Showing papers in "Water Resources Research in 1986"
TL;DR: The Borden aquifer was examined in great detail by conducting permeability measurements on a series of cores taken along two cross sections, one along and the other transverse to the mean flow direction as discussed by the authors.
Abstract: The spatial variability of hydraulic conductivity at the site of a long-term tracer test performed in the Borden aquifer was examined in great detail by conducting permeability measurements on a series of cores taken along two cross sections, one along and the other transverse to the mean flow direction. Along the two cross sections, a regular-spaced grid of hydraulic conductivity data with 0.05 m vertical and 1.0 m horizontal spatial discretization revealed that the aquifer is comprised of numerous thin, discontinuous lenses of contrasting hydraulic conductivity. Estimation of the three-dimensional covariance structure of the aquifer from the log-transformed data indicates that an exponential covariance model with a variance equal to 0.29, an isotropic horizontal correlation length equal to about 2.8 m, and a vertical correlation length equal to 0.12 m is representative. A value for the longitudinal macrodispersivity calculated from these statistical parameters using three-dimensional stochastic transport theory developed by L. W. Gelhar and C. L. Axness (1983) is about 0.6 m. For the vertically averaged case, the two-dimensional theory developed by G. Dagan (1982, 1984) yields a longitudinal djspersivity equal to 0.45 m. Use of the estimated statistical parameters describing the ln (K) variability in Dagan's transient equations closely predicted the observed longitudinal and horizontal transverse spread of the tracer with time. Weak vertical and horizontal dispersion that is controlled essentially by local-scale dispersion was obtained from the analysis. Because the dispersion predicted independently from the statistical description of the Borden aquifer is consistent with the spread of the injected tracer, it is felt that the theory holds promise for providing meaningful estimates of effective transport parameters in other complex-structured aquifers.
1,307 citations
TL;DR: In this article, a survey of parameter identification procedures in groundwater hydrology is presented, which includes the evaluation of methods used for computing the sensitivity matrix and statistics which can be used to estimate the parameter uncertainty.
Abstract: The purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem. Parameter identification methods are classified under the error criterion used in the formulation of the inverse problem. The problem of ill-posedness in connection with the inverse problem is addressed. Typical inverse solution techniques are highlighted. The review also includes the evaluation of methods used for computing the sensitivity matrix. Statistics which can be used to estimate the parameter uncertainty are outlined. Attempts have been made to compare and contrast representative inverse procedures, and direction for future research is suggested.
1,132 citations
TL;DR: In this article, a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions, including the initial head distribution, which can also be estimated if the system is originally at a steady state.
Abstract: 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.
860 citations
TL;DR: In this paper, the authors analyzed particle migration through porous media at typical groundwater flow velocities and found that retention of a relatively small solid volume within media pores can reduce media permeability by orders of magnitude.
Abstract: Transport of suspended participate matter is widely recognized to occur in subsurface environments. Field data indicate that viruses, bacteria, and clay minerals can migrate considerable distances and that small particles and macromolecules are implicated in the transport of organic contaminants and radio-nuclides. Furthermore, media permeability can be significantly altered by changes in aqueous chemistry through particle release and capture. Quantitative models for predicting particle transport are available within the water filtration literature that account for the mechanisms of particle-media collisions and the conditions for attachment. Predictions from the filtration models are used to analyze particle migration through porous media at typical groundwater flow velocities. As particles accumulate within media pores, available models become less predictive because of the coupling between particle retention and permeability reduction. An examination of filtration data reveals that retention of a relatively small solid volume within media pores can reduce media permeability by orders of magnitude. The fact that contaminants adsorbed to particles are mobile has important implications in understanding and predicting contaminant transport. The design of laboratory experiments and the collection of field samples often neglect contaminants transported by suspended colloids and particles.
843 citations
TL;DR: In this paper, the authors used perturbation-based spectral theory to estimate the head variance, effective conductivity tensor, and macrodispersivity tensors in a field, and used these results to answer important questions about the large-scale behavior of naturally heterogeneous aquifers.
Abstract: Research on stochastic analysis of subsurface flow has developed rapidly in the last decade, but applications of this approach have been very limited. The purpose of this paper is to illustrate how currently available techniques and results can be used to answer important questions about the large-scale behavior of naturally heterogeneous aquifers. Perturbation-based spectral theory, which presumes local statistical homogeneity, provides generic theoretical results for the head variance, effective conductivity tensor, and macrodispersivity tensor in a field. These results emphasize the key role of the variance and spatial correlation scales of the log hydraulic conductivity field. Field information of variances and correlation scales of natural materials is summarized. The validity of some of the generic stochastic results is evaluated through comparisons with Monte Carlo simulations and field observations. A specific field application example is developed to illustrate how the stochastic results are used to estimate large-scale parameters and determine the reliability of three-dimensional numerical simulations. Using typical log conductivity covariance parameters, the effective hydraulic conductivity tensor, and the macrodispersivity tensor are estimated. The calculated head variance, based on the simulated mean hydraulic gradient, is used as a measure of the adequacy of the calculation of the steady state flow model. Discussion emphasizes limitations and extensions of this approach, and ongoing field evaluations of the results.
773 citations
TL;DR: This paper showed 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.
Abstract: 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.
754 citations
TL;DR: In this paper, 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.
Abstract: 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.
710 citations
TL;DR: In this paper, the authors describe a methodology for parameterization of a distributed components approach to watershed simulation, which is designed to aid in the efficient parameterization and organization of watershed data as input to hydrologic simulation models.
Abstract: Digital elevation models are used to automatically map the stream channel and divide networks of a watershed. These topographic skeletons are used to partition the watershed into a set of fundamental, runoff producing subregions, each of which drains into one stream link. Construction of a code describing the network topology, along with parallel files containing attribute information of each drainage area and associated stream link may form the basis for an efficient watershed information system. Registration of remotely sensed imagery and maps of important soils information to the digital elevation model allows an effective organization of this data as input to hydrologic simulation models. The methodology described here is designed to aid in the efficient parameterization of a distributed components approach to watershed simulation.
680 citations
TL;DR: In this paper, 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.
Abstract: 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.
641 citations
TL;DR: A large-scale field experiment on natural gradient transport of solutes in groundwater has been conducted at a site in Borden, Ontario as discussed by the authors, where over 19,900 samples have been collected over a 3-year period.
Abstract: A large-scale field experiment on natural gradient transport of solutes in groundwater has been conducted at a site in Borden, Ontario. Well-defined initial conditions were achieved by the pulse injection of 12 m3 of a uniform solution containing known masses of two inorganic tracers (chloride and bromide) and five halogenated organic chemicals (bromoform, carbon tetrachloride, tetrachloroethylene, 1,2-dichlorobenzene, and hexachloroethane). A dense, three-dimensional array of over 5000 sampling points was installed throughout the zone traversed by the solutes. Over 19,900 samples have been collected over a 3-year period. The tracers followed a linear horizontal trajectory at an approximately constant velocity, both of which compare well with expectations based on water table contours and estimates of hydraulic head gradient, porosity, and hydraulic conductivity. The vertical displacement over the duration of the experiment was small. Spreading was much more pronounced in the horizontal longitudinal than in the horizontal transverse direction; vertical spreading was very small. The organic solutes were retarded in mobility, as expected.
634 citations
TL;DR: In this article, a discussion of the question, Under what conditions is the aquifer inverse problem well-posed? After defining the terms uniqueness, identifiability, and stability, theoretical considerations and synthetic examples are used to demonstrate that ill-posedness can be mitigated by including prior information about the parameters in the estimation criterion to be minimized.
Abstract: Paper 2 of this three-part series starts with a discussion of the question, Under what conditions is the aquifer inverse problem well-posed? After defining the terms uniqueness, identifiability, and stability, theoretical considerations and synthetic examples are used to demonstrate that ill-posedness can be mitigated by including prior information about the parameters in the estimation criterion to be minimized. At the same time, the inclusion of such information is shown to be insufficient to guarantee uniqueness and stability in all cases. Several test problems in the recent literature, which have resulted in pessimistic conclusions about the solvability of the aquifer inverse problem, are shown to be ill-posed; a question is thus raised about the validity of these conclusions in the general case. Various conjugate gradient algorithms, coupled with the adjoint state finite element method for computing the gradient of the estimation criterion, and with Newton's method for determining the optimum step size downgradient, are compared. A marked improvement in the rate at which these algorithms converge is shown to be achieved by switching from one method to another when the former slows down or fails to converge.
TL;DR: A review of the current conceptual understanding of the basic processes of water flow and chemical transport in the untsaturated (vadose) zone and of various deterministic mathematical models that are being used to describe these processes can be found in this article.
Abstract: This paper gives a review of our current conceptual understanding of the basic processes of water flow and chemical transport in the untsaturated (vadose) zone and of various deterministic mathematical models that are being used to describe these processes. During the past few decades, tremendous effort has been directed toward unravelling the complexities of various interactive physical, chemical, and microbiological mechanisms affecting unsaturated flow and transport, with contributions being made by soil scientists, geochemists, hydrologists, soil microbiologists, and others. Unfortunately, segmented, disciplinary research has contributed to a lack of experimental and theoretical understanding of the vadose zone, which, in turn, has precluded the accurate prediction and management of flow and contaminant transport through it. Thus a more unified and interdisciplinary approach is needed that considers the most pertinent physical, chemical, and biological processes operative in the unsaturated zone. Challenges for both fundamental and applied researchers to reveal the intricacies of the zone and to integrate these with currently known concepts are numerous, as is the urgency for progress inasmuch as our soil and ground water resources are increasingly subjected to the dangers of long-term pollution. Specific research areas in need of future investigation are outlined.
TL;DR: In this article, the authors proposed a unified statistical approach to groundwater flow and transport problems at three fundamental scales: the pore scale, the log hydraulic conductivity, and the log transmissivity integral scales.
Abstract: The statistical approach has been applied increasingly to groundwater flow problems in the last decade, as is illustrated in Figure 3 by the cumulative number of articles published in this field in Water Resources Reseach. This development has been motivated by the recognition of the fact that porous formations are heterogeneous, i.e., with properties which vary in an irregular manner in space. Flow domains are characterized by the length scale L of their spatial extent and three such scales of a fundamental nature are introduced: the laboratory, the local, and the regional scale. Heterogeneity is characterized by the spatial correlation scale I of the property of interest, the three scales corresponding to the above ones being the pore scale, the log hydraulic conductivity, and the log transmissivity integral scales. The medium properties and related flow variables are regarded as random space functions which satisfy two basic requirements: they enjoy some type of stationarity and I ≪ L. An additional scale D is the measurement or computational scale, characterizing the size of the measurement device of a flow variable or the element over which the variable is averaged for computational purposes. In both cases, the interest resides in the space average of the flow variable over a volume or area of length scale D. The primary aim of the theory of flow and transport through porous media is to determine the statistical moments of the space-averaged variables, given the statistical structure of the spatially variable property. The main objective of the study is to show that flow and transport problems at the three fundamental scales can be treated by a unified statistical approach, along this line. The specific aspects of each scale are examined separately, and areas of interest for future research are indicated. In the concluding remarks it is submitted that the statistical approach to groundwater flow has become a comprehensive theory, beyond the stage of an ad hoc modeling technique.
TL;DR: Sklash et al. as mentioned in this paper reported 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.
Abstract: 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).
TL;DR: In this paper, the authors used stable environmental isotopes of water, a naturally occuring conservative tracer, to test an acid precipitation neutralization mechanism in the Hubbard Brook Experimental Forest, New Hampshire.
Abstract: As part of the construction of a simulation model to test an acid precipitation neutralization mechanism, the stream hydrograph was separated into its baseflow and event water components using stable environmental isotopes of water, a naturally occuring conservative tracer. Three snowmelt events and one storm event during the winter and spring of 1984 were studied at an instrumented watershed in the Hubbard Brook Experimental Forest, New Hampshire. Conditions for use of the isotopic tracer were not always met, however. During the latter part of the snowmelt and the storm, the isotopic content of the groundwater and event water were not distinguishable. Furthermore the isotopic content of the meltwater varied considerably over time, thereby reducing the precision of the hydrograph separation. Frequent sampling of the meltwater is mandatory to assess this variability. Because the concentration of major cations and anions were measured as well, chemical tracers could be compared to the isotopic tracer, when the isotopic hydrograph separation was reliable, to test whether the chemical tracer was conservative. Dissolved silica was found to act as a conservative tracer for this watershed.
TL;DR: The unsatisfactory state of hydrology is, in the final analysis, the result of the dichotomy between the theoretical recognition of Hydrology as a science in its own right and the practical impossibility of studying it as a primary discipline but only as an appendage of hydraulic engineering, geography, geology, etc.
Abstract: The unsatisfactory state of hydrology is, in the final analysis, the result of the dichotomy between the theoretical recognition of hydrology as a science in its own right and the practical impossibility of studying it as a primary discipline but only as an appendage of hydraulic engineering, geography, geology, etc. As a consequence, the perspectives of hydrologists tend to be heavily biased in the direction of their nonhydrologic primary disciplines and their hydrologic backgrounds have wide gaps which breed a large variety of misconceptions. This state of affairs often paralyzes hydrologists' ability to differentiate between hydrology and water management, hydrology and statistics, facts and assumptions, science and convenience, etc., with consequent dangers both to scientific development of hydrology and to its practical utility. The danger increases with the proliferation of computerized “hydrologic” models whose cheaply arranged ability to fit data is presented as proof of their soundness and as a justification for using them for user-attractive but hydrologically indefensible extrapolations. These points are illustrated, among other things, by discussion of flood frequency analysis. The paper concludes with some thoughts concerning minimum standards for the testing of hydrologic simulation models that would ensure at least a modest level of credibility, and with a few suggestions for ingredients of a long-term cure that can prevent hydrology from joining alchemy and astrology in the annals of dilettantism.
TL;DR: In this paper, it is shown that an economically efficient water allocation system must integrate quantity and quality management and would be neither a priority nor a proportional rights system and that the nature of the water rights system may not be very important if short-term rental markets are operative.
Abstract: Exchange through markets is one way of allocating water. In many settings this method possesses a number of desirable attributes to a greater degree than alternative allocative mechanisms: flexibility, security, predictability, fairness …. Markets have shortcomings, too, especially related to quantity and quality return flow effects, but these can be mitigated through changes in the administrative framework of the water rights system. It is shown that an economically efficient water allocation system must integrate quantity and quality management and would be neither a priority nor a proportional rights system. However, the nature of the water rights system may not be very important if short-term rental markets are operative. The potential for intrastate and interstate water markets is discussed.
TL;DR: In this article, Borden et al. developed equations for simulating the simultaneous growth, decay, and transport of microorganisms, as well as the transport and removal of hydrocarbon and oxygen.
Abstract: Many hydrocarbons and related organic contaminants are rapidly degradable in the presence of oxygen. Unfortunately, exchange of oxygen with subsurface contaminant plumes is often slow. In this paper, equations are developed for simulating the simultaneous growth, decay, and transport of microorganisms, as well as the transport and removal of hydrocarbon and oxygen. These equations are solved by conventional numerical techniques to study the impact of microbial kinetics, horizontal mixing, adsorption, and vertical exchange with the unsaturated zone on biodegradation. In the region near the hydrocarbon source, any available oxygen will be rapidly consumed. In the body of the hydrocarbon plume, oxygen transport will be rate limiting and the consumption of oxygen and hydrocarbon can be approximated as an instantaneous reaction. The major sources of oxygen to the plume appear to be transverse mixing, advective fluxes when adsorption is significant and vertical exchange with the unsturated zone. In a companion paper (R. C. Borden et al., this issue), hydrocarbon transport is simulated at a hazardous waste site where oxygen-limited biodegradation is known to occur.
TL;DR: The search for regularities in hydrologic relationships is discussed against the background of the general types of predictive models used in science and various approaches to the study of water are compared and contrasted.
Abstract: 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.
TL;DR: In this article, the authors synthesize the diverse contributions of various disciplines to the problem of flow in low-permeability environments, and discuss the problems hindering analysis and suggest approaches to overcome them.
Abstract: Certain geologic media are known to have small permeability; subsurface environments composed of these media and lacking well developed secondary permeability have groundwater flow sytems with many distinctive characteristics. Moreover, groundwater flow in these environments appears to influence the evolution of certain hydrologic, geologic, and geochemical systems, may affect the accumulation of pertroleum and ores, and probably has a role in the structural evolution of parts of the crust. Such environments are also important in the context of waste disposal. This review attempts to synthesize the diverse contributions of various disciplines to the problem of flow in low-permeability environments. Problems hindering analysis are enumerated together with suggested approaches to overcoming them. A common thread running through the discussion is the significance of size- and time-scale limitations of the ability to directly observe flow behavior and make measurements of parameters. These limitations have resulted in rather distinct small- and large-scale approaches to the problem. The first part of the review considers experimental investigations of low-permeability flow, including in situ testing; these are generally conducted on temporal and spatial scales which are relatively small compared with those of interest. Results from this work have provided increasingly detailed information about many aspects of the flow but leave certain questions unanswered. Recent advances in laboratory and in situ testing techniques have permitted measurements of permeability and storage properties in progressively “tighter” media and investigation of transient flow under these conditions. However, very large hydraulic gradients are still required for the tests; an observational gap exists for typical in situ gradients. The applicability of Darcy's law in this range is therefore untested, although claims of observed non-Darcian behavior appear flawed. Two important nonhydraulic flow phenomena, osmosis and ultrafiltration, are experimentally well established in prepared clays but have been incompletely investigated, particularly in undisturbed geologic media. Small-scale experimental results form much of the basis for analyses of flow in low-permeability environments which occurs on scales of time and size too large to permit direct observation. Such large-scale flow behavior is the focus of the second part of the review. Extrapolation of small-scale experimental experience becomes an important and sometimes controversial problem in this context. In large flow systems under steady state conditions the regional permeability can sometimes be determined, but systems with transient flow are more difficult to analyze. The complexity of the problem is enhanced by the sensitivity of large-scale flow to the effects of slow geologic processes. One-dimensional studies have begun to elucidate how simple burial or exhumation can generate transient flow conditions by changing the state of stress and temperature and by burial metamorphism. Investigation of the more complex problem of the interaction of geologic processes and flow in two and three dimensions is just beginning. Because these transient flow analyses have largely been based on flow in experimental scale systems or in relatively permeable systems, deformation in response to effective stress changes is generally treated as linearly elastic; however, this treatment creates difficulties for the long periods of interest because viscoelastic deformation is probably significant. Also, large-scale flow simulations in argillaceous environments generally have neglected osmosis and ultrafiltration, in part because extrapolation of laboratory experience with coupled flow to large scales under in situ conditions is controversial. Nevertheless, the effects are potentially quite important because the coupled flow might cause ultra long lived transient conditions. The difficulties associated with analysis are matched by those of characterizing hydrologic conditions in tight environments; measurements of hydraulic head and sampling of pore fluids have been done only rarely because of the practical difficulties involved. These problems are also discussed in the second part of this paper.
TL;DR: In this article, a model for simulating microbial growth-degradation processes in porous media is developed, where the bulk of microorganisms in an aquifer grow in microcolonies attached to matrix surfaces.
Abstract: A model for simulating microbial growth-degradation processes in porous media is developed. It is assumed that the bulk of microorganisms in an aquifer grow in microcolonies attached to matrix surfaces. As developed, the model applies to the growth and decay of aerobic, heterotrophic microorganisms whose growth is limited by lack of a carbon and energy source (substrate), an oxygen source or both simultaneously as described by modified Monod kinetics. Transport of substrate and oxygen in the porous medium is assumed to be governed by advection-dispersion equations with surface adsorption. A total of five coupled equations result describing substrate and oxygen concentrations in the pore fluid, substrate and oxygen concentrations in the microcolonies and colony density, which is assumed sufficiently small so that aquifer hydraulic conductivity is not diminished. An iterative process involving an Eulerian-Lagrangian numerical procedure that is highly resistant to numerical dispersion in the presence of small dispersivities is used to solve the overall model, with parameter values selected from the literature or estimated. Results indicate that biodgradation would be expected to have a major effect on contaminant transport when proper conditions for growth exist. For one-dimensional transport in a column, the most rapid microbial growth always occurred at the influent boundary where oxygen and substrate concentrations were held constant independent of colony density. Anaerobic conditions develop rapidly and aerobic biodegradation ceases if large amounts of substrate are added to the system.
TL;DR: In this article, the effect of parameter uncertainty is examined in a Bayesian framework with emphasis on the derivation of the Bayesian distribution (and its first two moments) of unknown quantities given some measurements.
Abstract: Linear estimation has found many applications in the inference of spatial functions in surface and subsurface hydrology. The effect of parameter uncertainty is examined in a Bayesian framework with emphasis on the derivation of the Bayesian distribution (and its first two moments) of unknown quantities given some measurements. This distribution accounts not only for natural variability but also for parameter uncertainty. For known covariance parameters the Bayesian distribution is Gaussian (for Gaussian processes) with the mean being a given linear function of the data. This linear estimator is equivalent to the conventional Gaussian conditional mean estimator for a priori known drift coefficients and is the same with kriging for diffuse prior distribution of the drift coefficients; however, the developed procedure is more general. When both drift and covariance function parameters are uncertain, the Bayesian distribution is generally not Gaussian, and the Bayesian conditional mean is a nonlinear estimator. The case of diffuse priors is examined in some detail; it is shown that the posterior distribution of the covariance function parameters is given by the restricted likelihood function, i.e., the likelihood function of generalized increments. The results provide insight into the applicability of maximum likelihood versus restricted maximum likelihood parameter estimation, and conventional linear versus kriging estimation. A more general procedure which includes these methods as special cases is presented.
TL;DR: In this article, a Monte Carlo study employing the two-parameter lognormal distribution was conducted to extract the equivalent of an additional 10-30 years of gage record from a 50-year period of historical observation.
Abstract: An investigation is made of flood quantile estimators which can employ “historical” and paleoflood information in flood frequency analyses. Two categories of historical information are considered: “censored” data, where the magnitudes of historical flood peaks are known; and “binomial” data, where only threshold exceedance information is available. A Monte Carlo study employing the two-parameter lognormal distribution shows that maximum likelihood estimators (MLEs) can extract the equivalent of an additional 10–30 years of gage record from a 50-year period of historical observation. The MLE routines are shown to be substantially better than an adjusted-moment estimator similar to the one recommended in Bulletin 17B of the United States Water Resources Council Hydrology Committee (1982). The MLE methods performed well even when floods were drawn from other than the assumed lognormal distribution.
TL;DR: The long-term behavior of five organic solutes during transport over a period of 2 years in ground water under natural gradient conditions was characterized quantitatively by means of moment estimates as mentioned in this paper.
Abstract: The long-term behavior of five organic solutes during transport over a period of 2 years in ground water under natural gradient conditions was characterized quantitatively by means of moment estimates. Total mass was conserved for two of the organic compounds, carbon tetrachloride and tetrachloroethylene, while the total mass declined for three other compounds, bromoform, 1,2-dichlorobenzene, and hexachloroethane. The declines in mass for the latter three compounds are interpreted as evidence of transformation of the compounds. Retardation factors for the organic solutes, relative to chloride, ranged from 1.5 to 9.0, being generally greater for the more strongly hydrophobic compounds. The retardation is attributed to sorption. The apparent retardation factor increased markedly for all compounds over the duration of the experiment, by as much as 150%. Results from temporal and spatial sampling were in good agreement when compared at the same scale of time and distance.
TL;DR: In this paper, the roles of old and new water during three storm events (return periods from 4 weeks to 3 months) in September 1983 were evaluated using hydrometric and natural tracer (oxygen 18, deuterium, electrical conductivity, chloride) observations.
Abstract: Previous hydrometric and dye tracer studies in Maimai 8, a highly responsive catchment in the Tawhai State Forest, Westland, New Zealand, suggest that storm runoff generation is by rapid transmission of “new” (current storm rain) water to the stream via macropores. We used hydrometric and natural tracer (oxygen 18, deuterium, electrical conductivity, chloride) observations in two first- and one second-order stream and in six throughflow pits, to evaluate the roles of “old” (stored) and new water during three storm events (return periods from 4 weeks to 3 months) in September 1983. New water contributions were small (<25% of the hydrograph volume) and could be accounted for by saturation overland flow. Hillslope response varied areally but all sites issued old water-dominated throughflow. Ridge top sites had larger new water contributions (∼ 30–40%) than valley sites (< 10%). Macropore flow of new water therefore cannot explain streamflow or throughflow response in the Maimai catchments.
TL;DR: In this article, 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.
Abstract: 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.
TL;DR: In this paper, Carrera and Neuman proposed a method to estimate model parameters under a variety of conditions, and applied it to a synthetic test case and to a set of field data from the southwestern United States.
Abstract: The last paper of this three-part series illustrates and explores various features of the methodology we have proposed in papers 1 and 2 (J. Carrera and S. P. Neuman, this issue (a, b)) by applying it to a synthetic test case and to a set of field data from the southwestern United States. In addition to demonstrating the ability of our method to estimate model parameters under a variety of conditions, the synthetic example is used to investigate the relative worth of transient and steady state data in terms of their ability to bring about an improvement in the quality of the estimates. A similar investigation is performed with regard to the role that prior information may play in reducing the variance of the estimation errors. The paper demonstrates the potential utility of our inverse methodology to the optimum design of observation and measurement networks in space and time. Based on a synthetic example, the paper shows that the model structure identification criteria introduced in paper 1 (J. Carrera and S. P. Neuman, this issue (a)) can be used successfully to choose the best parameter zonation pattern among a number of given alternatives. In particular, a criterion due to R. L. Kashyap (1982) is found to be the most adequate for this purpose because it responds in the most convincing manner to noise in the data. The field example illustrates a case where one must account for temporal autocorrelation between water level data at a given observation point. By validating the model against data which have not been used for parameter estimation, one finds that the validation results improve when the temporal error structure of the water level data is represented by a lag-one autocorrelation model. Both the synthetic and the field examples are used to obviate the advantages of performing the analysis of the estimation errors in the eigenspace instead of the original parameter space and to relate the results of this analysis to the fundamental questions of identifiability, uniqueness, and stability where appropriate.
TL;DR: In this article, the most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method, where censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores.
Abstract: A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensored observations, for determining the best performing parameter estimation method for any particular data det. The most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method. With this method, censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log-probability regression method still had the smallest errors for the mean and standard deviation,more » but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification.« less
TL;DR: Theoretical equations for calculating the unit stream power of both sheet and rill flow were developed and used to predict the sediment transport capacity of such flows in this paper, and the results were very good and demonstrated the simplicity and robustness of the method.
Abstract: Theoretical equations for calculating the unit stream power of both sheet and rill flow were developed and used to predict the sediment transport capacity of such flows. Independent data sets from three sources representing both finely aggregated clay soils and coarse textured nonaggregated soils, sheet, rill, and composite sheet rill flow systems, and a range of slopes were used to test the utility of the method. The results were very good and demonstrated the simplicity and robustness of the method. For shallow overland flow the best results were obtained when the critical unit stream power at incipient sediment motion was treated as a constant value that was independent of slope. The results also suggest that a unique value of critical unit stream power for rill initiation exists that is independent of soil type. For noncohesive loams or fine sands and finely aggregated clay soils the sediment transport capacity can be accurately predicted from a knowledge of the physical characteristics of the soil or bed material alone. For aggregated clay soils this requires information on the aggregate size distribution and the effects of soil particle size differentiation as flow rates and unit stream powers increase with the transition from sheet to rill flow.
TL;DR: In this article, the tradeoffs between reliability, vulnerability, and resilience were examined using multiobjective mixed-integer, linear programming, and it was found that as reliability is increased or as the maximum length of consecutive shortfalls decreases (resilience increases), the vulnerability of the water system to larger deficits increases.
Abstract: Reliability in water supply reservoir operation is commonly thought of as the probability of failing to achieve some target release. Here we explore two additional proposed descriptions of reservoir performance: the maximum shortfall from the target (system vulnerability) and the maximum number of consecutive periods of deficit during a record (system resilience). The larger the maximum shortfall, the greater the vulnerability. The shorter the maximum length of deficits, the more resilient the system. Using multiobjective mixed-integer, linear programming, the tradeoffs between reliability, vulnerability, and resilience are examined. It is found that as reliability is increased or as the maximum length of consecutive shortfalls decreases (resilience increases), the vulnerability of the water system to larger deficits increases.