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1.
As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations.  相似文献   

2.
Within the framework of stochastic theory and the spectral perturbation techniques, three-dimensional dispersion in partially saturated soils with fractal log hydraulic conductivity distribution is analyzed. Our analysis is focused on the impact of fractal dimension of log hydraulic conductivity distribution, local dispersivity, and unsaturated flow parameters, such as the soil poresize distribution parameter and the moisture distribution parameter, on the spreading behavior of solute plume and the concentration variance. Approximate analytical solutions to the stochastic partial differential equations are derived for the variance of asymptotic solute concentration and asymptotic macrodispersivities.  相似文献   

3.
J. Lewis 《Ground water》2016,54(5):740-744
This technical note describes an effective and inexpensive field technique for measuring the saturated hydraulic conductivity of both undisturbed cores and repacked soil samples. The method requires no specialized equipment; everything that is required can be obtained in a hardware store. The method is a straightforward field implementation of the widely used falling‐head laboratory analysis directly derived from Darcy's law. As such, it sidesteps the need for empirical assumptions about soil texture and the relationship between saturated and unsaturated flow components which many permeameter‐based methods rely upon. The method is shown to produce results that are consistent with K values obtained elsewhere in the same homogeneous sand formation. Furthermore, the proposed method is useful for measuring hydraulic conductivity in drill cuttings obtained from direct push or auguring drill techniques, which cannot be done with any other field method. The range of hydraulic conductivity values that this test is appropriate for is on the order of 1E ? 7 m/s to 1E ? 3 m/s.  相似文献   

4.
The impact of three-dimensional subsurface heterogeneity in the saturated hydraulic conductivity on hillslope runoff generated by excess infiltration (so-called Hortonian runoff) is examined. A fully coupled, parallel subsurface–overland flow model is used to simulate runoff from an idealized hillslope. Ensembles of correlated, Gaussian random fields of saturated hydraulic conductivity are used to create uncertainty in spatial structure. A large number of cases are simulated in a parametric manner with the variance of the hydraulic conductivity varied over orders of magnitude. These cases include rainfall rates above, equal and below the geometric mean of the hydraulic conductivity distribution. These cases are also compared to theoretical representations of runoff production based on simple assumptions regarding (1) the rainfall rate and the value of hydraulic conductivity in the surface cell using a spatially-indiscriminant approach; and (2) a percolation-theory type approach to incorporate so-called runon. Simulations to test the ergodicity of hydraulic conductivity on hillslope runoff are also performed. Results show that three-dimensional stochastic representations of the subsurface hydraulic conductivity can create shallow perching, which has an important effect on runoff behavior that is different than previous two-dimensional analyses. The simple theories are shown to be very poor predictors of the fraction of saturated area that might runoff due to excess infiltration. It is also shown that ergodicity is reached only for a large number of integral scales (∼30) and not achieved for cases where the rainfall rate is less than the geometric mean of the saturated hydraulic conductivity.  相似文献   

5.
The hydraulic properties of the topsoil control the partition of rainfall into infiltration and runoff at the soil surface. They must be characterized for distributed hydrological modelling. This study presents the results of a field campaign documenting topsoil hydraulic properties in a small French suburban catchment (7 km2) located near Lyon, France. Two types of infiltration tests were performed: single ring infiltration tests under positive head and tension‐disk infiltration using a mini‐disk. Both categories were processed using the BEST—Beerkan Estimation of Soil Transfer parameters—method to derive parameters describing the retention and hydraulic conductivity curves. Dry bulk density and particle size data were also sampled. Almost all the topsoils were found to belong to the sandy loam soil class. No significant differences in hydraulic properties were found in terms of pedologic units, but the results showed a high impact of land use on these properties. The lowest dry bulk density values were obtained in forested soils with the highest organic matter content. Permanent pasture soils showed intermediate values, whereas the highest values were encountered in cultivated lands. For saturated hydraulic conductivity, the highest values were found in broad‐leaved forests and small woods. The complementary use of tension‐disk and positive head infiltration tests highlighted a sharp increase of hydraulic conductivity between near saturation and saturated conditions, attributed to macroporosity effect. The ratio of median saturated hydraulic conductivity to median hydraulic conductivity at a pressure of − 20 mm of water was about 50. The study suggests that soil texture, such as used in most pedo‐transfer functions, might not be sufficient to properly map the variability of soil hydraulic properties. Land use information should be considered in the parameterizations of topsoil within hydrological models to better represent in situ conditions, as illustrated in the paper. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

6.
The identification of groundwater parameters in heterogeneous systems is a major challenge in groundwater modeling. Flexible parameterization methods are needed to assess the complexity of the spatial distributions of these parameters in real aquifers. In this article, we introduce an adaptative parameterization to identify the distribution of hydraulic conductivity within the large‐scale (4400 km2) Upper Rhine aquifer. The method is based on adaptative multiscale triangulation (AMT) coupled with an inverse problem procedure that identifies the parameters' distributions by reducing the error between measured and simulated heads. The AMT method has the advantage of combining both zonation and interpolation approaches. The AMT method uses area‐based interpolation rather than an interpolation based on stochastic features. The method is applied to a standard 2D groundwater model that takes into account the interactions between the aquifer and surface water bodies, groundwater recharge, and pumping wells. The simulation period covers 204 months, from January 1986 to December 2002. Recordings at 109 piezometers are used for model calibration. The simulated heads are globally quite accurate and reproduce the main dynamics of the system. The local hydraulic conductivities resulting from the AMT method agree qualitatively with existing local experimental observations across the Rhine aquifer.  相似文献   

7.
Pumping test data for surficial aquifers are commonly analyzed under the assumption that the base of the aquifer corresponds to the bottom of the test wells (i.e., the aquifer is truncated). This practice can lead to inaccurate hydraulic conductivity estimates, resulting from the use of low saturated thickness values with transmissivity estimates, and not accounting for the effects of partially penetrating wells. Theoretical time-drawdown data were generated at an observation well in a hypothetical unconfined aquifer for various values of saturated thickness and were analyzed by standard curve-matching techniques. The base of the aquifer was assumed to be the bottom of the pumping and observation wells. The overestimation of horizontal hydraulic conductivity was found to be directly proportional to the error in assumed saturated thickness, and to the (actual) ratio of vertical to horizontal hydraulic conductivity (Kv/Kh). Inaccurately high estimates of hydraulic conductivity obtained by aquifer truncation can lead to overestimates of ground water velocity and contaminant plume spreading, narrow capture zone configuration estimates, and overestimates of available ground water resources.  相似文献   

8.
The strong vertical gradient in soil and subsoil saturated hydraulic conductivity is characteristic feature of the hydrology of catchments. Despite the potential importance of these strong gradients, they have proven difficult to model using robust physically based schemes. This has hampered the testing of hypotheses about the implications of such vertical gradients for subsurface flow paths, residence times and transit time distribution. Here we present a general semi‐analytical solution for the simulation of 2D steady‐state saturated‐unsaturated flow in hillslopes with saturated hydraulic conductivity that declines exponentially with depth. The grid‐free solution satisfies mass balance exactly over the entire saturated and unsaturated zones. The new method provides continuous solutions for head, flow and velocity in both saturated and unsaturated zones without any interpolation process as is common in discrete numerical schemes. This solution efficiently generates flow pathlines and transit time distributions in hillslopes with the assumption of depth‐varying saturated hydraulic conductivity. The model outputs reveal the pronounced effect that changing the strength of the exponential decline in saturated hydraulic conductivity has on the flow pathlines, residence time and transit time distribution. This new steady‐state model may be useful to others for posing hypotheses about how different depth functions for hydraulic conductivity influence catchment hydrological response. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

9.
Numerical modeling of groundwater-surface water interactions provides vital information necessary for determining the extent of nutrient transport, quantifying water budgets, and delineating zones of ecological support. The hydrologic data that drive these models are often collected at disparate scales and subsequently incorporated into numerical models through upscaling techniques such as piecewise constancy or geostatistical methods. However, these techniques either use basic interpolation methods, which often simplifies the system of interest, or utilize complex statistical methods that are computationally expensive, time consuming, and generate complex subsurface configurations. We propose a bulk parameter termed “vertically integrated hydraulic conductivity” (KV), and defined as the depth-integrated resistance to fluid flow sensed at the groundwater-surface water interface, as an alternative to hydraulic conductivity when investigating vertical fluxes across the groundwater-surface water interface. This bulk parameter replaces complex subsurface configurations in situations dominated by vertical fluxes and where heterogeneity is not of primary importance. To demonstrate the utility of KV, we extracted synthetic temperature time series data from a forward numerical model under a variety of scenarios and used those data to quantify vertical fluxes using the amplitude ratio method. These quantified vertical fluxes and the applied hydraulic head gradient were subsequently input into Darcy's Law and used to quantify KV. This KV was then directly compared to the equivalent hydraulic conductivity (KT) assuming an infinitely extending layer. Vertically integrated hydraulic conductivity allows for more accurate and robust flow modeling across the groundwater-surface water interface in instances where complex heterogeneities are not of primary concern.  相似文献   

10.
Abstract. MRCON is an interactive computer program designed to approximate soil moisture retention ( Θ-Ψ ) and/or unsaturated hydraulic conductivity (K- Θ ) for soils. MRCON, which is written in BASIC, uses empirical methods obtained from the literature to calculate K- Θ and a modified method to calculate Θ-Ψ . Input data for the program consist of a saturated moisture content and a minimum of three values of Θ-Ψ . A measured value of saturated hydraulic conductivity can be used as input to better approximate the K -Θ curves to field conditions.  相似文献   

11.
Modeling unsaturated flow in porous media requires constitutive relations that describe the soil water retention and soil hydraulic conductivity as a function of either potential or water content. Often, the hydraulic parameters that describe these relations are directly measured on small soil cores, and many cores are needed to upscale to the entire heterogeneous flow field. An alternative to the forward upscaling method using small samples are inverse upscaling methods that incorporate soft data from geophysical measurements observed directly on the larger flow field. In this paper, we demonstrate that the hydraulic parameters can be obtained from cross borehole ground penetrating radar by measuring the first arrival travel time of electromagnetic waves (represented by raypaths) from stationary antennae during a constant flux infiltration experiment. The formulation and coupling of the hydrological and geophysical models rely on a constant velocity wetting front that causes critical refraction at the edge of the front as it passes by the antennae. During this critical refraction period, the slope of the first arrival data can be used to calculate (1) the wetting velocity and (2) the hydraulic conductivity of the wet (or saturated) soil. If the soil is undersaturated during infiltration, then an estimate of the saturated water content is needed before calculating the saturated hydraulic conductivity. The hydraulic conductivity value is then used in a nonlinear global optimization scheme to estimate the remaining two parameters of a Broadbridge and White soil.  相似文献   

12.
We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions.  相似文献   

13.
We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions.  相似文献   

14.
Testing infiltrometer techniques to determine soil hydraulic properties is necessary for specific soils. For a loam soil, the water retention and hydraulic conductivity predicted by the BEST (Beerkan Estimation of Soil Transfer parameters) procedure of soil hydraulic characterization was compared with data collected by more standard laboratory and field techniques. Six infiltrometer techniques were also compared in terms of saturated soil hydraulic conductivity, Ks. BEST yielded water retention values statistically similar to those obtained in the laboratory and Ks values practically coinciding with those determined in the field with the pressure infiltrometer (PI). The unsaturated soil hydraulic conductivity measured with the tension infiltrometer (TI) was reproduced satisfactorily by BEST only close to saturation. BEST, the PI, one‐potential experiments with both the TI and the mini disk infiltrometer (MDI), the simplified falling head (SFH) technique and the bottomless bucket (BB) method yielded statistically similar estimates of Ks, differing at the most by a factor of three. Smaller values were obtained with longer and more soil‐disturbing infiltration runs. Any of the tested infiltration techniques appears usable to obtain the order of magnitude of Ks at the field site, but the BEST, BB and PI data appear more appropriate to characterize the soil at some stage during a rainfall event. Additional investigations on both similar and different soils would allow development of more general procedures to apply infiltrometer techniques for soil hydraulic characterization. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

15.
The process of attempting to model ground-water systems requires a good understanding of the spatial variation of aquifer hydraulic properties. The capabilities of the more recent innovative flowmeters such as the electromagnetic and heat pulse flowmeters provide the sensitivity to measure ambient flows and pump-induced flows. These flowmeters provide the measurements of pump-induced vertical flows which are analyzed to obtain vertical variations in horizontal hydraulic conductivity, K(z). With discrete areal K-values, K(x, y), and vertical profiles of K, provided by multiwell testing, the essential elements are present to produce a three-dimensional hydraulic conductivity field. The advent of these new flow measuring devices has contributed much to the motivation behind this paper. This paper presents the results of applying deterministic and stochastic methodology to the three-dimensional interpolation of hydraulic properties, specifically, hydraulic conductivity, K. Three of the approaches applied in this paper are deterministic in nature, inverse-distance weighting, inverse-distance-squared weighting, and ordinary kriging, while the fourth is a stochastic approach based on self-affine fractals. All of the methods are applied to measured data collected from 14 wells at a site in the United States near Mobile, Alabama. The three-dimensional K-distributions generated by each of the methods are used as inputs to an advective based transport model with the resulting model output compared to a two-well tracer study run previously at the same site.  相似文献   

16.
Characterization of shale reservoirs, which are typically of low permeability, is very difficult because of the presence of multiscale structures. While three-dimensional (3D) imaging can be an ultimate solution for revealing important complexities of such reservoirs, acquiring such images is costly and time consuming. On the other hand, high-quality 2D images, which are widely available, also reveal useful information about shales’ pore connectivity and size. Most of the current modeling methods that are based on 2D images use limited and insufficient extracted information. One remedy to the shortcoming is direct use of qualitative images, a concept that we introduce in this paper. We demonstrate that higher-order statistics (as opposed to the traditional two-point statistics, such as variograms) are necessary for developing an accurate model of shales, and describe an efficient method for using 2D images that is capable of utilizing qualitative and physical information within an image and generating stochastic realizations of shales. We then further refine the model by describing and utilizing several techniques, including an iterative framework, for removing some possible artifacts and better pattern reproduction. Next, we introduce a new histogram-matching algorithm that accounts for concealed nanostructures in shale samples. We also present two new multiresolution and multiscale approaches for dealing with distinct pore structures that are common in shale reservoirs. In the multiresolution method, the original high-quality image is upscaled in a pyramid-like manner in order to achieve more accurate global and long-range structures. The multiscale approach integrates two images, each containing diverse pore networks – the nano- and microscale pores – using a high-resolution image representing small-scale pores and, at the same time, reconstructing large pores using a low-quality image. Eventually, the results are integrated to generate a 3D model. The methods are tested on two shale samples for which full 3D samples are available. The quantitative accuracy of the models is demonstrated by computing their morphological and flow properties and comparing them with those of the actual 3D images. The success of the method hinges upon the use of very different low- and high-resolution images.  相似文献   

17.
Measurement of the saturated hydraulic conductivity of material in the unsaturated zone beneath proposed surface impoundments is important for predicting seepage rates of water and contaminants. Hazardous waste disposal facilities are commonly sited on the basis of the low permeability of the geologic materials beneath the site. Field measurement of the saturated hydraulic conductivity of low-permeability materials may be accomplished using air-entry permeameters and borehole permeameters. The results of a coordinated field and laboratory investigation of low-permeability materials at a hazardous waste facility are presented. The different methods of testing and analysis are compared and discussed. In general, air-entry permeameters and borehole permeameters are useful for measuring the saturated hydraulic conductivity of low-permeability materials.  相似文献   

18.
Characterization of groundwater contaminant source using Bayesian method   总被引：2，自引：1，他引：1  
Contaminant source identification in groundwater system is critical for remediation strategy implementation, including gathering further samples and analysis, as well as implementing and evaluating different remediation plans. Such problem is usually solved with the aid of groundwater modeling with lots of uncertainty, e.g. existing uncertainty in hydraulic conductivity, measurement variance and the model structure error. Monte Carlo simulation of flow model allows the input uncertainty onto the model predictions of concentration measurements at monitoring sites. Bayesian approach provides the advantage to update estimation. This paper presents an application of a dynamic framework coupling with a three dimensional groundwater modeling scheme in contamination source identification of groundwater. Markov Chain Monte Carlo (MCMC) is being applied to infer the possible location and magnitude of contamination source. Uncertainty existing in heterogonous hydraulic conductivity field is explicitly considered in evaluating the likelihood function. Unlike other inverse-problem approaches to provide single but maybe untrue solution, the MCMC algorithm provides probability distributions over estimated parameters. Results from this algorithm offer a probabilistic inference of the location and concentration of released contamination. The convergence analysis of MCMC reveals the effectiveness of the proposed algorithm. Further investigation to extend this study is also discussed.  相似文献   

19.
Highly resolved simulations of groundwater flow, chemical migration and contaminant recovery processes are used to test the applicability of stochastic models of flow and transport in a typical field setting. A simulation domain encompassing a portion of the upper saturated aquifer materials beneath the Lawrence Livermore National Laboratory was developed to hierarchically represent known hydrostratigraphic units and more detailed stochastic representations of geologic heterogeneity within them. Within each unit, Gaussian random field models were used to represent hydraulic conductivity variation, as parameterized from well test data and geologic interpretation of spatial variability. Groundwater flow, transport and remedial extraction of two hypothetical contaminants were made in six different statistical realizations of the system. The effective flow and transport behavior observed in the simulations compared reasonably with the predictions of stochastic theories based upon the Gaussian models, even though more exacting comparisons were prevented by inherent nonidealities of the geologic model and flow system. More importantly, however, biases and limitations in the hydraulic data appear to have reduced the applicability of the Gaussian representations and clouded the utility of the simulations and effective behavior based upon them. This suggests a need for better and unbiased methods for delineating the spatial distribution and structure of geologic materials and hydraulic properties in field systems. High performance computing can be of critical importance in these endeavors, especially with respect to resolving transport processes within highly variable media.©1998 Elsevier Science Limited. All rights reserved  相似文献   

20.
The renormalization group (RG) approach is a powerful theoretical framework, more suitable for upscaling strong heterogeneity than low-order perturbation expansions. Applications of RG methods in subsurface hydrology include the calculation of (1) macroscopic transport parameters such as effective and equivalent hydraulic conductivity and dispersion coefficients, and (2) anomalous exponents characterizing the dispersion of contaminants due to long-range conductivity correlations or broad (heavy-tailed) distributions of the groundwater velocity. First, we review the main ideas of RG methods and their hydrological applications. Then, we focus on the hydraulic conductivity in saturated porous media with isotropic lognormal heterogeneity, and we present an RG calculation based on the replica method. The RG analysis gives rigorous support to the exponential conjecture for the effective hydraulic conductivity [Water Resour. Res. 19 (1) (1983) 161]. Using numerical simulations in two dimensions with a bimodal conductivity distribution, we demonstrate that the exponential expression is not suitable for all types of heterogeneity. We also introduce an RG coarse-grained conductivity and investigate its applications in estimating the conductivity of blocks or flow domains with finite size. Finally, we define the fractional effective dimension, and we show that it justifies fractal exponents in the range 1−2/dα<1 (where d is the actual medium dimension) in the geostatistical power average.  相似文献   

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