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1.
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   

2.
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   

3.
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   

4.
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   

5.
This paper comparatively assesses the performance of five data assimilation techniques for three-parameter Muskingum routing with a spatially lumped or distributed model structure. The assimilation techniques used include direct insertion (DI), nudging scheme (NS), Kalman filter (KF), ensemble Kalman filter (EnKF) and asynchronous ensemble Kalman filter (AEnKF), which are applied to river reaches in Texas and Louisiana, USA. For both lumped and distributed routing, results from KF, EnKF and AEnKF are sensitive to the error specification. As expected, DI outperformed the other models in the case of lumped modelling, while in distributed routing, KF approaches, particularly AEnKF and EnKF, performed better than DI or nudging, reflecting the benefit of updating distributed states through error covariance modelling in KF approaches. The results of this work would be useful in setting up data assimilation systems that employ increasingly abundant real-time observations using distributed hydrological routing models.  相似文献   

6.
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   

7.
The Argo temperature and salinity profiles in 2005–2009 are assimilated into a coastal ocean general circulation model of the Northwest Pacific Ocean using the ensemble adjustment Kalman filter (EAKF). Three numerical tests, including the control run (CTL) (without data assimilation, which serves as the reference experiment), ensemble free run (EnFR) (without data assimilation), and EAKF experiment (with Argo data assimilation using EAKF), are carried out to examine the performance of this system. Using the restarts of different years as the initial conditions of the ensemble integrations, the ensemble spreads from EnFR and EAKF are all kept at a finite value after a sharp decreasing in the first few months because of the sensitive of the model to the initial conditions, and the reducing of the ensemble spread due to Argo data assimilation is not much. The ensemble samples obtained in this way can well represent the probabilities of the real ocean states, and no ensemble inflation is necessary for this EAKF experiment. Different experiment results are compared with satellite sea surface temperature (SST) data and the Global Temperature-Salinity Profile Program (GTSPP) data. The comparison of SST shows that modeled SST errors are reduced after data assimilation; the error reduction percentage after assimilating the Argo profiles is about 10?% on average. The comparison against the GTSPP profiles, which are independent of the Argo profiles, shows improvements in both temperature and salinity. The comparison results indicated a great error reduction in all vertical layers relative to CTL and the ensemble mean of EnFR; the maximum value for temperature and salinity reaches to 85?% and 80?%, respectively. The standard deviations of sea surface height are employed to examine the simulation ability, and it is shown that the mesoscale variability is improved after Argo data assimilation, especially in the Kuroshio extension area and along the section of 10°N. All these results suggest that this system is potentially useful for improving the simulation ability of oceanic numerical models.  相似文献   

8.
Catchment scale hydrological models are critical decision support tools for water resources management and environment remediation. However, the reliability of hydrological models is inevitably affected by limited measurements and imperfect models. Data assimilation techniques combine complementary information from measurements and models to enhance the model reliability and reduce predictive uncertainties. As a sequential data assimilation technique, the ensemble Kalman filter (EnKF) has been extensively studied in the earth sciences for assimilating in-situ measurements and remote sensing data. Although the EnKF has been demonstrated in land surface data assimilations, there are no systematic studies to investigate its performance in distributed modeling with high dimensional states and parameters. In this paper, we present an assessment on the EnKF with state augmentation for combined state-parameter estimation on the basis of a physical-based hydrological model, Soil and Water Assessment Tool (SWAT). Through synthetic simulation experiments, the capability of the EnKF is demonstrated by assimilating the runoff and other measurements, and its sensitivities are analyzed with respect to the error specification, the initial realization and the ensemble size. It is found that the EnKF provides an efficient approach for obtaining a set of acceptable model parameters and satisfactory runoff, soil water content and evapotranspiration estimations. The EnKF performance could be improved after augmenting with other complementary data, such as soil water content and evapotranspiration from remote sensing retrieval. Sensitivity studies demonstrate the importance of consistent error specification and the potential with small ensemble size in the data assimilation system.  相似文献   

9.
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   

10.
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   

11.
A series of numerical experiments for data assimilation with the Ensemble Kalman Filter (EnKF) in a shallow water model are reported. Temperature profiles measured at a North Sea location, 55°30ˊ North and 0°55ˊ East (referred to as the CS station of the NERC North Sea project), are assimilated in 1-D simulations. Comparison of simulations without assimilation to model results obtained when assimilating data with the EnKF allows us to assess the filter performance in reproducing features of the observations not accounted for by the model. The quality of the model error sampling is tested as well as the validity of the Gaussian hypothesis underlying the analysis scheme of the EnKF. The influence of the model error parameters and the frequency of the data assimilation are investigated and discussed. From these experiments, a set of optimal parameters for the model error sampling are deduced and used to test the behavior of the EnKF when propagating surface information into the water column.  相似文献   

12.
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   

13.
太湖叶绿素a同化系统敏感性分析   总被引：1，自引：1，他引：0  
太湖叶绿素a同化系统对于不同参数的敏感性将直接影响到该系统能否精确的估算太湖叶绿素a的浓度分布.利用2009年4月21日环境一号卫星(HJ-1B CCD2)影像数据反演太湖叶绿素a浓度场信息.以此作为背景场信息,结合基于集合均方根滤波的太湖叶绿素a同化系统,分析和评价了样本数目、同化时长、背景场误差、观测误差和模型误差对于同化系统性能的影响.结果表明:从计算成本、系统运行时间和同化效果等方面分析,当集合样本数目达到30~40左右时同化系统取得了较好的结果;同化系统对于背景场误差的估计变化不是很敏感,即初始场的估计是否准确对于同化系统的性能影响不是很大;同化系统对于模型误差和观测误差的变化较为敏感,不同的测试点位由于水体动力学性质不一,其敏感性的表现形式有所差异;利用数据同化方法可以有效地估算太湖叶绿素a浓度.  相似文献   

14.
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15.
Multiphase dynamic data integration into high resolution subsurface models is an integral aspect of reservoir and groundwater management strategies and uncertainty assessment. Over the past two decades, advances in computing and the development and implementation of robust algorithms for automatic history matching have considerably reduced the time and effort associated with subsurface characterization and reduced the subjectivity associated with manual model calibration. However, reliable and accurate subsurface characterization continues to be challenging due to the large number of model unknowns to be estimated using a relatively smaller set of measurements. For ensemble-based methods in particular, the difficulties are compounded by the need for a large number of model replicates to estimate sample-based statistical measures, specifically the covariances and cross-covariances that directly impact the spread of information from the measurement locations to the model parameters. Statistical noise resulting from modest ensemble sizes can overwhelm and degrade the model updates leading to geologically inconsistent subsurface models. In this work we propose to address the difficulties in the implementation of the ensemble Kalman filter (EnKF) for operational data integration problems. The methods described here use streamline-derived information to identify regions within the reservoir that will have a maximum impact on the dynamic response. This is achieved through spatial localization of the sample-based cross-covariance estimates between the measurements and the model unknowns using streamline trajectories. We illustrate the approach with a synthetic example and a large field-study that demonstrate the difficulties with the traditional EnKF implementation. In both the numerical experiments, it is shown that these challenges are addressed using flow relevant conditioning of the cross-covariance matrix. By mitigating sampling error in the cross-covariance estimates, the proposed approach provides significant computational savings through the use of modest ensemble sizes, and consequently offers the opportunity for use with large field-scale groundwater and reservoir characterization studies.  相似文献   

16.
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   

17.
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   

18.
In this study, we implement Particle Filter (PF)-based assimilation algorithms to improve root-zone soil moisture (RZSM) estimates from a coupled SVAT-vegetation model during a growing season of sweet corn in North Central Florida. The results from four different PF algorithms were compared with those from the Ensemble Kalman Filter (EnKF) when near-surface soil moisture was assimilated every 3 days using both synthetic and field observations. In the synthetic case, the PF algorithm with the best performance used residual resampling of the states and obtained resampled parameters from a uniform distribution and provided reductions of 76% in root mean square error (RMSE) over the openloop estimates. The EnKF provided the RZSM and parameter estimates that were closer to the truth than the PF with an 84% reduction in RMSE. When field observations were assimilated, the PF algorithm that maintained maximum parameter diversity offered the largest reduction of 16% in root mean square difference (RMSD) over the openloop estimates. Minimal differences were observed in the overall performance of the EnKF and PF using field observations since errors in model physics affected both the filters in a similar manner, with maximum reductions in RMSD compared to the openloop during the mid and reproductive stages.  相似文献   

19.
The effectiveness of an ensemble Kalman filter (EnKF) is assessed in the Selat Pauh of Singapore using observing system simulation experiment. Perfect model experiments are first considered. The perfect model experiments examine the EnKF in reducing the initial perturbations with no further errors than those in the initial conditions. Current velocity at 15 observational sites from the true ocean is assimilated every hour into the false ocean. While EnKF reduces the initial velocity error during the first few hours, it fails after one tidal cycle (approximately 12 h) due to the rapid convergence of the ensemble members. Successively, errors are introduced in the surface wind forcing. A random perturbation ε is applied independently to each ensemble member to maintain the ensemble spread. The assimilation results showed that the success of EnKF depends critically on the presence of ε, yet it is not sensitive to the magnitude of ε, at least in the range of weak to moderate perturbations. Although all experiments were made with EnKF only, the results could be applicable in general to all other ensemble-based data assimilation methods.  相似文献   

20.
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