摘要:

Relating the variability of permeability to the variability of head is a central part of linear estimation techniques such as cokriging. Only a few analytic relationships between log permeability covariances and head covariances presently exist. This paper describes a general numerical procedure which computes head covariances (ordinary or generalized) and cross covariances for any proper log permeability covariance. The numerical spectral method, a discrete analog of Fourier‐Stieltjes analysis, employs the pertinent linearized (small‐perturbation approximation) equations describing the physics of flow. The domain is taken as finite, with boundary effects considered negligible. The numerical spectral method can reproduce all pertinent analytic results with excellent agreement. Furthermore, we demonstrate the method's generality by finding the covariance relations for a case where no analytical results presently ex

ISSN:0043-1397    

DOI:10.1029/WR025i011p02287

年代:1989

数据来源: WILEY

摘要:

We describe and evaluate two previously undocumented methods of bulk permeability (K) determination and compare results obtained with results of conventional smaller‐scale tests on the same thick clayey till deposit. Analysis of the downward propagation of seasonal water table fluctuations yielded bulkKof approximately 10−10m s−1, in close agreement with results of laboratory consolidation and permeameter tests, slug tests, and distribution of vertical hydraulic gradient with depth in the deposit. This agreement suggests that for such materials, high‐gradient tests conducted at small scales of distance and time can provide reasonable estimates of bulkK. The results also imply groundwater residence times in the till of thousands of years. The flow pattern observed near a large excavation in the till was consistent with the initial recoveries of piezometers installed in much smaller boreholes, assuming perturbation of hydraulic head in the formation due to borehole excavation. Time scales of these perturbations, which prevent interpretation of measured hydraulic head using conventional well hydraulic methods, varied from months to tens o

ISSN:0043-1397    

DOI:10.1029/WR025i011p02299

年代:1989

数据来源: WILEY

摘要:

The estimation of design floods is, in practice, often based on small samples of data, which may cause a severe uncertainty. For a particular version of the partial duration series (exponentially distributed exceedances and Poissonian occurrence times) the distribution of theT‐year design estimatexˆTis derived along with the distribution ofRT; defined as the true risk of exceedingxˆTwithin a given disposal period. For a fixed flood level the distributions of the return period estimatorTˆand the estimator of the risk in lifetimeRˆare also presented. Analytical closed‐form expressions for mean value and standard deviation are derived for these variables, except forTˆ, which does not possess moments. The concept of “expected risk” is introduced, and an analytical expression describing this property is derived. A risk‐based design technique, which is essentially different from the traditional procedure, is presented, and its applicability is verified using Monte Ca

ISSN:0043-1397    

DOI:10.1029/WR025i011p02319

年代:1989

数据来源: WILEY

摘要:

Stochastic analyses of subsurface transport indicate that the concentration distributions of individual solute plumes may deviate significantly from those predicted by unconditional ensemble statistics, particularly in near‐source regions. This paper presents a method for developing improved concentration predictions which are tailored to site‐specific conditions. The improved predictions are obtained by conditioning ensemble moments on field observations of log hydraulic conductivity, head, and solute concentration. The conditional moments are obtained from a distributed parameter Kaiman filter which is recursively linearized about the most recent estimates of solute concentration and velocity. The conditioning procedure is illustrated for two synthetic random solute plumes. Reasonably good estimates of the solute concentration distributions are obtained by conditioning the ensemble moments on a small number of measurements located in regions of high concentration uncertainty. The sampling networks adapt to the unique characteristics of each plume as they evolve over time. The example indicates that it is important to capture the dominant trends of the velocity field at as early a time as possible. As more measurements become available, advection accounts for a greater portion of small‐scale velocity variability, and the magnitude of the macrodispersion term diminishes. This is reflected in the behavior of the conditional ensemble mo

ISSN:0043-1397    

DOI:10.1029/WR025i011p02331

年代:1989

数据来源: WILEY

摘要:

Sorptive processes which accompany unidimensional solute flow through a porous medium can be modeled in terms of rate‐limiting isotherms. Both the rate limitations and dispersive processes combine to degrade or distend an otherwise sharp solute front initially introduced to the “column” as a step. Whenever dispersion is the dominant distending mechanism, the model simulation can be well approximated by replacement of the isotherm with a local equilibrium assumption (LEA). Conversely, if kinetics dominate distension, the neglect of dispersion can provide an efficacious approximant. I develop and illustrate the double Laplace‐like approximation (DLA) as a useful approximant when neither of these extremes is realized. The development is for a simulation model of unidimensional dispersive and advective transport which, in its most general form, incorporates combined linear Freundlich and rate‐limited isotherms, and first‐order loss, as formulated in paper 1 of this series (Lassey, 1988a). The DLA is about as computationally onerous as the LEA and the nondispersive assumption (NDA). The DLA‐predicted gradients of solute and sorbed concentration at the front are related to the Péclet and Damköhler numbers (characteristic of dispersion and kinetics, respectively), and include as special cases those predicted by the LEA and NDA. A numerical survey of the three approximants indicates that, for a propagating solute front of relatively minor distension, the DLA is the super

ISSN:0043-1397    

DOI:10.1029/WR025i011p02357

年代:1989

数据来源: WILEY

摘要:

Volumetric water contentθand soil electrical conductivity σ may be measured in situ using time domain reflectometry (TDR). The parallel‐wire or two‐wire transmission line TDR probes currently in field use suffer from unwanted noise and information loss due to impedance mismatch between the probe and the coaxial connecting cable. Here we describe symmetric, multiwire probes designed to minimize these problems and eliminate the need for a balancing transformer between probe and TDR device. Analysis of the electric field distributions around these new probes shows that they emulate a coaxial transmission line, and their measured characteristic probe impedances approach that of coaxial probes. Signals from the new probes permit more reliable and accurateθand σ measurement and are superior to those of two‐wire probes with balancing transformer. The enhanced signal clarity of the new probes extends to sample diameters of at least 0.2 m. We show that electrical conductivity determined with the new probes is identical to that found with a coaxial cell and substantially different from that measured by a two‐wire probe. Our results indicate that values of σ, determined using the Giese‐Tiemann thin sample approach and measured characteristic probe impedances of coaxial or multiwire probes, agree with values of σ measured using an ac bridge for both electrolyte solutions and soil samples to within ±10%, provided σ exceeds 10 mS m−1. Finally, we give an example of the use of multiplexed three‐wire probes in following rainfall infiltration and redistribution during and after a simulated rainfall event in the field. Infiltrated quantities of water estimated from the TDR water content profiles agreed within ±10% w

ISSN:0043-1397    

DOI:10.1029/WR025i011p02367

年代:1989

数据来源: WILEY

摘要:

Pulse interference tests, which are conducted by monitoring the response in an observation well to a slug test conducted in a source well, are an attractive alternative to the pumping test method for determining the transmissivity and storativity of low‐storativity geological formations. An analytical model for analyzing the results of pulse interference tests affected by well bore storage in the observation well is developed in this paper using the Laplace transform method. By numerically inverting the Laplace space solution the practical range of the pulse interference test method and the influence of radial distance and well bore storage on the response in the observation well are explored. Results show that the influence of observation well storage can be significant, particularly for larger well bore storage coefficients and for almost all practical radial distances. In addition, a graphical method, based on the analytical model, is developed for analyzing the results of pulse interference tests in which observation well bore storage is negligible and for the case where the source and observation well storage coefficients are equal. A field example is also presented to illustrate and compare the use of the analytical model and graphical method for the field case where observation well storage is present and the case where it is no

ISSN:0043-1397    

DOI:10.1029/WR025i011p02377

年代:1989

数据来源: WILEY

摘要:

In this paper a generalized analytical frequency domain method for the evaluation of transmissivity tests is presented. For a confined homogeneous aquifer the Kelvin functions represent a satisfactory set of solutions for the equation of radial flow in the frequency domain. Depending on the type of transmissivity test, simple analytical frequency‐dependent transfer functions can be defined, which relate the reaction of the aquifer to any pressure disturbance. Hence a numerical Fourier transform of the field data can be performed to determine a transfer function of data, which can be fitted with the analytical one. In order to estimate the hydraulic parameters a special logarithmic Fourier transform was used to analyze synthetic data of a slug test to verify this approach. The consideration of transmissivity tests in the frequency domain leads to some promising prospects. With this method a radius of penetration for each excitation frequency can be defined. Furthermore, analytical solutions for radial symmetric permeability distributions are available (e.g., consideration of a gravel pack or a developed zone). The frequency domain approach is also extended to a new type of low‐cost transmissivity test, the hydraulic impedance t

ISSN:0043-1397    

DOI:10.1029/WR025i011p02388

年代:1989

数据来源: WILEY

ISSN:0043-1397    

DOI:10.1029/WR025i011p02397

年代:1989

数据来源: WILEY

ISSN:0043-1397    

DOI:10.1029/WR025i011p02398

年代:1989

数据来源: WILEY