fluctuations are the result of a time‐varying injection well concentration. The integral scale of the fluctuations increases with distance from the source and the observation well spectra are characteristic of a dispersive‐type filter. On the basis of these qualitative attenuation characteristics, a theoretical filter is constructed and transport parameters are estimated. The analysis indicates that environmental tracers may provide a useful extension to controlled tests over large length scales (> 100 m). Although current research has concentrated on the importance of intrinsic variability such as porous media heterogeneities, the present study addresses the control exerted by extrinsic variability as exhibited by source strength fluctuations.
A modified linear programming gradient method for optimal design of looped water distribution networks
Authors: Fujiwara O. , Jenchaimahakoon B. , Edirishinghe N. C. P.
Published: February 2008

A modified linear programming gradient (LPG) method is presented for solving looped water distribution network problems, together with a mathematically rigorous derivation of the LPG model. The LPG method of Alperovits and Shamir is modified in terms of both search direction and step size. A quasi‐Newton search direction is proposed instead of the steepest descent direction, and the step size is determined by a backtracking line search method instead of a fixed step size. The modified method is applied to a numerical example, where it provides an improved solution in comparison to the original LPG method.
Use of stochastic dynamic programming for reservoir management
Authors: Trezos Thanos , Yeh William W‐G.
Published: February 2008

Hydropower production plays an important role in the operation of electric energy production‐distribution systems. Since most of the economically feasible hydroelectric sites have already been developed, it is necessary to examine and develop practical, real‐time operational models which can be used to increase the output from existing hydropower plants. Three main issues are addressed by this research: the potential of increasing the output from existing hydropower plants, the alleviation of dimensionality problems for multistate dynamic programming, and the use of probabilistic forecast in the decision‐making process. An optimization model is developed which can be used as an analytical tool in the decision‐making process for reservoir operation. The model takes into consideration the uncertainty of forecast at the time a policy must be established. The uncertainty is expressed in terms of the second moments of the forecast probability distributions. There is no limitation on the type of distribution, and it is assumed that forecast is made by a conceptual type of watershed model. The proposed methodology is applicable to constrained stochastic systems with quadratic objective functions and linear dynamics. It uses the decomposition principle of dynamic programming without discretizing the state or control variable and therefore the method can be used for large‐scale systems. It is an iterative procedure which requires an initially feasible solution and solves a series of quadratic programming problems at each iteration. The applicability of the research is demonstrated through case studies.
Parameter estimation in groundwater: Classical, Bayesian, and deterministic assumptions and their impact on management policies
Authors: Loaiciga Hugo A. , Mariño Miguel A.
Published: February 2008

This work deals with a theoretical analysis of parameter uncertainty in groundwater management models. The importance of adopting classical, Bayesian, or deterministic distribution assumptions on parameters is examined from a mathematical standpoint. In the classical case, the parameters (e.g., hydraulic conductivities or storativities) are assumed fixed (i.e., nonrandom) but unknown. The Bayesian assumption considers the parameters as random entities with some probability distribution. The deterministic case, also called certainty equivalence, assumes that the parameters are fixed and known. Previous work on the inverse problem has emphasized the numerical solution for parameter estimates with the subsequent aim to use them in the simulation of field variables. In this paper, the role of parameter uncertainty (measured by their statistical variability) in groundwater management decisions is investigated. It is shown that the classical, Bayesian, and deterministic assumptions lead to analytically different management solutions. Numerically, the difference between such solutions depends upon the covariance of the parameter estimates. The theoretical analyses of this work show the importance of specifying the proper distributional assumption on groundwater parameters, as well as the need for using efficient and statistically consistent methods to solve the inverse problem. The distributional assumptions on groundwater parameters and the covariance of their sample estimators are shown to be the dominant parameter uncertainty factors affecting groundwater management solutions. An example illustrates the conceptual findings of this work.
Estimation of Brooks‐Corey Parameters from water retention data
Authors: Milly P. C. D.
Published: February 2008

The parameters of the Brooks‐Corey soil moisture characteristic may be determined by either graphical or automatic numerical procedures. A popular log‐log procedure for automatic estimation leads to a linear least squares optimization problem. Apparently, it has been applied incorrectly in the past when all measurements were used for parameter estimation, and this realization explains the inconsistencies in some published data. Its proper application generally requires the solution of more than one linear problem for each data set. Alternatively, a nonlinear procedure will yield parameter estimates directly. In either case there may exist multiple local minima in the sum of squared deviations between model and measurements, and the parameter estimates so derived are demonstrably unreliable; this appears to be a result of the distinct air‐entry suction implicit in the Brooks‐Corey model and usually absent in field‐measured characteristic curves. A new procedure based on an integral objective function overcomes the problems cited.
Stochastic considerations in optimal design of a microcatchment layout of runoff water harvesting
Authors: Oron Gideon , Enthoven Gerda
Published: February 2008

A management model was defined and solved for optimal runoff water use in arid zones via microcatchment. The microcatchment layout consists of hexagons. In determining their optimal size, stochastic characteristics of the rain and runoff generation were taken into account.
Introduction of the Stream Function Concept to the analysis of hydrodynamic dispersion in porous media
Authors: Batu Vedat
Published: February 2008

The stream function concept is introduced to the analysis of hydrodynamic dispersion in porous media. The governing partial differential equation for the stream function for two‐dimensional flow under steady state water and solute transport conditions in an isotropic porous medium is derived. For a uniform seepage velocity, the corresponding differential equation is obtained as a special case. The equation for axially symmetric solute transport case is also derived. It is shown that the isoconcentration curves and the hydrodynamic dispersion stream lines are not orthogonal to each other. For the uniform seepage velocity field case, general solutions are presented for concentration distribution and hydrodynamic dispersion stream function (HDSF) for strip sources having variable concentration distributions. Special solutions are presented for concentration, HDSF, and convective‐dispersive flux components for a strip source having constant concentration. The concept of hydrodynamic dispersion bounding streamline separating the solute transport zone from the other zones is also introduced. The methodology of the HDSF concepts and the solutions for some idealized cases can be applied for contaminant plume analysis, computer model validation, and other hydrogeological studies.
From field data to fracture network modeling: An example incorporating spatial structure
Authors: Long Jane C. S. , Billaux Daniel M.
Published: February 2008

This paper describes a technique for processing field data for a fracture network model which accounts for the observed spatial variability. This has been done by generating a network subregion by subregion where the properties of each subregion are predicted through geostatistics. Once the geometry of a particular realization is specified, flow through the network is studied. We develop the method for a two‐dimensional analysis based on data from Fanay‐Augeres, a uranium mine in France. We plan to extend the analysis to three dimensions and compare the results with in situ test results. In particular, we have focused on the data collected in a long section of a drift where fractures have been mapped and steady state permeability tests have been performed in 10 boreholes. In order to generate fractures in a statistically heterogeneous region we first divided the region into statistically homogeneous subregions. In each subregion and for each fracture set we must specify the areal fracture density and the orientation, length, and aperture distributions. We divided the fractures into five sets based on tectonic history and observed that for each set, fractures spaced close together tended to have similar orientations. This was built into the simulation. An estimate of the aperture distribution for each set was made by assuming that the hydraulic apertures of the fractures intersecting a well test zone were proportional to the fracture opening observed in the core. Data input to the geostatistical analysis for each set consisted of 16 values of mean length and density of fractures in each 5 m by 2 m section of the drift wall. The results of the simulation are tables of values for mean length and fracture density for each of the five sets. The value of density simulated for each subregion was used directly to determine the number of fractures to be generated of that set in the subregion. The value of mean length was used as the mean of the length distribution in the subregion. The local coefficient of variation for length was the same in every subregion. Using the data described above, we generated a 100 m by 100 m fracture network in a series of 100 statistically homogeneous subregions. The fractured region generated has a total of 65,740 fractures. A 70 m by 70 m region was isolated for directional permeability testing. Results show that the system is barely connected. About 0.1% of the fractures essentially control permeability. In the language of percolation theory this mesh is close to the critical density for which infinite clusters of fractures are found. Problems remaining include that (1) the analysis should be extended to three dimensions, (2) the geostatistical simulation and network simulation should be combined, rather than used as two separate operations, and (3) the nature of flow through single fractures at Fanay‐Augeres should be investigated.
Kinematic wave approximation to the transport of Escherichia coli in the vadose zone
Authors: Germann P. F. , Smith M. S. , Thomas G. W.
Published: February 2008

Threshold values for macropore flow parameters that are thought to be critical in the transport of microbial suspensions through macroporous soils were established through the application of a kinematic wave approach to bacterial breakthrough curves. According to the presented examples, moisture content w and conductance b in the macropore systems of four different soils had simultaneously to exceed 0.015 (m3/m3) and 0.1 (m/s), respectively, before substantial microbial breakthrough was observed at the bottom of undisturbed columns of macroporous soils with lengths ranging from 0.21 to 0.32 m. The application of these thresholds in a modeling approach to large‐scale flow revealed that hardly any microbes can be transported deeper than 2–3 m in soils when durations and intensities of naturally occurring precipitation events were entered into the model. It was also shown, however, that prolonged or intensified water input to the soil surface may efficiently carry microbes deeper than 100 m into the vadose zone.
A new method for the real‐time operation of reservoir systems
Authors: Georgakakos Aristidis P. , Marks David H.
Published: February 2008

This paper introduces a new method for the real‐time operation of reservoir systems. The system is represented by a set of stochastic differential equations describing the reservoir and river dynamics in state space form. The formulated reservoir operation problem calls for finding policies which maximize the expected benefits of one system's objective while satisfying the remaining objectives at prespecified reliability levels. The solution is obtained by a new method named extended linear quadratic Gaussian (ELQG) controller. ELQG draws on and extends stochastic control theory results, and it is well suited for the optimization of constrained dynamical systems. It is a trajectory iteration algorithm theoretically expected to exhibit reliability and computational efficiency. The new method is tested and evaluated in a real‐world case study.
Use of current meters for continuous measurement of flows in large rivers
Authors: Derecki Jan A. , Quinn Frank H.
Published: February 2008

Flows in the unregulated Great Lakes connecting channels, the St. Clair and Detroit Rivers, are normally determined using mathematical flow models with calibration based on periodic discharge measurements taken during the open‐water seasons. Consequently, the calculated flows normally exhibit good accuracy during ice‐free periods, but may contain large errors during winter months with extensive ice cover. The St. Clair River is particularly prone to large ice jams because of practically unlimited ice flow supply provided by Lake Huron and an extensive river delta that retards the passage of these ice flows. This study describes the experimental results of continuous flow measurements using electro magnetic (EM) current meters and an acoustic Doppler current profiler (ADCP) meter during the 1983–1985 period. A record ice jam in the St. Clair River occurred in April 1984 and provided an excellent opportunity for testing the current meter program. Verification of current meter results was provided by flows transferred from the Detroit River, which was ice‐free and permitted accurate flow simulation. The current meter flow measurement program illustrated high consistency of exponential (logarithmic) vertical distribution of velocities. Results indicate that accurate estimates of mean river flows can be obtained with a single well‐placed current meter. However, the EM current meters are direct contact single‐point sensors that are affected by frazil ice during winter and weed effects during most of the year. The ADCP meter is a remote sensor of velocities in the overhead water column and is not affected by the frazil ice and weed problems.
An energy balance approach to determine regional evapotranspiration based on planetary boundary layer similarity theory and regularly recorded data
Authors: Abdulmumin S. , Myrup Leonard O. , Hatfield Jerry L.
Published: February 2008

An energy balance procedure was developed to determine regional evapotranspiration using only regularly recorded solar radiation and rawinsonde data. The major input terms in the basic energy balance equation are daily surface net radiation and sensible heat flux. Net radiation was determined by empirical and semiempirical radiation balance equations and the sensible heat flux term from an aerodynamic mass transfer equation derived from concepts of planetary boundary layer similarity theory. The procedure gave better results for a small (100 ha) agricultural watersheds than a comparable procedure based on purely aerodynamic mass transfer considerations, especially on 1‐ and 2‐day periods. For a larger (1000 ha) hydrologic watershed the model achieved acceptable accuracy for monthly estimates of regional evapotranspiration. On this time scale, comparison with observation yielded slopes from 0.97 to 1.14 with correlations between 0.90 and 0.91. For the monthly comparison, the purely aerodynamical model achieved virtually the same accuracy. These results were obtained using the same data set that was used to calibrate the model. When independent data were used, the accuracy for the monthly estimate degraded (slope 0.75, correlation 0.40). For bimonthly estimates, accuracy improved (slope 0.92, correlation 0.73).
Laboratory investigation of longitudinal dispersion in anisotropic porous media
Authors: Silliman S. E. , Konikow L. F. , Voss C. I.
Published: February 2008

In this study, laboratory experiments were used to investigate mechanisms that may cause anisotropy in the dispersion coefficient and to investigate the relation between anisotropy in hydraulic conductivity and anisotropy in longitudinal dispersion. Measurements of sodium chloride concentration (used as a tracer) were made at 105 in situ sampling locations in a new type of sand box designed to allow flow in either of two perpendicular directions. Two types of hydraulic anisotropy were examined. The first consisted of structured zones of increased hydraulic conductivity within a lower‐conductivity medium. The second type involved low‐conductivity platelike inclusions within a homogeneous, isotropic medium. The plates were aligned such that the tortuosity was increased only in one principal direction of permeability. Results using two examples of the first type of media showed that the apparent longitudinal dispersivities for flow parallel to the high‐conductivity direction were greater than those perpendicular to this direction. Two examples of the second type of media produced smaller apparent longitudinal dispersivities for flow parallel to the high‐conductivity direction. The results suggest that the mechanisms causing dispersive anisotropy can be related, conceptually, to the factors causing hydraulic anisotropy.
Cycles in finite samples and cumulative processes of higher orders
Authors: Klemeš Vít , Klemeš Ivo
Published: February 2008

The process formed by a sequence of cumulative departures from the mean or from some other constant (residual mass curve, cusum chart) is a popular tool for the representation and analysis of time series in many sciences, for example, in hydrology, climatology, economics, game theory. In these and other natural and social sciences, similar cumulative processes also often arise naturally; examples include fluctuations of storage in a dam with a constant release rate, lake levels, volume of glaciers, biomass, inventories, and bank accounts. Moreover, many natural economic and other phenomena may represent, or contain, components of cumulative processes of higher orders, i.e., cumulative processes of cumulative processes. In this paper we show that for a sample {yt(0)}≡{xt} of any finite size N, the pure cumulative process of nth order, yt(n)≡∑i=1t(yi(n−1) − μ(n−1)), where μ(n−1) is the sample mean of {yt(n−1)} and t=1, 2, …, N, converges for n→∞ to a sine wave with a period equal to an integral fraction of the sample size N. This happens for any initial sample {yt(0)} and the convergence is of an exponential order. For samples from most stochastic as well as deterministic processes, the period of the limiting sine wave is equal to the sample size N. This behavior is demonstrated by examples involving samples from various processes ranging from pure random series to various deterministic series and including time series of some natural processes such as streamflow, lake levels, and glacier volumes. The paper includes a demonstration of effects of noise superimposed on, and of error in the value of, sample mean on the rate of convergence, and a discussion of some practical implications of the phenomenon described; it brings together some aspects of the work of Slutzky (1937), Hurst (1951), and Yule (1926).
Hydrologic detection of abandoned wells near proposed injection wells for hazardous waste disposal
Authors: Javandel Iraj , Tsang Chin Fu , Witherspoon Paul A. , Morganwalp David
Published: February 2008

Deep saline aquifers are being used for disposal of hazardous liquid wastes. A thorough knowledge of the competency of such aquifers and their confining geologic beds in permanently isolating the hazardous substances is the key to successful disposal operations. Characterization of such systems, and in particular the detection of any conduit that may permit hydraulic communication between the host aquifer and nearby freshwater aquifers, must be carried out prior to the initiation of disposal projects. In deep, multi‐aquifer systems, leaky faults, abandonded wells, highly conductive fractures, or shear zones may all provide leakage paths. If not initially detected, such conduits may show no apparent effect until contaminants in the freshwater aquifer reach detectable levels at the discharge point. By then, of course, detection is generally too late. This paper is an attempt to address the problem of initial detection of improperly plugged or open abandoned wells. A new analytic solution has been derived to calculate the amount of leakage from an abandoned well and the corresponding drawdown at monitoring wells. A method is proposed that can be used to detect such deep abandoned wells in the area of influence of a proposed deep injection well in a multiple‐aquifer system.
Numerical analysis of the nonsteady transport of interacting solutes through unsaturated soil: 2. Layered systems
Authors: Russo David
Published: February 2008

Transient one‐dimensional vertical transport of interacting solutes through a saturated‐unsaturated stratified soil profile during infiltration was studied using a modified version of the transport model described in part 1 [Russo, this issue], taking into account the depth variations of the coupling interacting soil input parameters. The solute transport was analyzed for two sequences of soil layering: a fine‐textured soil overlying coarser textured soils and a coarse‐textured soil overlying finer textured soils. Each sequence was analyzed for two different initial conditions and a given surface boundary condition pertinent to a common irrigation practice using nonsaline water. Results of the analyses suggested that the effect of soil‐matrix‐soil‐solution interactions on the transport of water and solutes may be significant and generally depends on the sequence of the soil layering and on the shape of the initial soil solutions's sodium adsorption ratio (SAR) profile. For a given initial soil solution's SAR profile the effect of soil‐solution‐soil‐matrix interactions on the transport process is greater when a fine‐textured soil is overlying coarser textured soils. For a given sequence of layering the movement of the interacting solutes may be retarded or accelerated relative to a reference inert state, depending on the shape of the initial soil solution's SAR profile relative to the sequence of the layering. The possible effects of soil‐solution‐soil‐matrix interacting on the spatial variability of solutes on a field scale are discussed briefly.
Unidimensional solute transport incorporating equilibrium and rate‐limited isotherms with first‐order loss: 1. Model conceptualizations and analytic solutions
Authors: Lassey Keith R.
Published: February 2008

I derive analytic solutions to the advection‐dispersion equation for unidimensional solute or tracer transport. The tracer undergoes both sorption and first‐order loss. Sorption is via a linear Freundlich isotherm in tandem with rate‐limited exchange (after Lapidus and Amundson). An arbitrary tracer input is postulated, with pulse input and step input specializations given detailed consideration. Many distinct conceptual models of unidimensional transport are mathematically equivalent to this formulation, including a model of exchange between mobile and immobile water, and including models with selective first‐order removal processes. Ambiguities in interpreting model simulations of experimental data have two origins: more than one conceptual model is a contending simulator; a conceptual model may be mathematically overspecified with parameters. The implications of such ambiguities are discussed.
Variability of yield of an irrigated crop and its causes: 1. Statement of the problem and methodology
Authors: Bresler Eshel , Dagan Gedeon
Published: February 2008

Crop yield depends on a large number of soil‐, water‐, and atmosphere‐related parameters. Some of these parameters are spatially variable and most of them are subject to uncertainty. Consequently, the yield is also spatially variable and its prediction is uncertain. The aims of this study were to (1) estimate the degree of yield variability as a function of variability of various parameters and (2) attempt to single out those parameters, the variability of which are estimated to have the largest impact upon the variability of yield of an irrigated crop. The first part of the study presents the general methodology developed in order to achieve these aims. It consists of a numerical deterministic model which predicts crop yield relative to its potential yield for a given irrigation regime and quality of water and for given soil and atmospheric conditions. Subsequently, the model is used to derive the values of expectation and variance of the relative irrigated crop yield as functions of these values of the various parameters.
Variability of yield of an irrigated crop and its causes: 2. Input data and illustration of results
Authors: Bresler Eshel , Dagan Gedeon
Published: February 2008

The data needed in order to evaluate the impact of the variability of different parameters upon crop yield variability were collected from various sources in the literature. Two fields (Paoche in the United States and Bet Dagan in Israel), which had been studied extensively in the past, were selected as representative for a wide range of soil conditions. In a similar manner, standard values of the expectations and extreme values of variances of other soil‐plant‐atmospheric parameters were inferred from the literature. The adopted values are summarized in a table. The dependence of the relative yield and its derivatives upon each of 19 parameters, while the remaining ones are kept fixed at their standard expected value, is illustrated.
Buoyancy flow at a two‐fluid interface in a porous medium: Analytical studies
Authors: Hellström Göran , Tsang Chin‐Fu , Claesson Johan
Published: February 2008

Analytical solutions for the pressure distribution and the flow field are derived for several idealized situations involving an injection well and a vertical plane or cylindrical interface between two fluids of different density and viscosity in an infinite anisotropic aquifer bounded by two horizontal planes. The interface, or transition zone, between the two fluids may be either sharp or of finite width. The buoyancy flow induced by the density difference will cause the two‐fluid interface to tilt. A characteristic time scale for the buoyancy tilting rate is deduced. The conditions at the well are found to have only a small influence on the buoyancy flow except very close to the well. The buoyancy flow decreases with increasing width of the transition zone.
Optimal dewatering schemes in the foundation design of an electronuclear plant
Authors: Galeati Giorgio , Gambolati Giuseppe
Published: February 2008

A three‐dimensional finite element model combined with an optimization approach based on linear mixed integer programming is developed and applied to assist in the design of the dewatering system for the electronuclear plant to be built by the Italian Electric Agency (ENEL) in Trino Vercellese, northwestern Italy. The foundations site is encompassed by a 25‐ to 35‐m deep plastic wall with the purpose of protecting the unconfined aquifer from the significant water table lowering required by the construction project. To reduce further the propagation of the depression cone a large amount of the water pumped out is reinjected through “ad hoc” recharge ditches. The finite element optimization model includes both the natural and the artificial constraints and provides several optimal withdrawal strategies for the dewatering system design concerning the distribution of the abstraction wells and the corresponding pumping rates. Physical and economical objective functions are explored and the related solutions are discussed.
A single decision‐maker approach to irrigation reservoir and farm management decision making
Authors: Dudley Norman J.
Published: February 2008

A model for optimizing short‐, intermediate‐, and long‐run irrigation decisions for surface water reservoirs is developed for a river valley irrigation system controlled by one decision maker. The modeled valley is characterized by highly variable reservoir inflows and crop growing conditions, and irrigable land supplies which are plentiful relative to available water. It advances similar work of the early 1970s pertaining to a corn monoculture by using a complex soil water‐plant growth simulation model for cotton developed by crop scientists over a number of years, and by employing an extra simulation model to simulate the effects of using optimal decisions derived by dynamic programming. The results indicate a potential for disagreement about reservoir management strategies and level of irrigation development between irrigators, other members of the local economy, and national economy policy makers. The assumption of one decision maker internalizes the derivation and communication of supply and demand probabilities, giving the results a level of economic efficiency which makes them a standard against which to judge the results of decentralized models.
A new analytic function for modeling partially penetrating wells
Authors: Haitjema Henk M. , Kraemer Stephen R.
Published: February 2008

A new analytic function is presented to model three‐dimensional flow near a partially penetrating well. The function represents a sink distribution along the well axis, whereby equipotential conditions along the well perimeter are approximately satisfied by adjusting several degrees of freedom of the function. This procedure is well known and has led to rather accurate solutions provided a sufficient number of free parameters were incorporated. The values for these parameters are obtained by solving a system of linear equations. The function presented in this paper achieves the same accuracy as past solutions with a significant reduction in the number of degrees of freedom required and hence fewer equations to be solved. This increased efficiency is of little consequence when the well is modeled by itself. However, when combined with the solutions to the many other flow features in a regional aquifer, the savings become significant. In fact, if each of the individual solutions would have many degrees of freedom, the resulting system of equations may become unmanageable, thus restricting applications. To demonstrate the use of the new function, a hypothetical groundwater contamination problem is solved, whereby contaminants are intercepted by a partially penetrating well.
Comparison of Newton‐type and direct search algorithms for calibration of conceptual rainfall‐runoff models
Authors: Hendrickson Jene' D. , Sorooshian Soroosh , Brazil Larry E.
Published: February 2008

An examination of the calibration aspect of conceptual rainfall‐runoff models was undertaken using the Sacramento soil moisture accounting model and a study comparing the performance of a Newton‐type optimization algorithm with that of a direct search algorithm. Results indicate that the direct search algorithm is the more robust of the two because the Newton‐type algorithm is more susceptible to poor conditioning of the response surface. Graphical studies of the response surface of the model's parameter space confirmed the presence of discontinuities and a rough‐textured surface, particularly in the derivatives.
On the diffusion wave model for overland flow: 1. Solution for steep slopes
Authors: Govindaraju R. S. , Jones S. E. , Kavvas M. L.
Published: February 2008

A new solution technique for analyzing the overland flows on lands adjacent to stream networks is presented. Some of the practical short‐comings of the state‐of‐the‐art kinematic wave model are discussed and the more comprehensive diffusion wave model is adopted. As boundary conditions for steep slopes, homogeneous end conditions of zero depth at the upstream and zero‐depth gradient at the downstream are found to represent the physical situation adequately. A weighted residual method is used to develop an approximate solution to the problem. The trial functions are taken to be the spatial eigenfunctions of the corresponding homogeneous problem. It is demonstrated that the resulting approximation converges rapidly and the results agree well with the full Saint Venant solution and the kinematic wave approximation. It is also shown that the numerical solution to the diffusion wave approximation agrees very well with the weighted residual approximation for only a small number of terms. Both the rising and recession phases of the outflow hydrograph have been considered. The approximation can easily accommodate time and space variation in rainfall.
Multidimensional modeling of cumulative rainfall: Parameter estimation and model adequacy through a continuum of scales
Authors: Islam Shafiqul , Bras Rafael L. , Rodriguez‐Iturbe Ignacio
Published: February 2008

This paper presents the multidimensional representation of the cumulative rainfall process and derives a closed‐form expression for the mean and space‐time covariance functions. A parameter estimation procedure is developed. Sensitivity analysis provides useful information for devising the parameter estimation strategy. The cumulative rainfall model is applied to 8 years of digitized rain gage data from the Walnut Gulch Experimental Watershed. The most useful feature of the model is its self‐consistency, implying that even after using information from a given limited set of data it still leads to realistic parameters which reproduce historical statistics at several levels of time and space scales.
A distributed parameter approach for evaluating the accuracy of groundwater model predictions: 1. Theory
Authors: McLaughlin Dennis , Wood Eric F.
Published: February 2008

A systematic stochastic analysis suggests that groundwater model accuracy depends on natural heterogeneity, data availability, model approximations, and method used to estimate model inputs. Distributed parameter estimation theory is used to develop a description of the modeling process which includes all of these factors. This description is based on a set of hybrid state equations which clearly distinguish between the heterogeneous distributed variables of the natural (reference) system and the aggregated variables of the discretized model. Approximate expressions for the first and second moments of the model's prediction error are derived directly from the state equations. The derived moments provide a convenient way to examine a number of questions related to sampling design, robust input estimation, and model performance. They also may be used to design modeling studies before extensive resources are committed to data collection and model development.
Microscale haline convection‐A proposed mechanism for transport and mixing at the water table region
Authors: Ronen Daniel , Magaritz Mordeckai , Paldor Nathan
Published: February 2008

Field measurements of chloride profiles in the water table region of a deep aquifer are interpreted in terms of haline convection at the microscale level. Under natural flow conditions the flow field is characterized by a small Peclet number (between 6.25×10−2 and 6.25×10−3) so that molecular diffusion dominates over mechanical dispersion. It is suggested that haline convection is a major transport and mixing mechanism at the water table region of granular aquifers under natural flow conditions wherever the intervention of man changed the chemical composition of natural replenishment. In the studied region it is estimated that the critical density difference which overcomes viscous drag forces is 0.23–0.28 kg/m3. This value agrees with the magnitude of the critical free convection parameter (modified Rayleigh number) of earlier models.
A method for locating wells in a groundwater monitoring network under conditions of uncertainty
Authors: Meyer Philip D. , Brill E. Downey
Published: February 2008

A method is presented for locating wells in a monitoring network under conditions of uncertainty. The method couples the use of a simulation model of contaminant transport and a facility location model. The Monte Carlo technique is used with the simulation model to translate uncertainty in the simulation model parameters into uncertainty in the contaminant concentration distribution. The simulation model determines which well locations would detect a given realization of a contaminant plume with a concentration above a specified limit. The facility location model is then used to select a fixed number of well locations so that a maximum number of such plume realizations are detected. The selected well network maximizes the probability of detection. The method is applied to an example problem. Although the technique is computationally intensive, the results indicate that practical problems are tractable.
Gradient dynamic programming for stochastic optimal control of multidimensional water resources systems
Authors: Foufoula‐Georgiou Efi , Kitanidis Peter K.
Published: February 2008

A new computational algorithm is presented for the solution of discrete time linearly constrained stochastic optimal control problems decomposable in stages. The algorithm, designated gradient dynamic programming, is a backward moving stagewise optimization. The main innovations over conventional discrete dynamic programming (DDP) are in the functional representation of the cost‐to‐go function and the solution of the single‐stage problem. The cost‐to‐go function (assumed to be of requisite smoothness) is approximated within each element defined by the discretization scheme by the lowest‐order polynomial which preserve its values and the values of its gradient with respect to the state variables at all nodes of the discretization grid. The improved accuracy of this Hermitian interpolation scheme reduces the effect of discretization error and allows the use of coarser grids which reduces the dimensionality of the problem. At each stage, the optimal control is determined on each node of the discretized state space using a constrained Newton‐type optimization procedure which has quadratic rate of convergence. The set of constraints which act as equalities is determined from an active set strategy which converges under lenient convexity requirements. This method of solving the single‐stage optimization is much more efficient than the conventional way based on enumeration or iterative methods with linear rate of convergence. Once the optimal control is determined, the cost‐to‐go function and its gradient with respect to the state variables is calculated to be used at the next stage. The proposed technique permits the efficient optimization of stochastic systems whose high dimensionality does not permit solution under the conventional DDP framework and for which successive approximation methods are not directly applicable due to stochasticity. Results for a four‐reservoir example are presented.
Fog drip as a source of groundwater recharge in northern Kenya
Authors: Ingraham Neil L. , Matthews Robert A.
Published: February 2008

Fog drip, or mist precipitation, has generally been neglected by hydrogeologists as a source of water, largely because of the difficulty in tracing fog through the hydrosphere. In the arid climate of northern Kenya, light stable isotopes aided in assessing the importance of fog drip. Fog was collected at localized fog‐laden montane areas and determined to have δD values of about +3 to +16.6‰. Rain‐derived groundwater was found to have δD values of about −25‰. However, groundwater in the fog‐laden areas have δD values of about −12.5‰ and appear to be a mixture of fog and rain. It is thought that in special environments such as northern Kenya, fog drip may be an important source of infiltration and groundwater recharge.