初始扰动振幅和集合样本数对CNOPs集合预报的影响

初始扰动振幅的大小和集合样本数对于集合预报取得更高预报技巧具有重要意义。本文将正交条件非线性最优扰动方法（orthogonal conditional nonlinear optimal perturbations,简称CNOPs）应用于概念模型Lorenz-96模式探讨了初始扰动振幅和集合样本数对集合预报技巧的影响,从而为使用更复杂模式进行集合预报提供指导。结果表明,由于CNOPs扮演了非线性系统中的最优初始扰动,从而使得当初始扰动振幅小于初始分析误差的大小时,CNOPs集合预报获得更高的预报技巧,并且CNOPs集合预报的最高预报技巧总是高于奇异向量法（singular vectors,简称SVs）集合预报的最高预报技巧。结果还表明,CNOPs集合预报倾向于具有一个合适的样本数时,达到最高技巧。更好的集合离散度——预报误差关系和更为平坦的Talagrand图（Talagrand diagram）进一步证明了CNOPs集合预报系统的可靠性,从而夯实了上述结果的合理性。因此,针对CNOPs集合预报,本文认为采用一个适当小于初始分析误差的初始扰动振幅和一个合适的集合样本数,有利于CNOPs集合预报达到最高预报技巧。     

A comparison study of the methods of conditional nonlinear optimal perturbations and singular vectors in ensemble prediction

The authors apply the technique of conditional nonlinear optimal perturbations (CNOPs) as a means of providing initial perturbations for ensemble forecasting by using a barotropic quasi-geostrophic (QG) model in a perfect-model scenario. Ensemble forecasts for the medium range (14 days) are made from the initial states perturbed by CNOPs and singular vectors (SVs). 13 different cases have been chosen when analysis error is a kind of fast growing error. Our experiments show that the introduction of CNOP provides better forecast skill than the SV method. Moreover, the spread-skill relationship reveals that the ensemble samples in which the first SV is replaced by CNOP appear superior to those obtained by SVs from day 6 to day 14. Rank diagrams are adopted to compare the new method with the SV approach. The results illustrate that the introduction of CNOP has higher reliability for medium-range ensemble forecasts.     

热带气旋奇异向量在GRAPES全球集合预报中的初步应用

基于副热带奇异向量的初值扰动方法已应用于GRAPES （Global and Regional Assimilation PrEdiction System）全球集合预报系统,但存在热带气旋预报路径离散度不足的问题。通过分析发现,热带气旋附近区域初值扰动结构不合理导致预报集合不能较好地估计热带气旋预报的不确定性,是路径集合离散度不足的可能原因之一。通过建立热带气旋奇异向量求解方案,将热带气旋奇异向量和副热带奇异向量共同线性组合生成初值扰动,以弥补热带气旋区域初值扰动结构不合理这一缺陷,进而改进热带气旋集合预报效果。利用GRAPES全球奇异向量计算方案,以台风中心10个经纬度区域为目标区构建热带气旋奇异向量求解方案,针对台风“榕树”个例进行集合预报试验,并开展批量试验,利用中国中央气象台最优台风路径和中国国家气象信息中心的降水观测资料进行检验,对比分析热带气旋奇异向量结构特征和初值扰动特征,评估热带气旋奇异向量对热带气旋路径集合预报和中国区域24 h累计降水概率预报技巧的影响。结果表明,热带气旋奇异向量具有局地化特征,使用热带气旋奇异向量之后,热带气旋路径离散度增加,路径集合平均预报误差和离散度的关系得到改善,路径集合平均预报误差有所减小,集合成员更好地描述了热带气旋路径的预报不确定性;中国台风降水的小雨、中雨、大雨、暴雨各量级24 h累计降水概率预报技巧均有一定提高。总之,当在初值扰动的生成中考虑热带气旋奇异向量后,可改进热带气旋初值扰动结果,并有助于改善热带气旋路径集合预报效果。      

GRAPES全球集合预报初始条件及模式物理过程不确定性方法研究

为描述GRAPES全球模式初始条件的不确定性,基于适合集合预报应用的GRAPES全球奇异向量技术,依据大气初始误差符合正态分布的特征,采用高斯取样奇异向量来构造全球集合预报初始扰动,在此基础上建立了GRAPES全球集合预报系统(GRAPES-GEPS)。利用GRAPES全球同化分析场,对采用初始扰动的GRAPES-GEPS连续试验预报结果进行检验和分析。结果表明:GRAPES-GEPS中高度场、风场及温度场预报的集合离散度能有效快速增加,集合平均均方根误差与集合离散度的关系合理;相对控制预报的均方根误差,集合平均的预报优势在预报中期非常显著。为进一步体现GRAPES-GEPS中模式物理过程的不确定性,发展了模式物理过程倾向随机扰动技术(SPPT)。试验结果表明:SPPT方案的应用有效提高了GRAPES-GEPS在南、北半球和热带地区等压面要素预报的集合离散度,同时一定程度减小了集合平均误差,进而改进了集合平均误差与集合离散度的关系,其中SPPT方案在热带地区的改进最为显著。本文发展的基于奇异向量的初始扰动方法和模式扰动SPPT方案在中国气象局2018年12月业务化运行的GRAPES-GEPS中得到了应用。     

Reducing the prediction uncertainties of high-impact weather and climate events: An overview of studies at LASG

This paper summarizes recent progress at the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences in studies on targeted observations, data assimilation, and ensemble prediction, which are three effective strategies to reduce the prediction uncertainties and improve the forecast skill of weather and climate events. Considering the limitations of traditional targeted observation approaches, LASG researchers have developed a conditional nonlinear optimal perturbation-based targeted observation strategy to optimize the design of the observing network. This strategy has been employed to identify sensitive areas for targeted observations of the El Niño–Southern Oscillation, Indian Ocean dipole, and tropical cyclones, and has been demonstrated to be effective in improving the forecast skill of these events. To assimilate the targeted observations into the initial state of a numerical model, a dimension-reducedprojection- based four-dimensional variational data assimilation (DRP-4DVar) approach has been proposed and is used operationally to supply accurate initial conditions in numerical forecasts. The performance of DRP-4DVar is good, and its computational cost is much lower than the standard 4DVar approach. Besides, ensemble prediction, which is a practical approach to generate probabilistic forecasts of the future state of a particular system, can be used to reduce the prediction uncertainties of single forecasts by taking the ensemble mean of forecast members. In this field, LASG researchers have proposed an ensemble forecast method that uses nonlinear local Lyapunov vectors (NLLVs) to yield ensemble initial perturbations. Its application in simple models has shown that NLLVs are more useful than bred vectors and singular vectors in improving the skill of the ensemble forecast. Therefore, NLLVs represent a candidate for possible development as an ensemble method in operational forecasts. Despite the considerable efforts made towards developing these methods to reduce prediction uncertainties, much challenging but highly important work remains in terms of improving the methods to further increase the skill in forecasting such weather and climate events.     

GRAPES全球集合预报系统不同随机物理扰动方案影响分析

为了更好地理解不同随机物理扰动方案对全球中期集合预报的影响差异,本研究基于GRAPES全球集合预报系统（GRAPES-GEPS）对比分析了随机物理倾向扰动（Stochastically Perturbed Parameterization Tendencies,SPPT）、随机动能补偿（Stochastic Kinetic Energy Backscatter,SKEB）及联合使用SPPT与SKEB三种模式扰动方案所产生的扰动特征及其对集合预报的影响。为避免初值扰动影响,考察随机物理方案所产生的扰动特征时,不使用初值扰动。通过扰动与误差相关性分析（PECA）发现,不同随机物理扰动方案所产生的扰动对预报误差均具有一定的描述能力,而且联合使用SPPT与SKEB方案时,扰动对误差的描述能力最好。对所有扰动方案来说,扰动总能量最初主要集中在热带地区对流层中高层以及平流层低层。随着预报时效的延长,扰动总能量不断增大,其大值区不断向热带外地区转移。从扰动总能量的谱结构来看,扰动能量均呈现升尺度发展的特征。在基于奇异向量初值扰动的GRAPES-GEPS中,随机物理扰动方案的使用均能够显著增加不同地区等压面要素的集合离散度,并在一定程度上改善集合平均误差。由于集合离散度的增大,预报失误率显著减小。连续分级概率评分也有所减小,尤其是在热带地区,改进更为明显。此外,中国地区不同量级（小雨、中雨、大雨和暴雨）降水概率预报技巧在一定程度上得到改善。上述改进均在联合使用SPPT与SKEB方案时最好,这与扰动总能量、扰动与误差相关分析结果一致。      

基于奇异矢量的优化短期集合预报

在1-2 d的短期预报中,由奇异矢量构建的初始扰动主要是线性发展,为了防止在积分终止时刻,由同一奇异矢量导出的正负初始扰动的积分在集合平均时互相抵消,文中首先通过理论推导和实际计算证明了对集合成员进行优化的必要性,以及从不同奇异矢量导出的集合成员中,表现好于控制预报的一组成员相对于控制预报的离差恒大于或恒小于表现劣于控制预报的另一组成员,利用这个特征,在做集合预报时,把奇异矢量导出的正负两组预报分成离差相对大一组、离差相对小一组,就可以避免求集合平均时成员相互抵消,从而提出了一种优化基于奇异矢量的短期集合预报的方法.文中使用NCAR/PSU(美国国家大气研究中心/宾夕法尼亚大学)中尺度有限区域模式MM5第1版,及其对应切线性、伴随模式,对1999年夏季发生的两个梅雨锋低涡个例作了分析,在计算奇异矢量时采用了干能量模,分析结果表明:相对于正负两个初始扰动都入选的集合,严格按照这种方法挑选出来的优化集合可以有效地提高集合平均的精确度.在生成初始扰动的方法上,文中的计算表明,相对于用单个奇异矢量生成初始扰动,把正交的多个奇异矢量累加起来导出的初始扰动具有更大的增长率,能有效地增大集合成员间的离差,提高集合成员的预报精度.     

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 in ation, 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 ofensemble 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.     

The Sensitive Regions Identified by CNOPs of Three Typhoon Events

In this paper, several sets of observing system simulation experiments (OSSEs) were designed for three typhoon cases to determine whether or not the additional observation data in the sensitive regions identified by conditional nonlinear optimal perturbations (CNOPs) could improve the short-range forecast of typhoons. The results show that the CNOPs capture the sensitive regions for typhoon forecasts, which implies that conducting additional observation in these specific regions and eliminating initial errors could reduce forecast errors. It is inferred from the results that dropping sondes in the CNOP sensitive regions could lead to improvements in typhoon forecasts.     

Ensemble hindcasts of ENSO events over the past 120 years using a large number of ensembles

Based on an intermediate coupled model (ICM), a probabilistic ensemble prediction system (EPS) has been developed. The ensemble Kalman filter (EnKF) data assimilation approach is used for generating the initial ensemble conditions, and a linear, first-order Markov-Chain SST anomaly error model is embedded into the EPS to provide model-error perturbations. In this study, we perform ENSO retrospective forecasts over the 120 year period 1886–2005 using the EPS with 100 ensemble members and with initial conditi...     

Optimal initial perturbations for El Nino ensemble prediction with ensemble Kalman filter

A method for selecting optimal initial perturbations is developed within the framework of an ensemble Kalman filter (EnKF). Among the initial conditions generated by EnKF, ensemble members with fast growing perturbations are selected to optimize the ENSO seasonal forecast skills. Seasonal forecast experiments show that the forecast skills with the selected ensemble members are significantly improved compared with other ensemble members for up to 1-year lead forecasts. In addition, it is found that there is a strong relationship between the forecast skill improvements and flow-dependent instability. That is, correlation skills are significantly improved over the region where the predictable signal is relatively small (i.e. an inverse relationship). It is also shown that forecast skills are significantly improved during ENSO onset and decay phases, which are the most unpredictable periods among the ENSO events.     

基于背景场奇异向量的CMA全球集合预报试验

目前中国气象局全球集合预报系统（China Meteorological Administration Global Ensemble Prediction System,CMA-GEPS）利用CMA全球数值预报系统分析场计算奇异向量（ANSV）,欧洲中期天气预报中心采用同化背景场计算奇异向量（FCSV）,在业务流程上先于计算ANSV,可优化集合预报系统运行时间。为此,在CMA-GEPS中探索采用FCSV进行集合预报的可行性,分析ANSV和FCSV的空间分布及相似指数,进而针对夏秋季节10个个例开展采用ANSV和FCSV的全球集合预报试验,从等压面要素集合预报技巧、中国地区24 h累积降水概率预报技巧、台风路径集合预报技巧、台风中心最低海平面气压预报技巧等方面对比二者结果。结果表明:ANSV和FCSV的主要结构特征相似,两组集合预报结果相当,表明在CMA-GEPS中使用FCSV可行,可作为未来高分辨率CMA-GEPS业务系统建设的选项。     

Dust storm ensemble forecast experiments in East Asia

The ensemble Kalman filter (EnKF), as a unified approach to both data assimilation and ensemble forecasting problems, is used to investigate the performance of dust storm ensemble forecasting targeting a dust episode in the East Asia during 23–30 May 2007. The errors in the input wind field, dust emission intensity, and dry deposition velocity are among important model uncertainties and are considered in the model error perturbations. These model errors are not assumed to have zero-means. The model error me...     

Ensemble forecasting of tropical cyclone motion: comparisonbetween regional bred modes and random perturbations

Summary Random perturbations (RPs) and a modified version for breeding of growing modes are used with a regional baroclinic mesoscale model to perform ensemble forecasting of tropical cyclone motion. Based on a sample of six cases, similar conclusions are found as in previous barotropic modeling studies. Even after introducing a larger spatial correlation into the RPs using a multi-quadric analysis scheme, the skill of this ensemble mean track prediction is almost always lower than that of the control forecast in the cases considered. The track prediction performance of the ensemble using regional bred modes (RBMs) as perturbations has a higher average skill. At nearly all forecast intervals except less than 24 h when the initial position error still dominates, the ensemble mean tracks in all six cases are improved over the control forecast. In the 6 h–24 h range, the success rate (ratio of the cases with a forecast improvement to the total number of cases) has a value of 10/24. In the 30 h–48 h range, the success rate increases to 20/24, but drops to 18/24 in the 54 h–72 h range. A relative skill score (RSS) is used to compare the skills of the two perturbation methodologies. It is found that the average RSSs of using RBMs are significantly higher than the corresponding ones of RPs at the 99% confidence level in all three 24-h periods. Note that the above conclusion is only based on ensemble mean forecasts. All of the possibilities from an ensemble-based probabilistic track distribution are not explored in this paper. The ensemble spreads in these RBM ensembles are large enough to include the verifying tracks in all the cases considered. It is also found that the ensemble spread is well correlated with the average error in an ensemble when using RBMs, but not with the ensemble mean forecast error in both methodologies. Received February 7, 2001/Revised April 18, 2001     

时间滞后与奇异向量初值生成方法的比较试验

简单介绍了国家气象中心基于奇异向量初值生成方法的神威集合预报准业务系统, 它主要包括资料的前处理、客观分析、预报模式、初值扰动的生成、后处理、产品制作和系统监控七个部分, 共有 32 个成员。 提出了 12 个成员的时间滞后法集合预报系统的实施方案, 并与奇异向量法进行了对比试验。 结果表明, 不论是距平相关系数还是均方根误差, 奇异向量法在绝大多数区域和预报时效都比时间滞后法好。     

Ensemble forecasting of tropical cyclone motion using a barotropic model. Part III: Combining perturbations of the environment and the vortex

Summary This is the third in a series of papers to investigate the applicability of the ensemble forecasting (EF) technique in the prediction of tropical cyclone (TC) motion. In the previous two papers, either the environment or the vortex was perturbed and the other unperturbed component was then merged onto the perturbed component at the initial time. In the present study, the separately-perturbed environment and vortex fields are combined at this time. The objective is to determine the extent to, and the synoptic pattern under which, such a combination can improve the TC motion forecast compared with perturbing only one component.The study makes use of the same barotropic model as the previous studies and the same dataset – 66 cases from the Tropical Cyclone Motion Experiment TCM90. Perturbations of the environment and those of the vortex are first generated separately using the breeding of growing modes (BGM) method, and then combined at the initial forecast time. The performance of this combined scheme, labeled as BGMC, is then compared with that of the scheme with only the environment or the vortex perturbations (termed BGME and BGMV, respectively).The BGMC distribution of ensemble forecast tracks are found to be basically similar to those in BGME but the spread is reduced. Some poor forecast members in BGME also become close to the best track in BGMC. The relative skill scores of the BGMC forecasts relative to the best track are almost all positive but those under the perfect model assumption are negative because the control forecast is better. While both BGMC and BGME schemes can improve TC forecast track under transition synoptic conditions, BGMC also achieve a higher success rate under complicated vortex and environment interactions. In general, the BGMC scheme is superior to the BGMV scheme.     

条件非线性最优扰动方法在适应性观测研究中的初步应用

针对适应性观测中敏感性区域的确定问题，考虑初始误差对预报结果的影响, 比较了条件非线性最优扰动(CNOP)与第一线性奇异向量(FSV)在两个降水个例中的空间结构的差异，考察了它们总能量范数随时间发展演变的异同。结合敏感性试验的分析，揭示了预报结果对CNOP类型的初始误差的敏感性要大于对FSV类型的初始误差的敏感性，因而减少初值中CNOP类型误差的振幅比减少FSV类型的收益要大。这一结果表明可以把CNOP方法应用于适应性观测来识别大气的敏感区。关于将CNOP方法有效地应用于适应性观测所面临的挑战及需要采取的对策等也进行了讨论。     

Ensemble Forecast： A New Approach to Uncertainty and Predictability

Ensemble techniques have been used to generate daily numerical weather forecasts since the 1990s in numerical centers around the world due to the increase in computation ability. One of the main purposes of numerical ensemble forecasts is to try to assimilate the initial uncertainty （initial error） and the forecast uncertainty （forecast error） by applying either the initial perturbation method or the multi-model/multiphysics method. In fact, the mean of an ensemble forecast offers a better forecast than a deterministic （or control） forecast after a short lead time （3-5 days） for global modelling applications. There is about a 1-2-day improvement in the forecast skill when using an ensemble mean instead of a single forecast for longer lead-time. The skillful forecast （65% and above of an anomaly correlation） could be extended to 8 days （or longer） by present-day ensemble forecast systems. Furthermore, ensemble forecasts can deliver a probabilistic forecast to the users, which is based on the probability density function （PDF） instead of a single-value forecast from a traditional deterministic system. It has long been recognized that the ensemble forecast not only improves our weather forecast predictability but also offers a remarkable forecast for the future uncertainty, such as the relative measure of predictability （RMOP） and probabilistic quantitative precipitation forecast （PQPF）. Not surprisingly, the success of the ensemble forecast and its wide application greatly increase the confidence of model developers and research communities.     

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 components 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 perturbation(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.     

Sensitivity to Tendency Perturbations of Tropical Cyclone Short-range Intensity Forecasts Generated by WRF

The present study uses the nonlinear singular vector(NFSV)approach to identify the optimally-growing tendency perturbations of the Weather Research and Forecasting(WRF)model for tropical cyclone(TC)intensity forecasts.For nine selected TC cases,the NFSV-tendency perturbations of the WRF model,including components of potential temperature and/or moisture,are calculated when TC intensities are forecasted with a 24-hour lead time,and their respective potential temperature components are demonstrated to have more impact on the TC intensity forecasts.The perturbations coherently show barotropic structure around the central location of the TCs at the 24-hour lead time,and their dominant energies concentrate in the middle layers of the atmosphere.Moreover,such structures do not depend on TC intensities and subsequent development of the TC.The NFSV-tendency perturbations may indicate that the model uncertainty that is represented by tendency perturbations but associated with the inner-core of TCs,makes larger contributions to the TC intensity forecast uncertainty.Further analysis shows that the TC intensity forecast skill could be greatly improved as preferentially superimposing an appropriate tendency perturbation associated with the sensitivity of NFSVs to correct the model,even if using a WRF with coarse resolution.