共查询到20条相似文献，搜索用时 15 毫秒
1.
《Advances in water resources》1999,23(1):1-13
The self-calibrated method has been extended for the generation of equally likely realizations of transmissivity and storativity conditional to transmissivity and storativity data and to steady-state and transient hydraulic head data. Conditioning to transmissivity and storativity data is achieved by means of standard geostatistical co-simulation algorithms, whereas conditioning to hydraulic head data, given its non-linear relation to transmissivity and storativity, is achieved through non-linear optimization, similar to standard inverse algorithms. The algorithm is demonstrated in a synthetic study based on data from the WIPP site in New Mexico. Seven alternative scenarios are investigated, generating 100 realizations for each of them. The differences among the scenarios range from the number of conditioning data, to their spatial configuration, to the pumping strategies at the pumping wells. In all scenarios, the self-calibrated algorithm is able to generate transmissivity–storativity realization couples conditional to all the sample data. For the specific case studied here the results are not surprising. Of the piezometric head data, the steady-state values are the most consequential for transmissivity characterization. Conditioning to transient head data only introduces local adjustments on the transmissivity fields and serves to improve the characterization of the storativity fields. 相似文献
2.
José E. Capilla J. Rodrigo J. J. Gómez-Hernández 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(3):171-190
A common approach for the performance assessment of radionuclide migration from a nuclear waste repository is by means of
Monte-Carlo techniques. Multiple realizations of the parameters controlling radionuclide transport are generated and each
one of these realizations is used in a numerical model to provide a transport prediction. The statistical analysis of all
transport predictions is then used in performance assessment. In order to reduce the uncertainty on the predictions is necessary
to incorporate as much information as possible in the generation of the parameter fields. In this regard, this paper focuses
in the impact that conditioning the transmissivity fields to geophysical data and/or piezometric head data has on convective
transport predictions in a two-dimensional heterogeneous formation. The Walker Lake data based is used to produce a heterogeneous
log-transmissivity field with distinct non-Gaussian characteristics and a secondary variable that represents some geophysical
attribute. In addition, the piezometric head field resulting from the steady-state solution of the groundwater flow equation
is computed. These three reference fields are sampled to mimic a sampling campaign. Then, a series of Monte-Carlo exercises
using different combinations of sampled data shows the relative worth of secondary data with respect to piezometric head data
for transport predictions. The analysis shows that secondary data allows to reproduce the main spatial patterns of the reference
transmissivity field and improves the mass transport predictions with respect to the case in which only transmissivity data
is used. However, a few piezometric head measurements could be equally effective for the characterization of transport predictions. 相似文献
3.
José E. Capilla J. Rodrigo J. J. Gómez-Hernández 《Stochastic Hydrology and Hydraulics》1998,12(3):171-190
A common approach for the performance assessment of radionuclide migration from a nuclear waste repository is by means of
Monte-Carlo techniques. Multiple realizations of the parameters controlling radionuclide transport are generated and each
one of these realizations is used in a numerical model to provide a transport prediction. The statistical analysis of all
transport predictions is then used in performance assessment. In order to reduce the uncertainty on the predictions is necessary
to incorporate as much information as possible in the generation of the parameter fields. In this regard, this paper focuses
in the impact that conditioning the transmissivity fields to geophysical data and/or piezometric head data has on convective
transport predictions in a two-dimensional heterogeneous formation. The Walker Lake data based is used to produce a heterogeneous
log-transmissivity field with distinct non-Gaussian characteristics and a secondary variable that represents some geophysical
attribute. In addition, the piezometric head field resulting from the steady-state solution of the groundwater flow equation
is computed. These three reference fields are sampled to mimic a sampling campaign. Then, a series of Monte-Carlo exercises
using different combinations of sampled data shows the relative worth of secondary data with respect to piezometric head data
for transport predictions. The analysis shows that secondary data allows to reproduce the main spatial patterns of the reference
transmissivity field and improves the mass transport predictions with respect to the case in which only transmissivity data
is used. However, a few piezometric head measurements could be equally effective for the characterization of transport predictions. 相似文献
4.
Determination of hydraulic head, H, as a function of spatial coordinates and time, in ground water flow is the basis for aquifer management and for prediction of contaminant transport. Several computer codes are available for this purpose. Spatial distribution of the transmissivity, T(x,y), is a required input to these codes. In most aquifers, T varies in an erratic manner, and it can be characterized statistically in terms of a few moments: the expected value, the variance, and the variogram. Knowledge of these moments, combined with a few measurements, permits one to estimate T at any point using geostatistical methods. In a review of transmissivity data from 19 unconsolidated aquifers, Hoeksema and Kitanidis (1985) identified two types of the logtransmissivity Y= ln(T) variations: correlated variations with variance sigma2Yc and correlation scale, I(Y), on the order of kilometers, and uncorrelated variations with variance sigma2Yn. Direct identification of the logtransmissivity variogram, Gamma(Y), from measurements is difficult because T data are generally scarce. However, many head measurements are commonly available. The aim of the paper is to introduce a methodology to identify the transmissivity variogram parameters (sigma2Yc, I(Y), and sigma2Yn) using head data in formations characterized by large logtransmissivity variance. The identification methodology uses a combination of precise numerical simulations (carried out using analytic element method) and a theoretical model. The main objective is to demonstrate the application of the methodology to a regional ground water flow in Eagle Valley basin in west-central Nevada for which abundant transmissivity and head measurements are available. 相似文献
5.
Estimation of heterogeneous aquifer parameters from piezometric data using ridge functions and neural networks 总被引：1，自引：1，他引：0
Inverse modeling aims to estimate transmissivity and other parameters needed by distributed aquifer models, using piezometric measurements. While these parameters are highly variable in space, the two-dimensional aquifer area is essentially empty of measurements (curse of dimensionality). To address this problem, a representation of the two-dimensional transmissivity map based on ridge functions and neural networks is introduced and applied to inverse aquifer modeling. The proposed representation has good expressive power, i.e. it is concise and convergences quickly as the number of parameters are increased, and it is expected to express complex transmissivity variations with relatively few parameters which can be estimated from the piezometric measurements. A simple regularization that can dampen erratic high frequency terms in the estimated parameters is suggested. Several examples indicate that the proposed parameterization can handle diverse types of transmissivity variations while it is particularly suited when the true transmissivity map exhibits specific sorts of heterogeneity with large anisotropies or abrupt changes along lines. 相似文献
6.
7.
The use of data to condition single random fields has a well-established history. However, the joint use of data from several cross-correlated random fields is not as well developed. For example, the use of both transmissivity and head data in a steady state 2-d stochastic flow problem is essentially an inverse problem that is very important for both flow and transport predictions. This problem is addressed here by using a combination of numerical simulation and analytical methods and its application illustrated. The type of information conveyed by the different data categories is explored. The results presented are especially interesting in that head and transmissivity each give different information: Head values would appear to constrain the geometry of the paths while transmissivity data yields information about travel times. The linearized model is expanded to an iterative procedure and the true conditional distribution at several locations is compared with the iterative solution.The problem mentioned above is one with a special transfer function specified by the flow equation. In the second part of the paper a Fast Fourier Transform method for generation and conditioning of two or more random fields is introduced. This procedure is simple to implement, fast and very flexible. 相似文献
8.
Gutjahr A. Bullard B. Hatch S. Hughson L. 《Stochastic Environmental Research and Risk Assessment (SERRA)》1994,8(1):79-108
The use of data to condition single random fields has a well-established history. However, the joint use of data from several cross-correlated random fields is not as well developed. For example, the use of both transmissivity and head data in a steady state 2-d stochastic flow problem is essentially an inverse problem that is very important for both flow and transport predictions. This problem is addressed here by using a combination of numerical simulation and analytical methods and its application illustrated. The type of information conveyed by the different data categories is explored. The results presented are especially interesting in that head and transmissivity each give different information: Head values would appear to constrain the geometry of the paths while transmissivity data yields information about travel times. The linearized model is expanded to an iterative procedure and the true conditional distribution at several locations is compared with the iterative solution.The problem mentioned above is one with a special transfer function specified by the flow equation. In the second part of the paper a Fast Fourier Transform method for generation and conditioning of two or more random fields is introduced. This procedure is simple to implement, fast and very flexible. 相似文献
9.
MODFLOW 2000 head uncertainty,a first-order second moment method 总被引：1，自引：0，他引：1
A computationally efficient method to estimate the variance and covariance in piezometric head results computed through MODFLOW 2000 using a first-order second moment (FOSM) approach is presented. This methodology employs a first-order Taylor series expansion to combine model sensitivity with uncertainty in geologic data. MODFLOW 2000 is used to calculate both the ground water head and the sensitivity of head to changes in input data. From a limited number of samples, geologic data are extrapolated and their associated uncertainties are computed through a conditional probability calculation. Combining the spatially related sensitivity and input uncertainty produces the variance-covariance matrix, the diagonal of which is used to yield the standard deviation in MODFLOW 2000 head. The variance in piezometric head can be used for calibrating the model, estimating confidence intervals, directing exploration, and evaluating the reliability of a design. A case study illustrates the approach, where aquifer transmissivity is the spatially related uncertain geologic input data. The FOSM methodology is shown to be applicable for calculating output uncertainty for (1) spatially related input and output data, and (2) multiple input parameters (transmissivity and recharge). 相似文献
10.
C. R. Dietrich G. N. Newsam 《Stochastic Environmental Research and Risk Assessment (SERRA)》1989,3(4):293-316
In recent years, geostatistical concepts have been applied to the inverse problem of transmissivity estimation from piezometric head data. It has been claimed that such methods overcome various difficulties encountered in other approaches. However, the reconstruction of transmissivity from head measurements is ill-posed as it depends on derivatives of the head field. Consequently, any accurate method for its solution is likely to encounter numerically ill-conditioned systems. This paper reviews the geostatistical approach, and uses the stability analyses of linear algebra to show that, as the amount of available data increases and the discretization of the system is refined, both a numerically ill-conditioned parameter estimation problem and ill-conditioned cokriging equations may appear. Therefore, while the geostatistical approach does have conceptual appeal, it does not avoid the fundamental difficulties arising out of the ill-posed nature of transmissivity identification. Instead, the method is likely to be quite sensitive to these difficulties, so care must be taken in its formulation to minimize their effects. A means to stabilize the geostatistical method is suggested and numerical experiments that highlight key points of our analysis are given. 相似文献
11.
In this study, we examine the effects of conditioning spatially variable transmissivity fields using head and/or transmissivity measurements on well-capture zones. In order to address the challenge posed by conditioning a flow model with spatially varying parameters, an innovative inverse algorithm, the Representers method, is employed. The method explicitly considers this spatial variability.
A number of uniform measurement grids with different densities are used to condition transmissivity fields using the Representers method. Deterministic and stochastic analysis of well-capture zones are then examined. The deterministic study focuses on comparison between reference well-capture zones and their estimated mean conditioned on head data. It shows that model performance due to head conditioning on well-capture zone estimation is related to pumping rate. At moderate pumping rates transmissivity observations are more crucial to identify effects arising from small-scale variations in pore water velocity. However, with more aggressive pumping these effects are reduced, consequently model performance, through incorporating head observations, markedly improves. In the stochastic study, the effect of conditioning using head and/or transmissivity data on well-capture zone uncertainty is examined. The Representers method is coupled with the Monte Carlo method to propagate uncertainty in transmissivity fields to well-capture zones. For the scenario studied, the results showed that a combination of 48 head and transmissivity data could reduce the area of uncertainty (95% confidence interval) in well-capture zone location by over 50%, compared to a 40% reduction using either head or transmissivity data. This performance was comparable to that obtained through calibrating on three and a half times the number of head observations alone. 相似文献
12.
A calibration method to solve the groundwater inverse problem under steady- and transient-state conditions is presented. The method compares kriged and numerical head field gradients to modify hydraulic conductivity without the use of non-linear optimization techniques. The process is repeated iteratively until a close match with piezometric data is reached. The approach includes a damping factor to avoid divergence and oscillation of the solution in areas of low hydraulic gradient and a weighting factor to account for temporal head variation in transient simulations. The efficiency of the method in terms of computing time and calibration results is demonstrated with a synthetic field. It is shown that the proposed method provides parameter fields that reproduce both hydraulic conductivity and piezometric data in few forward model solutions. Stochastic numerical experiments are conducted to evaluate the sensitivity of the method to the damping function and to the head field estimation errors. 相似文献
13.
Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data 总被引：1，自引：0，他引：1
Harrie-Jan Hendricks Franssen Jaime Gómez-Hernández Andrés Sahuquillo 《Journal of Hydrology》2003,281(4):281-295
This paper presents the extension of the self-calibrating method to the coupled inverse modelling of groundwater flow and mass transport. The method generates equally likely solutions to the inverse problem that display the variability as observed in the field and are not affected by a linearisation of the state equations. Conditioning to the state variables is measured by an objective function including, among others, the mismatch between the simulated and measured concentrations. Conditioning is achieved by minimising the objective function by gradient-based methods. The gradient contains the partial derivatives of the objective function with respect to: log conductivities, log storativities, prescribed heads at boundaries, retardation coefficients and mass sources. The derivatives of the objective function with respect to log conductivity are the most cumbersome and need the most CPU-time to be evaluated. For this reason, to compute this derivative only advective transport is considered. The gradient is calculated by the adjoint-state method. The method is demonstrated in a controlled, synthetic study, in which the worth of concentration data is analysed. It is shown that concentration data are essential to improve transport predictions and also help to improve aquifer characterisation and flow predictions, especially in the upstream part of the aquifer, even in the case that a considerable amount of other experimental data like conductivities and heads are available. Besides, conditioning to concentration data reduces the ensemble variances of estimated transmissivity, hydraulic head and concentration. 相似文献
14.
An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering 总被引：4，自引：0，他引：4
The ensemble Kalman filter (EnKF) is a commonly used real-time data assimilation algorithm in various disciplines. Here, the EnKF is applied, in a hydrogeological context, to condition log-conductivity realizations on log-conductivity and transient piezometric head data. In this case, the state vector is made up of log-conductivities and piezometric heads over a discretized aquifer domain, the forecast model is a groundwater flow numerical model, and the transient piezometric head data are sequentially assimilated to update the state vector. It is well known that all Kalman filters perform optimally for linear forecast models and a multiGaussian-distributed state vector. Of the different Kalman filters, the EnKF provides a robust solution to address non-linearities; however, it does not handle well non-Gaussian state-vector distributions. In the standard EnKF, as time passes and more state observations are assimilated, the distributions become closer to Gaussian, even if the initial ones are clearly non-Gaussian. A new method is proposed that transforms the original state vector into a new vector that is univariate Gaussian at all times. Back transforming the vector after the filtering ensures that the initial non-Gaussian univariate distributions of the state-vector components are preserved throughout. The proposed method is based in normal-score transforming each variable for all locations and all time steps. This new method, termed the normal-score ensemble Kalman filter (NS-EnKF), is demonstrated in a synthetic bimodal aquifer resembling a fluvial deposit, and it is compared to the standard EnKF. The proposed method performs better than the standard EnKF in all aspects analyzed (log-conductivity characterization and flow and transport predictions). 相似文献
15.
Andrea Zanini Peter K. Kitanidis 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(5):565-577
The estimation of field parameters, such as transmissivity, is an important part of groundwater modeling. This work deals
with the quasilinear geostatistical inverse approach to the estimation of the transmissivity fields from hydraulic head measurements.
The standard quasilinear approach is an iterative method consisting of successive linearizations. We examine a synthetic case
to evaluate the basic methodology and some modifications and extensions. The first objective is to evaluate the performance
of the quasilinear approach when applied to strongly heterogeneous (or “high-contrast”) transmissivity fields and, when needed,
to propose improvements that allow the solution of such problems. For large-contrast cases, the standard quasilinear method
often fails to converge. However, by introducing a derivative-free line search as a polishing step after each Gauss–Newton
iteration, we have found that convergence can be practically assured. Another issue is that the quasilinear procedure, which
uses linearization about the best estimate to evaluate estimation variances, may lead to inaccurate estimation of the variance
of the estimated variable. Our numerical results suggest that this may not be a particularly serious problem, though it is
hard to say whether this conclusion will apply to other cases. Nevertheless, since the quasilinear approach is an approximation,
we propose a potentially more accurate but computer-intensive Markov Chain Monte Carlo (MCMC) procedure based on conditional
realizations generated through the quasilinear approach and accepted or rejected according to the Metropolis–Hastings algorithm.
Six transmissivity fields with increasing contrast were generated and one thousand conditional realizations were computed
for each studied case. The MCMC procedure proposed in this work gives an overall more accurate picture than the quasilinear
approach but at a considerably higher computational cost. 相似文献
16.
For good groundwater flow and solute transport numerical modeling, it is important to characterize the formation properties. In this paper, we analyze the performance and important implementation details of a new approach for stochastic inverse modeling called inverse sequential simulation (iSS). This approach is capable of characterizing conductivity fields with heterogeneity patterns difficult to capture by standard multiGaussian-based inverse approaches. The method is based on the multivariate sequential simulation principle, but the covariances and cross-covariances used to compute the local conditional probability distributions are computed by simple co-kriging which are derived from an ensemble of conductivity and piezometric head fields, in a similar manner as the experimental covariances are computed in an ensemble Kalman filtering. A sensitivity analysis is performed on a synthetic aquifer regarding the number of members of the ensemble of realizations, the number of conditioning data, the number of piezometers at which piezometric heads are observed, and the number of nodes retained within the search neighborhood at the moment of computing the local conditional probabilities. The results show the importance of having a sufficiently large number of all of the mentioned parameters for the algorithm to characterize properly hydraulic conductivity fields with clear non-multiGaussian features. 相似文献
17.
18.
M. Giudici F. Delay G. de Marsily G. Parravicini G. Ponzini A. Rosazza 《Stochastic Hydrology and Hydraulics》1998,12(3):191-204
The Differential System Method (DSM) permits identification of the physical parameters of finite-difference groundwater flow
models in a confined aquifer when piezometric head and source terms are known at each point of the finite-difference lattice
for at least two independent flow situations for which the hydraulic gradients are not parallel. Since piezometric head data
are usually few and sparse, interpolation of the measured data onto a regular grid can be performed with geostatistical techniques.
We apply kriging to the sparse data of a synthetic aquifer to evaluate the stability of the DSM with respect to uncorrelated
measurement errors and interpolation errors. The numerical results show that the DSM is stable. 相似文献
19.
M. Giudici F. Delay G. de Marsily G. Parravicini G. Ponzini A. Rosazza 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(3):191-204
The Differential System Method (DSM) permits identification of the physical parameters of finite-difference groundwater flow
models in a confined aquifer when piezometric head and source terms are known at each point of the finite-difference lattice
for at least two independent flow situations for which the hydraulic gradients are not parallel. Since piezometric head data
are usually few and sparse, interpolation of the measured data onto a regular grid can be performed with geostatistical techniques.
We apply kriging to the sparse data of a synthetic aquifer to evaluate the stability of the DSM with respect to uncorrelated
measurement errors and interpolation errors. The numerical results show that the DSM is stable. 相似文献
20.
《水文科学杂志》2013,58(6)
Abstract Abstract Characterization of heterogeneity at the field scale generally requires detailed aquifer properties such as transmissivity and hydraulic head. An accurate delineation of these properties is expensive and time consuming, and for many if not most groundwater systems, is not practical. As an alternative approach, stochastic representation of random fields is used and presented in this paper. Specifically, an iterative stochastic conditional simulation approach was applied to a hypothetical and highly heterogeneous pre-designed aquifer system. The approach is similar to the classical co-kriging technique; it uses a linear estimator that depends on the covariance functions of transmissivity (T), and hydraulic head (h), as well as their cross-covariances. A linearized flow equation along with a conditional random field generator constitutes the iterative process of the conditional simulation. One hundred equally likely realizations of transmissivity fields with pre-specified geostatistical parameters were generated, and conditioned to both limited transmissivity and head data. The successful implementation of the approach resulted in conditioned flow paths and travel-time distribution under different degrees of aquifer heterogeneity. This approach worked well for fields exhibiting small variances. However, for random fields exhibiting large variances (greater than 1.0), an iterative procedure was used. The results show that, as the variance of the ln[T] increases, the flow paths tend to diverge, resulting in a wide spectrum of flow conditions, with no direct discernable relationship between the degree of heterogeneity and travel time. The applied approach indicates that high errors may result when estimation of particle travel times in a heterogeneous medium is approximated by an equivalent homogeneous medium. 相似文献