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1.
Groundwater modelling calls for an effective and robust data integrating method to fill the gap between the model and observation data. The ensemble Kalman filter (EnKF), a real‐time data assimilation method, has been increasingly applied in multiple disciplines such as petroleum engineering and hydrogeology. In this approach, a groundwater model is updated sequentially with measured data such as hydraulic head and concentration. As an alternative to the EnKF, the ensemble smoother (ES) has been proposed for updating groundwater models using all the data together, with much less computational cost. To further improve the performance of the ES, an iterative ES has been proposed for continuously updating the model by assimilating measurements together. In this work, we compare the performance of the EnKF, the ES, and the iterative ES using a synthetic example in groundwater modelling. Hydraulic head data modelled on the basis of the reference conductivity field are used to inversely estimate conductivities at unsampled locations. Results are evaluated in terms of the characterization of conductivity and groundwater flow predictions. It is concluded that (a) the iterative ES works better than the standard ES because of its continuous updating and (b) the iterative ES could achieve results comparable with those of the EnKF, with less computational cost. These findings show that the iterative ES should be paid much more attention for data assimilation in groundwater modelling.  相似文献   

2.
The Kalman filter is an efficient data assimilation tool to refine an estimate of a state variable using measured data and the variable's correlations in space and/or time. The ensemble Kalman filter (EnKF) (Evensen 2004, 2009) is a Kalman filter variant that employs Monte Carlo analysis to define the correlations that help to refine the updated state. While use of EnKF in hydrology is somewhat limited, it has been successfully applied in other fields of engineering (e.g., oil reservoir modeling, weather forecasting). Here, EnKF is used to refine a simulated groundwater tetrachloroethylene (TCE) plume that underlies the Tooele Army Depot‐North (TEAD‐N) in Utah, based on observations of TCE in the aquifer. The resulting EnKF‐based assimilated plume is simulated forward in time to predict future plume migration. The correlations that underpin EnKF updating implicitly contain information about how the plume developed over time under the influence of complex site hydrology and variable source history, as they are predicated on multiple realizations of a well‐calibrated numerical groundwater flow and transport model. The EnKF methodology is compared to an ordinary kriging‐based assimilation method with respect to the accurate representation of plume concentrations in order to determine the relative efficacy of EnKF for water quality data assimilation.  相似文献   

3.
Groundwater models are critical decision support tools for water resources management and environmental remediation. However, limitations in site characterization data and conceptual models can adversely affect the reliability of groundwater models. Therefore, there is a strong need for continuous model uncertainty reduction. Ensemble filters have recently emerged as promising high-dimensional data assimilation techniques. Two general categories of ensemble filters exist in the literature: perturbation-based and deterministic. Deterministic ensemble filters have been extensively studied for their better performance and robustness in assimilating oceanographic and atmospheric data. In hydrogeology, while a number of previous studies demonstrated the usefulness of the perturbation-based ensemble Kalman filter (EnKF) for joint parameter and state estimation, there have been few systematic studies investigating the performance of deterministic ensemble filters. This paper presents a comparative study of four commonly used deterministic ensemble filters for sequentially estimating the hydraulic conductivity parameter in low- and moderately high-dimensional groundwater models. The performance of the filters is assessed on the basis of twin experiments in which the true hydraulic conductivity field is assumed known. The test results indicate that the deterministic ensemble Kalman filter (DEnKF) is the most robust filter and achieves the best performance at relatively small ensemble sizes. Deterministic ensemble filters often make use of covariance inflation and localization to stabilize filter performance. Sensitivity studies demonstrate the effects of covariance inflation, localization, observation density, and conditioning on filter performance.  相似文献   

4.
Ensemble Kalman filter, EnKF, as a Monte Carlo sequential data assimilation method has emerged promisingly for subsurface media characterization during past decade. Due to high computational cost of large ensemble size, EnKF is limited to small ensemble set in practice. This results in appearance of spurious correlation in covariance structure leading to incorrect or probable divergence of updated realizations. In this paper, a universal/adaptive thresholding method is presented to remove and/or mitigate spurious correlation problem in the forecast covariance matrix. This method is, then, extended to regularize Kalman gain directly. Four different thresholding functions have been considered to threshold forecast covariance and gain matrices. These include hard, soft, lasso and Smoothly Clipped Absolute Deviation (SCAD) functions. Three benchmarks are used to evaluate the performances of these methods. These benchmarks include a small 1D linear model and two 2D water flooding (in petroleum reservoirs) cases whose levels of heterogeneity/nonlinearity are different. It should be noted that beside the adaptive thresholding, the standard distance dependant localization and bootstrap Kalman gain are also implemented for comparison purposes. We assessed each setup with different ensemble sets to investigate the sensitivity of each method on ensemble size. The results indicate that thresholding of forecast covariance yields more reliable performance than Kalman gain. Among thresholding function, SCAD is more robust for both covariance and gain estimation. Our analyses emphasize that not all assimilation cycles do require thresholding and it should be performed wisely during the early assimilation cycles. The proposed scheme of adaptive thresholding outperforms other methods for subsurface characterization of underlying benchmarks.  相似文献   

5.
Modeling the spread of subsurface contaminants requires coupling a groundwater flow model with a contaminant transport model. Such coupling may provide accurate estimates of future subsurface hydrologic states if essential flow and contaminant data are assimilated in the model. Assuming perfect flow, an ensemble Kalman filter (EnKF) can be used for direct data assimilation into the transport model. This is, however, a crude assumption as flow models can be subject to many sources of uncertainty. If the flow is not accurately simulated, contaminant predictions will likely be inaccurate even after successive Kalman updates of the contaminant model with the data. The problem is better handled when both flow and contaminant states are concurrently estimated using the traditional joint state augmentation approach. In this paper, we introduce a dual estimation strategy for data assimilation into a one-way coupled system by treating the flow and the contaminant models separately while intertwining a pair of distinct EnKFs, one for each model. The presented strategy only deals with the estimation of state variables but it can also be used for state and parameter estimation problems. This EnKF-based dual state-state estimation procedure presents a number of novel features: (i) it allows for simultaneous estimation of both flow and contaminant states in parallel; (ii) it provides a time consistent sequential updating scheme between the two models (first flow, then transport); (iii) it simplifies the implementation of the filtering system; and (iv) it yields more stable and accurate solutions than does the standard joint approach. We conducted synthetic numerical experiments based on various time stepping and observation strategies to evaluate the dual EnKF approach and compare its performance with the joint state augmentation approach. Experimental results show that on average, the dual strategy could reduce the estimation error of the coupled states by 15% compared with the joint approach. Furthermore, the dual estimation is proven to be very effective computationally, recovering accurate estimates at a reasonable cost.  相似文献   

6.
The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.Responsible Editor: Jörg-Olaf Wolff  相似文献   

7.
A new parameter estimation algorithm based on ensemble Kalman filter (EnKF) is developed. The developed algorithm combined with the proposed problem parametrization offers an efficient parameter estimation method that converges using very small ensembles. The inverse problem is formulated as a sequential data integration problem. Gaussian process regression is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen–Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative regularized EnKF algorithm. The filter is converted to an optimization algorithm by using a pseudo time-stepping technique such that the model output matches the time dependent data. The EnKF Kalman gain matrix is regularized using truncated SVD to filter out noisy correlations. Numerical results show that the proposed algorithm is a promising approach for parameter estimation of subsurface flow models.  相似文献   

8.
This paper describes an application of the ensemble Kalman filter (EnKF) in which streamflow observations are used to update states in a distributed hydrological model. We demonstrate that the standard implementation of the EnKF is inappropriate because of non-linear relationships between model states and observations. Transforming streamflow into log space before computing error covariances improves filter performance. We also demonstrate that model simulations improve when we use a variant of the EnKF that does not require perturbed observations. Our attempt to propagate information to neighbouring basins was unsuccessful, largely due to inadequacies in modelling the spatial variability of hydrological processes. New methods are needed to produce ensemble simulations that both reflect total model error and adequately simulate the spatial variability of hydrological states and fluxes.  相似文献   

9.
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   

10.
Reactive contaminant transport models are used by hydrologists to simulate and study the migration and fate of industrial waste in subsurface aquifers. Accurate transport modeling of such waste requires clear understanding of the system’s parameters, such as sorption and biodegradation. In this study, we present an efficient sequential data assimilation scheme that computes accurate estimates of aquifer contamination and spatially variable sorption coefficients. This assimilation scheme is based on a hybrid formulation of the ensemble Kalman filter (EnKF) and optimal interpolation (OI) in which solute concentration measurements are assimilated via a recursive dual estimation of sorption coefficients and contaminant state variables. This hybrid EnKF-OI scheme is used to mitigate background covariance limitations due to ensemble under-sampling and neglected model errors. Numerical experiments are conducted with a two-dimensional synthetic aquifer in which cobalt-60, a radioactive contaminant, is leached in a saturated heterogeneous clayey sandstone zone. Assimilation experiments are investigated under different settings and sources of model and observational errors. Simulation results demonstrate that the proposed hybrid EnKF-OI scheme successfully recovers both the contaminant and the sorption rate and reduces their uncertainties. Sensitivity analyses also suggest that the adaptive hybrid scheme remains effective with small ensembles, allowing to reduce the ensemble size by up to 80% with respect to the standard EnKF scheme.  相似文献   

11.
Traditional Ensemble Kalman Filter (EnKF) data assimilation requires computationally intensive Monte Carlo (MC) sampling, which suffers from filter inbreeding unless the number of simulations is large. Recently we proposed an alternative EnKF groundwater-data assimilation method that obviates the need for sampling and is free of inbreeding issues. In our new approach, theoretical ensemble moments are approximated directly by solving a system of corresponding stochastic groundwater flow equations. Like MC-based EnKF, our moment equations (ME) approach allows Bayesian updating of system states and parameters in real-time as new data become available. Here we compare the performances and accuracies of the two approaches on two-dimensional transient groundwater flow toward a well pumping water in a synthetic, randomly heterogeneous confined aquifer subject to prescribed head and flux boundary conditions.  相似文献   

12.
Sampling strategies and square root analysis schemes for the EnKF   总被引：27，自引：1，他引：26  
The purpose of this paper is to examine how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF. It is shown that by selecting the initial ensemble, the model noise and the measurement perturbations wisely, it is possible to achieve a significant improvement in the EnKF results, using the same number of members in the ensemble. The results are also compared with a square root implementation of the EnKF analysis scheme where the analyzed ensemble is computed without the perturbation of measurements. It is shown that the measurement perturbations introduce sampling errors which can be reduced using improved sampling schemes in the standard EnKF or fully eliminated when the square root analysis algorithm is used. Further, a new computationally efficient square root algorithm is proposed which allows for the use of a low-rank representation of the measurement error covariance matrix. It is shown that this algorithm in fact solves the full problem at a low cost without introducing any new approximations.  相似文献   

13.
Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state–parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model.  相似文献   

14.
This paper, based on a real world case study (Limmat aquifer, Switzerland), compares inverse groundwater flow models calibrated with specified numbers of monitoring head locations. These models are updated in real time with the ensemble Kalman filter (EnKF) and the prediction improvement is assessed in relation to the amount of monitoring locations used for calibration and updating. The prediction errors of the models calibrated in transient state are smaller if the amount of monitoring locations used for the calibration is larger. For highly dynamic groundwater flow systems a transient calibration is recommended as a model calibrated in steady state can lead to worse results than a noncalibrated model with a well-chosen uniform conductivity. The model predictions can be improved further with the assimilation of new measurement data from on-line sensors with the EnKF. Within all the studied models the reduction of 1-day hydraulic head prediction error (in terms of mean absolute error [MAE]) with EnKF lies between 31% (assimilation of head data from 5 locations) and 72% (assimilation of head data from 85 locations). The largest prediction improvements are expected for models that were calibrated with only a limited amount of historical information. It is worthwhile to update the model even with few monitoring locations as it seems that the error reduction with EnKF decreases exponentially with the amount of monitoring locations used. These results prove the feasibility of data assimilation with EnKF also for a real world case and show that improved predictions of groundwater levels can be obtained.  相似文献   

15.
The local ensemble transform Kalman filter (LETKF) is implemented with the Weather Research and Forecasting (WRF) model, and real observations are assimilated to assess the newly-developed WRF-LETKF system. The WRF model is a widely-used mesoscale numerical weather prediction model, and the LETKF is an ensemble Kalman filter (EnKF) algorithm particularly efficient in parallel computer architecture. This study aims to provide the basis of future research on mesoscale data assimilation using the WRF-LETKF system, an additional testbed to the existing EnKF systems with the WRF model used in the previous studies. The particular LETKF system adopted in this study is based on the system initially developed in 2004 and has been continuously improved through theoretical studies and wide applications to many kinds of dynamical models including realistic geophysical models. Most recent and important improvements include an adaptive covariance inflation scheme which considers the spatial and temporal inhomogeneity of inflation parameters. Experiments show that the LETKF successfully assimilates real observations and that adaptive inflation is advantageous. Additional experiments with various ensemble sizes show that using more ensemble members improves the analyses consistently.  相似文献   

16.
The application of interferometric synthetic aperture radar (InSAR) has been increasingly used to improve capabilities to model land subsidence in hydrogeologic studies. A number of investigations over the last decade show how spatially detailed time‐lapse images of ground displacements could be utilized to advance our understanding for better predictions. In this work, we use simulated land subsidences as observed measurements, mimicking InSAR data to inversely infer inelastic specific storage in a stochastic framework. The inelastic specific storage is assumed as a random variable and modeled using a geostatistical method such that the detailed variations in space could be represented and also that the uncertainties of both characterization of specific storage and prediction of land subsidence can be assessed. The ensemble Kalman filter (EnKF), a real‐time data assimilation algorithm, is used to inversely calibrate a land subsidence model by matching simulated subsidences with InSAR data. The performance of the EnKF is demonstrated in a synthetic example in which simulated surface deformations using a reference field are assumed as InSAR data for inverse modeling. The results indicate: (1) the EnKF can be used successfully to calibrate a land subsidence model with InSAR data; the estimation of inelastic specific storage is improved, and uncertainty of prediction is reduced, when all the data are accounted for; and (2) if the same ensemble is used to estimate Kalman gain, the analysis errors could cause filter divergence; thus, it is essential to include localization in the EnKF for InSAR data assimilation.  相似文献   

17.
Accurate forecasting of snow properties is important for effective water resources management, especially in mountainous areas like the western United States. Current model-based forecasting approaches are limited by model biases and input data uncertainties. Remote sensing offers an opportunity for observation of snow properties, like areal extent and water equivalent, over larger areas. Data assimilation provides a framework for optimally merging information from remotely sensed observations and hydrologic model predictions. An ensemble Kalman filter (EnKF) was used to assimilate remotely sensed snow observations into the variable infiltration capacity (VIC) macroscale hydrologic model over the Snake River basin. The snow cover extent (SCE) product from the moderate resolution imaging spectroradiometer (MODIS) flown on the NASA Terra satellite was used to update VIC snow water equivalent (SWE), for a period of four consecutive winters (1999–2003). A simple snow depletion curve model was used for the necessary SWE–SCE inversion. The results showed that the EnKF is an effective and operationally feasible solution; the filter successfully updated model SCE predictions to better agree with the MODIS observations and ground surface measurements. Comparisons of the VIC SWE estimates following updating with surface SWE observations (from the NRCS SNOTEL network) indicated that the filter performance was a modest improvement over the open-loop (un-updated) simulations. This improvement was more evident for lower to middle elevations, and during snowmelt, while during accumulation the filter and open-loop estimates were very close on average. Subsequently, a preliminary assessment of the potential for assimilating the SWE product from the advanced microwave scanning radiometer (AMSR-E, flown on board the NASA Aqua satellite) was conducted. The results were not encouraging, and appeared to reflect large errors in the AMSR-E SWE product, which were also apparent in comparisons with SNOTEL data.  相似文献   

18.
Data assimilation techniques have been proven as an effective tool to improve model forecasts by combining information about observed variables in many areas. This article examines the potential of assimilating surface soil moisture observations into a field‐scale hydrological model, the Root Zone Water Quality Model, to improve soil moisture estimation. The Ensemble Kalman Filter (EnKF), a popular data assimilation technique for nonlinear systems, was applied and compared with a simple direct insertion method. In situ soil moisture data at four different depths (5, 20, 40, and 60 cm) from two agricultural fields (AS1 and AS2) in northeastern Indiana were used for assimilation and validation purposes. Through daily update, the EnKF improved soil moisture estimation compared with the direct insertion method and model results without assimilation, having more distinct improvement at the 5 and 20 cm depths than for deeper layers (40 and 60 cm). Local vertical soil property heterogeneity in AS1 deteriorated soil moisture estimates with the EnKF. Removal of systematic bias in the forecast model was found to be critical for more successful soil moisture data assimilation studies. This study also demonstrates that a more frequent update generally contributes in enhancing the open loop simulation; however, large forecasting error can prevent more frequent update from providing better results. In addition, results indicate that various ensemble sizes make little difference in the assimilation results. An ensemble of 100 members produced results that were comparable with results obtained from larger ensembles. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

19.
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a sufficiently large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos expansion (PCE) to represent and propagate the uncertainties in parameters and states. However, PCKF suffers from the so-called “curse of dimensionality”. Its computational cost increases drastically with the increasing number of parameters and system nonlinearity. Furthermore, PCKF may fail to provide accurate estimations due to the joint updating scheme for strongly nonlinear models. Motivated by recent developments in uncertainty quantification and EnKF, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected at each assimilation step; the “restart” scheme is utilized to eliminate the inconsistency between updated model parameters and states variables. The performance of RAPCKF is systematically tested with numerical cases of unsaturated flow models. It is shown that the adaptive approach and restart scheme can significantly improve the performance of PCKF. Moreover, RAPCKF has been demonstrated to be more efficient than EnKF with the same computational cost.  相似文献   

20.
An implementation of the Ensemble Kalman filter (EnKF) with a coupled ice–ocean model is presented. The model system consists of a dynamic–thermodynamic ice model using the elastic-viscous-plastic (EVP) rheology coupled with the HYbrid Coordinate Ocean Model (HYCOM). The observed variable is ice concentration from passive microwave sensor data (SSM/I). The assimilation of ice concentration has the desired effect of reducing the difference between observations and model. Comparison of the assimilation experiment with a free-run experiment shows that there are large differences, especially in summer. In winter the differences are relatively small, partly because the atmospheric forcing used to run the model depends upon SSM/I data. The assimilation has the strongest impact close to the ice edge, where it ensures a correct location of the ice edge throughout the simulation. An inspection of the model ensemble statistics reveals that the error estimates of the model are too small in winter, partly a result of too low model ice-concentration variance in the central ice pack. It is found that the ensemble covariance between ice concentration and sea-surface temperature in the same grid cell is of the same sign (negative) throughout the year. The ensemble covariance between ice concentration and salinity is more dependent upon the physical mechanisms involved, with ice transport and freeze/melt giving different signs of the covariances. The ice-transport and ice-melt mechanisms also impact the ice-concentration variance and the covariance between ice concentration and ice thickness. The ensemble statistics show a high degree of complexity, which to some extent merits the use of computationally expensive assimilation methods, such as the Ensemble Kalman filter. The present study focuses on the assimilation of ice concentration, but it is understood that assimilation of other datasets, such as sea-surface temperature, would be beneficial.Responsible Editor: Jin-Song von Storch  相似文献   

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