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At least 1,045 records · Page 58Linked to original sources
USGS2010

Transport of reacting solutes subject to a moving dissolution boundary: Numerical methods and solutions

A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters. Although the water flow rate does not explicitly appear in the equation for the velocity of the moving boundary, the speed of the boundary depends more on the flux rate than on the dispersion coefficient. The discontinuity in the gradient of the solute concentration profile at the boundary increases with convection and with the initial concentration of the mineral. Our implicit method is extended to allow participation of the solutes in complexation reactions as well as the precipitation-dissolution reaction. This extension is easily made and does not change the basic method.

Water Resources Research↗
USGS2010

Stochastic model for the long-term transport of stored sediment in a river channel

We develop a stochastic model for the transport of stored sediment down a river channel. The model is based on probabilities of transition of particles among four different sediment storage reservoirs, called active (often mobilized), semiactive, inactive, and stable (hardly ever mobilized). The probabilities are derived from computed sediment residence times. Two aspects of sediment storage are investigated: flushing times of sediment out of a storage reservoir and changes in the quantity of sediment stored in different reservoirs due to seasonal sediment transport into, and out of, a reach. We apply the model to Redwood Creek, a gravel bed river in northern California. Although the Redwood Creek data set is incomplete, the application serves as an example of the sorts of analyses that can be done with the method. The application also provides insights into the sediment storage process. Sediment flushing times are highly dependent on the degree of interaction of the stable reservoir with the more mobile sediment reservoirs. The most infrequent and highest intensity storm events, which mobilize the stable reservoir, are responsible for the long-term shifts in sediment storage. Turnover times of channel sediment in all but the stable reservoir are on the order of 750 years, suggesting this is all the time needed for thorough interchange between these sediment compartments and cycling of most sediment particles from the initial reservoir to the ocean. Finally, the Markov model has adequately characterized sediment storage changes in Redwood Creek for 1947–1982, especially for the active reservoir. The model replicates field observation of the passage of a slug of sediment through the active reservoir of the middle reach of Redwood Creek in the 18 years following a major storm in 1964 that introduced large quantities of landslide debris to the channel.

California↗
USGS2010

Selective transport of hydrocarbons in the unsaturated zone due to aqueous and vapor phase partitioning

Long-term groundwater contamination can result from vapors and solutes emanating from organic liquids spilled in the unsaturated zone. The mathematical modeling analysis presented in this paper demonstrates for gasoline-range hydrocarbons, and other volatile organics commonly spilled, that diffusive transport in the unsaturated zone is a significant transport mechanism which can cause aqueous and vapor plumes to spread away from the immiscible liquid source, resulting in increasing groundwater contaminating potential. An analytical solution to a one-dimensional version of the transport model allows for the definition of a retardation coefficient which is dependent on phase-partitioning coefficients and moisture content. Significant differences in migration rates should be anticipated between hydrocarbons. A numerical solution was developed for a radially symmetric version of the model defining transport for a multiconstituent contaminant like gasoline. Differences in anticipated migration rates between aromatic and nonaromatic hydrocarbons was clearly demonstrated. A simulation based on the composition of an actual gasoline revealed that aromatic constituents, although constituting a fraction of the initial gasoline composition, completely defined the groundwater contaminating potential. This potential changes in time as constituents are selectively removed from the unsaturated zone. Further, the groundwater contaminating potential is quite sensitive to the ground surface boundary characterization.

Water Resources Research↗
USGS2010

Laboratory investigation of longitudinal dispersion in anisotropic porous media

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

Water Resources Research↗
USGS2010

Further comments on sensitivities, parameter estimation, and sampling design in one-dimensional analysis of solute transport in porous media

Sensitivities of solute concentration to parameters associated with first-order chemical decay, boundary conditions, initial conditions, and multilayer transport are examined in one-dimensional analytical models of transient solute transport in porous media. A sensitivity is a change in solute concentration resulting from a change in a model parameter. Sensitivity analysis is important because minimum information required in regression on chemical data for the estimation of model parameters by regression is expressed in terms of sensitivities. Nonlinear regression models of solute transport were tested on sets of noiseless observations from known models that exceeded the minimum sensitivity information requirements. Results demonstrate that the regression models consistently converged to the correct parameters when the initial sets of parameter values substantially deviated from the correct parameters. On the basis of the sensitivity analysis, several statements may be made about design of sampling for parameter estimation for the models examined: (1) estimation of parameters associated with solute transport in the individual layers of a multilayer system is possible even when solute concentrations in the individual layers are mixed in an observation well; (2) when estimating parameters in a decaying upstream boundary condition, observations are best made late in the passage of the front near a time chosen by adding the inverse of an hypothesized value of the source decay parameter to the estimated mean travel time at a given downstream location; (3) estimation of a first-order chemical decay parameter requires observations to be made late in the passage of the front, preferably near a location corresponding to a travel time of √ 2 times the half-life of the solute; and (4) estimation of a parameter relating to spatial variability in an initial condition requires observations to be made early in time relative to passage of the solute front.

Water Resources Research↗
USGS2010

Geochemistry of groundwater in tertiary and cretaceous sediments of the southeastern Coastal Plain in eastern Georgia, South Carolina, and southeastern North Carolina

Geochemical samples of groundwater taken along hydrologic flow paths in eastern Georgia, South Carolina, and southeastern North Carolina, from noncalcareous sand aquifers, largely of Cretaceous age, are dominated by sodium and bicarbonate ions. Calcareous sand aquifers, largely of Tertiary age, contain water whose chemistry is dominated by calcium and bicarbonate ions, but may evolve downgradient to sodium and bicarbonate dominance. Water chemistry in both types of aquifer evolves to sodium chloride dominance as a result of fresh water mixing with subsurface brines or seawater present in the deeper downgradient parts of the aquifers. Principal aqueous chemical reactions appear to occur in five reaction zones in the aquifers and include feldspar hydrolysis to kaolinite, calcite dissolution, calcium-for-sodium cation exchange, and neoformation of sodium smectite in the downgradient parts of the aquifers. Redox reactions produce dissolved iron concentrations greater than 1 mg/L near the recharge areas. Organic matter in the aquifers is oxidized to CO 2 by iron reduction and sulfate reduction processes. Production of CO 2 by a methanogenic process may also occur. Geochemical mass-transfer models simulating the observed chemistry in western Alabama and eastern Mississippi have been extended to account for higher concentrations of sodium and bicarbonate observed in the South Carolina part of the aquifers.

Georgia, North Carolina, South Carolina↗
USGS2010

Response of well aquifer systems to Earth tides: Problem revisited

Two recent works cause us to reexamine Bredehoeft's (1967) analysis of earthtide response of water wells. Narasimhan et al. (1984) raise several questions regarding Bredehoeft's (1967) analysis and suggest that the analysis is internally inconsistent. They argue that one cannot directly estimate the specific storage, which characterizes the drained behavior of a porous medium, from earth tide response, which is an undrained phenomenon. We resolve the questions raised by Narasimhan et al. (1984) and show that Bredehoeft's analysis is internally consistent. In addition, we show that it is possible to determine the specific storage from undrained loading. While Bredehoeft's analysis is somewhat heuristic and neglects grain compressibility, Van der Kamp and Gale (1983) present a more rigorous analysis that is based on Biot's (1941) constitutive relationships and accounts for grain compressibility. However, their results reduce to Bredehoeft's results when grains are assumed incompressible. This suggests that Bredehoeft's analysis has incorporated all the essential features of Biot's relationships except for grain compressibility. Upon reexamining Bredehoeft's analysis we find that this is indeed the case.

Water Resources Research↗
USGS2010

Processes affecting the distribution of selenium in shallow groundwater of agricultural areas, western San Joaquin Valley, California

A study was undertaken to evaluate the processes affecting the chemistry of shallow groundwater associated with agricultural drainage systems in the western San Joaquin Valley, California. The study was prompted by a need for an understanding of selenium mobility in areas having high selenium concentrations in shallow groundwater. Groundwater samples were collected along transects in three artificially drained fields where the age of the drainage system varied (15, 6, and 1.5 years). Selenium concentrations in the drain water also varied (430, 58, and 3700 μg/L, respectively). Isotopic enrichment and chemical composition of the groundwater samples indicate that saline- and selenium-enriched water has evolved as a result of evaporation or transpiration of groundwater. This evaporated, isotopically enriched water is being displaced by more recent, less saline irrigation water percolating through the root zone. This displacement seems to be a process whereby sodium chloride and sodium sulfate water is being replaced by more dilute calcium sulfate and calcium bicarbonate water.

California↗
USGS2010

Internal inconsistencies in dispersion-dominated models that incorporate chemical and microbial kinetics

Current understanding of transport processes in aquifers is limited by lack of precise point chemical concentration measurements. Recently, however, some careful measurements of vertical chemical concentration profiles have been made at several locations around the world that appear to support a consistent picture concerning the persistence of large vertical concentration gradients in aquifers and, by implication, the existence of very small vertical transverse dispersivities. These data were obtained in aquifers supporting microbial activity. Data analysis using a mathematical model which considers microbial degradation coupled to nutrient and oxygen transport indicates that a vertical transverse dispersivity on the order of 0.1 cm or less is consistent with the concentration gradients that were measured. The existence of such large gradients and low dispersivities is not consistent with the use of two-dimensional vertically averaged (areal) models as currently applied, especially if one is interested in the development of transport models with predictive capability beyond that associated with standard calibration and extrapolation. Even three-dimensional models with large vertical transverse dispersivities compared to those measured will produce results inconsistent with measurements. Microbial-chemical activity is very sensitive to concentration distributions. Smearing of the oxygen profile can result in the prediction of aerobic activity where, in fact, none exists.

Water Resources Research↗
USGS2010

Effects of sulfur dioxide emissions on stream chemistry in the western United States

A 20-year record of water chemistry for seven headwater streams in the Rocky Mountain region of the western United States is compared to estimates of local and regional sulfur dioxide emissions for the same period. Emissions from smelters in the region comprise a significant part of sulfur dioxide emissions for the 11 states upwind of acid-sensitive watersheds in the Rocky Mountains, but smelter emissions have steadily decreased since 1970. Analysis of stream chemistry indicates conservative behavior of watershed sulfate, with atmospheric deposition as the dominant source of sulfate. No relation between regional stream chemistry and smelter or regional sulfur dioxide emissions is detected for the watersheds. Local emissions trends, however, do appear to affect sulfate concentrations in the streams. Year-to-year variability in stream sulfate concentration is much greater than any long-term trends that might be inferred.

Water Resources Research↗
USGS2010

Assessing the Birkenes Model of stream acidification using a multisignal calibration methodology

A revision of the Birkenes model of streamwater acidification has been attempted to incorporate additional chemical and hydrologic information gained in the last 6 years since its original construction. The first stage of this effort has been an analysis of the hydrologic submodel with the goal of extending it to predict concentrations of a conservative tracer in streamwater. An objective calibration of the model indicated that the model is overparameterized. Only one passive store is identifiabile, not two as currently contained in the model and the routing between the two reservoirs is not determined by the data. Inclusion of the conservative tracer improved the identifiability of the dimensional parameters, but had little effect on the rate or routing parameters. If the hydrologic structure is to be determined from the hydrograph and conservative tracer alone, it must be simplified to eliminate unidentifiable parameters. The validity of using more complex rainfall-runoff models in hydrochemical models which seek to test chemical mechanisms is called into question by this analysis.

Water Resources Research↗
USGS2010

The chemical evolution of a travertine-depositing stream: Geochemical processes and mass transfer reactions

This field study focuses on quantitatively defining the chemical changes occurring in Falling Spring Creek, a travertine-depositing stream located in Alleghany County, Virginia. The processes of CO 2 outgassing and calcite precipitation or dissolution control the chemical evolution of the stream. The observed chemical composition of the water was used with the computerized geochemical model WATEQF to calculate aqueous speciation, saturation indices, and CO 2 partial pressure values. Mass balance calculations were performed to obtain mass transfers of CO 2 and calcite. Reaction times, estimated from stream discharge, were used with the mass transfer results to calculate rates of CO 2 , outgassing and calcite precipitation between consecutive sampling points. The stream, which is fed by a carbonate spring, is supersaturated with respect to CO 2 along the entire 5.2-km flow path. Outgassing of CO 2 drives the solution to high degrees of supersaturation with respect to calcite. Metabolic uptake of CO 2 by photosynthetic plants is insignificant, because the high supply rate of dissolved carbon dioxide and the extreme agitation of the stream at waterfalls and rapids causes a much greater amount of inorganic CO 2 outgassing to occur. Calcite precipitation is kinetically inhibited until near the crest of a 20-m vertical waterfall. Calcite precipitation rates then reach a maximum at the waterfall where greater water turbulence allows the most rapid escape of CO 2 . Physical evidence for calcite precipitation exists in the travertine deposits which are first observed immediately above the waterfall and extend for at least 1.0 km below the falls. Net calcite precipitation occurs at all times of the year but is greatest during low-flow conditions in the summer and early fall.

Water Resources Research↗
USGS2010

Stochastic analysis of solute arrival time in heterogeneous porous media

Longitudinal advective solute movement in heterogeneous porous media is investigated by considering the solute arrival time at a plane perpendicular to the mean fluid velocity. The moments of the solute arrival time are defined in terms of the stochastic properties of a statistically anisotropic hydraulic conductivity field. The flux‐averaged concentration is specified by introducing the moments of the arrival time into a probability density function for the arrival time. The quadratic dependence of the arrival time variance on position in the vicinity of an injection point is indicative of a nondiffusive process. For the assumed spatial correlation of the hydraulic conductivity, the variance of the arrival time asymptotically approaches a linear dependence on the position from the injection point similar to a diffusion process. The impact of assuming solute movement to be a diffusive process from the onset of the solute injection causes erroneous estimates of flux‐averaged concentrations at distances from the injection point that are of the order of the correlation length of the hydraulic conductivity. The arrival time analysis and the particle position analysis given in Dagan (1982, 1984) are complementary interpretations of advective solute movement that yield different definitions of the solute concentration; the position analysis intrinsically defines the resident or volume‐averaged concentration, while the flux‐averaged concentration is defined from the arrival time analysis. The temporal variation of the resident and flux‐averaged concentration are similar at a given position for small values of the variance of the hydraulic conductivity, or at distances from the solute injection point that are large relative to correlation length of the hydraulic conductivity.

Water Resources Research↗
USGS2010

Using exogenous variables in testing for monotonic trends in hydrologic time series

One approach that has been used in performing a nonparametric test for monotonic trend in a hydrologic time series consists of a two-stage analysis. First, a regression equation is estimated for the variable being tested as a function of an exogenous variable. A nonparametric trend test such as the Kendall test is then performed on the residuals from the equation. By analogy to stagewise regression and through Monte Carlo experiments, it is demonstrated that this approach will tend to underestimate the magnitude of the trend and to result in some loss in power as a result of ignoring the interaction between the exogenous variable and time. An alternative approach, referred to as the adjusted variable Kendall test, is demonstrated to generally have increased statistical power and to provide more reliable estimates of the trend slope. In addition, the utility of including an exogenous variable in a trend test is examined under selected conditions.

Water Resources Research↗
USGS2010

Estimation of descriptive statistics for multiply censored water quality data

This paper extends the work of Gilliom and Helsel (1986) on procedures for estimating descriptive statistics of water quality data that contain “less than” observations. Previously, procedures were evaluated when only one detection limit was present. Here we investigate the performance of estimators for data that have multiple detection limits. Probability plotting and maximum likelihood methods perform substantially better than simple substitution procedures now commonly in use. Therefore simple substitution procedures (e.g., substitution of the detection limit) should be avoided. Probability plotting methods are more robust than maximum likelihood methods to misspecification of the parent distribution and their use should be encouraged in the typical situation where the parent distribution is unknown. When utilized correctly, less than values frequently contain nearly as much information for estimating population moments and quantiles as would the same observations had the detection limit been below them.

Water Resources Research↗
USGS2010

Nonparametric statistical methods for comparing two sites based on data with multiple nondetect limits

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.

California↗
USGS2010

A note on the recent natural gradient tracer test at the Borden Site

The variance in particle position, a measure of dispersion, is reviewed in the context of certain models of flow in random porous media. Asymptotic results for a highly stratified medium and an isotropic medium are particularly highlighted. Results of the natural gradient tracer test at the Borden site are reviewed in light of these models. This review suggests that the moments obtained for the conservative tracers at the Borden site could as well be explained by a model that more explicitly represents the three-dimensional nature of the flow field.

Borden Site↗
USGS2010

Analysis of accuracy of approximate, simultaneous, nonlinear confidence intervals on hydraulic heads in analytical and numerical test cases

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.

Water Resources Research↗