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1.
The localized normal-score ensemble Kalman filter (NS-EnKF) coupled with covariance inflation is used to characterize the spatial variability of a channelized bimodal hydraulic conductivity field, for which the only existing prior information about conductivity is its univariate marginal distribution. We demonstrate that we can retrieve the main patterns of the reference field by assimilating a sufficient number of piezometric observations using the NS-EnKF. The possibility of characterizing the conductivity spatial variability using only piezometric head data shows the importance of accounting for these data in inverse modeling. 相似文献
2.
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
3.
The ensemble particle filter (EnPF) in rainfall-runoff models 总被引：1，自引：1，他引：0
G. van Delft G. Y. El Serafy A. W. Heemink 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(8):1203-1211
Rainfall-runoff models play a very important role in flood forecasting. However, these models contain large uncertainties
caused by errors in both the model itself and the input data. Data assimilation techniques are being used to reduce these
uncertainties. The ensemble Kalman filter (EnKF) and the particle filter (PF) both have their own strengths. Research was
carried out to a possible combination between both types of filters that will lead to a new type of filters that joins the
strengths of both. The so called ensemble particle filter (EnPF) new combination is tested on flood forecasting problems in
both the hindcast mode as well as the forecast mode. Several proposed combinations showed considerable improvement when a
hindcast comparison on synthetic data was considered. Within the forecast comparison with field data, the suggested EnPF showed
remarkable improvements compared to the PF and slight improvements compared to the EnKF. 相似文献
4.
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
5.
Marc Leisenring Hamid Moradkhani 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(2):253-270
Using the U.S. National Weather Service’s SNOW-17 model, this study compares common sequential data assimilation methods,
the ensemble Kalman filter (EnKF), the ensemble square root filter (EnSRF), and four variants of the particle filter (PF),
to predict seasonal snow water equivalent (SWE) within a small watershed near Lake Tahoe, California. In addition to SWE estimation,
the various data assimilation methods are used to estimate five of the most sensitive parameters of SNOW-17 by allowing them
to evolve with the dynamical system. Unlike Kalman filters, particle filters do not require Gaussian assumptions for the posterior
distribution of the state variables. However, the likelihood function used to scale particle weights is often assumed to be
Gaussian. This study evaluates the use of an empirical cumulative distribution function (ECDF) based on the Kaplan–Meier survival
probability method to compute particle weights. These weights are then used in different particle filter resampling schemes.
Detailed analyses are conducted for synthetic and real data assimilation and an assessment of the procedures is made. The
results suggest that the particle filter, especially the empirical likelihood variant, is superior to the ensemble Kalman
filter based methods for predicting model states, as well as model parameters. 相似文献
6.
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
7.
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
8.
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
9.
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
10.
Reduction of Used Memory Ensemble Kalman Filtering (RumEnKF) is introduced as a variant on the Ensemble Kalman Filter (EnKF). RumEnKF differs from EnKF in that it does not store the entire ensemble, but rather only saves the first two moments of the ensemble distribution. In this way, the number of ensemble members that can be calculated is less dependent on available memory, and mainly on available computing power (CPU). RumEnKF is developed to make optimal use of current generation super computer architecture, where the number of available floating point operations (flops) increases more rapidly than the available memory and where inter-node communication can quickly become a bottleneck. RumEnKF reduces the used memory compared to the EnKF when the number of ensemble members is greater than half the number of state variables. In this paper, three simple models are used (auto-regressive, low dimensional Lorenz and high dimensional Lorenz) to show that RumEnKF performs similarly to the EnKF. Furthermore, it is also shown that increasing the ensemble size has a similar impact on the estimation error from the three algorithms. 相似文献
11.
Local extreme rain usually resulted in disasters such as flash floods and landslides. Upon today, it is still one of the most difficult tasks for operational weather forecast centers to predict those events accurately. In this paper, we simulate an extreme precipitation event with ensemble Kalman filter (EnKF) assimilation of Doppler radial-velocity observations, and analyze the uncertainties of the assimilation. The results demonstrate that, without assimilation radar data, neither a single initialization of deterministic forecast nor an ensemble forecast with adding perturbations or multiple physical parameterizations can predict the location of strong precipitation. However, forecast was significantly improved with assimilation of radar data, especially the location of the precipitation. The direct cause of the improvement is the buildup of a deep mesoscale convection system with EnKF assimilation of radar data. Under a large scale background favorable for mesoscale convection, efficient perturbations of upstream mid-low level meridional wind and moisture are key factors for the assimilation and forecast. Uncertainty still exists for the forecast of this case due to its limited predictability. Both the difference of large scale initial fields and the difference of analysis obtained from EnKF assimilation due to small amplitude of initial perturbations could have critical influences to the event's prediction. Forecast could be improved through more cycles of EnKF assimilation. Sensitivity tests also support that more accurate forecasts are expected through improving numerical models and observations. 相似文献
12.
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
13.
A. H. ELSheikh C. C. Pain F. Fang J. L. M. A. Gomes I. M. Navon 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(4):877-897
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
14.
Evaluating the utility of the ensemble transform Kalman filter for adaptive sampling when updating a hydrodynamic model 总被引：1，自引：0，他引：1
This paper compares two Monte Carlo sequential data assimilation methods based on the Kalman filter, for estimating the effect of measurements on simulations of state error variance made by a one-dimensional hydrodynamic model. The first method used an ensemble Kalman filter (EnKF) to update state estimates, which were then used as initial conditions for further simulations. The second method used an ensemble transform Kalman filter (ETKF) to quickly estimate the effect of measurement error covariance on forecast error covariance without the need to re-run the simulation model. The ETKF gave an unbiased estimate of EnKF analysed error variance, although differences in the treatment of measurement errors meant the results were not identical. Estimates of forecast error variance could also be made, but their accuracy deteriorated as the time from measurements increased due in part to model non-linearity and the decreasing signal variance. The motivation behind the study was to assess the ability of the ETKF to target possible measurements, as part of an adaptive sampling framework, before they are assimilated by an EnKF-based forecasting model on the River Crouch, Essex, UK. The ETKF was found to be a useful tool for quickly estimating the error covariance expected after assimilating measurements into the hydrodynamic model. It, thus, provided a means of quantifying the ‘usefulness’ (in terms of error variance) of possible sampling schemes. 相似文献
15.
An ensemble Kalman filter (EnKF) is developed to identify a hydraulic conductivity distribution in a heterogeneous medium by assimilating solute concentration measurements of solute transport in the field with a steady‐state flow. A synthetic case with the mixed Neumann/Dirichlet boundary conditions is designed to investigate the capacity of the data assimilation methods to identify a conductivity distribution. The developed method is demonstrated in 2‐D transient solute transport with two different initial instant solute injection areas. The influences of the observation error and model error on the updated results are considered in this study. The study results indicate that the EnKF method will significantly improve the estimation of the hydraulic conductivity field by assimilating solute concentration measurements. The larger area of the initial distribution and the more observed data obtained, the better the calculation results. When the standard deviation of the observation error varies from 1% to 30% of the solute concentration measurements, the simulated results by the data assimilation method do not change much, which indicates that assimilation results are not very sensitive to the standard deviation of the observation error in this study. When the inflation factor is more than 1.0 to enlarge the model error by increasing the forecast error covariance matrix, the updated results of the hydraulic conductivity by the data assimilation method are not good at all. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
16.
Martyn P. Clark David E. Rupp Ross A. Woods Xiaogu Zheng Richard P. Ibbitt Andrew G. Slater Jochen Schmidt Michael J. Uddstrom 《Advances in water resources》2008
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
17.
18.
Data assimilation in groundwater modelling: ensemble Kalman filter versus ensemble smoothers 
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下载免费PDF全文 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
19.
The performance of an inexpensive, ensemble-based optimal interpolation (EnOI) scheme that uses a stationary ensemble of model
anomalies to approximate forecast error covariances, is compared with that of an ensemble Kalman filter (EnKF). The model
to which the methods are applied is a pair of “perfect”, one-dimensional, linear advection equations for two related variables.
While EnOI is sub-optimal, it can give results that are comparable to those of the EnKF. The computational cost of EnOI is
typically about times less than that of EnKF, where is the ensemble size. We suggest that EnOI may provide a practical and cost-effective alternative to the EnKF for some applications
where computational cost is a limiting factor. We demonstrate that when the ensemble size is smaller than the dimension of
the model’s sub-space, both the EnKF and EnOI may require localisation around each observation to eliminate effects of sampling
error and to increase the effective number of independent ensemble members used to construct an analysis. However, localisation
can degrade an analysis if the length-scales of the localising function are too short. We demonstrate that, as the length-scale
of the localising function is decreased, localisation can significantly compromise the model’s dynamical balances. We also
find that localisation artificially amplifies high frequencies for applications of the EnKF. Based on our experiments, for
applications where localisation is necessary, the length-scales of the localisation should be larger than the decorrelation
length-scales of the variables being updated. 相似文献
20.
Evensen (2003) presents a modification of the Ensemble Kalman Filter (EnKF), in which the observation-error and background-error covariance matrices are both represented by ensembles, in contrast to the usual practice, where only the background error is so represented. It is shown that this modification can cause the ensemble to collapse to a single member, in the common situation where the number of observations is more than twice the number of ensemble members, and to be rank-deficient when the number of observations is greater than or equal to the ensemble size. It is also shown that some further modifications to the scheme, presented by Evensen as offering numerical efficiencies, can prevent this collapse. However, these latter modifications are shown in some simple numerical examples to require tuning to produce acceptable results, which are nevertheless inferior to those of the standard EnKF.Acknowledgements The author acknowledges useful discussions with Peter Steinle, and other participants at the EnKF workshop held in BMRC in November, 2003. 相似文献