The paper investigates the ability to retrieve the true soil moisture profile by assimilating near-surface soil moisture into a soil moisture model with an ensemble Kalman filter (EnKF) assimilation scheme, includin...The paper investigates the ability to retrieve the true soil moisture profile by assimilating near-surface soil moisture into a soil moisture model with an ensemble Kalman filter (EnKF) assimilation scheme, including the effect of ensemble size, update interval and nonlinearities in the profile retrieval, the required time for full retrieval of the soil moisture profiles, and the possible influence of the depth of the soil moisture observation. These questions are addressed by a desktop study using synthetic data. The "true" soil moisture profiles are generated from the soil moisture model under the boundary condition of 0.5 cm d^-1 evaporation. To test the assimilation schemes, the model is initialized with a poor initial guess of the soil moisture profile, and different ensemble sizes are tested showing that an ensemble of 40 members is enough to represent the covariance of the model forecasts. Also compared are the results with those from the direct insertion assimilation scheme, showing that the EnKF is superior to the direct insertion assimilation scheme, for hourly observations, with retrieval of the soil moisture profile being achieved in 16 h as compared to 12 days or more. For daily observations, the true soil moisture profile is achieved in about 15 days with the EnKF, but it is impossible to approximate the true moisture within 18 days by using direct insertion. It is also found that observation depth does not have a significant effect on profile retrieval time for the EnKF. The nonlinearities have some negative influence on the optimal estimates of soil moisture profile but not very seriously.展开更多
This study examines the performance of coupling the deterministic four-dimensional variational assimilation system (4DVAR) with an ensemble Kalman filter (EnKF) to produce a superior hybrid approach for data assim...This study examines the performance of coupling the deterministic four-dimensional variational assimilation system (4DVAR) with an ensemble Kalman filter (EnKF) to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme (E4DVAR) benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence: the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.展开更多
This study explored the impact of coastal radar observability on the forecast of the track and rainfall of Typhoon Morakot (2009) using a WRF-based ensemble Kalman filter (EnKF) data assimilation (DA) system. Th...This study explored the impact of coastal radar observability on the forecast of the track and rainfall of Typhoon Morakot (2009) using a WRF-based ensemble Kalman filter (EnKF) data assimilation (DA) system. The results showed that the performance of radar EnKF DA was quite sensitive to the number of radars being assimilated and the DA timing relative to the landfall of the tropical cyclone (TC). It was found that assimilating radial velocity (Vr) data from all the four operational radars during the 6 h immediately before TC landfall was quite important for the track and rainfall forecasts after the TC made landfall. The TC track forecast error could be decreased by about 43% and the 24-h rainfall forecast skill could be almost tripled. Assimilating Vr data from a single radar outperformed the experiment without DA, though with less improvement compared to the multiple-radar DA experiment. Different forecast performances were obtained by assimilating different radars, which was closely related to the first-time wind analysis increment, the location of moisture transport, the quasi-stationary rainband, and the local convergence line. However, only assimilating Vr data when the TC was farther away from making landfall might worsen TC track and rainfall forecasts. Besides, this work also demonstrated that Vr data from multiple radars, instead of a single radar, should be used for verification to obtain a more reliable assessment of the EnKF performance.展开更多
In this paper, firstly, the bias between observed radiances from the Advanced TIROS-N Operational Vertical Sounder (ATOVS) and those simulated from a model first-guess are corrected. After bias correction, the obser...In this paper, firstly, the bias between observed radiances from the Advanced TIROS-N Operational Vertical Sounder (ATOVS) and those simulated from a model first-guess are corrected. After bias correction, the observed minus calculated (O-B) radiances of most channels were reduced closer to zero, with peak values in each channel shifted towards zero, and the distribution of O-B closer to a Gaussian distribution than without bias correction. Secondly, ATOVS radiance data with and without bias correction are assimilated directly with an Ensemble Kalman Filter (EnKF) data assimilation system, which are then adopted as the initial fields in the forecast model T106L19 to simulate Typhoon Prapiroon (2006) during the period 2-4 August 2006. The prediction results show that the assimilation of ATOVS radiance data with bias correction has a significant and positive impact upon the prediction of the typhoon's track and intensity, although the results are not perfect.展开更多
In a limited number of ensembles, some samples do not adequately reflect the true atmospheric state and can in turn affect forecast performance. This study explored the feasibility of sample optimization using the ens...In a limited number of ensembles, some samples do not adequately reflect the true atmospheric state and can in turn affect forecast performance. This study explored the feasibility of sample optimization using the ensemble Kalman filter(EnKF) for a simulation of the 2014 Super Typhoon Rammasun, which made landfall in southern China in July 2014. Under the premise of sufficient ensemble spread, keeping samples with a good fit to observations and eliminating those with poor fit can affect the performance of En KF. In the sample optimization, states were selected based on the sample spatial correlation between the ensemble state and observations. The method discarded ensemble states that were less representative and, to maintain the overall ensemble size, generated new ensemble states by reproducing them from ensemble states with a good fit by adding random noise. Sample selection was performed based on radar echo data. Results showed that applying En KF with optimized samples improved the estimated track, intensity,precipitation distribution, and inner-core structure of Typhoon Rammasun. Therefore, the authors proposed that distinguishing between samples with good and poor fits is vital for ensemble prediction, suggesting that sample optimization is necessary to the effective use of En KF.展开更多
To accurately estimate winter wheat yields and analyze the uncertainty in crop model data assimilations, winter wheat yield estimates were obtained by assimilating measured or remotely sensed leaf area index (LAI) v...To accurately estimate winter wheat yields and analyze the uncertainty in crop model data assimilations, winter wheat yield estimates were obtained by assimilating measured or remotely sensed leaf area index (LAI) values. The performances of the calibrated crop environment resource synthesis for wheat (CERES-Wheat) model for two different assimilation scenarios were compared by employing ensemble Kalman filter (EnKF)-based strategies. The uncertainty factors of the crop model data assimilation was analyzed by considering the observation errors, assimilation stages and temporal-spatial scales. Overalll the results indicated a better yield estimate performance when the EnKF-based strategy was used to comprehen- sively consider several factors in the initial conditions and observations. When using this strategy, an adjusted coefficients of determination (R2) of 0.84, a root mean square error (RMSE) of 323 kg ha-1, and a relative errors (RE) of 4.15% were obtained at the field plot scale and an R2 of 0.81, an RMSE of 362 kg ha-1, and an RE of 4.52% were obtained at the pixel scale of 30 mx30 m. With increasing observation errors, the accuracy of the yield estimates obviously decreased, but an acceptable estimate was observed when the observation errors were within 20%. Winter wheat yield estimates could be improved significantly by assimilating observations from the middle to the end of the crop growing seasons. With decreasing assimilation frequency and pixel resolution, the accuracy of the crop yield estimates decreased; however, the computation time decreased. It is important to consider reasonable temporal-spatial scales and assimilation stages to obtain tradeoffs between accuracy and computation time, especially in operational systems used for regional crop yield estimates.展开更多
Reservoir inversion by production history matching is an important way to decrease the uncertainty of the reservoir description. Ensemble Kalman filter (EnKF) is a new data assimilation method. There are two problem...Reservoir inversion by production history matching is an important way to decrease the uncertainty of the reservoir description. Ensemble Kalman filter (EnKF) is a new data assimilation method. There are two problems have to be solved for the standard EnKF. One is the inconsistency between the updated model and the updated dynamical variables for nonlinear problems, another is the filter divergence caused by the small ensemble size. We improved the EnKF to overcome these two problems. We use the half iterative EnKF (HIEnKF) for reservoir inversion by doing history matching. During the H1EnKF process, the prediction data are obtained by rerunning the reservoir simulator using the updated model. This can guarantee that the updated dynamical variables are consistent with the updated model. The updated model can nonlinearly affect the prediction data. It is proved that HIEnKF is similar to the first iteration of the EnRML method. Covariance localization is introduced to alleviate filter divergence and spurious correlations caused by the small ensemble size. By defining the shape and size of the correlation area, spurious correlation between the gridblocks far apart is alleviated. More freedom of the model ensemble is preserved. The results of history matching and inverse problem obtained from the HIEnKF with covariance localization are improved. The results show that the model freedom increases with a decrease in the correlation length. Therefore the production data can be matched better. But too small a correlation length can lose some reservoir information and this would cause big errors in the reservoir model estimation.展开更多
Ensemble-based analyses are useful to compare equiprobable scenarios of the reservoir models.However,they require a large suite of reservoir models to cover high uncertainty in heterogeneous and complex reservoir mode...Ensemble-based analyses are useful to compare equiprobable scenarios of the reservoir models.However,they require a large suite of reservoir models to cover high uncertainty in heterogeneous and complex reservoir models.For stable convergence in ensemble Kalman filter(EnKF),increasing ensemble size can be one of the solutions,but it causes high computational cost in large-scale reservoir systems.In this paper,we propose a preprocessing of good initial model selection to reduce the ensemble size,and then,EnKF is utilized to predict production performances stochastically.In the model selection scheme,representative models are chosen by using principal component analysis(PCA)and clustering analysis.The dimension of initial models is reduced using PCA,and the reduced models are grouped by clustering.Then,we choose and simulate representative models from the cluster groups to compare errors of production predictions with historical observation data.One representative model with the minimum error is considered as the best model,and we use the ensemble members near the best model in the cluster plane for applying EnKF.We demonstrate the proposed scheme for two 3D models that EnKF provides reliable assimilation results with much reduced computation time.展开更多
Data assimilation in agricultural remote sensing research is of great significance to integrate with remote sensing observations and model simulations for parameters estimation. The present investigation not only desi...Data assimilation in agricultural remote sensing research is of great significance to integrate with remote sensing observations and model simulations for parameters estimation. The present investigation not only designed and realized the Ensemble Kalman Filtering algorithm (EnKF) assimilation by combing the crop growth model (CERES-Wheat) with remote sensing data, but also optimized and updated the key parameters (LAI) of winter wheat by using remote sensing data. Results showed that the assimilation LAI and the observation ones agreed with each other, and the R2 reached 0.8315. So assimilation remote sensing and crop model could provide reference data for the agricultural production.展开更多
The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to ...The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors (BVs) are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector (NLLV) scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram-Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more com- ponents in analysis errors than the BVs. In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random pertur- bation (RP) technique, and the BV method, as well as its improved version--the ensemble transform Kalman filter (ETKF) method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.展开更多
Correctly estimating the forecast error covariance matrix is a key step in any data assimilation scheme. If it is not correctly estimated, the assimilated states could be far from the true states. A popular method to ...Correctly estimating the forecast error covariance matrix is a key step in any data assimilation scheme. If it is not correctly estimated, the assimilated states could be far from the true states. A popular method to address this problem is error covariance matrix inflation. That is, to multiply the forecast error covariance matrix by an appropriate factor. In this paper, analysis states are used to construct the forecast error covariance matrix and an adaptive estimation procedure associated with the error covariance matrix inflation technique is developed. The proposed assimilation scheme was tested on the Lorenz-96 model and 2D Shallow Water Equation model, both of which are associated with spatially correlated observational systems. The experiments showed that by introducing the proposed structure of the forecast error eovariance matrix and applying its adaptive estimation procedure, the assimilation results were further improved.展开更多
The computational cost required by the Ensemble Kalman Filter (EnKF) is much larger than that of some simpler assimilation schemes, such as Optimal Interpolation (OI) or three-dimension variational as- similation ...The computational cost required by the Ensemble Kalman Filter (EnKF) is much larger than that of some simpler assimilation schemes, such as Optimal Interpolation (OI) or three-dimension variational as- similation (3DVAR). Ensemble optimal interpolation (EnOI), a crudely simplified implementation of EnKF, is sometimes used as a substitute in some oceanic applications and requires much less computational time than EnKF. In this paper, to compromise between computational cost and dynamic covariance, we use the idea of "dressing" a small size dynamical ensemble with a larger number of static ensembles in order to form an approximate dynamic covariance. The term "dressing" means that a dynamical ensemble seed from model runs is perturbed by adding the anomalies of some static ensembles. This dressing EnKF (DrEnKF for short) scheme is tested in assimilation of real altimetry data in the Pacific using the HYbrid Coordinate Ocean Model (HYCOM) over a four-year period. Ten dynamical ensemble seeds are each dressed by 10 static ensemble members selected from a 100-member static ensemble. Results are compared to two EnKF assimilation runs that use 10 and 100 dynamical ensemble members. Both temperature and salinity fields from the DrEnKF and the EnKF are compared to observations from Argo floats and an OI SST dataset. The results show that the DrEnKF and the 100-member EnKF yield similar root mean square errors (RMSE) at every model level. Error covariance matrices from the DrEnKF and the 100-member EnKF are also compared and show good agreement.展开更多
ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement fun...ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions: the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.展开更多
Though the ensemble Kalman filter (EnKF) has been successfully applied in many areas, it requires explicit and accurate model and measurement error information, leading to difficulties in practice when only limited ...Though the ensemble Kalman filter (EnKF) has been successfully applied in many areas, it requires explicit and accurate model and measurement error information, leading to difficulties in practice when only limited information on error mechanisms of observational in-struments for subsurface systems is accessible. To handle the uncertain errors, we applied a robust data assimilation algorithm, the ensemble H-infinity filter (EnHF), to estimation of aquifer hydraulic heads and conductivities in a flow model with uncertain/correlated observational errors. The impacts of spatial and temporal correlations in measurements were analyzed, and the performance of EnHF was compared with that of the EnKF. The results show that both EnHF and EnKF are able to estimate hydraulic conductivities properly when observations are free of error; EnHF can provide robust estimates of hydraulic conductivities even when no observational error information is provided. In contrast, the estimates of EnKF seem noticeably undermined because of correlated errors and inaccurate error statistics, and filter divergence was observed. It is concluded that EnHF is an efficient assimilation algorithm when observational errors are unknown or error statistics are inaccurate.展开更多
This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that o...This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, en- semble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition (also called phase transition) and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.展开更多
Temperature (T) and salinity (S) profiles from conductivity-temperature-depth data collected during the Northern South China Sea Open Cruise from August 16 to September 13, 2008 are assimilated using Ensemble Kalm...Temperature (T) and salinity (S) profiles from conductivity-temperature-depth data collected during the Northern South China Sea Open Cruise from August 16 to September 13, 2008 are assimilated using Ensemble Kalman Filter (EnKF). An adaptive observational error strategy is used to prevent filter from diverging. In the meantime, aiming at the limited improvement in some sites caused by the T and S biases in the model, a T-S constraint scheme is adopted to improve the assimilation performance, where T and S are separately updated at these locations. Validation is performed by comparing assimilated outputs with independent in situ data (satellite remote sensing sea level anomaly (SLA), the OSCAR velocity product and shipboard ADCP). The results show that the new EnKF assimilation scheme can significantly reduce the root mean square error (RMSE) of oceanic T and S compared with the control run and traditional EnKF. The system can also improve the simulation of circulations and SLA.展开更多
The Localized Weighted Ensemble Kalman Filter(LWEnKF)is a new nonlinear/non-Gaussian data assimilation(DA)method that can effectively alleviate the filter degradation problem faced by particle filtering,and it has gre...The Localized Weighted Ensemble Kalman Filter(LWEnKF)is a new nonlinear/non-Gaussian data assimilation(DA)method that can effectively alleviate the filter degradation problem faced by particle filtering,and it has great prospects for applications in geophysical models.In terms of operational applications,along-track sea surface height(AT-SSH),swath sea surface temperature(S-SST)and in-situ temperature and salinity(T/S)profiles are assimilated using the LWEnKF in the northern South China Sea(SCS).To adapt to the vertical S-coordinates of the Regional Ocean Modelling System(ROMS),a vertical localization radius function is designed for T/S profiles assimilation using the LWEnKF.The results show that the LWEnKF outperforms the local particle filter(LPF)due to the introduction of the Ensemble Kalman Filter(EnKF)as a proposal density;the RMSEs of SSH and SST from the LWEnKF are comparable to the EnKF,but the RMSEs of T/S profiles reduce significantly by approximately 55%for the T profile and 35%for the S profile(relative to the EnKF).As a result,the LWEnKF makes more reasonable predictions of the internal ocean temperature field.In addition,the three-dimensional structures of nonlinear mesoscale eddies are better characterized when using the LWEnKF.展开更多
The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful ch...The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful choice of an initial ensemble perturbation method that dynamically cycles ensemble perturbations is required for the optimal performance of the system. Based on the multivariate empirical orthogonal function (MEOF) method, a new ensemble initialization scheme is developed to generate balanced initial perturbations for the ensemble Kalman filter (EnKF) data assimilation, with a reasonable consideration of the physical relationships between different model variables. The scheme is applied in assimilation experiments with a global spectral atmospheric model and with real observations. The proposed perturbation method is compared to the commonly used method of spatially-correlated random perturbations. The comparisons show that the model uncertainties prior to the first analysis time, which are forecasted from the balanced ensemble initial fields, maintain a much more reasonable spread and a more accurate forecast error covariance than those from the randomly perturbed initial fields. The analysis results are further improved by the balanced ensemble initialization scheme due to more accurate background information. Also, a 20-day continuous assimilation experiment shows that the ensemble spreads for each model variable are still retained in reasonable ranges without considering additional perturbations or inflations during the assimilation cycles, while the ensemble spreads from the randomly perturbed initialization scheme decrease and collapse rapidly.展开更多
Hybrid data assimilation (DA) is a method seeing more use in recent hydrology and water resources research. In this study, a DA method coupled with the support vector machines (SVMs) and the ensemble Kalman filter...Hybrid data assimilation (DA) is a method seeing more use in recent hydrology and water resources research. In this study, a DA method coupled with the support vector machines (SVMs) and the ensemble Kalman filter (EnKF) technology was used for the prediction of soil moisture in different soil layers: 0-5 cm, 30 cm, 50 cm, 100 cm, 200 cm, and 300 cm. The SVM methodology was first used to train the ground measurements of soil moisture and meteorological parameters from the Meilin study area, in East China, to construct soil moisture statistical prediction models. Subsequent observations and their statistics were used for predictions, with two approaches: the SVM predictor and the SVM-EnKF model made by coupling the SVM model with the EnKF technique using the DA method. Validation results showed that the proposed SVM-EnKF model can improve the prediction results of soil moisture in different layers, from the surface to the root zone.展开更多
The remaining useful life(RUL)prediction is a crucial indicator for the lithium-ion battery health prognostic.The particle filter(PF),used together with an empirical model,has become one of the most well-accepted tech...The remaining useful life(RUL)prediction is a crucial indicator for the lithium-ion battery health prognostic.The particle filter(PF),used together with an empirical model,has become one of the most well-accepted techniques for RUL prediction.In this work,a novel filtering algorithm,named the Gaussian mixture model(GMM)-ensemble Kalman filter(EnKF)is proposed.It embeds the Gaussian mixture model in the EnKF framework to cope with the non-Gaussian feature of the system state space,and meanwhile address some of the major shortcomings of the PF.The GMM-EnKF and the PF are both applied on public data sets for RUL prediction and the simulation results show superiority of our proposed approach to the PF.展开更多
基金the National Natural Science Foundation of China(Grant Nos.40475012,90202014, 2001CB309404).
文摘The paper investigates the ability to retrieve the true soil moisture profile by assimilating near-surface soil moisture into a soil moisture model with an ensemble Kalman filter (EnKF) assimilation scheme, including the effect of ensemble size, update interval and nonlinearities in the profile retrieval, the required time for full retrieval of the soil moisture profiles, and the possible influence of the depth of the soil moisture observation. These questions are addressed by a desktop study using synthetic data. The "true" soil moisture profiles are generated from the soil moisture model under the boundary condition of 0.5 cm d^-1 evaporation. To test the assimilation schemes, the model is initialized with a poor initial guess of the soil moisture profile, and different ensemble sizes are tested showing that an ensemble of 40 members is enough to represent the covariance of the model forecasts. Also compared are the results with those from the direct insertion assimilation scheme, showing that the EnKF is superior to the direct insertion assimilation scheme, for hourly observations, with retrieval of the soil moisture profile being achieved in 16 h as compared to 12 days or more. For daily observations, the true soil moisture profile is achieved in about 15 days with the EnKF, but it is impossible to approximate the true moisture within 18 days by using direct insertion. It is also found that observation depth does not have a significant effect on profile retrieval time for the EnKF. The nonlinearities have some negative influence on the optimal estimates of soil moisture profile but not very seriously.
基金sponsored by the U.S. National Science Foundation (Grant No.ATM0205599)the U.S. Offce of Navy Research under Grant N000140410471Dr. James A. Hansen was partially supported by US Offce of Naval Research (Grant No. N00014-06-1-0500)
文摘This study examines the performance of coupling the deterministic four-dimensional variational assimilation system (4DVAR) with an ensemble Kalman filter (EnKF) to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme (E4DVAR) benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence: the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.
基金sponsored by the Special Fund for Meteorological Research in the Public Interest from the Ministry of Science and Technology of China(Grant No.GYHY201306004)the National Key Basic Research Program of China(Grant No.2013CB430104)+1 种基金the National Natural Science Foundation of China(Grant Nos.41461164006,41375048 and 41425018)supported by the Ministry of Science and Technology of Taiwan(Grant No.MOST103-2111-M-002-011-MY3)
文摘This study explored the impact of coastal radar observability on the forecast of the track and rainfall of Typhoon Morakot (2009) using a WRF-based ensemble Kalman filter (EnKF) data assimilation (DA) system. The results showed that the performance of radar EnKF DA was quite sensitive to the number of radars being assimilated and the DA timing relative to the landfall of the tropical cyclone (TC). It was found that assimilating radial velocity (Vr) data from all the four operational radars during the 6 h immediately before TC landfall was quite important for the track and rainfall forecasts after the TC made landfall. The TC track forecast error could be decreased by about 43% and the 24-h rainfall forecast skill could be almost tripled. Assimilating Vr data from a single radar outperformed the experiment without DA, though with less improvement compared to the multiple-radar DA experiment. Different forecast performances were obtained by assimilating different radars, which was closely related to the first-time wind analysis increment, the location of moisture transport, the quasi-stationary rainband, and the local convergence line. However, only assimilating Vr data when the TC was farther away from making landfall might worsen TC track and rainfall forecasts. Besides, this work also demonstrated that Vr data from multiple radars, instead of a single radar, should be used for verification to obtain a more reliable assessment of the EnKF performance.
基金supported by the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant Nos KZCX2-YW-202 and KZCX2-YW-Q03-3)the Chinese Special Scientific Research Project for Public Interest (Grant No GYHY200906004)
文摘In this paper, firstly, the bias between observed radiances from the Advanced TIROS-N Operational Vertical Sounder (ATOVS) and those simulated from a model first-guess are corrected. After bias correction, the observed minus calculated (O-B) radiances of most channels were reduced closer to zero, with peak values in each channel shifted towards zero, and the distribution of O-B closer to a Gaussian distribution than without bias correction. Secondly, ATOVS radiance data with and without bias correction are assimilated directly with an Ensemble Kalman Filter (EnKF) data assimilation system, which are then adopted as the initial fields in the forecast model T106L19 to simulate Typhoon Prapiroon (2006) during the period 2-4 August 2006. The prediction results show that the assimilation of ATOVS radiance data with bias correction has a significant and positive impact upon the prediction of the typhoon's track and intensity, although the results are not perfect.
基金National Key Project for Basic Research(973 project)(2015CB452802)National Natural Science Fund(41475102,41675099,41475061)+2 种基金Science and Technology Planning Project of Guangdong Province(2017B020218003,2017B030314140)Natural Science Foundation of Guangdong Province(2016A030313140,2017A030313225)Science and technology project of Guangdong Meteorological Bureau(GRMC2017Q01)
文摘In a limited number of ensembles, some samples do not adequately reflect the true atmospheric state and can in turn affect forecast performance. This study explored the feasibility of sample optimization using the ensemble Kalman filter(EnKF) for a simulation of the 2014 Super Typhoon Rammasun, which made landfall in southern China in July 2014. Under the premise of sufficient ensemble spread, keeping samples with a good fit to observations and eliminating those with poor fit can affect the performance of En KF. In the sample optimization, states were selected based on the sample spatial correlation between the ensemble state and observations. The method discarded ensemble states that were less representative and, to maintain the overall ensemble size, generated new ensemble states by reproducing them from ensemble states with a good fit by adding random noise. Sample selection was performed based on radar echo data. Results showed that applying En KF with optimized samples improved the estimated track, intensity,precipitation distribution, and inner-core structure of Typhoon Rammasun. Therefore, the authors proposed that distinguishing between samples with good and poor fits is vital for ensemble prediction, suggesting that sample optimization is necessary to the effective use of En KF.
基金supported by the National Natural Science Foundation of China (41401491,41371396,41301457,41471364)the Introduction of International Advanced Agricultural Science and Technology,Ministry of Agriculture,China (948 Program,2016-X38)+1 种基金the Agricultural Scientific Research Fund of Outstanding Talentsthe Open Fund for the Key Laboratory of Agri-informatics,Ministry of Agriculture,China (2013009)
文摘To accurately estimate winter wheat yields and analyze the uncertainty in crop model data assimilations, winter wheat yield estimates were obtained by assimilating measured or remotely sensed leaf area index (LAI) values. The performances of the calibrated crop environment resource synthesis for wheat (CERES-Wheat) model for two different assimilation scenarios were compared by employing ensemble Kalman filter (EnKF)-based strategies. The uncertainty factors of the crop model data assimilation was analyzed by considering the observation errors, assimilation stages and temporal-spatial scales. Overalll the results indicated a better yield estimate performance when the EnKF-based strategy was used to comprehen- sively consider several factors in the initial conditions and observations. When using this strategy, an adjusted coefficients of determination (R2) of 0.84, a root mean square error (RMSE) of 323 kg ha-1, and a relative errors (RE) of 4.15% were obtained at the field plot scale and an R2 of 0.81, an RMSE of 362 kg ha-1, and an RE of 4.52% were obtained at the pixel scale of 30 mx30 m. With increasing observation errors, the accuracy of the yield estimates obviously decreased, but an acceptable estimate was observed when the observation errors were within 20%. Winter wheat yield estimates could be improved significantly by assimilating observations from the middle to the end of the crop growing seasons. With decreasing assimilation frequency and pixel resolution, the accuracy of the crop yield estimates decreased; however, the computation time decreased. It is important to consider reasonable temporal-spatial scales and assimilation stages to obtain tradeoffs between accuracy and computation time, especially in operational systems used for regional crop yield estimates.
基金support from the Shandong Natural Science Foundation(Grant No.ZR2010EM053)the Fundamental Research Funds for the Central Universities(Grant No.10CX04042A)
文摘Reservoir inversion by production history matching is an important way to decrease the uncertainty of the reservoir description. Ensemble Kalman filter (EnKF) is a new data assimilation method. There are two problems have to be solved for the standard EnKF. One is the inconsistency between the updated model and the updated dynamical variables for nonlinear problems, another is the filter divergence caused by the small ensemble size. We improved the EnKF to overcome these two problems. We use the half iterative EnKF (HIEnKF) for reservoir inversion by doing history matching. During the H1EnKF process, the prediction data are obtained by rerunning the reservoir simulator using the updated model. This can guarantee that the updated dynamical variables are consistent with the updated model. The updated model can nonlinearly affect the prediction data. It is proved that HIEnKF is similar to the first iteration of the EnRML method. Covariance localization is introduced to alleviate filter divergence and spurious correlations caused by the small ensemble size. By defining the shape and size of the correlation area, spurious correlation between the gridblocks far apart is alleviated. More freedom of the model ensemble is preserved. The results of history matching and inverse problem obtained from the HIEnKF with covariance localization are improved. The results show that the model freedom increases with a decrease in the correlation length. Therefore the production data can be matched better. But too small a correlation length can lose some reservoir information and this would cause big errors in the reservoir model estimation.
基金supported by The Ministry of Trade,Industry,and Energy(20172510102090,20142520100440,20162010201980)Global PhD Fellowship Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2015H1A2A1030756)supported by the National Research Foundation of Korea(NRF)Grant(No.2018R1C1B5045260).
文摘Ensemble-based analyses are useful to compare equiprobable scenarios of the reservoir models.However,they require a large suite of reservoir models to cover high uncertainty in heterogeneous and complex reservoir models.For stable convergence in ensemble Kalman filter(EnKF),increasing ensemble size can be one of the solutions,but it causes high computational cost in large-scale reservoir systems.In this paper,we propose a preprocessing of good initial model selection to reduce the ensemble size,and then,EnKF is utilized to predict production performances stochastically.In the model selection scheme,representative models are chosen by using principal component analysis(PCA)and clustering analysis.The dimension of initial models is reduced using PCA,and the reduced models are grouped by clustering.Then,we choose and simulate representative models from the cluster groups to compare errors of production predictions with historical observation data.One representative model with the minimum error is considered as the best model,and we use the ensemble members near the best model in the cluster plane for applying EnKF.We demonstrate the proposed scheme for two 3D models that EnKF provides reliable assimilation results with much reduced computation time.
基金supported by the National Natural Science Foundation of China (40701120)the Beijing Natural Science Foundation, China (4092016)the Beijing Nova, China (2008B33)
文摘Data assimilation in agricultural remote sensing research is of great significance to integrate with remote sensing observations and model simulations for parameters estimation. The present investigation not only designed and realized the Ensemble Kalman Filtering algorithm (EnKF) assimilation by combing the crop growth model (CERES-Wheat) with remote sensing data, but also optimized and updated the key parameters (LAI) of winter wheat by using remote sensing data. Results showed that the assimilation LAI and the observation ones agreed with each other, and the R2 reached 0.8315. So assimilation remote sensing and crop model could provide reference data for the agricultural production.
文摘The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors (BVs) are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector (NLLV) scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram-Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more com- ponents in analysis errors than the BVs. In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random pertur- bation (RP) technique, and the BV method, as well as its improved version--the ensemble transform Kalman filter (ETKF) method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.
基金supported by the National Program on Key Basic Research Project of China (Grant No. 2010CB950703)the National Natural Science foundation of China General Program (Grant No. 40975062)the Young Scholars Fundation of Beijing Normal University (Grant No. 105502GK)
文摘Correctly estimating the forecast error covariance matrix is a key step in any data assimilation scheme. If it is not correctly estimated, the assimilated states could be far from the true states. A popular method to address this problem is error covariance matrix inflation. That is, to multiply the forecast error covariance matrix by an appropriate factor. In this paper, analysis states are used to construct the forecast error covariance matrix and an adaptive estimation procedure associated with the error covariance matrix inflation technique is developed. The proposed assimilation scheme was tested on the Lorenz-96 model and 2D Shallow Water Equation model, both of which are associated with spatially correlated observational systems. The experiments showed that by introducing the proposed structure of the forecast error eovariance matrix and applying its adaptive estimation procedure, the assimilation results were further improved.
基金supported by the Knowledge Innovation Program of Chinese Academy of Sciences (Grant No. KZCX1-YW-12-03)National Basic Research Program of China (2006CB403600)+3 种基金Project of Young Scientists Fund by National Natural Sciences Foundation of China (Grant No. 40606008)National Science and Technology Infrastructure Program(2006BAC03B04)supported by National Natural Sciences Foundation of China (Grant No.40531006)supported by a private donation from Trond Mohn c/o Frank Mohn AS, Bergenand the MERSEA project from the European Commission (Grant No. SIP3-CT-2003-502885)
文摘The computational cost required by the Ensemble Kalman Filter (EnKF) is much larger than that of some simpler assimilation schemes, such as Optimal Interpolation (OI) or three-dimension variational as- similation (3DVAR). Ensemble optimal interpolation (EnOI), a crudely simplified implementation of EnKF, is sometimes used as a substitute in some oceanic applications and requires much less computational time than EnKF. In this paper, to compromise between computational cost and dynamic covariance, we use the idea of "dressing" a small size dynamical ensemble with a larger number of static ensembles in order to form an approximate dynamic covariance. The term "dressing" means that a dynamical ensemble seed from model runs is perturbed by adding the anomalies of some static ensembles. This dressing EnKF (DrEnKF for short) scheme is tested in assimilation of real altimetry data in the Pacific using the HYbrid Coordinate Ocean Model (HYCOM) over a four-year period. Ten dynamical ensemble seeds are each dressed by 10 static ensemble members selected from a 100-member static ensemble. Results are compared to two EnKF assimilation runs that use 10 and 100 dynamical ensemble members. Both temperature and salinity fields from the DrEnKF and the EnKF are compared to observations from Argo floats and an OI SST dataset. The results show that the DrEnKF and the 100-member EnKF yield similar root mean square errors (RMSE) at every model level. Error covariance matrices from the DrEnKF and the 100-member EnKF are also compared and show good agreement.
基金supported by research grants from the NSERC (Natural Sciences and Engineering Research Council of Canada) Discovery Programthe National Natural Science Foundation of China (Grant Nos.41276029 and 40730843)the National Basic Research Program (Grant No.2007CB816005)
文摘ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions: the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.
基金supported by the National Natural Science Foundation of China(Grant No.41602250)the Project of the China Geological Survey(Grant No.DD20160293)
文摘Though the ensemble Kalman filter (EnKF) has been successfully applied in many areas, it requires explicit and accurate model and measurement error information, leading to difficulties in practice when only limited information on error mechanisms of observational in-struments for subsurface systems is accessible. To handle the uncertain errors, we applied a robust data assimilation algorithm, the ensemble H-infinity filter (EnHF), to estimation of aquifer hydraulic heads and conductivities in a flow model with uncertain/correlated observational errors. The impacts of spatial and temporal correlations in measurements were analyzed, and the performance of EnHF was compared with that of the EnKF. The results show that both EnHF and EnKF are able to estimate hydraulic conductivities properly when observations are free of error; EnHF can provide robust estimates of hydraulic conductivities even when no observational error information is provided. In contrast, the estimates of EnKF seem noticeably undermined because of correlated errors and inaccurate error statistics, and filter divergence was observed. It is concluded that EnHF is an efficient assimilation algorithm when observational errors are unknown or error statistics are inaccurate.
基金supported by U.S. National Science Foundation through Award Number ATM-0833985
文摘This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, en- semble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition (also called phase transition) and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.
基金The Strategic Priority Research Program of the Chinese Academy of Sciences under contract No.XDA10010405the Promgram of Guangdong Province Department of Science and Technology No.2012A032100004+1 种基金the National Natural Science Foundation of China under contract Nos 41476012,41521005 and 41406131the Knowledge Innovation Program of the Chinese Academy of Sciences under contract Nos SQ201001 and SQ201205
文摘Temperature (T) and salinity (S) profiles from conductivity-temperature-depth data collected during the Northern South China Sea Open Cruise from August 16 to September 13, 2008 are assimilated using Ensemble Kalman Filter (EnKF). An adaptive observational error strategy is used to prevent filter from diverging. In the meantime, aiming at the limited improvement in some sites caused by the T and S biases in the model, a T-S constraint scheme is adopted to improve the assimilation performance, where T and S are separately updated at these locations. Validation is performed by comparing assimilated outputs with independent in situ data (satellite remote sensing sea level anomaly (SLA), the OSCAR velocity product and shipboard ADCP). The results show that the new EnKF assimilation scheme can significantly reduce the root mean square error (RMSE) of oceanic T and S compared with the control run and traditional EnKF. The system can also improve the simulation of circulations and SLA.
基金The National Key Research and Development Program of China under contract No.2018YFC1406202the National Natural Science Foundation of China under contract No.41830964.
文摘The Localized Weighted Ensemble Kalman Filter(LWEnKF)is a new nonlinear/non-Gaussian data assimilation(DA)method that can effectively alleviate the filter degradation problem faced by particle filtering,and it has great prospects for applications in geophysical models.In terms of operational applications,along-track sea surface height(AT-SSH),swath sea surface temperature(S-SST)and in-situ temperature and salinity(T/S)profiles are assimilated using the LWEnKF in the northern South China Sea(SCS).To adapt to the vertical S-coordinates of the Regional Ocean Modelling System(ROMS),a vertical localization radius function is designed for T/S profiles assimilation using the LWEnKF.The results show that the LWEnKF outperforms the local particle filter(LPF)due to the introduction of the Ensemble Kalman Filter(EnKF)as a proposal density;the RMSEs of SSH and SST from the LWEnKF are comparable to the EnKF,but the RMSEs of T/S profiles reduce significantly by approximately 55%for the T profile and 35%for the S profile(relative to the EnKF).As a result,the LWEnKF makes more reasonable predictions of the internal ocean temperature field.In addition,the three-dimensional structures of nonlinear mesoscale eddies are better characterized when using the LWEnKF.
基金supported by the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KZCX1-YW-12-03)the National Basic Research Program of China (Grant No. 2010CB951901)the National Natural Science Foundation of China (Grant No. 40805033)
文摘The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful choice of an initial ensemble perturbation method that dynamically cycles ensemble perturbations is required for the optimal performance of the system. Based on the multivariate empirical orthogonal function (MEOF) method, a new ensemble initialization scheme is developed to generate balanced initial perturbations for the ensemble Kalman filter (EnKF) data assimilation, with a reasonable consideration of the physical relationships between different model variables. The scheme is applied in assimilation experiments with a global spectral atmospheric model and with real observations. The proposed perturbation method is compared to the commonly used method of spatially-correlated random perturbations. The comparisons show that the model uncertainties prior to the first analysis time, which are forecasted from the balanced ensemble initial fields, maintain a much more reasonable spread and a more accurate forecast error covariance than those from the randomly perturbed initial fields. The analysis results are further improved by the balanced ensemble initialization scheme due to more accurate background information. Also, a 20-day continuous assimilation experiment shows that the ensemble spreads for each model variable are still retained in reasonable ranges without considering additional perturbations or inflations during the assimilation cycles, while the ensemble spreads from the randomly perturbed initialization scheme decrease and collapse rapidly.
基金supported by the National Basic Research Program of China (the 973 Program,Grant No.2010CB951101)the Program for Changjiang Scholars and Innovative Research Teams in Universities,the Ministry of Education,China (Grant No. IRT0717)
文摘Hybrid data assimilation (DA) is a method seeing more use in recent hydrology and water resources research. In this study, a DA method coupled with the support vector machines (SVMs) and the ensemble Kalman filter (EnKF) technology was used for the prediction of soil moisture in different soil layers: 0-5 cm, 30 cm, 50 cm, 100 cm, 200 cm, and 300 cm. The SVM methodology was first used to train the ground measurements of soil moisture and meteorological parameters from the Meilin study area, in East China, to construct soil moisture statistical prediction models. Subsequent observations and their statistics were used for predictions, with two approaches: the SVM predictor and the SVM-EnKF model made by coupling the SVM model with the EnKF technique using the DA method. Validation results showed that the proposed SVM-EnKF model can improve the prediction results of soil moisture in different layers, from the surface to the root zone.
基金supported by Natural Science Basic Research Program of Shaanxi Province of China(No.2020JQ-683)Key Research&Design Project of Shaanxi Province(No.2019TSLGY04-06)。
文摘The remaining useful life(RUL)prediction is a crucial indicator for the lithium-ion battery health prognostic.The particle filter(PF),used together with an empirical model,has become one of the most well-accepted techniques for RUL prediction.In this work,a novel filtering algorithm,named the Gaussian mixture model(GMM)-ensemble Kalman filter(EnKF)is proposed.It embeds the Gaussian mixture model in the EnKF framework to cope with the non-Gaussian feature of the system state space,and meanwhile address some of the major shortcomings of the PF.The GMM-EnKF and the PF are both applied on public data sets for RUL prediction and the simulation results show superiority of our proposed approach to the PF.