摘要:

Numerical models that solve governing equations for subsurface fluid flow and transport are commonly applied to analyze quantitatively the effects of heterogeneity. These models require maps of spatially variable hydraulic properties. Because complete three‐dimensional information about hydraulic properties is never obtainable, numerous methods have been developed to interpolate between data values and use geologic, hydrogeologic, and geophysical information to create images of aquifer properties. Image creation approaches fall into three general categories: structure‐imitating, process‐imitating, and descriptive. Structure‐imitating methods rely on one or more of the following to constrain the geometry of spatial patterns in geologic media: correlated random fields, probabilistic rules, and deterministic constraints developed from facies relations. Structure‐imitating methods include spatial statistical algorithms and geologically based sedimentation pattern‐matching approaches. Process‐imitating models include aquifer model calibration methods and geologic process models. Aquifer model calibration methods use governing equations for subsurface fluid flow and transport to relate hydraulic properties to heads and solute information through history and steady state data matching. Geologic process models combine fundamental laws of conservation of mass and momentum with sediment transport equations to simulate spatial patterns in grain size distributions. At the sedimentary basin scale, multiprocess models include thermomechanical mechanisms of basin subsidence. Descriptive methods couple geologic observations with facies relations to divide an aquifer into zones of characteristic hydraulic properties. All approaches are capable of reproducing heterogeneity over a range of scales and considering some types of geologic information. Some approaches are strictly spatial while some are linked to the time evolution of sedimentation. Some approaches can be conditioned on measurements. Recent advances aimed at infusing geologic information into images of the subsurface include extracting more information from sedimentological facies models, incorporating qualitative geologic information into random field generators and simulating depositional processes. Classes of research missing from the literature include multiprocess models that incorporate diagenesis and three‐dimensional surface water flow, hybrid methods that combine features of existing approaches, and approaches that can make use of all available geologic, geophysical, and

ISSN:0043-1397    

DOI:10.1029/96WR00025

年代:1996

数据来源: WILEY

摘要:

The identification of aquifer heterogeneities, particularly flow paths and barriers, has become a critical research topic in hydrology. Cross‐well seismic tomography may provide the needed resolution when used in conjunction with hydraulic head and tracer concentration measurements. We demonstrate a field application and sensitivity analysis of the split inversion method (SIM), which combines seismic, hydraulic, and tracer data to estimate the three‐dimensional zonation of aquifer properties along with the hydraulic properties for these zones. For the Kesterson aquifer in the San Joaquin Valley, California, we first invert seismic travel times measured between six well pairs to obtain seismic slowness (1/seismic velocity) cross sections, or tomograms. We then use conditional simulation to provide three‐dimensional seismic slowness realizations. Next, the SIM is used to split several realizations into three lithologic zones and assign hydraulic properties to the zones to best match six tracer concentration hist

ISSN:0043-1397    

DOI:10.1029/96WR01269

年代:1996

数据来源: WILEY

摘要:

In this paper we show that given prior information in terms of a lower and upper bound, a prior bias, and constraints in terms of measured data, minimum relative entropy (MRE) yields exact expressions for the posterior probability density function (pdf) and the expected value of the linear inverse problem. In addition, we are able to produce any desired confidence intervals. In numerical simulations, we use the MRE approach to recover the release and evolution histories of plume in a one‐dimensional, constant known velocity and dispersivity system. For noise‐free data, we find that the reconstructed plume evolution history is indistinguishable from the true history. An exact match to the observed data is evident. Two methods are chosen for dissociating signal from a noisy data set. The first uses a modification of MRE for uncertain data. The second method uses “presmoothing” by fast Fourier transforms and Butterworth filters to attempt to remove noise from the signal before the “noise‐free” variant of MRE inversion is used. Both methods appear to work very well in recovering the true signal, and qualitatively appear superior to that ofSkaggs and Kabala[1994]. We also solve for a degenerate case with a very high standard deviation in the noise. The recovered model indicates that the MRE inverse method did manage to recover the salient features of the source history. Once the plume source history has been developed, future behavior of a plume can then be cast in a probabilistic framework. For an example simulation, the MRE approach not only was able to resolve the source function from noisy data but also was able to correctly predict fu

ISSN:0043-1397    

DOI:10.1029/95WR03818

年代:1996

数据来源: WILEY

摘要:

Tension disc infiltrometers are becoming increasingly popular devices for in situ measurement of the unsaturated hydraulic properties of soil. Tension infiltration data are generally used to evaluate the parametersKsand α in Gardner's exponential model of the unsaturated hydraulic conductivity. Either two measurements using different disc diameters or measurements with a single disc but using multiple pressure heads are then used. In this paper we describe a parameter estimation procedure which combines the Levenberg‐Marquardt nonlinear parameter optimization method involving weighted least squares, with a quasi‐three‐dimensional numerical model which solves the variably saturated flow equation. By numerical inversion of Richards' equation the unknown parameters in van Genuchten's model of the unsaturated soil‐hydraulic properties are estimated from observed cumulative infiltration data during transient water flow. Additional measurements of the pressure head or water content, as well as a penalty function for constraining the unknown parameters to remain in some feasible region (Bayesian estimation), can be optionally included into the parameter estimation procedure. The problem of optimal sampling design, that is, selecting the best points in space and time for making measurements, is addressed by studying the sensitivity of the objective function to changes in the optimized hydraulic parameters. We calculate objective functions based on available cumulative infiltration, pressure head, and water content measurements and also on several combinations of these data. The behavior of the objective function in three‐dimensional parameter space is evaluated by means of a series of two‐dimensional response surfaces. The utility of the parameter estimation procedure is demonstrated using numerically generated data. The sensitivity of the procedure to different initial estimates of the model parameters is al

ISSN:0043-1397    

DOI:10.1029/96WR01525

年代:1996

数据来源: WILEY

摘要:

The soil water retention model developed by Kosugi was modified to be compatible with Mualem's model in order to derive an analytical expression for the relative hydraulic conductivityKr. The modified water retention model is to be derived by applying a lognormal distribution law to the soil pore radius distribution function. Parameters of this retention model have physical significance on the water content (θ)– capillary pressure (ψ) curve and are related directly to the statistics of the pore radius distribution. The accuracy of the resulting combined water‐retention‐hydraulic‐conductivity model is verified for observed data sets for six soils. Results showed that the proposed model produces acceptable matches with observed water retention curves and adequate predictions of hydraulic conductivities in five out of six cases. The θ − ψ andKr− ψ (orKr− θ) curves generated by this model are generally similar to those generated by va

ISSN:0043-1397    

DOI:10.1029/96WR01776

年代:1996

数据来源: WILEY

摘要:

A three‐dimensional interpretation of the Borden Site experiment is proposed with the aid of a recently developed stochastic model that incorporates transiency of the piezometric head gradient. The behavior of the second‐order central transverse plume moments is analyzed with the aim of explaining the underprediction of experimental results by existing steady state models. The model assumes uniformity in space, but time varying mean head gradient, stationary and anisotropic log conductivity, and a first‐order approximation in the log conductivity variance. The solution for the trajectory covariances, assumed to be equal to the plume spatial second moments under ergodic conditions, is evaluated with the aid of a few quadratures. An analysis of the parameters and plume spatial moments found in the literature precedes application of the model. It is found that unsteadiness leads to an increase in the transverse, horizontal, second moment compared with the one based on a steady state flow model. Still, application of Borden Site data leads to values lower than the ones inferred from concentration measurements. We conclude that unsteadiness of the mean head gradient does not fully explain the magnitude of observed transverse spreading. However, the impact of transients on spreading is significant in the transverse direction, and the definition of a Fickian transverse dispersion coefficient may not be a simple task for transport occurring under natural flow condi

ISSN:0043-1397    

DOI:10.1029/96WR01629

年代:1996

数据来源: WILEY

摘要:

Recently, an exact Eulerian‐Lagrangian theory of advective transport in space‐time random velocity fields was developed by one of us. We present a formal extension of this theory that accounts for anisotropic local dispersion. The resultant (conditional) mean transport equation is generally nonlocal in space‐time. To assess the impact of local dispersion on the prediction of transport under uncertainty, we adopt a first‐order pseudo‐Fickian approximation for this equation. We then solve it numerically by Galerkin finite elements for two‐dimensional transport from an instantaneous square source in a uniform (unconditional) mean flow field subject to isotropic local dispersion. We use a higher‐order approximation to compute explicitly the standard deviation and coefficient of variation of the predicted concentrations. Our theory shows (in an exact manner), and our numerical results demonstrate (under the above closure approximations), that the effect of local dispersion on first and second concentration moments varies monotonically with the magnitude of the local dispersion coefficient. When this coefficient is small relative to macrodispersion, its effect on the prediction of nonreactive transport under uncertainty can, for all practical purposes, be disregarded. This is contrary to some recent assertions in the literature that local dispersion must always be taken into account, no mat

ISSN:0043-1397    

DOI:10.1029/96WR01335

年代:1996

数据来源: WILEY

摘要:

By using analytic elements to model steady state, two‐dimensional, Dupuit‐Forchheimer groundwater flow and its contribution to surface water flow, average base flows and groundwater flows in a groundwater and surface water system can be represented. Changing boundary conditions are modeled by adding or removing streams from the groundwater flow domain according to the availability of water in the stream. This dynamic representation of boundary conditions allows for the anticipation of unknown effects due to future aquifer stresses or stream withdrawals. The model does not account for transient streamflow but significantly improves the realism of steady state surface water and groundwater interactions by simulating average base flows and limiting the infiltration rates of losing streams. When steady state groundwater flow is modeled without considering the limits of available streamflow, recharge rates or hydraulic conductivities that are estimated during model calibration can be substantially in error. The capability to model groundwater and surface water conjunctively is accomplished without substantial increases in model complexity or data requireme

ISSN:0043-1397    

DOI:10.1029/96WR00900

年代:1996

数据来源: WILEY

摘要:

A dual‐porosity fractal model is derived that considers transient flow from block to fissure, skin between the fissure and the block, and storage capacity and skin effect on the pumping well. Type curves for different flow dimensions are provided. They concern the pumping well and observation wells located either in the fissure system or in a matrix block. The interpretation of a field case using this model shows good agreement between the theoretical drawdown and the observed data, with consistent results from the pumping well and the observation well. A flow dimension of 1.45 is obtaine

ISSN:0043-1397    

DOI:10.1029/96WR01464

年代:1996

数据来源: WILEY

摘要:

Adsorbing solute transport in two‐dimensional heterogeneous unsaturated soil was studied by means of stochastic numerical simulations. Heterogeneities in the soil's hydraulic properties and in the adsorption isotherm were simulated using random fields having specified statistical structures. Macrodispersion was analyzed using the spatial moments of numerically generated solute plumes. Among different realizations of the heterogeneous soil, the discrepancies between second‐order moments and macrodispersion coefficients were large. Macrodispersivities of unsaturated soils increased with decreasing water content. Also, heterogeneous adsorption of solute enhanced the solute spreading. When the adsorption coefficient was negatively correlated with the saturated hydraulic conductivity, solute spreading was greater than when adsorption was uncorrelated or positively correlated with the conductiv

ISSN:0043-1397    

DOI:10.1029/96WR01101

年代:1996

数据来源: WILEY