摘要:

A new approach for the treatment, of dispersive transport in a simplified porous medium is presented. Use of a volume averaging approach allows the development of a separate point macroscopic balance equation for the dispersion quantity that appears in the averaged transport equation. The new equation is a more general representation, which avoids the complications and questions that arise concerning the coefficients associated with the Fickian approximation for dispersion. Constitutive relationships are developed for a number of the source terms arising in the averaged dispersion equation. The coupled transport and dispersion equations along with Darcy's law and the macroscopic continuity equation constitute a closed, second‐order model for dispersion in a porous mediu

ISSN:0043-1397    

DOI:10.1029/WR022i005p00591

年代:1986

数据来源: WILEY

摘要:

The second‐order dispersion model developed by Tompson and Gray (this issue) is reduced to a one‐dimensional form in terms of dimensionless variables and is applied to the simple problem of solute transport in pipes and capillaries. Numerical experiments allow the dimensionless constitutive coefficients appearing in the model to be evaluated under several flow regimes. Simple functional relationships for these coefficients in terms of the Peclet number are developed. The model performs well using these scale independent coefficients, even at early times and short travel distances, when the traditional first‐order Fickian model is inade

ISSN:0043-1397    

DOI:10.1029/WR022i005p00601

年代:1986

数据来源: WILEY

摘要:

The disjunctive kriging method described in this paper produces a nonlinear unbiased estimator with the characteristic minimum variance of errors. Disjunctive kriging is as good, or otherwise better than linear estimators in the sense of reduced kriging variance and exactness of estimation. It does not suffer from the difficulties associated with computing the conditional expectation and can be thought of as its estimator. Disjunctive kriging also provides an estimate of the conditional probability that a random variable located at a point or averaged over a block in two‐dimensional space is above some specified cutoff or tolerance level and this can be written in terms of the probability distribution or the density function. The method has important implications in aiding management decisions by providing a quantitative input (which is not readily obtained from the linear kriging estimators), based on the available data, which is the best nonlinear unbiased estimator short of the conditional expectation. A major disadvantage in using disjunctive kriging is the increased computational time. This, however, is mitigated by increased information about the estimat

ISSN:0043-1397    

DOI:10.1029/WR022i005p00615

年代:1986

数据来源: WILEY

摘要:

The disjunctive kriging (DK) method described in detail in the previous paper of this series is illustrated by two examples. The first example is for the electrical conductivity (EC) which is approximately lognormally distributed. In the second example the natural logarithm of the EC is used to produce an approximately normally distributed data set. The data set was chosen since the Hermite coefficients for a normal and lognormal distribution could be determined analytically as well as to facilitate a comparison between ordinary and disjunctive kriging. The capability of DK to be a nonlinear estimator and an estimator of the conditional probability is explored. The results indicate that DK is a better estimator than linear estimators (i.e., ordinary kriging) in the sense of reduced variance of errors and average kriging variance even when the data are approximately normally or lognormally distributed. Also, using DK one can obtain an estimate of the conditional probability.

ISSN:0043-1397    

DOI:10.1029/WR022i005p00623

年代:1986

数据来源: WILEY

摘要:

A simple hillslope hydrological model predicting discharge from sloping shallow soils is analyzed. Unlike most existing hillslope models, this model is fully analytic and thus straightforward to apply. It compares favorably to more complex models, and its application is illustrated for experimental data collected at the Coweeta Hydrological Laboratory.

ISSN:0043-1397    

DOI:10.1029/WR022i005p00631

年代:1986

数据来源: WILEY

摘要:

A 14‐ayear record of convective‐dispersive flow in the unsaturated zone was reconstructed using the difference between the environmental tritium content of rain and of irrigation water. Samples were taken from a loess profile in the northern Negev, Israel, in an area where precipitation is 200 mm/winter and irrigation is 650 mm/summer. The difference between the measured tritium profile and the input tritium profile was interpreted in terms of mobile and immobile water domains. The percentage of the total water which is immobile was estimated to be about 40% at the surface and 55% at 8.5 m depth. This leads to the estimate that 8 ± 1% of the rain and irrigation water percolated downward, with a velocity of 0.66 ± 0.03 m yr−1and a maximal effective dispersion coefficient of 5 × 10−11m2s−1. Using these values, we determined the limits of dispersivity (0.5–1.5 mm) and of tortuosity (0.05–0.11) in th

ISSN:0043-1397    

DOI:10.1029/WR022i005p00635

年代:1986

数据来源: WILEY

摘要:

Chemical impact of irrigation return flows upon receiving waters has historically focussed on salt and sediment production. Transport of other agricultural pollutants which are preferentially associated with suspended sediment is largely unknown in western Canada and poorly addressed elsewhere because of the traditional emphasis upon whole and filtered water chemistry. This study examines the role of suspended sediment in the flux of phosphorus and metals from large‐scale irrigation in semiarid southern Alberta. It establishes temporal patterns of chemical flux over the irrigation season, identifies the chemical species of phosphorus and metals, and assesses the potential for phosphorus and heavy metal impact from irrigation return flows upon receiving riverine systems. Whole and filtered water chemistry is found to be not especially useful in determining either chemical enrichment of return flows nor for evaluating impact upon receiving waters. Suspended sediment plays a major role in transport of phosphorus and heavy metals. Evidence from parent materials, prairie soils, chemical speciation, statistical relationships for metals and for phosphorus, and comparative data for suspended sediment during spring high flow in receiving rivers when sediments originate from eroding diffuse sources, all indicate that sediment‐associated phosphorus and metals in irrigation return flows are not anthropogenically enriched and do not represent an impact beyond that which is naturally occurring in receiving riv

ISSN:0043-1397    

DOI:10.1029/WR022i005p00643

年代:1986

数据来源: WILEY

摘要:

A practical approach is developed for frequency analysis of multiyear drought durations of annual streamflow series. The proposed approach utilizes a technique which smooths the frequency‐curve irregularity of drought durations and, therefore, reduces the statistical uncertainties associated with sample‐size limitations. Several hazard‐function models are examined with regard to their ability to represent the duration‐dependent termination rate of a drought data set. The logistic model with an exponential correction for short durations is considered to have sufficient flexibility for describing most portions of the termination‐rate function. The parameters of the logistic model are identified using a piecewise linear regression for the linearized termination probability curve. Once the form of the hazard model is specified arid its parameters are estimated, the probability distribution and exceedance probability of drought durations can be determined from their corresponding relationships with the hazard model. The historic droughts of Feather River, California, are used to demonstrate the methodology. Results indicate that the observed nine‐year drought of Feather River has a return period o

ISSN:0043-1397    

DOI:10.1029/WR022i005p00655

年代:1986

数据来源: WILEY

摘要:

The problem of solute transport in steady nonuniform flow created by a recharging and discharging well pair is investigated. Numerical difficulties encountered with the standard Galerkin formulation in Cartesian coordinates are illustrated. An improved finite element solution strategy is presented to overcome the numerical problem. The strategy is based on a formulation performed in three‐dimensional curvilinear coordinates. This formulation is developed especially for the simulation of two‐well injection‐withdrawal tracer tests conducted in homogeneous or stratified aquifers. The formulation can also be applied to other types of problems involving transport in homogeneous and stratified aquifers. A three‐dimensional finite element approximation is derived by two successive applications of upstream weighted‐residual and subdomain collocation procedures. First, the weighted residual procedure is formulated in the horizontal flow plane using curvilinear coordinates along and normal to streamlines. Upstream weighting is included but automatically controlled and limited to one dimension along the main flow direction. Second, the subdomain collocation procedure is formulated in the vertical dimension. Spatial discretization of the three‐dimensional flow region is performed using a curvilinear finite element mesh that is point‐centered in the horizontal plane and block‐centered in the vertical direction. General algorithms are developed for mesh generation, time stepping and matrix reduction. The solution algorithm is designed to accommodate several thousand nodal unknowns with minimal core storage and CPU time requirement. Two simulation examples are presented to verify and validate the numerical model in two dimensions using an analytical solution and experimental laboratory and field data. A comparative study shows that the proposed formulation is superior to the standard Galerkin formulation in Cartesian coordinates both in terms of accuracy and computational efficiency. The field simulation example indicates the need to conduct a more elaborate three‐dimensional simulation study allowing for vertical variation in hydraulic conductivity. Such a study has been completed and is reported in the follow‐up p

ISSN:0043-1397    

DOI:10.1029/WR022i005p00663

年代:1986

数据来源: WILEY

摘要:

Many so‐called sandstone aquifers are actually multiple‐aquifer systems consisting of discontinuous sand bodies distributed complexly in a matrix of lower‐permeability silts and clays. The arrangement and Interconnectedness of these various lithofacies strongly influence spatial patterns of hydraulic conductivity (K) and, in turn, groundwater flow and mass transport. A promising technique of estimating such patterns ofKinvolves careful analysis of both subsurface geologic and subsurface hydrologic data. In this study the three‐dimensional distribution ofKwas estimated for a numerical flow model of part of the Wilcox aquifer system in Texas, usingKdata from core samples and pumping tests and more than 100 geophysical logs. The aquifer system, which is up to 320 m thick, consists of multiple, elongate sand bodies and silts and clays deposited in a fluvial environment and is similar to many other systems found in the Gulf Coast and other sedimentary basins. The resulting deterministic‐conceptual flow model demonstrates the importance and methods of incorporating geologic information in groundwater models. Flow in the aquifer is shown to be controlled not so much byKof the sands as by their continuity and Interconnectedness. Much of the aquifer system consists of large zones in which the fluvial channel‐fill sands are sparse and apparently disconnected, resulting in groundwater flow rates lower by a factor of 101to 103than in adjacent, well‐interconnected belts of fluvial channel‐fill sand belts. Modeling results also raise serious doubts regarding our ability to predict regional scale flow and mass transport in complex aquifers such as the Wilcox, using current technology. Though sand body Interconnectedness is critically important, it is also very difficult to estimate. One or two well‐connected sands among a system of otherwise disconnected sands can completely alter a velocity field. This is particularly true if the sands are connected vertically and nonzero vertical hydraulic gradients exist. Because the model is three‐dimensional, sensitivity of hydraulic head to heterogeneity or Interconnectedness is much less than normally observed in two‐dimensional models, and therefore heads computed by the model give little to no indication of the location of well‐interconnected zones. Thus such zones can easily go undetected, even in carefully calibrated models which yield reasonably accurate hydraulic heads. This is a significant point for model

ISSN:0043-1397    

DOI:10.1029/WR022i005p00679

年代:1986

数据来源: WILEY