bluuebunny/crossref_metadata_2025 huggingface dataset:
Hydrologic Mechanisms Governing Fluid Flow in a Partially Saturated, Fractured, Porous Medium
Authors: Wang J. S. Y. , Narasimhan T. N.
Published: February 2008

In contrast to the saturated zone within which fluid moves rapidly along fractures, the fractures (with apertures large relative to the size of matrix pores) will desaturate first during the drainage process, and the bulk of fluid flow would be through interconnected pores in the matrix. Within a partially drained fracture, the presence of a relatively continuous air phase will produce practically an infinite resistance to liquid flow in the direction parallel to the fracture. The residual liquid will be held by capillary force, in regions around fracture contact areas where the apertures are small. Normal to the fracture surfaces, the drained portion of the fractures will reduce the effective area for liquid flow from one matrix block to another matrix block. A general statistical theory is constructed for flow along the fracture and for flow between the matrix blocks to the fractures under partially saturated conditions. Results are obtained from an aperture distribution model for fracture saturation, hydraulic conductivity, and effective matrix‐fracture flow areas as functions of pressure. The effects of distortion of flow paths by the air pockets are taken into account by a phase‐separation constriction factor in a generalized cubic law for fracture flow under a partially saturated condition. The reduction of matrix‐fracture flow area is taken into account by summing the aperture distribution function to a saturation cutoff aperture, which is inversely proportional to the suction head. Drainage from a column of fractured tuff is simulated using available parameters for the densely welded tuff of the Topopah Spring Member at Yucca Mountain, southern Nevada. The column is bounded by discrete vertical fractures and dissected by horizontal fractures with the fracture spacings determined by the frequencies and orientations of fractured cores. The fraction of fracture surfaces with coatings is assumed to correspond to the fraction of in situ fracture contact area. The characteristic curves for the matrix are based on laboratory measurements of tuff samples. From the cases simulated for the fractured, porous columns with discrete vertical and horizontal fractures and porous matrix blocks explicitly taken into account, it is observed that the highly transient changes from fully saturated conditions to partially saturated conditions are extremely sensitive to the fracture properties. However, the quasi‐steady changes of the fluid flow of a partially saturated, fractured, porous system could be approximately simulated without taking the fractures into account.
Origin and Distribution of Sulfate in a Fractured Till in Southern Alberta, Canada
Authors: Hendry M. J. , Cherry J. A. , Wallick E. I.
Published: February 2008

Glacial till in a 22‐km2 area of the Interior Plains Region of southern Alberta, Canada consists of an upper brown gypsiferous weathered zone (up to 20 m thick) and a lower discontinuous grey nonweathered zone (up to 25 m thick). Although the total sulfur content of the two till zones is the same (0.34%), the mean total sulfate content of the weathered till (4.0 mg g−1) exceeds that of the nonweathered till (0.8 mg g−1). Similarities suggest that all SO42− in the nonweathered till and 20% of the sulfate in the weathered till was derived from sulfate‐rich bedrock fragments incorporated in the till during deposition. Laboratory experiments and δ18O and δ34S analyses of total SO42− and the sulfur forms in the two zones show that the majority of the sulfate in the weathered till was derived from the oxidation of organic S at some time after the till was deposited. Mass balance and flux calculations indicate that this oxidation occurred under partially saturated conditions. Groundwater flow simulations suggest that the water table was much lower and that a thick partially saturated zone was possible during the drier Altithermal period (11,000 to 3000 years B.P.). The following chemical processes account for the major ions that are found in the groundwater but were generated when the partially saturated zone existed. The oxidation of reduced S produced SO42− and H+. The H+ reacted with carbonate minerals under elevated PCO2, with Ca2+ loss by exchange for Na+ and gypsum precipitation. Volume shrinkage in the weathered till resulting from these geochemical processes may have enhanced the development of fractures and caused the associated increased hydraulic conductivity.
River Loads Underestimated by Rating Curves
Authors: Ferguson R. I.
Published: February 2008

Statistical considerations show that the sediment, solute, or pollutant load of a river is likely to be underestimated by methods in which unmeasured concentrations are estimated from discharge using a least squares regression for the logarithm of concentration. The degree of underestimation increases with the degree of scatter about the rating curve and can reach 50%. A simple correction factor is proposed and tested successfully on simulated and real data sets.
Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 1. Maximum Likelihood Method Incorporating Prior Information
Authors: Carrera Jesus , Neuman Shlomo P.
Published: February 2008

In this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions. The parameters include values and directions of principal hydraulic conductivities (or transmissivities) in anisotropic media, specific storage (or storativity), interior and boundary recharge or leakage rates, coefficients of head‐dependent interior and boundary sources, and boundary heads. In transient situations, the initial head distribution can also be estimated if the system is originally at a steady state. Paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters. The inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters. Since not all the factors which contribute to the prior errors can be quantified statistically at the outset, the covariance matrices of these errors are expressed in terms of several parameters which, if unknown, can be estimated jointly with the hydraulic parameters by a stagewise optimization process. When transient head data are separated by a fixed time interval, the temporal structure of these data is approximated by a lag‐one autoregressive model with a correlation coefficient that can be treated as another unknown parameter. Estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace. Paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature, all of which are based on the maximum likelihood concept, might be useful for selecting the best groundwater model (or the best method of parameterizing a particular model) among a number of given alternatives.
A Transfer Function Model of Solute Transport Through Soil: 3. The Convection‐Dispersion Equation
Authors: Sposito Garrison , White Robert E. , Darrah Peter R. , Jury William A.
Published: February 2008

The two‐component convection‐dispersion equation (CDE) model is developed as a special case of the transfer function model (TFM) of solute transport. It is shown that the two‐component CDE model can be reformulated as an integral equation for the “fast” solute component which has the same form and interpretation as the TFM integral equation specialized to (1) steady water flow conditions and (2) solute input or loss restricted to the entrance or exit surface of a soil unit. The travel time probability density function (pdf) for a solute according to the two‐component CDE model then is calculated analytically as a Laplace transform. Numerical inversion of the transformed pdf is carried out for several different sets of values of the four adjustable parameters in the CDE model. The effects of convection, dispersion, and linear sorption processes, as well as the influence of the “slow” solute component, are illustrated by the numerically simulated travel time pdf. It is suggested that the fractional transport volume is the most significant physical parameter in the model in terms of impact on the shape of the travel time pdf.
Paleoflood Hydrology and Flood Frequency Analysis
Authors: Hosking J. R. M. , Wallis J. R.
Published: February 2008

Techniques recently developed in paleohydrology enable the estimation of discharges and dates of occurrence of flood events which occurred thousands of years ago. We use computer simulation to assess whether a single paleoflood estimate, when included in a single‐site or regional flood frequency analysis procedure, gives a worthwhile increase in the accuracy of estimates of extreme floods. We find that the main factors affecting the utility of this kind of paleological information are the specification of the fitted flood frequency distribution (whether it has two or three unknown parameters) and the size of the measurement error of paleodischarge estimates. Errors in estimating the date of the paleoflood are of minor importance. We conclude that paleological information is most useful when estimating a three‐parameter flood frequency distribution for a single site possessing only a short gauged record. When several independent and homogeneous gauged records from different sites are used in a regional flood frequency analysis, the value of paleological information is, within the limits of this study, negligible.
Simulation of Fluid Flow and Energy Transport Processes Associated With High‐Level Radioactive Waste Disposal in Unsaturated Alluvium
Authors: Pollock David W.
Published: February 2008

Many parts of the Great Basin have thick zones of unsaturated alluvium which might be suitable for disposing of high‐level radioactive wastes. A mathematical model accounting for the coupled transport of energy, water (vapor and liquid), and dry air was used to analyze one‐dimensional, vertical transport above and below an areally extensive repository. Numerical simulations were conducted for a hypothetical repository containing spent nuclear fuel and located 100 m below land surface. Initial steady state downward water fluxes of zero (hydrostatic) and 0.0003 m yr−1 were considered in an attempt to bracket the likely range in natural water flux. Predicted temperatures within the repository peaked after approximately 50 years and declined slowly thereafter in response to the decreasing intensity of the radioactive heat source. The alluvium near the repository experienced a cycle of drying and rewetting in both cases. The extent of the dry zone was strongly controlled by the mobility of liquid water near the repository under natural conditions. In the case of initial hydrostatic conditions, the dry zone extended approximately 10 m above and 15 m below the repository. For the case of a natural flux of 0.0003 m yr−1 the relative permeability of water near the repository was initially more than 30 times the value under hydrostatic conditions, consequently the dry zone extended only about 2 m above and 5 m below the repository. In both cases a significant perturbation in liquid saturation levels persisted for several hundred years. This analysis illustrates the extreme sensitivity of model predictions to initial conditions and parameters, such as relative permeability and moisture characteristic curves, that are often poorly known.
Prediction of Surface Saturation Zones in Natural Catchments by Topographic Analysis
Authors: O'Loughlin E. M.
Published: February 2008

The topography of hillslopes or whole catchments is analyzed numerically to calculate local geometric and drainage attributes that can be combined to test for the expectation of soil waterlogging. At locations where accumulated drainage flux from upslope exceeds the product of soil transmissivity and the local slope, saturation to the soil surface occurs. Results of the analysis of specific landscapes are presented as a location dependent function. The function may be mapped as isolines to define successive boundaries of zones of soil saturation, depending on the wetness state of the landscape as a whole. The analysis is applied to two catchments, to predict the growth or contraction of zones of waterlogging for a range of drainage fluxes and to simulate the effects of transpiration changes in part or all of the catchment. In the second application, the predicted boundaries of saturated zones are used to calculate the minimum proportion of a catchment's area that produces rapid surface runoff. This proportion is shown to depend on the value of a normalized wetness parameter. Storm runoff data support the predicted form of the relationship.
Application of Functional Analysis to Optimization of a Variable Head Multireservoir Power System for Long‐Term Regulation
Authors: Soliman S. A. , Christensen G. S.
Published: February 2008

Functional analysis and minimum norm formulation are employed for solving the optimal long‐term problem of a hydro power system for maximum total expected benefits (benefits from energy generated by a hydro power system over the planning period plus the expected future returns from water left in storage at the end of that period). The proposed method takes into account the stochasticity of the river inflows; we assume that their probability properties are preestimated from past history. The adequate fulfillment of other system functions such as flood control and water supply is guaranteed via constraints on storage and release variables. Numerical results are presented for a real system in operation consisting of three rivers; each river has two series reservoirs.
Monte Carlo Simulation of Snow Depth in a Forest
Authors: Woo Ming‐Ko , Steer Peter
Published: February 2008

Snow depth in a forest is highly variable and to reduce the cost of extensive field sampling for obtaining mean depths, a simulation model was developed. First, the location of individual trees in a representative portion of the forest is either surveyed in the field or simulated based on the statistical characteristics pertaining to the distribution of trees. In this forest, a large number of randomly located sample points is generated by Monte Carlo technique. The azimuth and distance from each point to the nearest tree is determined, and a snow depth simulated based on the observed snow depth distribution around individual trees. The model was applied successfully to a northern spruce forest in subarctic Ontario, showing that this simulation provides a useful approach to determine mean snow depth.
Simulations of Two‐Well Tracer Tests in Stratified Aquifers at the Chalk River and the Mobile Sites
Authors: Huyakorn Peter S. , Andersen Peter F. , Molz Fred J. , Güven Oktay , Melville Joel G.
Published: February 2008

A simulation study of two‐well injection‐withdrawal tracer tests in stratified granular aquifers at two widely separated sites is presented. The first site is located near the Chalk River Nuclear Laboratories in Canada, and the second site is located in Mobile, Alabama. Field data and test conditions at these sites are substantially different in terms of vertical distributions of hydraulic conductivity, well spacings, flow rates, test durations, and tracer travel distances. Furthermore, the test at the Chalk River site was conducted in a recirculating mode, whereas the test at the Mobile site was conducted in a nonrecirculating mode. Simulations of these tests were performed in three dimensions using the curvilinear finite element model developed in the previous paper of this series. The simulations incorporated measured vertical variations in relative hydraulic conductivity and local dispersivity values that are small fractions (between 1/1000 and 1/100) of the spacing between the injection and the withdrawal wells. The local dispersivities are used to account for local hydrodynamic dispersion and are chosen independently so that they are not affected by the scales of the tests. Simulation results obtained from the model are presented. Interpretation of these results is made in conjunction with measured breakthrough curves at the withdrawal well and multilevel observation wells. For the Chalk River site, predicted and measured breakthrough curves at the withdrawal well are in good agreement over the earlier part of the test duration. Deviation of the field data from the model prediction occurs over the second part, where the predicted breakthrough curves show a declining trend but the field data plot does not. For the Mobile site, predicted and measured breakthrough curves at the withdrawal well show similar trends throughout the entire test duration and are in good agreement overall. Model predictions of the effect of hydraulic conductivity stratification on temporal distributions of concentration are generally consistent with data from multilevel observation wells at both sites. The model results also show interesting effects of stratification on spatial distributions of concentration, and on the evolution and spreading pattern of tracer plumes. These effects have not been fully assessed in the field measurement and should be investigated further.
Laboratory Studies of Gas Flow Through a Single Natural Fracture
Authors: Schrauf T. W. , Evans D. D.
Published: February 2008

The relationship between the aperture and gas conductivity of a single natural fracture was investigated in the laboratory. Fracture conductivity was evaluated as a function of both the applied fluid pressure gradient and average fracture aperture, the latter ranging from 600 to 200 μm. Fracture apertures were determined independently on the basis of both fracture deformation and fracture volume measurements. Flow generally occurred in the linear and transitional flow regime between linear and fully nonlinear flow. The transition was found to be smooth and well described by an equation of the form: −(dp/dx) = av + bv2, where dp/dx is the pressure gradient and v is the fluid velocity. The linear and nonlinear fracture conductivities were found to be functions of the aperture and surface roughness of the fracture in agreement with existing empirical equations. A new physical model for fracture flow is also formulated based on an analogy to pipe flow.
Study on Generation of Periodical Large Surface Eddies in a Composite Channel Flow
Authors: Tamai Nobuyuki , Asaeda Takashi , Ikeda Hirokazu
Published: February 2008

A set of comparative experiments are employed to identify a predominant factor in the generation of large eddies on the water surface at the interface between the main channel and the floodplain in a composite channel flow. It is indicated that the large surface eddies are not phenomena whose action resembles boiling but tornadolike vortices generated by the local shear layer at the interface. Flow visualization technique showed that there existed a complicated three‐dimensional structure in the form of inclined vortex tubes which behaved like longitudinal vortices near the top edge of the floodplain as well as periodically generated large surface eddies. The periodicity of those phenomena is explained as the preferred mode of the local shear layer with two‐dimensional stability analysis.
Storm Runoff Generation in Humid Headwater Catchments: 1. Where Does the Water Come From?
Authors: Pearce A. J. , Stewart M. K. , Sklash M. G.
Published: February 2008

Production of storm runoff in highly responsive catchments is not well understood. We report in these papers a comprehensive set of hydrometric and natural tracer data for rainfall, soil water, and streamflow for catchments in the Tawhai State Forest, Westland, New Zealand, which reveal some of the important runoff processes. The catchments are small (< 4 ha), with short (< 300 m) steep (average 34°) slopes and thin (< 1 m) permeable soils. Long‐term (1977–1980) weekly observations of oxygen 18, electrical conductivity, and chloride in the stream, groundwater, and rain in the main study catchment indicate that catchment outflow reflects a well‐mixed reservoir with a mean residence time of approximately 4 months. A preliminary storm hydrograph separation using oxygen 18 (for a storm hydrograph exceeded by only 22% of events since 1979) indicates that only 3% of storm runoff could be considered “new” (i.e., current storm) water. Rapid subsurface flow, such as macropore flow, of new water therefore cannot explain streamflow response in the study area. More detailed hydrograph separation studies on throughflow as well as streamflow are described in parts 2 (M. G. Sklash et. al., this issue) and 3 (M. G. Sklash et. al., unpublished manuscript, 1986).
Modeling the Effects of Acid Deposition: Control of Long‐Term Sulfate Dynamics by Soil Sulfate Adsorption
Authors: Cosby B. J. , Hornberger G. M. , Wright R. F. , Galloway J. N.
Published: February 2008

A dynamic model based on a simple nonlinear relationship between adsorbed and dissolved sulfate in soils is used to examine the implied long‐term control exerted on drainage water sulfate concentration by mineral soil adsorption. The model assumes reversible adsorption and does not consider biological sulfur transformations or variable adsorption arising from changes in soil organic matter or pH. The model is used to simulate the effects of more than a century of increased atmospheric sulfur deposition into low‐order, mountainous catchments. The response time of simulated drainage water sulfate concentration is a function of the hydrological retention time and the amount of sulfate adsorbed on the soil. Simulated catchments with small adsorption capacity respond at essentially the hydrological response time (months to a year). Simulated catchments with large adsorption capacity respond much more slowly (decades). These response times decrease dramatically as adsorbed sulfate accumulates. There has been a tendency to classify catchments as those that respond to changes in sulfur deposition and those that do not. Our results suggest that (at least for low‐order, shallow soil catchments) responses to sulfur deposition are continuous, not dichotomous, and response times will decrease under prolonged atmospheric deposition.
Slug Test Analysis
Authors: Sageev Abraham
Published: February 2008

The pressure or head response of an aquifer to a slug test in a fully penetrating well with wellbore storage and skin is presented. Three kinds of type curves are discussed: early time log‐log, intermediate time semilog, and late time log‐log. The early time response of the slug test depends on the presence of wellbore skin; hence two kinds of early time type curves are presented. When the active well has wellbore skin, the early time correlating parameter is the product of the skin and dimensionless storage. When wellbore skin is not present, the early time response is proportional to the square root of time, with dimensionless storage as the correlating parameter. The intermediate time semilog type curves are applicable when wellbore skin is not present. The late time type curves may be used when the dimensionless storage is greater than one and wellbore skin is positive or when the dimensionless storage is smaller than one and wellbore skin is negligible. The radius of investigation of the slug test is also examined with and without wellbore skin at the active well. Although the presence of wellbore skin reduces the magnitude of the dimensionless head responses at observation wells, the detectable radius of investigation is not significantly dependent on wellbore skin.
Urban Water Balance: 2. Results From a Suburb of Vancouver, British Columbia
Authors: Grimmond C. S. B. , Oke T. R.
Published: February 2008

The paper demonstrates the use of the C. S. B. Grimmond et al. (this issue) water balance model. It is used to calculate the daily, monthly, and annual water balance components for a suburban catchment in Vancouver, British Columbia. The budget results for one complete year are presented and where possible are compared with those from other cities. The balance is also compared with that for a rural area in the region, thereby illustrating the effects of suburban development. In interpreting the results special consideration is directed toward elucidating the role of irrigation (mainly garden sprinkling) in the suburban water balance. The temporal pattern of external water use is related to prevailing weather conditions. In particular, it is shown to be closely related to evapotranspiration. The relationship is a complex feedback system involving human as well as biophysical controls. The model is run both with, and without, an irrigation input to gauge its impact on the water budget. Together the results provide both quantitative and qualitative support for the idea that irrigation is the source of water supporting the relatively large rates of suburban evapotranspiration reported in energy balance studies.
The Relationship Between a Continuous‐Time Renewal Model and a Discrete Markov Chain Model of Precipitation Occurrence
Authors: Small Mitchell J. , Morgan David J.
Published: February 2008

A relationship between a continuous wet‐dry renewal model with gamma distributed dry intervals and a Markov chain model for daily rainfall is derived. The relationship requires numerical evaluation for the general case, but closed‐form solutions are available for the Markov process case in which dry intervals are exponentially distributed. The Markov process equations are equivalent to those derived by J. R. Green (1964) for first‐order transition probabilities, but are presented in a simplified, nonrecursive form. The Markov process relationships are examined for convergence and accuracy with simulation studies and comparison to observed rainfall records. The Markov process model is shown to provide a good representation in certain parts of the United States. In other areas where the Markov property is inappropriate due to event clustering or other phenomena the gamma model provides an improved characterization of the relationship between continuous and discrete rainfall occurrence.
Transport of Conservative Tracers in the Field Under Intermittent Flood Irrigation
Authors: Bowman Robert S. , Rice Robert C.
Published: February 2008

The velocity of downward percolating water measured using tracer concentration profiles was compared to the macroscopic velocity calculated from a water balance. Experiments were performed in a 37‐m2 field plot under intermittent flood irrigation. Five different soil water tracers were used to follow the movement of six applied water pulses over a period of 10 months under two irrigation regimes. Mean water velocities measured with the tracers averaged 60–70% greater than the calculated macroscopic velocity. The results indicated that a significant portion of the applied water moved downward through preferential flow paths even under unsaturated conditions. The measured velocities were not sensitive to irrigation frequency as long as total water applied remained constant. The data indicate that simple water balance models may overestimate arrival times of surface‐applied water and chemicals to ground water.
The Value of Historical Data in Flood Frequency Analysis
Authors: Hosking J. R. M. , Wallis J. R.
Published: February 2008

A common problem in flood frequency analysis is estimation, from a short gauged record, of the flood corresponding to a return period of 50–1000 years. One would expect that an estimate of the historical maximum event; i.e., the maximum flood in a period of perhaps 100–200 years, would, if properly included in the estimation procedure, improve the resulting estimate of the flood magnitude at the given return period. We attempt to assess the value of historical information using computer simulation. An annual flood sequence and a historical maximum event are generated from ah extreme‐value distribution (of type I or II) and quantitiles of the distribution are estimated by maximum likelihood, both including the excluding the historical event. After many such simulations have been performed the accuracy of the quantile estimates is assessed. We also consider the effect of errors in the magnitude of historical discharge estimates and the use of historical data in regional flood frequency analysis.
Dissolved‐oxygen depressions under ice cover in two Yukon rivers
Authors: Whitfield Paul H. , McNaughton B.
Published: February 2008

Concentrations of dissolved oxygen under winter ice cover were studied during the winter of 1982–1983 in two Yukon rivers, the Nordenskiold and Takhini. Oxygen in both rivers became depleted during the winter. The depletion of oxygen was more severe in the river with higher organic carbon concentrations. The development and progression of the depressions appears to be related to physical processes as well as biological consumption. About 80% of the depression takes place during the formation of the ice cover. The results are in agreement with earlier reports of depressions of dissolved oxygen under ice. The depression of oxygen we observed during formation of the ice was much more rapid than had been previously described. The level of dissolved oxygen in these rivers was found to return to the saturation concentration before the ice cover broke up.
Effect of radial flow on deviations from local equilibrium during sorbing solute transport through homogeneous soils
Authors: Valocchi Albert J.
Published: February 2008

Several laboratory and theoretical studies of sorbing solute transport through one‐dimensional homogeneous soil columns have recently addressed the validity of the local chemical equilibrium assumption (LEA).This paper extends previous theoretical results to the case of ideal radial flow in homogeneous aquifers. Sorption kinetics are assumed to follow a first‐order reversible rate law. Two sample problems are considered: one involves injection of a contaminant pulse into a diverging radial flow field; the other, extraction of polluted groundwater by a purge well in a converging radial flow field. An analytical time moment analysis is performed to derive formulas for solute breakthrough curve time moments. Comparison of time moment formulas for the kinetic and equilibrium models leads to the definition of criteria for LEA validity. These criteria explicitly show the effect of basic system parameters (e.g., pumping rate, dispersion coefficient, distribution coefficient, reaction rate coefficient) upon deviations from equilibrium behavior. For the case of converging radial flow, formulas are derived to calculate the impact of desorption kinetics upon the time required for aquifer decontamination. The results also show that significant nonequilibrium effects are confined to the vicinity close to the injection‐extraction wells.
An equivalent continuum model for coupled stress and fluid flow analysis in jointed rock masses
Authors: Oda Masanobu
Published: February 2008

To provide a set of governing equations for solving the coupled stress and fluid flow, a rock mass, which commonly contains a large number of geological discontinuities, is treated as an anisotropic, elastic porous medium with the corresponding elastic compliance and permeability tensors, hydro‐mechanical equivalents to the discontinuous mass. The hydromechanical equivalents, with the special emphasis on the permeability tensor, are formulated on the assumption that any crack can be replaced by a set of parallel planar plates connected by two springs. Two‐dimensional numerical analyses on seepage flow networks support the validity of the permeability tensor. Some field evidence is analyzed to examine the applicability of the present model for the practical purpose of rock hydraulics.
A natural gradient experiment on solute transport in a sand aquifer: 2. Spatial moments and the advection and dispersion of nonreactive tracers
Authors: Freyberg David L.
Published: February 2008

The three‐dimensional movement of a tracer plume containing bromide and chloride is investigated using the data base from a large‐scale natural gradient field experiment on groundwater solute transport. The analysis focuses on the zeroth‐, first‐, and second‐order spatial moments of the concentration distribution. These moments define integrated measures of the dissolved mass, mean solute velocity, and dispersion of the plume. Moments are estimated from the point observations using quadrature approximations tailored to the density of the sampling network. The estimators appear to be robust, with acceptable sampling variability. Estimates of the mass in solution for both bromide and chloride demonstrate that the tracers behaved conservatively, as expected. Analysis of the first‐order moment estimates indicates that the experimental tracer plumes traveled along identical trajectories. The horizontal trajectory is linear and aligned with the hydraulic gradient. The vertical trajectory is curvilinear, concave upward. The total vertical displacement is small, however, so that the vertical component of the mean solute velocity vector is negligible. The estimated mean solute velocity is identical for both tracers (0.091 m/day) and is spatially and temporally uniform for the first 647 days of travel time. After 647 days of transport, the plume apparently encountered a relatively large‐scale heterogeneity in the velocity field, leading to a distinct vertical layering, and slowing the rate of advance of the center of mass of the plume as a whole. The estimated horizontal components of the covariance tensor evolve over time in a manner consistent with the qualitative shape changes observed from plots of the concentration data. The major principal axis, initially aligned roughly perpendicular to the hydraulic gradient, rotates smoothly over time until it is nearly aligned with the mean solute velocity vector, as the plume itself elongates and orients its long axis with the direction of movement. Plots of the components of the covariance tensor as functions of time show evidence of what is commonly called “scale‐dependent” dispersion: the rate of growth of the covariance over time is not linear. The theoretical results of G. Dagan (1984) calibrate well to the estimated covariance data for the first 647 days of transport. The calibrated values of the parameters of the hydrualic conductivity distribution closely match independently measured values from the site. The asymptotic longitudinal dispersivity obtained from the calibration is 0.49 m, although asymptotic conditions were apparently not reached. The estimated covariance terms for the last sampling session, 1038 days after injection, are inconsistent with the earlier data and with the Dagan model, particularly for the transverse and off‐diagonal components. This behavior is probably attributable to the observed large‐scale heterogeneity in the velocity field.
Looking for hydrologic laws
Authors: Dooge James C. I.
Published: February 2008

The search for regularities in hydrologic relationships is discussed against the background of the general types of predictive models used in science. The various approaches to the study of water are compared and contrasted. The ideas discussed are illustrated by examples from the development of techniques in flood hydrology and by personal conclusions on the sources for new hypotheses in flood hydrology and the possibility of their verification.
Stochastic modeling of large‐scale transient unsaturated flow systems
Authors: Mantoglou Aristotelis , Gelhar Lynn W.
Published: February 2008

A new framework for modeling large‐scale transient unsaturated flow systems in spatially variable soils is proposed in order to overcome the problem of limited information about the local details of spatial soil variability. A stochastic approach, which assumes that local soil properties are realizations of three‐dimensional random fields, is followed for derivation of a large‐scale model representation (structure). The three dimensionality of the local flow and the nonlinear dependence of the local flow output on the local soil properties are considered. The large‐scale model structure is derived by averaging the local governing flow equation over the ensemble of realizations of the underlying soil property random fields. The resulting mean model representation is in the form of a partial differential equation in which averaged or effective model parameters occur. These effective model parameters (i.e., effective hydraulic conductivity and effective specific moisture capacity) are evaluated using a quasi‐linearized fluctuation equation and a spectral representation of stationary processes. The large‐scale model representation considers the large‐scale effects of soil property variability and has relatively few parameters. The general conclusions of this study are that soil property variability produces large‐scale hysteresis and anisotropy of the effective parameters. The potential theoretical and practical ramifications of these results in the area of unsaturated flow modeling need to be investigated. The general stochastic modeling framework developed here is applicable not only to unsaturated flow but also to other distributed parameter systems (e.g., saturated flow and transport, geothermal and oil reservoir modeling).
Effect of regional heterogeneity on flood frequency estimation
Authors: Lettenmaier Dennis P. , Wallis James R. , Wood Eric F.
Published: February 2008

Recent work on regional flood frequency estimation has shown that accurate flood quantile estimates are possible when the underlying flood frequency distributions are identical at all sites in the region except for a scaling factor, particularly when the underlying distribution has a two‐parameter form. The class of regional probability‐weighted moment (PWM) estimators is investigated for robustness to mis‐specification of the assumed distributional form and to regional heterogeneity in moments of order higher than one. Whereas two‐parameter distributions belonging to the extreme value family perform quite well when the form of the underlying distribution is close to that of the fitted distribution, large biases can result when the distribution is misspecified. The three‐parameter generalized extreme value distribution (GEV), when fitted using the regional PWM method, has been shown to be relatively insensitive to violations of the distributional assumption, and to have low variability and bias. In this paper it is shown that regional estimation methods using the three‐parameter GEV distribution are relatively insensitive to modest regional heterogeneity in the coefficient of variation and quite insensitive to regional variation in the skew coefficient. The key determinant of the performance of the regional estimators is shown to be the regional mean coefficient of variation. For high values of the mean coefficient of variation, such as might be encountered in arid regions, an alternate PWM estimation method based on the GEV distribution that accommodates the regional heterogeneity in the higher order moments is preferred. The trade‐off between this alternate method and the approach that assumes regional homogeneity in moments higher than order one is sensitive to the record lengths.
Stochastic theory of field‐scale fickian dispersion in anisotropic porous media
Authors: Neuman Shlomo P. , Winter C. Larrabee , Newman Charles M.
Published: February 2008

A three‐dimensional theory is described for field‐scale Fickian dispersion in anisotropic porous media due to the spatial variability of hydraulic conductivities. The study relies partly on earlier work by the authors the attributes of which are briefly reviewed. It leads to results which differ in important ways from earlier theoretical conclusions about dispersion in anisotropic media. We express the dispersion tensor D as the sum of a local component d and a field‐scale component Δ. The local component is assumed to be independent of velocity (which is most appropriate if it represents molecular diffusion) and its principal terms are taken to act parallel and normal to the mean velocity vector μ. The field‐scale component is written as αμ, where α is a dispersivity tensor and μ= |μ|. We show that at large Peclet numbers P, the dispersivity tensor reduces to a single principal component parallel to the mean velocity, regardless of how μ is oriented. This result, valid for arbitrary covariance functions of log‐hydraulic conductivity, differs from that of L. W. Gelhar and C. L. Axness (1983), according to whom the asymptotic dispersivity tensor may possess more than one nonzero eigen value. They calculate the direction of the largest principal dispersivity to be offset from the mean velocity toward the direction of least spatial correlation (or away from the stratification in typical layered media). We show that this principal dispersivity is offset in the opposite direction at small and intermediate Peclet numbers but rotates toward the mean velocity as P increases. The largest eigen value is constant and dominated by field‐scale velocity fluctuations at large P values. The other two eigen values diminish asymptotically in proportion to P−1 and are controlled by d as well as by field‐scale differential convection. The range of small Peclet numbers has not been previously investigated under anisotropic conditions yet is of much importance for transport in low‐permeability rocks or soils. We show that at low P values all three principal dispersivities are proportional to P and thus Δ is proportional to μ2 (a phenomenon reminiscent of Taylor diffusion). When the mean velocity is inclined to the axes of anisotropy, the eigen values of Δ are neither parallel nor normal to μ. However, since D is dominated by d at small Peclet numbers, the principal dispersion coefficients are asymptotically (as P→0) parallel and normal to the mean velocity just like when P is large; their maximum deviation from these directions occurs at intermediate P values.
Soil water saturation: Dielectric determination
Authors: Alharthi A. , Lange J.
Published: February 2008

Dielectric measurements of moist soils are used to determine water saturations. The degree of saturation of water is determined using a mixing law for the composite structure (soil, water, and air) which is verified experimentally. For the lower water saturation range (<60%), a particularly simple form for the relationship between fractional water content θ and measured dielectric constant can be formulated. In particular, for sandy soils at 23°C, the fractional water content is given by θ = 0.128(ϵc)½ − 0.204.
Evaluation of a groundwater corrective action at the Chem‐Dyne Hazardous Waste Site using a telescopic mesh refinement modeling approach
Authors: Ward David S. , Buss David R. , Mercer James W. , Hughes Shereen S.
Published: February 2008

The available data base and hydrogeologic information for the Chem‐Dyne hazardous waste site, located in southwestern Ohio, are typical of many Superfund sites. Data are localized because investigations conducted at these sites are for the purpose of defining contaminant plumes. Little or no data are available to characterize the regional flow systems which impart a controlling influence on the rate and direction of contaminant migration. To simulate groundwater flow and contaminant transport in this setting, a telescopic mesh refinement (TMR) approach is appropriate. This approach provides the means of accurately incorporating regional controlling factors into smaller model domains and also increased grid resolution in areas of critical importance. At the Chem‐Dyne site a finite‐difference model was applied at three scales: regional, local, and site. This application of TMR integrates the regional and local flow system characteristics to analyze the effectiveness of a proposed remedial action at the site scale. The TMR modeling approach permits effective flow and transport model construction and calibration to provide quantitative analysis of system response to a groundwater extraction‐injection well clean‐up system. Calibration of the flow models demonstrates the regional importance of induced river infiltration to groundwater pumping centers and the control of surface water features on the direction of plume migration. The site‐scale transport model reveals that a significant portion of the volatile organic contaminants are not captured by the preliminary proposed system.
On maximum likelihood estimators for the multisite lag‐one streamflow model: Complete and incomplete data cases
Authors: Kuczera George
Published: February 2008

Two practical problems may arise when using the traditional estimators of the parameters in the multisite lag‐one streamflow model: (1) the estimated covariance matrix may not be positive definite thereby preventing its decomposition, a necessary step for synthetic streamflow generation, and (2) if there are missing observations, streamflow data must be truncated to the shortest record resulting in a loss of useful information. This note draws attention to the existence of maximum likelihood estimators which overcome both problems. In the complete data case, explicit maximum likelihood estimators exist. However, in the incomplete data case, iterative maximum likelihood procedures must be used. In particular, the expectation maximization (EM) algorithm is considered in a state‐space framework compatible with the multisite streamflow model; this algorithm has robust convergence properties, is simple to implement, and produces smoothed estimates of the missing data. An example is presented illustrating problems with decomposition of the traditional covariance matrix estimate and also illustrating application of the EM algorithm.
A Markov Renewal Model for rainfall occurrences
Authors: Foufoula‐Georgiou Efi , Lettenmaier Dennis P.
Published: February 2008

A probabilistic model for the temporal description of daily rainfall occurrences at a single location is presented. By defining an event as a day with measurable precipitation the model is cast into the discrete‐time point process framework. In the proposed model the sequence of times between events is formed by sampling from two geometric distributions, according to transition probabilities specified by a Markov chain. The model belongs to the class of Markov renewal processes and exhibits clustering relative to the independent Bernoulli process. As a special case, it reduces to a renewal model with a mixture distribution for the interarrival times. The rainfall occurrence model coupled with a mixed exponential distribution for the nonzero daily rainfall amounts was applied to the daily rainfall series for Snoqualmie Falls, Washington, and was successful in preserving the short‐term structure of the occurrence process, as well as the distributional properties of the seasonal rainfall amounts.
A robust‐resistant spatial analysis of soil water infiltration
Authors: Cressie N. A. C. , Horton R.
Published: February 2008

Data taken at adjacent spatial locations often exhibit correlation which must be taken into account in their analysis. Geostatistical methods, originally developed for the mining industry, have proven to be adaptable to hydrological problems. This paper concentrates on estimating the spatial correlations between soil water infiltration observations, with special emphasis on resistant methods to remove nonstationarity. After this removal, robust semivariogram estimators are used to examine the spatial dependencies for various tillage treatments. There is some indication that infiltration characteristics inherit different types of spatial dependency, depending on the tillage treatment applied.