bluuebunny/crossref_metadata_2025 huggingface dataset:
Water quality modeling: A review of the analysis of uncertainty
Authors: Beck M. B.
Published: February 2008

This paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction. More specifically, four problem areas are examined in detail: uncertainty about model structure, uncertainty in the estimated model parameter values, the propagation of prediction errors, and the design of experiments in order to reduce the critical uncertainties associated with a model. The review is rather lengthy, and it has therefore been prepared in effect as two papers. There is a shorter, largely nontechnical version, which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling. Enclosed by this shorter discussion is the main body of the review dealing in turn with (1) identifiability and experimental design, (2) the generation of preliminary model hypotheses under conditions of sparse, grossly uncertain field data, (3) the selection and evaluation of model structure, (4) parameter estimation (model calibration), (5) checks and balances on the identified model, i.e., model “verification” and model discrimination, and (6) prediction error propagation. Much time is spent in discussing the algorithms of system identification, in particular, the methods of recursive estimation, and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first‐order error analysis. There are two obvious omissions from the review. It is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty, although clearly some reference must be made to these topics. In brief, the review concludes (not surprisingly) that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality, and much remains to be done. A lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior, and there is ample evidence to show that the “larger,” more “comprehensive” models are easily capable of generating highly uncertain predictions of future behavior. For the future of the subject, it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification, a need for new questions to be posed in the problem of prediction, and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence.
The alpha, beta, gamma of evaporation from saline water bodies
Authors: Salhotra Atul M. , Adams E. Eric , Harleman Donald R. F.
Published: February 2008

Evaporation from a saline water body is less than that from a freshwater body because of two factors: a decrease in saturation vapor pressure and a partially compensating increase in water surface temperature. These factors are quantified by analyzing field data for eight evaporation pans containing solutions with different salinities and ionic compositions (extending the analysis of Salhotra et al. (1985)). A large saline lake (Dead Sea) is also analyzed using a one‐dimensional numerical model with coupled heat, salt, water, and mechanical energy balances. Further, the use of experiments involving evaporation pans, to study the effect of salinity on lake evaporation, is discussed in light of the fact that the two water bodies have different wind speed functions and hence different temperature feedback effects. Finally, data on the direct measurement of the saturation vapor pressure from mixtures of Mediterranean and Dead Sea waters are presented and compared with results from the analyses of the evaporation pan data.
A comparison of snow cover liquid water measurement techniques
Authors: Boyne H. S. , Fisk D.
Published: February 2008

The amount and distribution of liquid water are important for assessing the mechanical strength, meltwater generation, and meltwater transmission in snow. Liquid water also has a profound effect on the performance of active and passive remote sensing systems operating in the microwave and millimeter wave region of the electromagnetic spectrum. New methods of measuring liquid water have been reported which show considerable promise. Our purpose is to address the question of measurement equivalence by comparing the three direct methods of freezing calorimetry, alcohol calorimetry, and dilution and by comparing the precision of a calibrated capacitance probe with one of the direct methods. All comparisons were made in a laboratory cold room with snow having a mass liquid water content of 0–14 mkg per 100 mkg of snow. The comparisons show that the methods are equivalent with an uncertainty of ±1.8 mkg per 100 mkg of snow. However, the operational achievement of equivalence is strongly dependent on a variety of factors such as sample size, mixing of snow and working fluid, and operator skill.
Conditional simulations of fluid flow in three‐dimensional networks of discrete fractures
Authors: Andersson Johan , Dverstorp Björn
Published: February 2008

How to predict flow through a network of discrete fractures in a three‐dimensional domain is investigated. Fractures are modeled as circular discs of arbitrary size, orientation, transmissivity, and location. A fracture network is characterized by the statistical distributions of these quantities. Fracture traces observed on a wall form the basis for estimates of mean fracture radius, fracture orientation parameters, and fracture density. Fracture trace lengths are estimated with the scanline method and from areal sampling on circular regions. The traces observed on the wall can also be used to condition the network. This trace conditioning is achieved by forcing the network generator to always reproduce the observed traces. Conditioning might be a means of decreasing the variability of the fracture networks. A numerical simulation model has been developed which is capable of generating a fracture network of desired statistical properties and solving for the steady state flow. On each fracture disc the flow is discretized with the boundary element method. A series of hypothetical examples are analyzed. These examples consist of sets of Monte‐Carlo simulations of flow through a series of networks generated from the same statistical distributions. The examples lead to the following conclusions. Large fractures and high fracture density implies good connectivity in the networks. A high fracture density implies a small variance in the flow through the network. Trace conditioning decreases estimation variance only when the fracture network consists of large fractures. Fracture statistics can be estimated reasonably well from fracture traces observed on a wall.
Pressure change and surface expansion in salt marshes due to tidal inundation
Authors: Corapcioglu M. Yavuz , Mathur S.
Published: February 2008

Infiltration of water across the surface‐water interface of a marsh in areas flooded due to tides has been known to cause swelling of sediments. The sudden tidal inundation in an unflooded soil creates a head gradient at the surface of the unsaturated soil above the water table. When water infiltrates into the soil under this gradient, the suction head in the unsaturated domain decreases, and the pore pressure in the saturated zone increases with time, resulting in swelling of highly compressible marsh soils. A one‐dimensional mathematical model which consists of a mass conservation equation, quasi‐static equilibrium equations, stress strain relations for an assumed perfectly elastic solid matrix and a variable total stress expression has been employed to obtain a numerical solution for pore pressure change and swelling due to tidal inundation. Numerical results are presented graphically at the spatial and temporal points of interest for a constant depth of ponding of water at the marsh surface resulting from tidal inundation. Results show that swelling of soil is primarily governed by the initial head gradient across the marsh surface‐water interface.
Effects of spatial variability on annual average water balance
Authors: Milly P. C. D. , Eagleson P. S.
Published: February 2008

Spatial variability of soil and vegetation causes spatial variability of the water balance. For an area in which the water balance is not affected by lateral water flow, the frequency distributions of storm surface runoff, evapotranspiration, and drainage to groundwater are derivable from distributions of soil hydraulic parameters by means of a point water balance model and local application of the vegetal equilibrium hypothesis. Means and variances of the components of the budget can be found by Monte Carlo simulation or by approximate local expansions. For a fixed set of mean soil parameters, soil spatial variability may induce significant changes in the areal mean water balance, particularly if storm surface runoff occurs. Variability of the pore size distribution index and permeability has a much larger effect than that of effective porosity on the means and variances of water balance variables. The importance of the pore size distribution index implies that the microscopic similarity assumption may underestimate the effects of soil spatial variability. In general, the presence of soil variability reduces the sensitivity of water balance to mean properties. For small levels of soil variability, there exists a unique equivalent homogeneous soil type that reproduces the budget components and the mean soil moisture saturation of an inhomogeneous area.
Heat transfer in aquifers with finite caprock thickness during a thermal injection process
Authors: Voigt H. D. , Haefner F.
Published: February 2008

A two‐dimensional model has been developed to solve for the problem of thermal injection into confining aquifer with a caprock of finite thickness and a bedrock of infinite thickness. Heat transfer by horizontal convection within the aquifer and by vertical conduction in the caprock and bedrock is considered. The model also incorporates variable temperatures on the surface of the caprock. Thus it can be used to study problems in connection with aquifer thermal energy storage, heat recovery from, and cold water injection into aquifers near the surface. The derived analytical solutions show that the caprock thickness is important only in long‐time periods and at greater distance from the injection well. The application of this model to cold water injection into an aquifer with 1.75‐m caprock thickness shows that the influence of seasonal variations of the surface temperature on the aquifer is nearly ±2°C.
Groundwater contamination by Temik Aldicarb pesticide: The first 8 months
Authors: Wartenberg Daniel
Published: February 2008

In 1979, Temik aldicarb pesticide was detected in the groundwater of Suffolk County, New York. Concentrations detected in drinking water supplies exceeded health guidelines, causing concern among thousands of residents. In spite of suggestive evidence prior to detection and inquiries from local investigators, EPA did not consider contamination a likely event. Upon detection of the contamination, EPA officials instituted an emergency response. Then, when they were sure there was no acute hazard, they left the situation in the hands of local health authorities, who struggled without adequate resources or sufficient in‐house expertise. The local officials' failure to acknowledge these limitations led to public mistrust and discontent. From this case study one sees the consequences of limited implementation of the federal pesticide regulatory system. More stringent requirements would have likely prevented the contamination. In addition, an integrated response from agencies at many levels of government would have helped prevent similar contamination elsewhere and provided more comprehensive management of this episode on Long Island. Openness by government officials on the limitations of the health data would have helped defuse public animosity and encouraged a more satisfactory resolution of the contamination.
On the modeling of brine transport in porous media
Authors: Hassanizadeh S. Majid , Leijnse Toon
Published: February 2008

The problem of concentrated brine transport arises in the study of transport of pollutants released from a repository in a rock salt formation. An important characteristic of brine, as compared to other solutions normally encountered in groundwater problems, is that it contains a high concentration of solutes. This factor requires special attention in the development of mathematical models for brine transport problems. In this work we discuss certain important physical and mathematical differences between low‐ and high‐concentration situations. In particular, we consider three primary aspects of a model: basic equations, boundary conditions, and numerical techniques. Recognizing the fact that in high‐concentration situations, the fluid motion is not independent of the solutes movement, a new formulation of Darcy's and Fick's law are proposed. The basic equations comprise a set of two nonlinear coupled partial differential equations to be solved for the pressure p and the solute mass fraction ω. These equations have to be solved by means of iterative methods. Various possibilities involving finite difference methods have been studied. In one case, after discretizing the equations in a fully implicit way, the Newton‐Raphson method has been employed to solve the system of nonlinear difference equations simultaneously. In another case, after removing part of the nonlinearity by a transformation of the dependent variable ω, a procedure of sequential solution of the two equations by successive substitution is employed. It turns out that the latter method is considerably faster than the former one as a result of the quasi‐linearization. Finally, considering boundary conditions, it is shown that often they are also nonlinear and coupled. Appropriate conditions for a rock salt boundary and an outflow boundary are developed and their significance in high‐concentration situations are discussed. In particular, a nonlinear time‐dependent boundary condition at a rock salt boundary is developed which takes into account the process of salt dissolution and cap rock formation.
Simultaneous inversion of hydrogeologic and thermal data: 2. Incorporation of thermal data
Authors: Woodbury Allan D. , Smith Leslie
Published: February 2008

Introduction of a data set for a second potential field provides an approach to deal with data limitations in the inverse problem. We examine how temperature measurements can be used to improve the resolution of model parameters in constructing a model of a steady state groundwater flow system. The approach is applicable to cross‐sectional models with vertical components of fluid flow. In media with low hydraulic conductivity, the thermal regime is conductive and temperature measurements do not carry direct information on the hydrogeologic regime. In more permeable systems however, fluid velocities are sufficient to redistribute heat within the basin, perturbing the conductive regime. Parameter estimates developed in the inverse simulation are required to satisfy a weighted measure of both the hydrogeologic and thermal data. The effectiveness of this joint inverse depends upon the extent of the advective disturbance, which, in turn, is controlled by the magnitude of hydraulic conductivity, the length scale and location of hydraulic conductivity variations, the depth of active flow, and the regional configuration of the groundwater flow system. A series of hypothetical examples are presented to demonstrate how model misfit can be reduced when noisy hydraulic head data are augmented with thermal data. Because the extent of an advective disturbance depends upon the absolute value of hydraulic conductivity, addition of temperature measurements in an inverse simulation is particularly helpful in cases where there is uncertainty in boundary conditions, such as recharge rates. The approach is used to construct a model of the groundwater flow system at Downie Slide, north of Revelstoke, British Columbia. Results presented in part one suggest that the slide behaves as a homogeneous, isotropic medium (Woodbury et al., 1987). With a homogeneous hydraulic conductivity, only the ratio of fluid flux to hydraulic conductivity could be determined. By including thermal data, the value of hydraulic conductivity can be estimated.
Confronting the ironies of optimal design: Nonoptimal sampling designs with desirable properties
Authors: Casman Elizabeth A. , Naiman Daniel Q. , Chamberlin Charles E.
Published: February 2008

Two sampling designs are developed for the improvement of parameter estimate precision in nonlinear regression, one for when there is uncertainty in the parameter values, and the other for when the correct model formulation is unknown. Although based on concepts of optimal design theory, the design criteria emphasize efficiency rather than optimality. The development is illustrated using a Streeter‐Phelps dissolved oxygen‐biochemical oxygen demand model.
A continuum model for water movement in an unsaturated fractured rock mass
Authors: Peters R. R. , Klavetter E. A.
Published: February 2008

The movement of fluids in a fractured, porous medium has been the subject of considerable study. This paper presents a continuum model that may be used to evaluate the isothermal movement of water in an unsaturated, fractured, porous medium under slowly changing conditions. This continuum model was developed for use in evaluating the unsaturated zone at the Yucca Mountain site as a potential repository for high‐level nuclear waste. Thus its development has been influenced by the conditions thought to be present at Yucca Mountain. A macroscopic approach and a microscopic approach are used to develop a continuum model to evaluate water movement in a fractured rock mass. Both approaches assume that the pressure head in the fractures and the matrix are identical in a plane perpendicular to flow. Both approaches lead to a single‐flow equation for a fractured rock mass. The two approaches are used to calculate unsaturated hydrologic properties, i.e., relative permeability and saturation as a function of pressure head, for several types of tuff underlying Yucca Mountain, using the best available hydrologic data for the matrix and the fractures. Rock mass properties calculated by both approaches are similar.
Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties
Authors: Russo David
Published: February 2008

Parameter estimation procedures involving solution of the inverse flow problem pertinent to a transient experiment constitute a powerful method of determining the soil hydraulic properties. One of the problems associated with these procedures is the selection of an appropriate model to describe the soil hydraulic properties. Three different models were considered: those of van Genuchten (VG) and Brooks and Corey (BC) model, and the exponential model of Gardner for the hydraulic‐conductivity‐soil‐water‐pressure relationships, coupled with a new expression for the soil‐water‐content‐soil‐water‐pressure relationship (GR model). For a given model the soil hydraulic properties were determined from simulated and measured outflow experiments supplemented with water content at a soil water pressure head of −15,000 cm H2O, using the parameter estimation procedure of Kool et al. (1985a) and data from two soils: a hypothetical sandy loam soil (assumed to be described by the VG model) and a silt loam soil. Model validation tests were performed, and the most appropriate model was selected from the candidate models by discrimination tests using the Akaike Information Criterion (AIC). In the case of the hypothetical sandy loam, the VG model was found to be the most accurate and most consistent with the data. The performance of both the BC and the GR models (in terms of the AIC) was less good but very similar to each other. In the case of the silt loam soil, the VG model with additional parameter m, which accounts for the correlation between pores and for the flow path tortuosity (m=2.02) rather than a constant m=0.5, was found to be most accurate and most consistent with the data. The performance of the BC and the GR models was similar when m was considered as an unknown parameter instead of a constant.
Pseudopotential functions in construction of flow nets for contaminant transport modeling
Authors: Matanga George B.
Published: February 2008

Construction of flow nets in most hydrogeologic field problems is complicated by nonexistence of orthogonality between streamlines and hydraulic head lines in anisotropic porous media. The nonexistence of orthogonality can be circumvented by transformation of the anisotropic porous medium into an isotropic one. Flow nets are valuable in generation of a numerical solution grid for a contaminant transport equation formulated along the direction of flow and the direction orthogonal to flow. Effect of flow domain transformation on contaminant transport simulation is not known. The flow domain transformation can be avoided by constructing flow nets with streamlines and pseudopotential lines. The pseudopotential lines are based on the theory of pseudopotential function. A discussion of the theory in isotropic porous media exists in literature. To my knowledge, this is the first time that the theory is being extended to anisotropic porous media. An integration procedure is used to evaluate values of pseudopotential function and hydraulic head along a streamline. A comparison of flow nets based on pseudopotential lines and hydraulic head lines indicates that pseudopotential lines are more useful than hydraulic head lines in simulation of contaminant transport in saturated groundwater flow systems.
An explanation of scale‐dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry
Authors: Wheatcraft Stephen W. , Tyler Scott W.
Published: February 2008

Stochastic transport theories rely on the assumptions that the principles of stationarity and ergodicity are satisfied. These assumptions imply that the pattern of heterogeneity can be viewed as being spatially periodic, thus yielding a finite correlation scale. We examine a type of heterogeneity which does not satisfy these principles: self‐similar, or fractal heterogeneity, which exhibits a pattern (over a large range of scales) that is independent of the scale of observation and thus will possess a very large correlation scale. We review the basic concepts of fractal geometry and develop scaling relationships for fractal travel distance versus scale of observation. We then develop Lagrangian models for dispersion in a single fractal streamtube and for a set (or bundle) of fractal streamtubes. The results are compared to classical one‐dimensional advection‐dispersion theory, existing fractal and stochastic theories, and to a summary of field‐measured dispersivity data. For the single streamtube model, field‐measured dispersivity is proportional to the straight‐line travel distance raised to a power of D ‐ 1, where D is the fractal dimension. For the set of fractal streamtubes, field‐measured dispersivity is proportional to the straight‐line travel distance raised to a power of 2D ‐ 1. The analytical expressions are verified and elaborated by a fractal random walk computer model. The computer model is used to show the self‐similar nature of heterogeneity that is independent of the scale of observation. Comparisons of the field dispersivity data with our fractal models indicate that most tracer tests have been performed in media that approximate a set of fractal streamtubes.
Chemical‐hydrologic interactions in the near‐stream zone
Authors: Pionke H. B. , Hoover J. R. , Schnabel R. R. , Gburek W. J. , Urban J. B. , Rogowski A. S.
Published: February 2008

The chemical and hydrologic responses of a 9.9‐ha Pennsylvania hill‐land watershed to a typical summer storm event were determined and compared. Patterns and the relative magnitudes of NO3, NH4, total phosphorus (P), and orthophosphate (PO4) concentrations observed in seepage, surface runoff, storm flow, base flow, and rainfall fit those hypothesized from the storm hydrograph and associated water table responses observed in the near‐stream zone. Nitrate concentrations in seepage and base flow were similar and, typically, exceeded those in surface runoff, rainfall, and peak storm flow by 5–20 times. Conversely, NH4, total P, and PO4concentrations in surface runoff from the seep zone and in peak storm flows exceeded those in seepage and base flow by 2–20 times. The findings, presented in a hydrologically based framework for this watershed, provide a conceptual model of how the near‐storm zone operates during and following storm events.
Multivariate Periodic ARMA(1,1) Processes
Authors: Bartolini Paolo , Salas Jose D. , Obeysekera J. T. B.
Published: February 2008

The main objective of this paper is to investigate the properties of multivariate periodic autoregressive moving average (ARMA)(l, 1) processes. Such properties include the covariance structure, the parameter space, and estimation. The parameter space of such periodic processes is derived by aggregation (for instance, monthly models will aggregate to annual models). In particular, the parameter space and estimation are analyzed for contemporaneous ARMA (CARMA) models. It is shown that in general, the aggregation of a multivariate periodic ARMA(1, 1) model leads to a stationary multivariate ARMA(1, 1) model. However, not always a periodic CARMA(1, 1) model aggregates into a stationary CARMA(1, 1) model. Furthermore, it is shown that in estimating the aggregated model parameters, the method based on the periodic model and corresponding parameters, is superior to that based on the aggregated series.
A generalized radial flow model for hydraulic tests in fractured rock
Authors: Barker J. A.
Published: February 2008

Models commonly used for the analysis of hydraulic test data are generalized by regarding the dimension of the flow to be a parameter which is not necessarily integral and which must be determined empirically. Mathematical solutions for this generalized radial flow model are derived for the standard test conditions: constant rate, constant head, and slug tests. Solutions for the less common, sinusoidal test are contained within the general solutions given. Well bore storage and skin are included and the extension to dual‐porosity media outlined. The model is presented as a model of fractured media, for which it is most likely to find application because of the problem of choosing the appropriate flow dimension.
Benefits of increased streamflow: The case of the John Day River Steelhead Fishery
Authors: Johnson Neal S. , Adams Richard M.
Published: February 2008

Conflicts between instream water uses such as fish production and traditional out‐of‐stream uses are an important water resource issue. One criterion for evaluating the merits of alternative water allocations is economic efficiency. This study uses an integrated approach to measure the recreational steelhead fishery benefits of incremental streamflow changes in the John Day River in Oregon. The analysis combines a steelhead fishery production model with a contingent valuation assessment of changes in fishing quality to obtain estimates of the marginal value of water in producing fishing quality. The results suggest that increased summer flows to enhance fishing have a marginal value of about $2.40 acre‐foot. When expressed in terms of water actually consumed, the value may be up to 10 times higher. These values are sensitive to the location of flow alterations in the river, potential for downstream uses and number of anglers in the fishery.
Effective permeability and dispersion in locally heterogeneous aquifers
Authors: Poley Adriaan D.
Published: February 2008

The global effective permeability and hydrodynamic dispersion tensors due to steady flow in locally heterogeneous and statistically anisitropic aquifers are analysed using the “self‐consistent approximation.” For small perturbations the results for the statistically anisotropic case are shown to be consistent with those derived using stochastic continuum theory. However, for larger perturbations the stochastic continuum theory has not yet produced rigorous results that can be compared with those in this paper.
On a new functional form for the dispersive flux in porous media
Authors: Tompson Andrew F. B.
Published: February 2008

A recently developed second‐order model for local dispersive transport in porous media has been simplified to yield a new, closed‐form relationship for the dispersive flux. In situations characterized by negligible velocity gradients, the flux can generally be represented as a convolution or “memory” integral over time of previous concentration gradients. The strength of this memory is controlled by an exponential weighting factor related to the magnitudes of the velocity and local molecular diffusive flux. The form of this result is consistent with other models of diffusive and dispersive transport phenomena over various spatial scales. In circumstances where the memory strength is small, the integral can be simplified and cast in the form of a standard Fickian relationship with apparent time‐dependent dispersivity functions that grow to finite, asymptotic values. This specific formulation can be manipulated to yield a one‐equation transport balance law in the form of a telegraph equation. Nonphysical effects, such as spurious upstream dispersion and instantaneous propagation of mass to extremely distant points predicted with a Fickian law, are reduced or eliminated. Although the importance of the new result in transport simulations will depend on the spatial and temporal scales of interest, it should provide some insight in the interpretation and design of new experiments.
Interpretation of field tracer tests of a single fracture using a transient solute storage model
Authors: Raven K. G. , Novakowski K. S. , Lapcevic P. A.
Published: February 2008

The results and interpretation of five induced‐gradient tracer tests performed at five different average interborehole fluid velocities in a single fracture in monzonitic gneiss are described. The experiments were conducted using radioactive 82Br and a fluorescent dye as conservative tracers where the tracers were pulse injected into radial convergent and injection‐withdrawal flow fields. The flow fields were established between straddle packers isolating the fracture in three boreholes over distances of 12.7–29.8 m. The tracer breakthrough curves were determined from samples of the withdrawn groundwater and were interpreted using residence time distribution (RTD) theory and two deterministic simulation models. The RTD curves of the tracer experiments were interpreted by fitting to the field data a simple advection‐dispersion model and an advection‐dispersion model with transient solute storage in immobile fluid zones. Both models consider the different flow field geometries associated with injection‐withdrawal and radial convergent tests. Comparison of the fits obtained by the simulation models suggest that the initial period of solute transport in single fractures is advection dominated and with increasing tracer residence time or decreasing fluid velocity, transport progresses toward more Fickian‐like behavior. During the advective‐dominated period, the transient solute storage model is shown to adequately describe the asymmetries and long tails characteristic of the fracture RTDs. Interpretation of the tracer experiments using both simulation models further suggests that induced‐gradient tracer experiments are likely to underestimate the dispersive characteristics of single fractures under natural flow conditions.
Nonparametric statistical methods for comparing two sites based on data with multiple nondetect limits
Authors: Millard Steven P. , Deverel Steven J.
Published: February 2008

As concern over the effects of trace amounts of pollutants has increased, so has the need for statistical methods that deal appropriately with data that include values reported as “less than” the detection limit. It has become increasingly common for water quality data to include censored values that reflect more than one detection limit for a single analyte. For such multiply censored data sets, standard statistical methods (for example, to compare analyte concentration in two areas) are not valid. In such cases, methods from the biostatistical field of survival analysis are applicable. Several common two‐sample censored data rank tests are explained, and their behaviors are studied via a Monte Carlo simulation in which sample sizes and censoring mechanisms are varied under an assumed lognormal distribution. These tests are applied to shallow groundwater chemistry data from two sites in the San Joaquin Valley, California. The best overall test, in terms of maintained α level, is the normal scores test based on a permutation variance. In cases where the α level is maintained, however, the Peto‐Prentice statistic based on an asymptotic variance performs as well or better.
An efficient finite element method for modeling multiphase flow
Authors: Kaluarachchi J. J. , Parker J. C.
Published: February 2008

A two‐dimensional finite element model based on Galerkin's weighted residual approach and an upstream weighting technique was developed to predict simultaneous flow of water and oil in a three‐fluid phase system with gas assumed at constant pressure. Element matrices were computed using the influence coefficient method for both Picard and Newton‐Raphson nonlinear iteration schemes. A number of hypothetical simulations were performed in both one and two dimensions to evaluate the accuracy and efficiency of the various schemes with respect to handling of nonlinear soil properties, time marching, mass balance errors, soil nonhomogeneity, and effects of upstream weighting. Results indicate that the Picard scheme appears to be as effective as the Newton‐Raphson scheme while requiring substantially less computational effort if upstream weighting is employed. The Picard method without upstream weighting did not provide satisfactory convergence behavior. Results from problems involving extreme soil nonhomogeneity indicate that accurate solutions can be obtained with the Picard method with the proper use of upstream weighting. Saturation‐pressure derivative terms in the formulation can be evaluated using both analytical and chord‐slope methods. Results indicate that time averaging of these terms is critical for good mass balance results especially during redistribution. Overall mass balance is also sensitive to the fluid‐dependent scaling parameters of the constitutive relationships.
Effects of temperature variation on critical stream dissolved oxygen
Authors: Eheart J. Wayland , Park Heekyung
Published: February 2008

The classical assumption that the lowest dissolved oxygen (DO) occurs at the highest temperature may not always hold. The DO saturation concentration decreases monotonically with increasing temperature, lowering the DO, but the reaeration coefficient increases monotonically with increasing temperature, tending to raise it. The decay coefficient monotonically increases with increasing temperature, lowering the DO for single discharges but not necessarily for multiple discharges. (Lower decay rates attending lower temperatures could result in low DO at the point where the impact from one discharge meets that of another.) This paper addresses the question of whether DO might under some circumstances worsen with decreasing temperature. Using a linear programing model it is shown that for a uniform stream at constant streamflow, the pattern of discharge that maximizes the derivative of critical dissolved oxygen with respect to temperature is an infinite uniformly distributed load. This suggests that streams receiving a large number of discharges may be more susceptible to DO increasing with decreasing temperature than streams receiving a small number of discharges. The corresponding maximum value of the derivative is shown to be dCS/dT + (CS ‐ C*) ln Φ mg/L‐1 °C−1, where T is the temperature in °C, C* is the dissolved oxygen standard, CS is the DO saturation concentration (both in milligrams per liter), and Φ is the temperature adjustment factor for the reaeration coefficient. The maximum derivative value does not depend on the decay coefficient or its temperature adjustment factor. For the maximum reported value of Φ of 1.047, the maximum derivative value is 0.26273 ‐ 0.0028610T + 0.00013371T2 ‐ 0.0000035718T3 ‐ 0.045929C*, for which the assumption that DO decreases monotonically with increasing temperature is valid for C* greater than about 6 mg/L. However, this assumption breaks down for values of Φ just above the range reported in the literature and values of C* just below the normally chosen range of 5–6 mg/L.
Analysis of accuracy of approximate, simultaneous, nonlinear confidence intervals on hydraulic heads in analytical and numerical test cases
Authors: Hill M. C.
Published: February 2008

Inaccuracies in parameter values, parameterization, stresses, and boundary conditions of analytical solutions and numerical models of groundwater flow produce errors in simulated hydraulic heads. These errors can be quantified in terms of approximate, simultaneous, nonlinear confidence intervals presented in the literature. Approximate confidence intervals can be applied in both error and sensitivity analysis and can be used prior to calibration or when calibration was accomplished by trial and error. In this paper, the method is expanded for use in numerical problems, and the accuracy of the approximate intervals is evaluated using Monte Carlo runs. Four test cases are used to compare results. In two numerical test cases, the approximate, simultaneous confidence intervals are generally accurate and are calculated efficiently enough to indicate that the method is useful for real‐world problems. In one of the two analytical test cases considered, the approximate intervals are too wide to be of practical interest. Improving the method used to approximate the uncertainty of the model inputs could make the confidence intervals useful in more problems.
Convergent radial dispersion: A Laplace transform solution for aquifer tracer testing
Authors: Moench Allen F.
Published: February 2008

A Laplace transform solution was obtained for the injection of a tracer in a well situated in a homogeneous aquifer where steady, horizontal, radially convergent flow has been established due to pumping at a second well. The standard advection‐dispersion equation for mass transfer was used as the controlling equation. For boundary conditions, mass balances that account for mixing of the tracer with the fluid residing in the injection and pumped wells were used. The derived solution, which can be adapted for either resident or flux‐averaged concentration, is of practical use only for the pumped well. This problem is of interest because it is easily applied to field determination of aquifer dispersivity and effective porosity. Breakthrough curves were obtained by numerical inversion of the Laplace transform solution. It was found that tracer mixing with fluid in the pumped and injection wells, especially in low‐porosity aquifers, may have a significant influence on the shape of the tracer breakthrough curves.
Probability distribution of velocity in natural channel cross sections
Authors: Dingman S. Lawrence
Published: February 2008

The probability distribution of velocities in idealized parabolic channels and in regular and highly irregular natural stream cross sections follows a power law: F(v)=(v/V)c, where F(v) is the cumulative frequency distribution of velocity v, Vis the maximum velocity in the cross section, and c is a shape parameter. Values of Vand c can be estimated from current meter measurements via moments, maximum likelihood, or regression analysis; maximum likelihood is most precise. The distribution is useful in stream habitat studies because it provides immediate information about the fraction of a cross section containing velocities in any range. For stream gaging, one can use this distribution to estimate the mean cross‐sectional velocity E(v), where E(v)=[c/(c + 1)]V without invoking assumptions about the location of the mean velocity in each profile. One can also immediately determine the energy coefficient α as α=(c + 1)3/[c2(c + 3)] and use this information to improve the accuracy of field measurements of reach resistance.
Thin ice growth
Authors: Ashton George D.
Published: February 2008

The thickening of ice covers has traditionally been calculated using a method in which the thickness is assumed proportional to the square root of the accumulated freezing degree days. Particularly for newly formed thin ice this method overpredicts the ice thickness. Consideration of the thermal resistance between the top of the ice and the atmosphere results in a method which predicts linear growth with time for thin ice and transitions to the t½ growth at large thicknesses. The method proposed here is not new but seems to be rarely used even though it requires selection of only one coefficient. Data from several sources including initial river ice growth, sea ice growth, and sludge freezing are used to validate the method and bracket the coefficient.
Accounting for intracell flow in models with emphasis on water table recharge and stream‐aquifer interaction: 2. A procedure
Authors: Jorgensen Donald G. , Signor Donald C. , Imes Jeffrey L.
Published: February 2008

Intercepted intracell flow, especially if cell includes water table recharge and a stream ((sink), can result in significant model error if not accounted for. A procedure utilizing net flow per cell (Fn) that accounts for intercepted intracell flow can be used for both steady state and transient simulations. Germane to the procedure is the determination of the ratio of area of influence of the interior sink to the area of the cell (Ai/Ac). Ai is the area in which water table recharge has the potential to be intercepted by the sink. Determining Ai/Ac requires either a detailed water table map or observation of stream conditions within the cell. A proportioning parameter M, which is equal to 1 or slightly less and is a function of cell geometry, is used to determine how much of the water that has potential for interception is intercepted by the sink within the cell. Also germane to the procedure is the determination of the flow across the streambed (Fs), which is not directly a function of cell size, due to difference in head between the water level in the stream and the potentiometric surface of the aquifer underlying the streambed. The use of Fn for steady state simulations allows simulation of water levels without utilizing head‐dependent or constant head boundary conditions which tend to constrain the model‐calculated water levels, an undesirable result if a comparison of measured and calculated water levels is being made. Transient simulations of streams usually utilize a head‐dependent boundary condition and a leakance value to model a stream. Leakance values for each model cell can be determined from a steady state simulation, which used the net flow per cell procedure. For transient simulation, Fn would not include Fs. Also, for transient simulation it is necessary to check Fn at different time intervals because M and Ai/Ac are not constant and change with time. The procedure was used successfully in two different models of the aquifer system in the Ozarks. The use of Fn was essential to the two model studies because most model cells in both models contained water table recharge and multiple sinks.
The relationship of catchment topography and soil hydraulic characteristics to lake alkalinity in the northeastern United States
Authors: Wolock D. M. , Hornberger G. M. , Beven K. J. , Campbell W. G.
Published: February 2008

We undertook the task of determining whether base flow alkalinity of surface waters in the northeastern United States is related to indices of soil contact time and flow path partitioning that are derived from topographic and soils information. The influence of topography and soils on catchment hydrology has been incorporated previously in the variable source area model TOPMODEL as the relative frequency distribution of ln (a/Kb tan B), where ln is the Naperian logarithm, “a” is the area drained per unit contour, K is the saturated hydraulic conductivity, b is the soil depth, and tan B is the slope. Using digital elevation and soil survey data, we calculated the ln (a/Kb tan B) distribution for 145 catchments. Indices of flow path partitioning and soil contact time were derived from the ln (a/Kb tan B) distributions and compared to measurements of alkalinity in lakes to which the catchments drain. We found that alkalinity was, in general, positively correlated with the index of soil contact time, whereas the correlation between alkalinity and the flow path partitioning index was weak at best. A portion of the correlation between the soil contact time index and alkalinity was attributable to covariation with soil base saturation and cation exchange capacity, while another portion was found to be independent of these factors. Although our results indicate that catchments with long soil contact time indices are most likely to produce high alkalinity base flow, a sensitivity analysis of TOPMODEL suggests that surface waters of these same watersheds may be susceptible to alkalinity depressions during storm events, due to the role of flow paths.
Simple analytic functions for modeling three‐dimensional flow in layered aquifers
Authors: Fitts Charles R.
Published: February 2008

Analytic functions are presented for modeling three‐dimensional steady groundwater flow in stratified aquifers. The functions create discontinuity in the potential across an infinite plane while maintaining continuity of the potential gradient across the plane. These functions may be superimposed with other analytic functions to model three‐dimensional flow in stratified aquifers under a variety of boundary conditions. An interface between two layers of different hydraulic conductivity, an impermeable boundary, or a thin leaky layer may be modeled using such functions. These functions are simple compared to functions for doublet distributions over finite plane panels and are suitable for efficient modeling.
An assessment of bed load sediment transport formulae for gravel bed rivers
Authors: Gomez Basil , Church Michael
Published: February 2008

The performance is tested of 12 bed load sediment transport formulae developed for use in gravel bed channels. The formulae are applied in the manner intended by the original authors. To this end, the test data are restricted to ones obtained in approximately steady flow when the material in motion was similar to that present on the bed; that is, transport was not size selective. This represents the nearest approach to “equilibrium sediment transport” that can be realized with available data. Four sets of river data and three sets of flume data were chosen for the test, covering a range of eight orders of magnitude in unit bed load transport rate. The test data were not used in the development of the formulae. The analysis separates mean bias and local bias. No formula performs consistently well. Limitations of the test data, the constraints imposed by an operationally realistic test, and reasons based upon the physics of the transport phenomenon all may be adduced for this. To estimate the magnitude of transport with limited hydraulic information, stream power equations should be used because they provide the most straightforward scale correlation of the phenomenon. In particular, the approach of Bagnold deserves further study. When local hydraulic information is available, a formula should be selected that is sensitive to bed state or grain size distribution and, in this context, the formulae of Einstein, Parker, and Ackers‐White‐Day bear continued examination.