Comparison of Nonlinear Local Lyapunov Vectors with Bred Vectors, Random Perturbations and Ensemble Transform Kalman Filter Strategies in a Barotropic Model

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.

Ensemble Transform Sensitivity Method for Adaptive Observations

The Ensemble Transform（ET） method has been shown to be useful in providing guidance for adaptive observation deployment.It predicts forecast error variance reduction for each possible deployment using its corresponding transformation matrix in an ensemble subspace.In this paper,a new ET-based sensitivity（ETS） method,which calculates the gradient of forecast error variance reduction in terms of analysis error variance reduction,is proposed to specify regions for possible adaptive observations.ETS is a first order approximation of the ET;it requires just one calculation of a transformation matrix,increasing computational efficiency（60%-80%reduction in computational cost）.An explicit mathematical formulation of the ETS gradient is derived and described.Both the ET and ETS methods are applied to the Hurricane Irene（2011） case and a heavy rainfall case for comparison.The numerical results imply that the sensitive areas estimated by the ETS and ET are similar.However,ETS is much more efficient,particularly when the resolution is higher and the number of ensemble members is larger.

A Comparison of Breeding and Ensemble Transform Vectors for Global Ensemble Generation

To compare the initial perturbation techniques using breeding vectors and ensemble transform vectors, three ensemble prediction systems using both initial perturbation methods but with different ensemble member sizes based on the spectral model T213/L31 are constructed at the National Meteorological Center, China Meteorological Administration （NMC/CMA）. A series of ensemble verification scores such as forecast skill of the ensemble mean, ensemble resolution, and ensemble reliability are introduced to identify the most important attributes of ensemble forecast systems. The results indicate that the ensemble transform tech- nique is superior to the breeding vector method in light of the evaluation of anomaly correlation coefficient （ACC）, which is a deterministic character of the ensemble mean, the root-mean-square error （RMSE） and spread, which are of probabilistic attributes, and the continuous ranked probability score （CRPS） and its decomposition. The advantage of the ensemble transform approach is attributed to its orthogonality among ensemble perturbations as well as its consistence with the data assimilation system. Therefore, this study may serve as a reference for configuration of the best ensemble prediction system to be used in operation.

The Effects of Land Surface Process Perturbations in a Global Ensemble Forecast System

Atmospheric variability is driven not only by internal dynamics, but also by external forcing, such as soil states, SST, snow, sea-ice cover, and so on. To investigate the forecast uncertainties and effects of land surface processes on numerical weather prediction, we added modules to perturb soil moisture and soil temperature into NCEP＇s Global Ensemble Forecast System （GEFS）, and compared the results of a set of experiments involving different configurations of land surface and atmospheric perturbation. It was found that uncertainties in different soil layers varied due to the multiple timescales of interactions between land surface and atmospheric processes. Perturbations of the soil moisture and soil temperature at the land surface changed sensible and latent heat flux obviously, as compared to the less or indirect land surface perturbation experiment from the day-to-day forecasts. Soil state perturbations led to greater variation in surface heat fluxes that transferred to the upper troposphere, thus reflecting interactions and the response to atmospheric external forcing. Various verification scores were calculated in this study. The results indicated that taking the uncertainties of land surface processes into account in GEFS could contribute a slight improvement in forecast skill in terms of resolution and reliability, a noticeable reduction in forecast error, as well as an increase in ensemble spread in an under-dispersive system. This paper provides a preliminary evaluation of the effects of land surface processes on predictability. Further research using more complex and suitable methods is needed to fully explore our understanding in this area.

Impact of Perturbation Schemes on the Ensemble Prediction in a Coupled Lorenz Model

Based on a simple coupled Lorenz model,we investigate how to assess a suitable initial perturbation scheme for ensemble forecasting in a multiscale system involving slow dynamics and fast dynamics.Four initial perturbation approaches are used in the ensemble forecasting experiments:the random perturbation(RP),the bred vector(BV),the ensemble transform Kalman filter(ETKF),and the nonlinear local Lyapunov vector(NLLV)methods.Results show that,regardless of the method used,the ensemble averages behave indistinguishably from the control forecasts during the first few time steps.Due to different error growth in different time-scale systems,the ensemble averages perform better than the control forecast after very short lead times in a fast subsystem but after a relatively long period of time in a slow subsystem.Due to the coupled dynamic processes,the addition of perturbations to fast variables or to slow variables can contribute to an improvement in the forecasting skill for fast variables and slow variables.Regarding the initial perturbation approaches,the NLLVs show higher forecasting skill than the BVs or RPs overall.The NLLVs and ETKFs had nearly equivalent prediction skill,but NLLVs performed best by a narrow margin.In particular,when adding perturbations to slow variables,the independent perturbations(NLLVs and ETKFs)perform much better in ensemble prediction.These results are simply implied in a real coupled air–sea model.For the prediction of oceanic variables,using independent perturbations(NLLVs)and adding perturbations to oceanic variables are expected to result in better performance in the ensemble prediction.

Effect of Doubling the Ensemble Size on the Performance of Ensemble Prediction in the Warm Season Using MOGREPS Implemented at the KMA

Using the Met Office Global and Regional Ensemble Prediction System （MOGREPS） implemented at the Korea Meteorological Administration （KMA）, the effect of doubling the ensemble size on the performance of ensemble prediction in the warm season was evaluated. Because a finite ensemble size causes sampling error in the full forecast probability distribution function （PDF）, ensemble size is closely related to the efficiency of the ensemble prediction system. Prediction capability according to doubling the ensemble size was evaluated by increasing the number of ensembles from 24 to 48 in MOGREPS implemented at the KMA. The initial analysis perturbations generated by the Ensemble Transform Kalman Filter （ETKF） were integrated for 10 days from 22 May to 23 June 2009. Several statistical verification scores were used to measure the accuracy, reliability, and resolution of ensemble probabilistic forecasts for 24 and 48 ensemble member forecasts. Even though the results were not significant, the accuracy of ensemble prediction improved slightly as ensemble size increased, especially for longer forecast times in the Northern Hemisphere. While increasing the number of ensemble members resulted in a slight improvement in resolution as forecast time increased, inconsistent results were obtained for the scores assessing the reliability of ensemble prediction. The overall performance of ensemble prediction in terms of accuracy, resolution, and reliability increased slightly with ensemble size, especially for longer forecast times.

Comparison of Adaptive Simulation Observation Experiments of the Heavy Rainfall in South China and Sichuan Basin

This study examines the effectiveness of adaptive observation experiments using the ensemble transformation sensitivity(ETS) method to improve precipitation forecasts during heavy rainfall events in South China and the Sichuan Basin. High-resolution numerical models are employed to simulate adaptive observations. By identifying the sensitive areas of key weather system positions 42 hours before heavy rainfall events, the adaptive observations improve the prediction of jet streams, strong winds, and shear lines, which are essential for accurate heavy rainfall forecasting. This improvement is reflected in both the precipitation structure and location accuracy within the verification region. In South China, targeted observations enhance rainfall predictions by improving water vapor transport. In the Sichuan Basin, adaptive observations refine water vapor transport and adjust vortex dynamics. This research highlights the importance of accurately predicting shear lines and jet streams for forecasting heavy rainfall in these areas. Overall, this study found that adaptive observation enhances the precipitation forecast skills of the structure and location for heavy rainfall in South China and the Sichuan Basin, emphasizing their potential utility in operational numerical weather prediction.

Research on data assimilation strategy of turbulent separated flow over airfoil

In order to increase the accuracy of turbulence field reconstruction,this paper combines experimental observation and numerical simulation to develop and establish a data assimilation framework,and apply it to the study of S809 low-speed and high-angle airfoil flow.The method is based on the ensemble transform Kalman filter(ETKF)algorithm,which improves the disturbance strategy of the ensemble members and enhances the richness of the initial members by screening high flow field sensitivity constants,increasing the constant disturbance dimensions and designing a fine disturbance interval.The results show that the pressure distribution on the airfoil surface after assimilation is closer to the experimental value than that of the standard Spalart-Allmaras(S-A)model.The separated vortex estimated by filtering is fuller,and the eddy viscosity field information is more abundant,which is physically consistent with the observation information.Therefore,the data assimilation method based on the improved ensemble strategy can more accurately and effectively describe complex turbulence phenomena.

区域集合预报系统的集合变换卡尔曼滤波初始扰动的余弦分析约束方案

基于GRAPES区域集合预报系统,针对初始扰动对预报误差描述能力依然不足的问题,在动力降尺度构造集合初始扰动的基础上,本文利用集合变换卡尔曼滤波(ETKF)方法更新集合扰动以捕获更多中小尺度扰动信息,提出并发展了一种融合资料同化分析增量特征信息的新的分析约束扰动方法——余弦分析约束扰动,对ETKF更新后集合初始扰动的不合理信息进行适应性自主调整,使得不同空间尺度的初始扰动物理结构和振幅尽可能与相应的预报误差结构和振幅相一致。试验结果表明,随天气形式的持续演变,强降水区域分析约束调整的集合初始扰动的中小尺度信息明显更为丰富,且温度扰动显示出更明显的优势;在模式积分初期,余弦分析约束扰动方案的集合离散度和扰动能量在空间分布与演变特征等方面均表现出更为合理的发展趋势,初始扰动质量及预报性能由此得到了有效改善。

Study on ETKF-Based Initial Perturbation Scheme for GRAPES Global Ensemble Prediction

Initial perturbation scheme is one of the important problems for ensemble prediction. In this paper, ensemble initial perturbation scheme for Global/Regional Assimilation and PrEdiction System （GRAPES） global ensemble prediction is developed in terms of the ensemble transform Kalman filter （ETKF） method. A new GRAPES global ensemble prediction system （GEPS） is also constructed. The spherical simplex 14-member ensemble prediction experiments, using the simulated observation network and error characteristics of simulated observations and innovation-based inflation, are carried out for about two months. The structure characters and perturbation amplitudes of the ETKF initial perturbations and the perturbation growth characters are analyzed, and their qualities and abilities for the ensemble initial perturbations are given. The preliminary experimental results indicate that the ETKF-based GRAPES ensemble initial perturbations could identify main normal structures of analysis error variance and reflect the perturbation amplitudes. The initial perturbations and the spread are reasonable. The initial perturbation variance, which is approximately equal to the forecast error variance, is found to respond to changes in the observational spatial variations with simulated observational network density. The perturbations generated through the simplex method are also shown to exhibit a very high degree of consistency between initial analysis and short-range forecast perturbations. The appropriate growth and spread of ensemble perturbations can be maintained up to 96-h lead time. The statistical results for 52-day ensemble forecasts show that the forecast scores of ensemble average for the Northern Hemisphere are higher than that of the control forecast. Provided that using more ensemble members, a real-time observational network and a more appropriate inflation factor, better effects of the ETKF-based initial scheme should be shown.

Notes and correspondence on ensemble-based three-dimensional variational filters

Several ensemble-based three-dimensional variational (3D-Var) filters are compared. These schemes replace the static background error covariance of the traditional 3D-Var with the ensemble forecast error covariance, but generate analysis ensemble anomalies (perturbations) in different ways. However, it is demonstrated in this paper that they are all theoretically equivalent to the ensemble transformation Kalman filter (ETKF). Furthermore, a new method named EnPSAS is presented. The analysis shows that EnPSAS has a small condition number and can apply covariance localization more easily than other ensemble-based 3D-Var methods.