bluuebunny/crossref_metadata_2025 huggingface dataset:
A finite‐volume Eulerian‐Lagrangian Localized Adjoint Method for solution of the advection‐dispersion equation
Authors: Healy R. W. , Russell T. F.
Published: February 2004

A new mass‐conservative method for solution of the one‐dimensional advection‐dispersion equation is derived and discussed. Test results demonstrate that the finite‐volume Eulerian‐Lagrangian localized adjoint method (FVELLAM) outperforms standard finite‐difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion‐dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space‐time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.
Paleoflood evidence for a natural upper bound to flood magnitudes in the Colorado River Basin
Authors: Enzel Yehouda , Ely Lisa L. , House P. Kyle , Baker Victor R. , Webb Robert H.
Published: February 2004

The existence of an upper limit to the magnitude of floods in a region is a long‐standing and controversial hypothesis in flood hydrology. Regional envelope curves encompassing maximum flood magnitudes stabilize with progressive increases in the areal coverage and period of observation (Wolman and Costa, 1984). However, the short lengths of conventional gaging records limit substantial advances in testing whether this stabilization is evidence of an upper limit. In the Colorado River basin there are 32,120 station years of gage data, but the average period at a gaging station is only 20 years, with most stations having less than 70 years of observation. Paleoflood magnitudes derived from sediments of large prehistoric floods from 25 sites on rivers in Arizona and Utah provide additional data to extend the records of the largest floods. The paleoflood data identify the maximum flood discharges that have occurred on individual rivers over the last several hundred to several thousand years. Even with this increase in the observational period, the largest paleoflood discharges do not exceed the upper bound of maximum peak discharges delineated by the envelope curve derived from the available gaged and historical records. This result accords with the hypothesis of an upper physical limit for flood magnitudes and suggests that, for the Colorado River basin, the upper limit can be approximated by existing systematic and historical data for large floods. Similar relationships also hold when paleofloods and gaged records are presented for the subregion of southern Arizona.
Statistics of block conductivity through a simple bounded stochastic medium
Authors: Fenton Gordon A. , Griffiths D. V.
Published: February 2004

A Monte Carlo approach is employed to estimate the distribution of an equivalent conductivity measure, the block conductivity, which characterizes the total flow rate through a two‐dimensional bounded domain and which is itself a random variable. Chi‐square goodness‐of‐fit tests indicate that the lognormal distribution is an appropriate choice for the block conductivity distribution. For square domains, the mean and variance of the block conductivity are seen to be closely approximated using the statistics of local averages of log conductivity.
Two‐dimensional groundwater transport of reactive solutes with competitive adsorption
Authors: Kalatzis Athanasios , García‐Delgado Rafael A. , Pang Tak‐Kai , Koussis Antonis D. , Bowers Alan R.
Published: February 2004

Chemical contamination of groundwater is typically associated with multicomponent solutions, the migration of which is affected by preferential adsorption and solution reactions. Transport models should, therefore, account for advection and dispersion and for the reactions in the solution and on the solid phase. The two‐dimensional model METLI has been developed for the personal computer (PC) simulation of groundwater transport with competitive adsorption of a three‐species system consisting of a metal, a ligand, and their dominant complex at a given pH. The model structure, which employs spatial and process splitting algorithms, is described. One‐ and two‐dimensional application examples are used to demonstrate how chemical reactivity and affinity for adsorption of a species, adsorption capacity of soil, and the number of the adsorbing species affect pollutant plumes in groundwater. The model executes rapidly on PCs using grids of several hundred nodes.
A comprehensive set of analytical solutions for nonequilibrium solute transport with first‐order decay and zero‐order production
Authors: Toride Nobuo , Leij Feike J. , van Genuchten Martinus T.
Published: February 2004

Solute transport in the subsurface is often considered to be a nonequilibrium process. Predictive models for nonequilibrium transport may be based either on chemical considerations by assuming the presence of a kinetic sorption process, or on physical considerations by assuming two‐region (dual‐porosity) type formulations which partition the liquid phase into mobile and immobile regions. For certain simplifying conditions, including steady state flow and linear sorption, the chemical and physical nonequilibrium transport models can be cast in the same dimensionless form. This paper presents a comprehensive set of analytical solutions for one‐dimensional nonequilibrium solute transport through semi‐infinite soil systems. The models involve the one‐site, two‐site, and two‐region transport models, and include provisions for first‐order decay and zero‐order production. General solutions are derived for the volume‐averaged (or resident) solute concentration using Laplace transforms assuming both first‐ and third‐type inlet conditions, and arbitrary initial conditions, input solute concentrations, and solute production profiles. The solutions extend and generalize existing solutions for equilibrium and nonequilibrium solute transport. The general solutions are evaluated for some commonly used input and initial conditions, and zero‐order production profiles. Expressions for the flux‐averaged concentration are derived from the general and specific solutions assuming a third‐type inlet condition. Typical examples of calculated concentration distributions resulting from several sets of initial and input conditions and zero‐order production functions are also presented and briefly discussed.
Micromodel studies of three‐fluid porous media systems: Pore‐scale processes relating to capillary pressure‐saturation relationships
Authors: Soll W. E. , Celia M. A. , Wilson J. L.
Published: February 2004

An experimental approach to study physical processes affecting fluid behavior in three‐fluid porous media systems was designed and implemented. These experiments were designed to provide quantitative evidence of important pore‐scale displacement processes. A unique experimental approach using a two‐dimensional synthetic porous medium (micromodel) and digital image analysis (DIA) enabled both measurement of three‐fluid capillary pressure‐saturation relationships and analysis of fluid behavior at the pore level. Experiments were pressure controlled, and were designed to mimic measurements typically performed on laboratory cores. Only quasi‐static measurements were made, with a focus on capillary pressure‐saturation relations. Different orders of fluid infiltration with respect to wettability were studied. DIA made it possible to obtain quantitative information about the experiments, including fluid saturations, saturation changes between pressure steps, and movement of apparently isolated fluids through films. The results provide insights into important pore‐scale mechanisms and provide a basis for three‐fluid pore‐scale computations.
Stream temperature dynamics: Measurements and modeling
Authors: Sinokrot Bashar A. , Stefan Heinz G.
Published: February 2004

A numerical model based on a finite difference solution of the unsteady heat advection‐dispersion equation is formulated to predict water temperatures in streams at time increments of 1 hour. An energy balance accounts for the effects of air temperature, solar radiation, relative humidity, cloud cover, and wind speed on the net rate of heat exchange through the water surface, and heat conduction between water and streambed. Continuous stream temperature recordings in shallow streams show strong dynamic behavior including diurnal variations of several degrees Celsius which are lost in the standard daily records. These measured water temperatures are used to calibrate the model for the optimum percentages of Sun shading and wind sheltering. Stream exposure to solar radiation is shown to vary from 30 to 100% and wind exposure from 10 to 30% depending on the character of the stream. Values are related to stream width and season because of variable leaf cover of trees on stream banks. After calibration, accuracies of hourly and daily water temperature predictions over periods of several weeks are of the order of 0.2° to 1°C. Solar (shortwave) radiation is shown to be the most important component of the heat flux across the stream water surface, but none of the other components, i.e., long‐wave radiation, evaporation, and convection to the atmosphere, are negligible. Conductive heat exchange between the streambed and the water is a significant heat balance component in shallow streams.
Evaluation of vertical groundwater fluxes and thermal properties of aquifers based on transient temperature‐depth profiles
Authors: Taniguchi Makoto
Published: February 2004

A series of type curves is presented for estimating vertical groundwater fluxes in relatively shallow aquifers by using seasonal changes in groundwater temperature‐depth profiles. Vertical groundwater fluxes are estimated by fitting a dimensionless parameter to the type curves when the amplitude of annual variations of groundwater temperature at several depths and the thermal diffusivity of the aquifer are known or measured. Both upward and downward groundwater fluxes estimated by fitting temperatures observed in Nagaoka plain, Japan to the type curves agree well with the fluxes calculated from hydraulic conductivity and hydraulic gradient data. Measurements of seasonal changes in groundwater temperature and hydraulic gradients were analyzed to estimate the thermal diffusivity of the aquifer in situ that is close to the value reported in the literature.
Measurement of river level variations with satellite altimetry
Authors: Koblinsky C. J. , Clarke R. T. , Brenner A. C. , Frey H.
Published: February 2004

Quantitative assessment of water levels and river discharge is often made difficult by large distances, limited access, and low population densities in remote areas. Satellite altimetry provides a repetitive remote sensing approach to determining river levels at a number of locations within a river system, providing the orbital repeat cycle is short enough in time, the ground track maintains a stable repeat over previous locations, and the return power of the altimeter signal can be readily identified and located. The U.S. Navy's Geosat radar altimeter mission between 1985 and 1989 provided the first altimeter measurements with sufficient precision and extended duration to examine the utility of such measurements for long‐term monitoring of inland waters. These measurements have been examined over the Amazon basin. Satellite observations are retrieved at four locations that overlap with river gauge measurements. A technique is developed to isolate radar return signals from the river. Two years of satellite measurements are compared with the river gauge retrievals. The overall level of comparison is 0.7 m rms when the technique is applied manually, and 1.2 m rms when an automated version of the method is applied. At one location the average difference is 0.2 m rms. This level of accuracy may not be useful for routine hydrological measurements. However, there are a variety of difficulties that are specific to the Geosat altimeter measurement over rough terrain. Present altimeter satellites, ERS 1 (launched June 1991) and TOPEX/Poseidon (launched August 1992), correct many of these problems. This study suggests that the prospect for obtaining useful measurements of river level from space is promising.
Atmospheric and subsurface sources of stable and radioactive nuclides used for groundwater dating
Authors: Lehmann Bernhard E. , Davis Stanley N. , Fabryka‐Martin June T.
Published: February 2004

Theoretical calculations together with a review of data from Sweden, Switzerland and Canada indicate that given sufficient isolation time and U and Th in the aquifer matrix, deep subsurface production of 3H, 4He, 36Cl, 37Ar, 39Ar, 40Ar, 85Kr, 129I, and 222Rn can overshadow the normal atmospheric component of these nuclides in recharging groundwater. Although direct evidence is lacking, calculations suggest that small but measurable subsurface production of 3H and 14C could also take place in aquifers having high U and Th concentrations. Some ground water which has been recharged during the past 40 years will have 3H, 3He, 36Cl, 85Kr, and 129I concentrations which are dominantly anthropogenic. Dating methods with the least complications in interpretation appear to be 3H‐3He for postbomb waters and 81Kr for waters in the range of 5×104 to 1×106 a.
A comparison of linear regression with Clark's Method for estimating barometric efficiency of confined aquifers
Authors: Davis Donald R. , Rasmussen Todd C.
Published: February 2004

An estimate of barometric efficiency, often necessary for aquifer pump test interpretation, is difficult to obtain when there is a trend in water levels over time. Ordinary least squares (OLS) regression methods can be used to determine both the barometric efficiency and a trend function when the form of the trend is known. Clark's (1967) procedure, which does not require specification of the trend functional form, is shown to provide an unbiased and consistent estimate of barometric efficiency. OLS is only advantageous for a short data record providing the form of the trend is known. Clark's method may still be used with short data records with a linear trend when augmented by a recursive correction procedure. Both methods work best with constant barometric efficiency and rapid aquifer‐borehole water level equilibration.
Flow structure in a bouldery mountain stream with complex bed topography
Authors: Furbish David Jon
Published: February 2004

Bouldery, mountain streams often possess highly irregular banks and beds composed of bedrock outcrops and immobile clasts mingled with alluvial bed forms. This complex morphology can induce locally strong flow accelerations and distortions of the water surface. Despite the complexity of flow at a scale of one or two channel widths and smaller, it is possible to identify a filament of high stream wise velocity that exhibits a near‐oscillatory structure, albeit noisy, as it threads back and forth across the channel over tens of channel widths; and transverse water surface slopes locally mimic transverse bed slopes. These features are responses to shoaling of flow over an irregular, nearly random, bed topography. To clarify the mechanisms leading to this structure, linearized forms of the depth‐averaged equations of momentum and continuity are solved in the wavenumber domain, for the case of a straight channel with uniform width, using a doubly periodic description of bed topography as a forcing term. Systematic changes in the strength and phase of velocity and water surface responses with varying wavenumber of bed undulations reflect mutual interaction of streamwise and transverse flow accelerations and transverse water surface slopes. These results are cast in terms of spectral responses to a bed composed of many superimposed waveforms. Then the shapes of spectra describing transverse water surface slopes and the transverse coordinate of the high‐velocity filament, as measured from 100 equally spaced sections along North Boulder Creek, Colorado, are predicted by the analysis. The levels of the spectra are underestimated, however, due to factors not taken into account by the linear analysis, notably variations in width, and form drag associated with coarse roughness.
The value of streamflow data for storage design
Authors: Cloke Peter S. , Cordery Ian
Published: February 2004

It has long been assumed that the benefits of collecting streamflow data are greater than the costs of collection. However, factual information on the benefits of data collection programs are not available. To assess the value of one aspect of data use, the reduction in uncertainty of design storage size and the associated capital cost was determined for a range of lengths of available data. The results were applied to the 500 station data collection network in New South Wales, Australia to show that for this single use of data the benefits greatly exceed the cost of collection.
Factorial kriging analysis of springwater contents in the Dyle River Basin, Belgium
Authors: Goovaerts P. , Sonnet P. , Navarre A.
Published: February 2004

This paper describes a geostatistical method, known as factorial kriging analysis, which is well suited for analyzing multivariate spatial information. The method involves multivariate variogram modeling, principal component analysis, and cokriging. It uses several separate correlation structures, each corresponding to a specific spatial scale, and yields a set of regionalized factors summarizing the main features of the data for each spatial scale. The method is applied to springwater solute contents (Ca, Sr, Mg, K, Na, SO4, NO3 Cl, pH, electrical conductivity, alkalinity) measured in 86 springs situated in the Dyle River catchment area, Belgium. Two scales of spatial variation (1 and 9 km) are identified and interpreted. These correspond to local sources of contaminants due to human activities and regional changes in the geologic characteristics of the aquifer. At each scale, the correlation structure is analyzed and the regionalized factors are estimated by cokriging and then mapped. The results are compared with those of a classical multivariate approach, i.e., principal component analysis of the correlation matrix, which takes no account of the spatial location of the observations.
A quadratic Petrov‐Galerkin Solution for kinematic wave overland flow
Authors: Muñoz‐Carpena Rafael , Miller Cass T. , Parsons John E.
Published: February 2004

A Petrov‐Galerkin (PG) finite element method was developed to solve the kinematic wave formulation of the overland flow equations. The resultant model uses quadratic basis functions and test functions that are modified by polynomials of cubic and quartic order, yielding a formulation that includes four PH parameters. The PG model was found to reduce the mean sum of square error of the solution compared to a conventional Bubnov‐Galerkin finite element solution by about a factor of 3 as the Courant number (Cr) approached one. Good results were also achieved with the PG method for problems that resulted in shock formation, which are typical of many applied problems of concern. PG parameters were found to depend strongly upon the Courant number and weakly upon the number of nodes in the system. Polynomial expressions were derived to approximate the PG parameters over the range 0 < Cr < 1. As the number of nodes in the system increased, a single‐parameter version of the model yielded solutions approaching the accuracy of the four‐parameter model.
A tool for evaluating a need for variable selectivities in cation transport in soil
Authors: Mansell R. S. , Bloom S. A. , Bond W. J.
Published: February 2004

The empirical Rothmund‐Kornfeld equation was used to describe a collection of cation exchange isotherms for K and Ca in Brucedale soil over a range of total solution concentrations (CT). A comparison of variable binary exchange selectivity coefficients (KKCa) which vary with CT and solution phase ion concentrations (CK, CCa) with constant KKca values was thus possible. Percent differences between sorbed equilibrium concentrations calculated using variable and constant KKCa over a range of CT and CK were arranged into a contour map. Zones of potentially observable difference were limited, implying that simulations of cation transport using variable and constant KKCa values would be essentially identical. The predicted effect was examined using a numerical model for cation transport. The model successfully described observed spatial distributions for cation concentrations following constant‐flux infiltration of electrolyte solution into soil columns. Simulations using variable KKCa values provided only a slight improvement over simulations using constant KKCa values, thus validating the use of the contour map as a convenient method to evaluate the need to use variable selectivities in simulations of cation transport.
Adaptive calibration of a conceptual model for flash flood forecasting
Authors: Brath Armando , Rosso Renzo
Published: February 2004

The adaptive use of a conceptual model for real‐time flow forecasting is investigated. Maximum likelihood and ordinary least squares estimation criteria are considered, and the performance of maximum likelihood techniques for autocorrelated (AMLE) and heteroscedastic (HMLE) errors is analyzed jointly with that provided by the commonly used ordinary least squares estimation (OLSE) technique. Streamflow forecasts are compared for three rivers in central Italy, obtained by AMLE, HMLE, and OLSE adaptive calibration of a simple conceptual model describing the rainfall‐runoff transformation by accounting for Hortonian infiltration and linear basin response to rainfall excess. Although model residuals display both autocorrelation and heteroscedasticity, OLSE is found to provide a rather satisfactory performance. Because the OLSE technique also requires less computational effort compared to that for AMLE and HMLE, one could consider OLSE as a suitable option for real‐time model operation.
Permeability of Apache Leap Tuff: Borehole and core measurements using water and air
Authors: Rasmussen T. C. , Evans D. D. , Sheets P. J. , Blanford J. H.
Published: February 2004

Field and laboratory methods for estimating and interpreting parameters obtained from field borehole and laboratory core experiments are examined using permeability data interpreted from air and water injection tests in variably saturated fractured tuff at the Apache Leap Tuff Site in central Arizona. The tuff at the field site has a matrix porosity of approximately 17.5% and contains numerous near‐vertical fractures at an average spacing of 1.3 m. More than 270 m of 6.4‐cm‐diameter oriented core were collected from boreholes drilled to a maximum depth below the surface of 30 m and at a vertical angle of 45°. Laboratory estimates of absolute permeabilities using air and water as the test fluids were acquired at a range of matric potentials for 105, 5‐cm‐long core segments extracted at approximately 3‐m intervals containing no obvious fractures. Field scale estimates of fractured rock permeabilities using air and water as test fluids were obtained at ambient matric suctions and water saturated conditions, respectively. The field tests were conducted along 3‐m intervals within boreholes with the intervals centered on core sampling positions. Borehole and core permeabilities demonstrate substantial spatial variability, with variations exceeding three orders of magnitude. Laboratory core data show a strong relationship between permeabilities using saturated water and oven‐dry air injection tests with the latter demonstrating the Klinkenberg effect. The influence of matric suction on permeabilities is used to demonstrate that relative permeabilities do not sum to a constant for a wide range of matric suction. Only weak relationships exist between permeabilities measured in boreholes versus cores for both water and air. Permeabilities measured in boreholes using air are shown to provide good estimates of permeabilities measured using water into initially unsaturated, fractured rock at the Apache Leap Tuff Site.
Variable‐head ponded infiltration under constant or variable rainfall
Authors: Philip J. R.
Published: February 2004

This study of the effect of excess rainfall, ponded without runoff, on the dynamics of infiltration into a deep homogeneous soil uses the Green‐Ampt, or delta function, approximation. Exact solutions are given for constant and for piecewise constant rainfall. An inverse method yields solutions for arbitrary hyetographs. Ponding can increase markedly both the total duration of the infiltration event and the total amount infiltrated. The analysis suggests that capillary hysteresis emerges during the ponding recession phase toward the end of a storm. In long‐duration heavy rainstorms infiltration rate may increase with time, contrary to the classical picture. The asymptotic large time infiltration rate under continuous constant rainfall at rate R, with
(the conductivity parameter in the Green‐Ampt formulation) is an increasing function of both
and R. (With ponding neglected, it is simply
). An appendix gives some exact results on the influence of hyetograph shape on time to ponding.
A numerical dual‐porosity model with semianalytical treatment of fracture/matrix flow
Authors: Zimmerman Robert W. , Chen Gang , Hadgu Teklu , Bodvarsson Gudmundur S.
Published: February 2004

A new dual‐porosity model is developed for single‐phase fluid flow in fractured/porous media. Flow is assumed to take place through the fracture network and between the fractures and matrix blocks. The matrix blocks are treated in a lumped parameter manner, with a single average pressure used for each matrix block. Rather than assuming that fracture/matrix flux is proportional to the difference between the fracture pressure and matrix pressure at each point, as is done in the Warren‐Root model, we use a nonlinear equation which more accurately models the flux over all time regimes, including both early and late times. This flux equation is compared with analytical solutions for spherical blocks with prescribed pressure variations on their boundaries. The nonlinear flux equation is also used as a source/sink term in the numerical simulator TOUGH. The modified code allows more accurate simulations than the conventional Warren‐Root method, with a large savings (about 90%) in computational time compared to methods which explicitly discretize the matrix blocks.
Kinetic analysis of virus adsorption and inactivation in batch experiments
Authors: Grant Stanley B. , List E. John , Lidstrom Mary E.
Published: February 2004

The mobility and ecology of viruses in natural environments is strongly influenced by the adsorption of virus particles to sand or soil surfaces. This binding process is frequently studied by conducting batch experiments in which fluid suspensions of virus particles are contacted with the adsorbent of interest. In this report, a simple first‐order kinetic theory is presented which accounts for many of the complicated interactions that can occur when viruses contact an adsorbent in a batch system. Closed‐form solutions and numerical simulations of the model indicate that four classes of virus‐surface interactions can be identified, including quasi‐equilibrium adsorption, quasi‐equilibrium adsorption with surface sinks, quasi‐equilibrium adsorption with reduced inactivation, and direct irreversible adsorption. Based on these results, a new experimental approach for studying virus‐surface interactions is proposed and tested using a model system consisting of bacteriophage lambda and Ottawa sand. Fluid samples were collected from sand‐containing and sand‐free virus suspensions over the course of 5–6 days and analyzed for plaque forming units (PFU). These experiments were repeated using three different pH values and six different electrolyte compositions. Nondimensionalization of the PFU data from the sand‐free suspension collapsed all of the data onto a single line, as predicted by the kinetic model. When plotted in a nondimensional format, data from the sandcontaining suspensions exhibited behavior which tould readily be interpreted within the context of the kinetic model. These results suggest that the proposed approach offers a powerful alternative to conventional methods for studying virus adsorption at the solid‐liquid interface, and for predicting the potential mobility and fate of viruses in porous media.
Base cation chemistry of storm runoff in a forested headwater wetland
Authors: Hill Alan R.
Published: February 2004

Hydrologic data were combined with analysis of a natural isotope, oxygen 18, and solutes (Ca, Mg, K, Na) to examine saturation overland flow and stream base cation dynamics during storms in a headwater swamp. Laboratory experiments were also used to study the interaction of mixtures of throughfall and groundwater with swamp substrates in zones of saturation overland flow. Increased streamflow was associated with decreased concentrations of Ca, Mg, and Na, whereas K concentrations remained constant, or increased in some storms. A comparison of chemical and isotopic hydrograph separation indicated that Ca, Mg, and Na were conservative in storms with instantaneous event water contributions <25% and were reactive in storms with a larger event water component. Laboratory data suggested that these cations were only released rapidly from swamp substrates when mixed with water containing >40% throughfall (event water). Stream K concentrations appear to be controlled by the mixture of throughfall and groundwater in saturation overland flow during occasional storms with high throughfall K concentrations. Laboratory data suggested that for most storms which have throughfall K concentrations of <1 mg L−1, K was released as overland flow interacts with swamp substrates, resulting in constant stream K concentrations.
Stochastic models applied to cluster analysis of censored water quality data
Authors: Maul A. , El‐Shaarawi A. H.
Published: February 2004

A clustering method is presented which is appropriate when a mixture of multivariate distributions is used to model the data. The procedure assumes that the measurements made on several independent characteristics follow probability distributions of different nature (e.g., normal, Poisson, multinomial). Likelihood methods are used to both estimate the parameters of the models and perform the cluster analysis. The procedure is applicable when the data are subject to censoring. A data set on the concentrations of volatile halocarbon contaminant in Lake Ontario is used to illustrate the methods of this paper.
Economic and environmental impacts of water quality protection policies: 2. Application to the Central High Plains
Authors: Bernardo D. J. , Mapp H. P. , Sabbagh G. J. , Geleta S. , Watkins K. B. , Elliott R. L. , Stone J. F.
Published: February 2004

A three‐stage modeling framework is applied to evaluate the potential economic and environmental impacts of agricultural groundwater protection policies in the Central High Plains Region. Three alternative policies (limitations on total nitrogen applications, limitations on unit‐area nitrogen applications, and restrictions on the use of selected herbicides) are compared to a baseline scenario that reflects the absence of any form of groundwater quality protection measures. In general, nitrogen restrictions are more effective in reducing nitrate loadings in percolation water if implemented on a unit‐area basis rather than as a total (farm level) restriction. In contrast, the total restriction is more effective in controlling runoff losses of nitrogen. Both nitrogen restrictions have significant impacts on crop production levels and regional agricultural income, while the economic consequences of the pesticide restriction are much less pronounced. The proposed regional modeling framework provides critical information necessary to assess the economic and environmental tradeoffs of policy alternatives aimed at controlling agricultural nonpoint source pollution.
How much complexity is warranted in a rainfall‐runoff model?
Authors: Jakeman A. J. , Hornberger G. M.
Published: February 2004

Development of mathematical models relating the precipitation incident upon a catchment to the streamflow emanating from the catchment has been a major focus of surface water hydrology for decades. Generally, values for parameters in such models must be selected so that runoff calculated from the model “matches” recorded runoff from some historical period. Despite the fact that the physics governing the path of a drop of water through a catchment to the stream involves complex relationships, evidence indicates that the information content in a rainfall‐runoff record is sufficient to support models of only very limited complexity. This begs the question of what limits the observed data place on the allowable complexity of rainfall‐runoff models. Time series techniques are applied for estimating transfer functions to determine how many parameters are appropriate to describe the relationship between precipitation and streamflow in the case where data on only precipitation, air temperature, and streamflow are available. Statistics from an “information matrix” provide the clues necessary for determining allowable model complexity. Time series models are developed for seven catchments with widely varying physical characteristics in different temperate climatic regimes to demonstrate the method. It is found that after modulating the measured rainfall using a nonlinear loss function, the rainfall‐runoff response of all catchments is well represented using a linear model. Also, for all catchments a two‐component linear model with four parameters is the model of choice. The two components can be interpreted as defining a “quick flow” and “slow flow” response of the given catchment. The method therefore provides a statistically rigorous way to separate hydrographs and parameterize their response behavior. The ability to construct reliable transfer function models for describing the rainfall‐runoff process offers a new approach to investigate empirically the controls of physical catchment descriptors, land use change, climate change, etc., on the dynamic response of catchments through the extensive analysis of historical data sets.
Minimum relative entropy: Forward probabilistic modeling
Authors: Woodbury Allan D. , Ulrych T. J.
Published: February 2004

The pioneering work of Jaynes in Bayesian/maximum entropy methods has been successfully explored in many disciplines. The principle of maximum entropy (PME) is a powerful and versatile tool of inferring a probability distribution from constraints that do not completely characterize that distribution. Minimum relative entropy (MRE) is a method which has all the important attributes of the maximum entropy approach with the advantage that prior information may be easily included. In this paper we use MRE to determine the prior probability density function (pdf) of a set of model parameters based on limited information. The resulting pdf is used in Monte Carlo simulations to provide expected values in field variables such as concentration, and confidence limits. We compare the probabilistic results from a traditional advection‐dispersion (ADE) model based on volumetric averaging concepts with that of a model based on the assumption that the hydraulic conductivity is a stationary stochastic process. The results suggest that although Naff's (1990) model satisfies the observed data to a better degree than ADE model, the upper and lower confidence bands about the mean value are larger than the ADE results. This result we attribute to the fact that Naff's (1990) model simply contains more parameters, each of which is unknown and has to be estimated. There is no statistical difference between the expected values of second‐spatial moments for the two models. The examples presented in this paper illustrate problems associated with assigning Gaussian pdfs as priors in a probabilistic model. First, such an assumption for the input parameters actually injects more information into the problem than may actually exist, whether consciously or unconsciously. This fact is borne out by comparison with minimum relative entropy theory. Second, the output parameters as suggested from the Monte Carlo analysis cannot be assumed to be Gaussian distributed even when the prior pdf is Gaussian in form. In a practical setting, the significance of this result and the approximation of Gaussian form would depend on the toxicity and environmental standards that apply to the problem.
Runoff sensitivity to temporal and spatial rainfall variability at runoff plane and small basin scales
Authors: Ogden Fred L. , Julien Pierre Y.
Published: February 2004

Surface runoff sensitivity to spatial and temporal variability of rainfall is examined using physically based numerical runoff models. Rainfall duration tr and temporal sampling interval δt are varied systematically, and normalized by the time to equilibrium te. The relative sensitivity Rs is defined as the total volume of outflow variability over 50 Monte Carlo simulations normalized by the rainfall volume and the coefficient of variation of rainfall. Relative sensitivity to temporal rainfall variability increases with both tr and δt. An asymptotic Rs value proportional to (δt/te1/2) is approached as tr ≫ te. Two‐dimensional surface runoff simulations with spatially variable rainfall, without temporal variability, on two watersheds indicate that Rs decreases as tr/te increases. Normalized Rs versus tr/te curves are identical for two watersheds and a one‐dimensional overland flow plane. These findings indicate that spatial variability is dominant when tr < te, while temporal variability dominates when tr > te, particularly for larger values of δt/te.
A Borehole Field Method to determine unsaturated hydraulic conductivity
Authors: Shan Chao , Stephens Daniel B.
Published: February 2004

Unsaturated hydraulic conductivity is often the single most important soil property in vadose zone flow and transport. However, at depths below the root zone there is no field method available to determine it. The proposed method is directed toward developing a practical field tool to determine Unsaturated hydraulic conductivity in discrete intervals over any depth. The basic idea is to inject water at a point and monitor the steady state pressure distribution surrounding the source. We have developed an analytical solution to use either the observed steady state pressure heads at several points due to a single injection, or steady pressure heads at a single point due to multiple injections, to determine the unsaturated hydraulic conductivity. The approach is based on a linearization of the Unsaturated flow equation which uses the piecewise exponential model of unsaturated hydraulic conductivity. Examples of hydraulic conductivity calculations for three different soils give excellent results.
Estimating discharge of shallow groundwater by transpiration from greasewood in the Northern Great Basin
Authors: Nichols William D.
Published: February 2004

Evapotranspiration from bare soil and phreatophytes is a principal mechanism of groundwater discharge in arid and semiarid regions of the midwestern and western United States including the Great Basin. The imbalance between independent estimates of groundwater recharge from precipitation and of groundwater discharge based on estimates of groundwater evapotranspiration leads to large uncertainties in groundwater budgets. Few studies have addressed this problem. Energy budget micrometeorological field studies were conducted in a stand of sparse‐canopy greasewood growing in an area of shallow groundwater in the western Great Basin during the summer of 1989. The data were used to calculate above‐canopy fluxes of sensible and latent heat using the energy budget‐Bowen ratio method. The calculated energy budget fluxes were used, with soil surface and plant canopy temperature measurements, to calibrate and apply a two‐component, energy‐combination model that partitions the energy and heat fluxes between bare soil and the canopy. This permitted the separation of evaporation from the soil and transpiration from greasewood. The calibrated model was used to estimate daily transpiration of groundwater by greasewood growing in an area with a depth to water of about 2 m. The daily rate of groundwater discharge by transpiration during July and August was estimated to be 2.4 mm. A period of 100 days for groundwater discharge at this rate was assumed to estimate an annual discharge of groundwater of 24 cm at the study site.
A modeling study of rainfall rate‐reflectivity relationships
Authors: Smith James A. , Krajewski Witold F.
Published: February 2004

Power law models that relate rainfall rate and radar reflectivity factor are the principal topic of this paper. Two interrelated problems associated with these models are examined: (1) estimation of parameters of power law models, and (2) assessment of the accuracy of rainfall rate estimates derived from power law models. A statistical model of raindrop processes is used for analysis of both problems. The model provides explicit representations of power law model parameter estimates and the error of rainfall rate‐reflectivity relationships in terms of simple representations of raindrop processes. These results are used to examine issues related to parameterization of algorithms for radar rainfall estimation including (1) bounds on power law model parameter estimates, (2) climatological variability of power law model parameters, (3) seasonal variability of power law model parameters, and (4) multiplicative bias in radar rainfall estimates. Empirical analyses are carried out using drop size data from a number of sites. Detailed analyses are carried out for a data set from North Carolina.
Role of physical heterogeneity in the interpretation of small‐scale laboratory and field observations of bacteria, microbial‐sized microsphere, and bromide transport through aquifer sediments
Authors: Harvey Ronald W. , Kinner Nancy E. , MacDonald Dan , Metge David W. , Bunn Amoret
Published: February 2004

The effect of physical variability upon the relative transport behavior of microbial‐sized microspheres, indigenous bacteria, and bromide was examined in field and flow‐through column studies for a layered, but relatively well sorted, sandy glaciofluvial aquifer. These investigations involved repacked, sieved, and undisturbed aquifer sediments. In the field, peak abundance of labeled bacteria traveling laterally with groundwater flow 6 m downgradient from point of injection was coincident with the retarded peak of carboxylated microspheres (retardation factor, RF = 1.7) at the 8.8 m depth, but preceded the bromide peak and the retarded microsphere peak (RF = 1.5) at the 9.0 m depth. At the 9.5 m depth, the bacterial peak was coincident with both the bromide and the microsphere peaks. Although sorption appeared to be a predominant mechanism responsible for immobilization of microbial‐sized microspheres in the aquifer, straining appeared to be primarily responsible for their removal in 0.6‐m‐long columns of repacked, unsieved aquifer sediments. The manner in which the columns were packed also affected optimal size for microsphere transport, which in one experiment was near the size of the small (∼2 μm) groundwater protozoa (flagellates). These data suggest that variability in aquifer sediment structure can be important in interpretation of both small‐scale field and laboratory experiments examining microbial transport behavior.
A multiple species transport model with sequential decay chain interactions in heterogeneous subsurface environments
Authors: McNab W. W. , Narasimhan T. N.
Published: February 2004

The spatial and temporal distribution of solutes in groundwater is controlled by several physical and chemical processes. Among the chemical processes, sequential degradation phenomena play an important role in determining the fate of radioactive materials and certain types of organic compounds. We present a numerical model designed to evaluate the simultaneous transport and kinetically controlled sequential degradation (straight and branched chains) of several dissolved components in groundwater systems. The model utilizes a two‐step quasi‐linearization algorithm to solve the equations of chemical transport and transformation. The transport equations are solved explicitly using the integral finite difference method. The chemical transformation equations are solved using an implicit finite difference (in time) algorithm for each volume element in the discretized flow domain. Although this algorithm is designed to solve problems involving first‐order kinetics, it may be modified in certain instances to accommodate rate mechanisms other than first order. The chemical transformation module and the transport module are coupled via a source/sink term in the transport equation. This combination results in a numerical code that is computationally efficient. We have found that the model yields solutions which are in excellent agreement with available analytical solutions. Solution of a test problem based on the sequential degradation of the pesticide aldicarb demonstrates that the model can provide useful insights into the fate of solutes subject to certain degradation regimes in heterogeneous groundwater systems. Although the illustrative examples presented are one dimensional, the model itself is capable of handling two‐ and three‐dimensional problems. In addition, the modular structure of the model is built upon user‐specified chemical reactions. This allows for flexibility in problem definition, which may accommodate both reversible and irreversible reactions.
Advection and diffusion in a variable‐salinity confining layer
Authors: Konikow Leonard F. , Arévalo Javier Rodríguez
Published: February 2004

A numerical model that simulates groundwater flow and solute transport for cases in which fluid properties are variable was applied in one dimension (vertical) to the shallow, low‐permeability, clayey, confining layer in Doñana National Park in southwestern Spain. The salinity in the 80‐m‐thick confining layer decreases from a brine near the land surface to fresh water near its base. Results of model simulations indicate that the system could be in or close to a steady state condition. The model calibration was very sensitive to small variations in individual model parameters and was nonunique in the sense that equally good calibrations could be achieved by compensatory joint perturbations in the permeability, diffusion coefficient, and overall governing hydraulic gradient. At present, there is probably an upward flow of the order of 1 mm yr−1 to 1 cm yr−1 and a balance in the solute flux between upward advection and downward diffusion. The time scale of calculated responses to changes in boundary conditions in this low‐permeability system ranges from thousands to hundreds of thousands of years when considering extremes within the range of uncertainty of values of the evaluated parameters.