bluuebunny/crossref_metadata_2025 huggingface dataset:
Transport of reacting solutes in porous media: Relation between mathematical nature of problem formulation and chemical nature of reactions
Authors: Rubin Jacob
Published: February 2008

Examples involving six broad reaction classes show that the nature of transport‐affecting chemistry may have a profound effect on the mathematical character of solute transport problem formulation. Substantive mathematical diversity among such formulations is brought about principally by reaction properties that determine whether (1) the reaction can be regarded as being controlled by local chemical equilibria or whether it must be considered as being controlled by kinetics, (2) the reaction is homogeneous or heterogeneous, (3) the reaction is a surface reaction (adsorption, ion exchange) or one of the reactions of classical chemistry (e.g., precipitation, dissolution, oxidation, reduction, complex formation). These properties, as well as the choice of means to describe them, stipulate, for instance, (1) the type of chemical entities for which a formulation's basic, mass‐balance equations should be written; (2) the nature of mathematical transformations needed to change the problem's basic equations into operational ones. These and other influences determine such mathematical features of problem formulations as the nature of the operational transport‐equation system (e.g., whether it involves algebraic, partial‐differential, or integro‐partial‐differential simultaneous equations), the type of nonlinearities of such a system, and the character of the boundaries (e.g., whether they are stationary or moving). Exploration of the reasons for the dependence of transport mathematics on transport chemistry suggests that many results of this dependence stem from the basic properties of the reactions' chemical‐relation (i.e., equilibrium or rate) equations.
Time‐dependent linearized two‐dimensional infiltration and evaporation from nonuniform and periodic strip sources
Authors: Batu Vedat
Published: February 2008

Using a linearized partial differential equation describing unsaturated, homogeneous, and isotropic porous media flow, a general two‐dimensional time‐dependent mathematical model is presented for infiltration and infiltration‐evaporation cases from nonuniform and periodic strip sources located at the soil surface. The analysis is based on an exponential relationship between the unsaturated hydraulic conductivity and the soil water pressure head and also assumes a constant value for the derivative of unsaturated hydraulic conductivity with respect to water content. In the mathematical analysis, Laplace transform and Fourier analysis techniques are used simultaneously, and a general equation is obtained in series‐integral form for the distribution of matric flux potential. The solution for uniform infiltration from equally spaced strip sources and uniform evaporation from the rest of the strips is presented as a special case of the general model. Another special case is presented for infiltration from equally spaced strip sources. The results of this latter case are compared with Warrick and Lomen (1976), and it is observed that the agreement is reasonably good. All results are expressed in integral forms and are calculated by using a numerical integration method. Equations for the horizontal and vertical flux components for the special case are presented. The solutions predict the matric flux potential and flux components as functions of space and time. They are of interest in the design of irrigation systems and may be used also for different purposes in other engineering applications.
Estimating Demand for Intake Water by Self‐Supplied Firms
Authors: Ziegler Joseph A. , Bell Stephen E.
Published: February 2008

The proper specification of the price variable in estimating the demand for intake water by self‐supplied firms is a neglected subject in the literature. Previous studies have used measures of average cost, but neoclassical economic theory suggests firms respond to marginal costs. Using data from a sample of paper and chemical firms in Arkansas, the null hypothesis that there is no significant difference in the estimates of industrial water demand using either average or marginal costs is tested. It is shown that the use of average cost provides a better estimate of water use in terms of statistical fit and predictive capabilities.
A Dynamic Model of Basin Sediment Yield
Authors: Moore R. J.
Published: February 2008

A new model is presented to predict the hour‐to‐hour variation in basin suspended sediment yield which incorporates the phenomenon that yields are influenced by the availability of sediment, as well as the capacity of flow to transport sediment. This is achieved through the definition of three model functions: (1) an availability function, (2) a removal function, and (3) a translation function. The inverse Gaussian probability density function is introduced as a suitable translation function because of its shape and its physical interpretation in terms of the Saint Venant equations of open channel flow, the equations of groundwater flow, and the general convection‐diffusion equation. A “censored objective function” is employed to facilitate efficient model calibration in circumstances where significant sediment yields are produced by infrequently occurring flood events, but the changing availability of sediment between storm events demands that the model be run continuously over time. The paper ends with a discussion of the problems of model calibration when the sediment yield process is considered to exhibit threshold‐type behavior. Adoption of a modeling strategy based on the use of smooth but physically plausible functions was an important concern and motivation in developing the new model. It is concluded that the performance of basin sediment yield models must be severely limited on account of (1) the complexity of the sediment yield process at the basin scale and (2) the paucity of data usually available. This lack of definition at the basin scale provides a persuasive argument in favor of simple models which represent the dominant modes of behavior of the system.
Acid Mine Drainage From Reclaimed Coal Strip Mines 2. Simulation Results of Model
Authors: Jaynes D. B. , Pionke H. B. , Rogowski A. S.
Published: February 2008

Acid mine drainage from reclaimed coal strip mines is simulated by use of a comprehensive model described in an earlier paper. The simulated concentrations of key components are well within the ranges of measured values from reclaimed mines. In systems without iron‐oxidizing bacteria the simulations indicate that oxygen is the only important oxidizer of pyrite. The oxidation of ferrous to ferric iron by purely chemical means is too slow to affect the overall oxidation rate of pyrite and is not important in these systems. For the typical physical parameters used here the diffusion rate of oxygen is the primary factor controlling the rate of pyrite oxidation. The pyrite oxidation rate is decreased by decreased air‐filled porosity, by increased tortuosity of the oxygen diffusion path, by increased size of the spoil fragments, and by burying the pyritic material at deeper depths. Where oxygen resupply is not limiting the results indicate that iron‐oxidizing bacteria can greatly increase the rate of pyrite oxidation. Whether or not bacteria are important in these zones depends primarily on the pH of the spoil solution. In the optimal pH range, between reduced bacterial efficiency and reduced ferric iron solubility (2.0 ≲ pH ≲ 3.0), the pyrite oxidation rate is accelerated by bacterially produced ferric iron. The extent and type of chemical reactions between H+, produced by pyrite oxidation, and the spoil matrix appears to be crucial in establishing the pH of the spoil solution.
Some Exact Solutions for Solute Transport Through Soils Containing Large Cylindrical Macropores
Authors: van Genuchten M. T. , Tang D. H. , Guennelon R.
Published: February 2008

This paper presents several exact and approximate analytical solutions of the equations describing convective‐dispersive solute transport through large cylindrical macropores with simultaneous radial diffusion from the larger pores into the surrounding soil matrix. Adsorption effects were included through the introduction of linear isotherms for both the macropore region and the soil bulk matrix. In one formulation the macropores are surrounded by cylindrical soil mantles of finite thickness. Another formulation considers diffusion from a single cylindrical macropore into a radially infinite soil system. A relatively simple but very accurate approximate solution that ignores dispersion in the macropore region is also derived. The various analytical solutions in this paper can be used to calculate temporal and spatial concentration distributions in the macropore system. In addition, approximate solutions are presented for the radial concentration distribution within the adjacent soil matrix. By means of an example, it is demonstrated that at early times, little accuracy is lost when the radially finite soil mantle is replaced by an infinite system.
Stochastic Streamflow Models for Hydroelectric Systems
Authors: Pereira M. V. F. , Oliveira G. C. , Costa C. C. G. , Kelman J.
Published: February 2008

This paper describes the development of a monthly streamflow model for the Brazilian hydroelectric system. The model is based on the disaggregation of lag 1 autoregressive annual flows into monthly values. Model features include addition of new sites, nonparametric generation of monthly flows, and correction of negative values. A methodology for assessing model adequacy is described and applied in a case study comparing the proposed model and a multivariate monthly autoregressive model. The economic effect of model selection is illustrated in a realistic generation planning case study: it is shown that investment differences resulting from the application of different models may reach US $1 billion.
Sediment Yield and Storm Flow Response to Clear‐Cut Harvest and Site Preparation in the Ouachita Mountains
Authors: Miller Edwin L.
Published: February 2008

Clear‐cut harvest and site preparation, including crushing the residual vegetation, burning, and contour ripping, were applied to three small watersheds in Oklahoma. Three undisturbed forested watersheds served as controls. First‐year sediment losses averaged 282 and 36 kg/ha and storm flow water yields averaged 22.9 and 31.7 cm on clear‐cut and uncut watersheds, respectively. The lower water yield on cut watersheds may have been due to contour ripping. Treatment differences in sediment yield were significant the second and third, but not the fourth, year following treatment. Storm flow water yield from clear‐cut watersheds was significantly higher than from uncut watersheds the second year but not the third or fourth years. Absolute levels of sediment yield from clear‐cut and control watersheds were relatively low in all years of the study. The overall impact of harvest and site preparation on total suspended solids levels in runoff was small and short‐lived.
Daily Precipitation Modeling by Discrete Autoregressive Moving Average Processes
Authors: Chang Tiao J. , Kavvas M. L. , Delleur J. W.
Published: February 2008

To account for the statistical dependence among the daily precipitation magnitudes and among the daily precipitation occurrence times, various models from the discrete autoregressive moving average (DARMA) family are constructed for and applied to the daily precipitation data in Indiana. The structure of the DARMA family is specified by the marginal distribution of independent identically distributed (i.i.d.) discrete random variables and by their random linear combination. A fundamental property of the DARMA family is that its correlation structure can be specified independently of its marginal density. The DARMA correlation structure remains invariant under transformation of the marginal density. This property is satisfied by the Indiana daily precipitation data, and it facilitates their modeling by the DARMA family of processes. It is shown that the Markov chain, a popular model for the daily precipitation sequences, is a specified model within DARMA family. The Indiana daily precipitation data is transformed into a multistate discrete precipitation sequence by discretizing the daily precipitation amount into a number of magnitude states. The stochastic process of the daily precipitation sequences is analyzed in terms of the locally stationary seasons defined within the paper. In each season the candidate DARMA models are identified in terms of the covariance function within the season. The parameter estimation of these candidate models is done by fitting their theoretical autocorrelation functions to their empirical counterparts, and the state probabilities are obtained through the multistate mean run lengths. The theoretical run‐length distributions of the candidate models are derived for each of the precipitation magnitude states, including the dry state. The goodness‐of‐fit tests of the candidate models and the best model selection are based on the theoretical multistate run‐length distributions of the daily precipitation data.

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Quantitative Analysis of Existing Conditions and Production Strategies for the Baca Geothermal System, New Mexico
Authors: Faust Charles R. , Mercer James W. , Thomas Stephen D. , Balleau W. Pete
Published: February 2008

The Baca geothermal reservoir and adjacent aquifers in the Jemez Mountains of New Mexico comprise an integrated hydrogeologic system. Analysis of the geothermal reservoir either under natural conditions or subject to proposed development should account for the mass (water) and energy (heat) balances of adjacent aquifers as well as the reservoir itself. A three‐dimensional model based on finite difference approximations is applied to this integrated system. The model simulates heat transport associated with the flow of steam and water through an equivalent porous medium. The Baca geothermal reservoir is dominated by flow in fractures and distinct strata, but at the scale of application the equivalent porous media concept is appropriate. The geothermal reservoir and adjacent aquifers are simulated under both natural conditions and proposed production strategies. Simulation of natural conditions compares favorably with observed pressure, temperature, and thermal discharge data. The history matching simulations show that the results used for comparison are most sensitive to vertical permeability and the area of an assumed high‐permeability zone connecting the reservoir to a deep hydrothermal source. Simulations using proposed production strategies and optimistic estimates of certain hydrologic parameters and reservoir extent indicate that a 50‐MW power plant could be maintained for a period greater than 30 years. This production, however, will result in significant decreases in the total water discharge to the Jemez River.
Hysteresis Affected Water Movement in Scale Heterogeneous Profiles
Authors: Curtis A. A. , Watson K. K.
Published: February 2008

A method is presented for applying the concept of scale heterogeneity to infiltration and redistribution problems in heterogeneous porous materials. Where water movement is not monotonically constrained to either wetting or draining boundary curves, full soil water characteristics are needed to analyze the flow process numerically. Profile heterogeneity results in these characteristics becoming spatially dependent, with each position in the profile requiring its own set of soil water characteristics. Numerical techniques used to overcome the resulting problems of data storage and manipulation are outlined. These techniques include a simple interpolative soil water hysteresis model and a method of utilizing the dimensionless scaling factor to compute the requried soil water characteristics at any depth from a datum material. Results for unimpeded infiltration and redistribution and for infiltration into a bounded profile are compared with those for equivalent homogeneous profiles to demonstrate the utility of the method.
Flow Toward Storage Tunnels Beneath a Water Table: 2. Three‐Dimensional Flow
Authors: Tal A. , Dagan G.
Published: February 2008

In the first part of the study (Tal and Dagan, 1983) the problem of two‐dimensional flow of water toward storage tunnels was solved. This case corresponds to a falling water table in absence of sufficient natural recharge. In the present part we consider the case in which the water table is prevented from descending and is maintained in a steady position by a battery of recharging wells. The three‐dimensional flow problem is solved first by a simplified linearization approximation which is valid for flat water table which is sufficiently high above the gallery. The full nonlinear free surface problem is subsequently solved numerically by the boundary integral element method, and the range of validity of the linearized approximation is established. The solution provides the tools needed in order to design an optimal well system (spacing, length, discharge) for given gallery setup, product pressure, and water table height. Both cases of products of low and high vapor pressures are investigated.
An Analysis of Dispersion in a Stratified Aquifer
Authors: Güven Oktay , Molz Fred J. , Melville Joel G.
Published: February 2008

The dispersion of a conservative solute produced as a result of vertical variations of hydraulic conductivity in a horizontal stratified aquifer of finite thickness is analyzed by applying the moment method of Aris to solve the governing advection‐dispersion equation describing mass transport. In the analysis it is assumed that the aquifer is of constant thickness and of infinite lateral extent, the hydraulic conductivity is a known function of the vertical coordinate only, and the flow is unidirectional, parallel to the stratification. The applicable Aris moment equations are developed in a suitable nondimensional form. Analytical solutions are obtained for the zeroth and first moments and for the time derivative of the second moment of the longitudinal concentration distribution for the case of an instantaneous plane source for several idealized hydraulic conductivity profiles (parabolic, linear, step function, and cosine profiles and their even periodic extensions). The analysis gives the time‐dependent variation of the longitudinal macrodispersivity for these idealized cases throughout the transient development of the dispersion process. The results of the analysis are applied to a field‐measured hydraulic conductivity profile, and predicted values of the longitudinal macrodispersivity are compared with field results. An important conclusion from the analyses is that nonuniformities in the hydraulic conductivity profile which persist over long distances may produce rather large values of longitudinal macrodispersivity which are comparable to those observed in some aquifers and which are much larger than those predicted by some previous stochastic analyses. Implications of the analytical results for field dispersion problems are discussed.
A Model for Investigating Mechanical Transport in Fracture Networks
Authors: Endo H. K. , Long J. C. S. , Wilson C. R. , Witherspoon P. A.
Published: February 2008

A technique is presented to determine when anisotropic fracture systems can be modeled as equivalent porous media (continua) for transport. In order to use the continuum approach, one must demonstrate that the fracture system has the same transport behavior as an equivalent porous medium. Hydraulic effective porosity is calculated as the product of specific discharge and mean travel time, divided by linear length of travel. Specific discharge and hydraulic effective porosity are measured in different directions of flow in regions of varying size with constant hydraulic gradients. If the fracture system behaves like an equivalent porous medium, directional flow has the following properties: (1) specific discharge can be predicted from a permeability tensor and (2) hydraulic effective porosity is independent of direction of flow. A numerical model has been developed to simulate mechanical transport under steady flow in a discrete fracture network. The model is used to determine the distribution of travel times from inlet to outlet for fluid traveling in stream tubes. We have examined only systems with parallel fracture sets in which all fractures are long compared to the region under study. These systems satisfy criterion 1 in that flux can be calculated using a porous medium equivalent. However, these systems do not satisfy criterion 2 because hydraulic effective porosity is shown to be directionally dependent. Thus, even though flux can be accurately predicted using porous medium assumptions for some fracture systems, it may not be possible to accurately predict mechanical transport using these same assumptions.
A Spectral Theory of Rainfall Intensity at the Meso‐β Scale
Authors: Waymire Ed , Gupta Vijay K. , Rodriguez‐Iturbe Ignacio
Published: February 2008

The available empirical descriptions of extratropical cyclonic storms are employed to formulate a physically realistic stochastic representation of the ground level rainfall intensity field in space and time. The stochastic representation is based on three‐component stochastic point processes which possess the general features of the embedding of rain cells within small mesoscale areas within large mesoscale areas within synoptic storms. Certain scale idealizations, and assumptions on functional forms which qualitatively reflect the physical features, lead to a closed form expression for the covariance function, i.e., the real space‐time spectrum, of the rainfall intensity field. The theoretical spectrum explains the empirical spectral features observed by Zawadzki almost a decade ago. Of particular interest and importance in this connection is an explanation of the empirical observation that the Taylorian propogation of the fine scale structure, via a transformation of time to space through the storm velocity, holds only for a small time lag and not throughout. The results here indicate the extent of this lag in terms of the characteristic scales associated with cell durations, cellular birthrates and velocities, etc.
The Krafla Geothermal Field, Iceland: 1. Analysis of well test data
Authors: Bodvarsson Gudmundur S. , Benson Sally M. , Sigurdsson Omar , Stefansson Valgardur , Eliasson Einar T.
Published: February 2008

Extensive, modeling studies of the Krafla geothermal field in Iceland are presented in a series of four papers. This first paper describes the geological settings of the field and the analysis of well test data. The geothermal system at Krafla is very complex, with a single‐phase liquid reservoir overlying a two‐phase reservoir. The reservoir rocks are volcanic with sequences of basalt flows, hyloclastics, and intrusions. The fluid flow in the reservoir is fracture dominated. Considerable pressure transient data from injection tests have been gathered from the Krafla wells. These data are analyzed to yield the transmissivity distribution in the reservoir system. As the data are complicated by various factors (wellbore effects, nonisothermal effects, two‐phase flow, and fractured rocks) the applicability of conventional well test analysis methods is questionable. We have developed a methodology to analyze injection tests for such systems. The results obtained show that the transmissivity of the Krafla reservoir is low, averaging 2 Darcy meters (Dm). The average transmissivity of most commercially successful geothermal fields is an order of magnitude higher.
Note on the applicability of the James‐Stein Estimator in regional hydrologic studies
Authors: Landwehr J. Maciunas , Matalas N. C. , Wallis J. R.
Published: February 2008

The applicability of the James‐Stein estimator in regional hydrologic studies which entail the estimation of anN‐dimensional location parameter is discussed. Regional studies are frequently characterized by relatively short, generally correlated, samples drawn from nonsymmetric and bounded, i.e., nonnormal, populations. By means of computer simulation studies the James‐Stein estimator, subject to the Lindley modification and adoption of the positive part rule suggested by Efron and Morris and conditioned on the assumption of independence, was shown to be robust in the case of the hydrologically plausible distribution considered here, namely, Weibull distributions with coefficient of skewness ranging from 0 to 10. However, in contrast to traditional methods of regionalization the effect of cross correlation is a diminishment of the relative risk advantage of the James‐Stein estimator, even in the best case of normal variables : this is discussed and illustrated.
Hydrologic analyses of acidic and alkaline lakes
Authors: Chen C. W. , Gherini S. A. , Peters N. E. , Murdoch P. S. , Newton R. M. , Goldstein R. A.
Published: February 2008

Woods and Panther lakes in the Adirondack Mountains of New York respond differently to the same acidic deposition. A mathematical model study has shown that lake water becomes acidic when hydrologic conditions force precipitation to flow to the lakes as surface flow or as lateral flow through the shallow organic soil horizon. Hydrographic data, capacity of flow through inorganic soil horizons, runoff recession curves, and groundwater level fluctuations of Woods and Panther lake basins provide independent evidence to support the thesis that the acidic state of a lake depends on the paths the tributary water takes as it passes thorough the terrestrial system. It is concluded thot Panther Lake is more alkaline than Woods Lake, because a larger proportion of the precipitation falling on the basin passes through deeper mineral soil horizons.
Modeling persistence in hydrological time series using fractional differencing
Authors: Hosking J. R. M.
Published: February 2008

The class of autoregressive integrated moving average (ARIMA) time series models may be generalized by permitting the degree of differencing d to take fractional values. Models including fractional differencing are capable of representing persistent series (d > 0) or short‐memory series (d = 0). The class of fractionally differenced ARIMA processes provides a more flexible way than has hitherto been available of simultaneously modeling the long‐term and short‐term behavior of a time series. In this paper some fundamental properties of fractionally differenced ARIMA processes are presented. Methods of simulating these processes are described. Estimation of the parameters of fractionally differenced ARIMA models is discussed, and an approximate maximum likelihood method is proposed. The methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures.
A Multiphase Approach to the Modeling of Porous Media Contamination by Organic Compounds: 1. Equation Development
Authors: Abriola Linda M. , Pinder George F.
Published: February 2008

A multiphase approach to the modeling of aquifer contamination by organic compounds is developed. This approach makes it possible to describe the simultaneous transport of a chemical contaminant in three physical forms: as a nonaqueous phase, as a soluble component of an aqueous phase, and as a mobile fraction of a gas phase. The contaminant may be composed of, at most, two distinct components, one of which may be volatile and slightly water soluble and the other of which is both nonvolatile and insoluble in water. Equations which describe this complex system are derived from basic conservation of mass principles by the application of volume averaging techniques and the incorporation of various constitutive relations and approximations. Effects of matrix and fluid compressibilities, gravity, phase composition, interphase mass exchange, capillarity, diffusion, and dispersion are all considered. The resulting mathematical model consists of a system of three nonlinear partial differential equations subject to two equilibrium constraints. These equations relate five unknowns: two capillary pressures and three mass fractions.
Estimating the Parameters of a Cube Root Normal Distribution from Reduced Sample Data
Authors: Potratz C. J. , Steinhorst R. K. , Hanson C. L.
Published: February 2008

A procedure is presented which provides estimates for μ and σ2, the parameters of a cube root normal distribution, using only the sample mean and variance of the untransformed data. The technique employs Newton's algorithm and yields method of moments estimates which can be applied when only aggregated data are available.
A New Type Curve Method for the Analysis of Pumping Tests in Large‐Diameter Wells
Authors: Wikramaratna R. S.
Published: February 2008

An improved method is proposed for the analysis of pumping test data from large‐diameter wells in confined aquifers. An example is given which illustrates some of the problems which arise with the existing method and which shows the advantages of the proposed method.
Conditional Distributions of Neyman‐Scott Models for Storm Arrivals and Their Use in Irrigation Scheduling
Authors: Ramirez Jorge A. , Bras Rafael L.
Published: February 2008

This paper solves the deficit irrigation scheduling problem assuming that rainfall arrivals obey a Neyman‐Scott cluster model. The implied dependence between storms is represented by derived conditional distributions of the occurrence of rainfall based on the history of past storm arrivals. This new result is used on a physicostochastic model of the soil moisture history which in turn leads to an optimal control algorithm for making irrigation decisions. The decision of when and how much to irrigate now depends on measured soil moisture, available irrigation water, and time since the last rainfall occurrence.
Hydrograph Sensitivity to Storm Kinematics
Authors: Ngirane‐Katashaya G. G. , Wheater H. S.
Published: February 2008

Using synthetic urban catchments, represented by a distributed nonlinear rainfall‐runoff model, the effects of storm velocity on the runoff hydrograph are quantified for different catchment areas and response parameters. Results are considered in comparison with equivalent stationary storms and the implications for current design practice are examined.
Evaluation of the Polubarinova‐Kochina Formula for the Dam Problem
Authors: Hornung Ulrich , Krueger Thomas
Published: February 2008

The stationary problem of unconfined groundwater flow through a rectangular dam has been solved by P. Ya. Polubarinova‐Kochina. In this paper the analytical formulas are used to obtain accurate numerical values for the phreatic surface and for the height of the seepage face. These values provide a reference with which to compare numerical methods for seepage problems.
Stability of the Green‐Ampt Profile in a Delta Function Soil
Authors: Milly P. C. D.
Published: February 2008

The sharp wetting front of Green and Ampt represents a solution of the Richards equation for infiltration into a delta‐function soil. In order that the sharpness of this profile be maintained in the presence of a small perturbation of the profile shape, it is sufficient that the second derivative of hydraulic conductivity with respect to moisture content be positive for all values of moisture content. An inspection of theoretical and experimental data on the hydraulic conductivity suggests that this condition is usually satisfied. The profile is also stable if the first derivative of hydraulic conductivity with respect to moisture content is proportional to a delta function.
Flood Damage Mitigation: A Review of Structural and Nonstructural Measures and Alternative Decision Frameworks
Authors: Thampapillai Dodo J. , Musgrave Warren F.
Published: February 2008

Literature from diverse sources such as public expenditure economics, management science, geography, agriculture, and engineering reveals a wide range of decision frameworks for deriving flood mitigation strategies. These different types of decision frameworks are reviewed in this paper. The aim is to provide an understanding of these frameworks, along with their relative adequacies and inadequacies. Such an understanding reveals the directions along which the formulation of a more adequate framework should proceed. However, the formulation of a given decision framework is influenced by the types of economic benefits associated with the flood mitigation measures considered in that framework. Hence the various flood mitigation measures are reviewed, prior to the various decision frameworks.
Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 3. Observations and Applications
Authors: Yeh T.‐C. Jim , Gelhar Lynn W. , Gutjahr Allan L.
Published: February 2008

Results of stochastic theory for flow in heterogeneous soils are analyzed by comparisons with laboratory experiments and field observations, and through applications examples. The two key theoretical results are (1) the variability of capillary pressure or moisture content increases when mean capillary pressure increases and (2) the anisotropy ratio (horizontal/vertical) of effective (mean) unsaturated hydraulic conductivity increases when mean capillary pressure increases or mean moisture content decreases. Comparisons with the field data on moisture content and capillary pressure variability show trends similar to those predicted by the theory. Calculations of hydraulic conductivity anisotropy based on two actual soils show that the variations in soil texture produce large changes in anisotropy as the mean capillary pressure changes. Several previously reported field observations and laboratory experiments support the theoretical finding of a capillary pressure dependent hydraulic anisotropy for unsaturated flow. The importance of this anisotropy effect in applications involving groundwater recharge, irrigation, surface runoff generation, and waste isolation is discussed.
The Analysis of Structural Identifiability: Theory and Application to Conceptual Rainfall‐Runoff Models
Authors: Sorooshian Soroosh , Gupta Vijai Kumar
Published: February 2008

The identification of a conceptual hydrologic model involves two stages: selection of a suitable model structure and parameter estimation. These two stages cannot be treated as distinct, and it is important that the limitations of available parameter estimation methodologies be given serious consideration during the procedure of model structure selection. This paper focuses on the concepts and tools necessary for the evaluation of whether the structure of a hydrologic model is such that its parameters can be successfully identified. A definition of structural identifiability is advanced that is based purely on model properties and is independent of the stochastic nature of the output observation errors. The approach is used to develop a measure of local structural identifiability which is useful in the analysis of parameter sensitivity. A measure, called the sensitivity ratio, is introduced which is suitable for studying parameter interactions in the multidimensional parameter space. Also, the use of allowable reparameterizations to improve identifiability is discussed. The utility of the concepts discussed in this paper are demonstrated by a simulation example using a conceptual rainfall‐runoff model.
Multisite ARMA(1,1) and Disaggregation Models for Annual Streamflow Generation
Authors: Stedinger Jery R. , Lettenmaier Dennis P. , Vogel Richard M.
Published: February 2008

Disaggregation and multisite autoregressive moving average (ARMA)(1,1) time‐series models provide simple and efficient frameworks for generation of multisite synthetic streamflow sequences that exhibit long‐term persistence. This paper considers multisite ARMA(1,1) models whose Φ and Θ matrices are diagonal; a Monte Carlo study examined the efficiency of three procedures for estimating individual Φ‐θ values for each site and two estimators of the covariance matrix of the innovations. Also included in the study was a univariate ARMA(1,1) model of the aggregate flows with a simple disaggregation algorithm to generate flows at the individual sites. In the realm of most hydrologic interest, simple diagonal multisite ARMAl(1,1) models performed adequately and it is not necessary to fit the more cumbersome nondiagonal models. The disaggregation procedure coupled with an ARMA(1,1) aggregate flow model did as well as the multivariate diagonal ARMA(1,1) models.
On the probabilistic structure of storm surface runoff
Authors: Córdova José R , Rodríguez‐Iturbe Ignacio
Published: February 2008

The mean and variance of storm surface runoff are derived under the assumption that storm events are rectangular pulses with a bivariate exponential distribution for the intensity and duration of the storm. The Philip infiltration equation is used to make the transformation between rainfall and surface runoff. The probability of zero storm surface runoff is also calculated under the same assumptions. It is shown that the correlation between intensity and duration of the storm has an important impact on the probabilistic structure of storm surface runoff.
Synthesis of radar rainfall data
Authors: Krajewski Witold F. , Georgakakos Konstantine P.
Published: February 2008

A method of generating synthetic radar‐rainfall data is described. The data are generated by imposing random noise on a given, high‐quality radar‐rainfall field. Certain conditions are imposed on the resultant rainfall field so that the noise parameters are prespecified. The conditions pertain to the second order statistics of the generated rainfall fields: the mean, the variance, the correlation, and the variance of the logarithmic ratio of the resultant field to the original field. Accuracy of the generation method is evaluated from implementing a test case using Global Atmospheric Research Program Atlantic Tropical Experiment radar data. The method can be used in a number of different, mainly hydrologic, applications. These include validation of radar and rain gage data merging procedures, testing of various methods for computation of mean areal precipitation, and sensitivity analysis of rainfall‐runoff models.
Hypergame Analysis of the Lake Biwa Conflict
Authors: Okada Norio , Hipel Keith W. , Oka Yoshiharu
Published: February 2008

When there are misunderstandings among participants in a water resources conflict, hypergame analysis can be used to systematically model the conflict and predict the compromise resolutions. In order to demonstrate the efficacy of using hypergame analysis for studying water resources management problems, it is applied to the Lake Biwa conflict in Japan. This dispute constitutes a typical example of a water allocation conflict where downstream users would like more water from the upstream controllers of the major source of the water. Furthermore, each participant or player in the Lake Biwa dispute has misperceptions about the other players' preferences. Besides predicting the different resolutions which each of the players envisioned, hypergame analysis correctly forecasts the compromise resolution that occurred historically.
Optimization Modeling of Water Quality in an Uncertain Environment
Authors: Burn Donald H. , McBean Edward A.
Published: February 2008

An optimization model with an ability to reflect uncertainties present in water quality problems is described. The technique employed is chance constrained programming wherein probabilistic constraints in a water quality optimization problem are replaced with their deterministic equivalents. The uncertainty inherent in the random elements of the problem is characterized using first‐order uncertainty analysis for the case study described.
Approximate Analysis of the Borehole Permeameter in Unsaturated Soil
Authors: Philip J. R.
Published: February 2008

An approximate analysis of the steady constant‐head uncased borehole permeameter in homogeneous unsaturated soil is presented. A bulb‐shaped region of saturated soil, the “saturated bulb,” adjoins the water‐filled length of the hole. The problem is solved by matching approximate models of the “inner” saturated flow within the bulb and of the “outer” flow in the surrounding unsaturated soil. The quasilinear analysis, with sorptive number α characterizing the capillary properties of the soil, is applied to the outer, unsaturated flow. Certain approximations made are geometrical, and others simplify the physics by treating gravity and capillarity as separable. The results agree well with the limited body of relevant detailed numerical solutions, and the model is consistent also with saturated flow results and formulae. In general, the capillary properties of the soil cannot be ignored: for a borehole of radius 0.05 m, the error committed in ignoring capillarity increases from 2.8 to 280% as α decreases from 10 to 0.1 m−1. The concepts and methods (the saturated bulb, use of the quasi‐linear analysis, matching inner and outer flows) apply to a range of steady mixed saturated‐unsaturated flow systems with water applied under positive hydrostatic pressure to an initially unsaturated soil mass. The study leads to some doubt about the practicality of using the borehole permeameter to measure saturated hydraulic conductivity in the absence of an independent determination of α.
A Frequency Domain Approach to Water Quality Modeling in Groundwater: Theory
Authors: Duffy C. J. , Gelhar L. W.
Published: February 2008

A method for the analysis of complex temporal variations of environmental tracers or pollution time series in groundwater is examined using spectral analysis and linear filter theory for stationary stochastic processes. The interpretation of solute fluctuations subject to a time varying source is accomplished via frequency domain solutions to stochastic differential equations for three widely applied transport models: (1) a lumped parameter or linear reservoir model; (2) convective (advective) transport in a curvilinear flow field; and (3) convective‐dispersive transport in a uniform flow field. Frequency domain solutions are presented in terms of the theoretical transfer function and phase spectra which describe the amplitude attenuation and phase lag between frequencies in the input and output. A comparison of the frequency response of the three models indicates that the unique filtering characteristics of each may provide a diagnostic tool for matching the appropriate theory to a sampled water quality “signal.” A procedure is suggested for parameter estimation which involves comparison of the theoretical and field estimated transfer function and phase spectra.
Errors and Parameter Estimation in Precipitation‐Runoff Modeling: 1. Theory
Authors: Troutman Brent M.
Published: February 2008

Errors in complex conceptual precipitation‐runoff models may be analyzed by placing them into a statistical framework. This amounts to treating the errors as random variables and defining the probabilistic structure of the errors. By using such a framework, a large array of techniques, many of which have been presented in the statistical literature, becomes available to the modeler for quantifying and analyzing the various sources of error. A number of these techniques are reviewed in this paper, with special attention to the peculiarities of hydrologic models. Known methodologies for parameter estimation (calibration) are particularly applicable for obtaining physically meaningful estimates and for explaining how bias in runoff prediction caused by model error and input error may contribute to bias in parameter estimation.
A Comparison of Several Methods of Solving Nonlinear Regression Groundwater Flow Problems
Authors: Cooley Richard L.
Published: February 2008

Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear‐regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi‐linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi‐Newton method, and last was the Fletcher‐Reeves method, which did not converge in 100 iterations for two of the problems. The fastest method per iteration was the Fletcher‐Reeves method, and this was followed closely by the quasi‐Newton method. The Marquardt and quasi‐linearization methods were slower. For all four methods the speed per iteration was directly related to the number of parameters in the model. However, this effect was much more pronounced for the Marquardt and quasi‐linearization methods than for the other two. Hence the quasi‐Newton (and perhaps Fletcher‐Reeves) method might be more efficient than either the Marquardt or quasi‐linearization methods if the number of parameters in a particular model were large, although this remains to be proven. The Marquardt method required somewhat less central memory than the quasi‐linearization metilod for three of the four problems. For all four problems the quasi‐Newton method required roughly two thirds to three quarters of the memory required by the Marquardt method, and the Fletcher‐Reeves method required slightly less memory than the quasi‐Newton method. Memory requirements were not excessive for any of the four methods.
Illustration and Verification of Adjoint Sensitivity Theory for Steady State Groundwater Flow
Authors: Wilson John L. , Metcalfe Douglas E.
Published: February 2008

The application of adjoint sensitivity theory to steady state ground water flow is illustrated with three one‐dimensional flow problems. Adjoint states are analytically derived for four performance measures of these test problems: hydraulic head at a point, spatially average hydraulic head, Darcy velocity at a point, and flux from a prescribed head boundary. Sensitivity coefficients are analytically calculated for average head. The adjoint states are interpreted and their usefulness is discussed. The implementation of a numerical adjoint sensitivity flow code to solve for these adjoint states is described, and the computed adjoint states are used in the code to evaluate the sensitivities of model results to model input parameters. The one‐dimensional flow problems provide a set of verification tests for the numerical code. The numerical code successfully reproduces both the analytically derived adjoint states, including those involving jump conditions, and the sensitivity coefficients for model output values that are nonlinear with respect to model parameters.
Radiation Balances of Melting Snow Covers at an Open Site in the Central Sierra Nevada, California
Authors: Aguado Edward
Published: February 2008

The radiation balances of melting snowpacks for three seasons at an open site at the Central Sierra Snow Laboratory near Soda Springs, California were examined. The snow covers were examples of below‐normal, near‐normal and much‐above‐normal water equivalents. Two of the snow covers melted under generally clear skies in late spring while the other melted under cloudier conditions and at a time when less extraterrestrial radiation was available. Moreover, the snow covers were of very different densities, thereby allowing examination of a possible relationship between that characteristic and albedo. No such relationship was observed. Despite the dissimilarities in the conditions under which melt occurred, the disposition of solar radiation was similar for the three melt seasons. Albedos and their rates of decline through the melt season were similar for the three seasons. Absorbed solar radiation and a cloudiness index were useful predictors for daily net radiation, accounting for 71% of the total variance.