条件非线性最优扰动方法在黑潮目标观测研究中的应用

对近年来利用条件非线性最优扰动（Conditional Nonlinear Optimal Perturbation,CNOP）方法开展的黑潮目标观测研究进行了总结,主要包括日本南部黑潮路径变异的目标观测研究、黑潮延伸体模态转变的目标观测研究和源区黑潮流量变化的目标观测研究。通过计算这些事件的CNOP型扰动,发现这些事件的CNOP型扰动具有局地特征,可以作为实施目标观测的敏感区。理想回报试验结果表明,如果在由CNOP方法识别的敏感区内实施目标观测,则会大幅度提高上述事件的预报技巧。     

条件非线性最优扰动方法在台风“风神”和“凤凰”相互作用过程中的应用研究

利用条件非线性最优扰动(CNOP)方法,对2002年发生在西太平洋上的台风“风神”和“凤凰”之间的相互作用进行研究。CNOP方法可揭示出“风神”对“凤凰”单向引导作用的过程,表现为若将“凤凰”所在区域作为验证区域,用CNOP方法识别的敏感区主要位于“风神”所在区域,呈现出环绕“风神”的半环状结构;若将“风神”所在区域作为验证区域,则CNOP方法所识别的敏感区主要位于“风神”与副高交界的地方,远离“凤凰”所在的区域,可见,“风神”主要受副高的影响。敏感性试验表明,CNOP所识别的敏感区内误差的发展要大于台风中心周围区域内初始误差的发展,且在全场误差的发展中占有较大的比重,说明CNOP所识别的敏感区对验证区域的预报有较大的影响。      

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。     

条件非线性最优扰动(CNOP):简介与数值求解

介绍了条件非线性最优扰动(Conditional Nonlinear Optimal Perturbation,CNOP)的定义及其在大气和海洋等可预报性研究中的应用。根据研究对象不同,CNOP分为与初始扰动有关的CNOP(CNOP-I)方法、与模式参数扰动有关的CNOP(CNOP-P)方法和同时考虑初始扰动和模式参数扰动的CNOP方法。目前,CNOP-I方法已经应用于ENSO、黑潮和阻塞可预报性以及热盐环流和草原生态系统稳定性的研究。此外,CNOP-I方法也被应用于探讨台风目标观测的研究,利用CNOP-I方法能够识别出台风预报的初值敏感区,通过观测系统模拟试验表明在初值敏感区增加观测能够有效改进台风的预报技巧。CNOP-P方法也在ENSO和黑潮可预报性以及热盐环流和草原生态系统稳定性研究中得到了应用。为了将CNOP方法应用于更多的领域,本文利用一个简单的Burgers方程,介绍了如何通过建立Burgers方程的切线性模式和伴随模式,从而利用非线性最优化算法计算获得CNOP。这一数值试验为将CNOP方法应用于更多的领域提供了借鉴。     

一种求解条件非线性最优扰动的快速算法及其在台风目标观测中的初步检验

条件非线性最优扰动(CNOP)是Mu等2003年提出的一个新的理论方法,它是线性奇异向量在非线性情形的推广,克服了线性奇异向量不能代表非线性系统最快发展扰动的缺陷,成为非线性系统可预报性和敏感性等研究新的有效工具.然而,由于以往CNOP的求解需要采用伴随技术,计算量相当巨大,限制了该方法的推广应用.为了克服这一困难,本文基于经验正交分解(EOF),提出了一种求解CNOP的快速算法,利用GRAPES区域业务预报模式实现了CNOP快速计算,并在台风"麦莎"的目标观测研究中得到初步检验,通过观测系统模拟实验(OSSE)检验了该方法确定敏感性区域(瞄准区)的有效性和可行性.试验结果表明,用快速算法求解的CNOP,其净能量随时间快速地发展,而且发展呈非线性.在台风"麦莎"个例的目标观测试验中,用快速算法得到的预报时间为24 h的CNOP可以有效地识别瞄准区,并通过瞄准区内初值的改善,可明显减少目标区域(检验区)内24 h累计降水预报误差.尤其,累计降水预报的这种改进效果能够延伸到更长时间(如72 h),尽管检验时间是设在第24小时.进一步分析发现,24 h累计降水预报误差的减少是通过利用瞄准区内改善的初值改进初始时刻台风暖心结构、高空相对涡度以及水汽条件等而得以实现的.     

条件非线性最优扰动在可预报性问题研究中的应用

本文总结了近年来条件非线性最优扰动方法的应用研究的主要进展.主要包括四个方面:(1)将条件非线性最优扰动(CNOP)方法拓展到既考虑初始扰动又考虑模式参数扰动,形成了拓展的CNOP方法.拓展的CNOP方法不仅能够应用于研究分别由初始误差和模式参数误差导致的可预报性问题,而且能够用于探讨初始误差和模式参数误差同时存在的情形;(2)将拓展的CNOP方法分别应用于ENSO和黑潮可预报性研究,考察了初始误差和模式参数误差对其可预报性的影响,揭示了初始误差在导致ENSO和黑潮大弯曲路径预报不确定性中的重要作用;(3)考察了阻塞事件发生的最优前期征兆(OPR)以及导致其预报不确定性的最优增长初始误差(OGR),揭示了OPR和OGR空间模态及其演变机制的相似性及其局地性特征;(4)研究了台风预报的目标观测问题,用CNOP方法确定了台风预报的目标观测敏感区,通过观测系统模拟试验(OSSEs)和/或观测系统试验(OSEs),表明了CNOP敏感区在改进台风预报中的有效性.具体地,台风OGR的主要误差分布在某一特定区域,空间分布具有明显的局地性特征,在台风OGR的局地性区域增加观测,有效改进了台风的预报技巧,该区域代表了台风预报的初值敏感区.事实上,上述El Ni(n)o事件、黑潮路径变异以及阻塞事件的OGR的空间分布也具有明显的局地性特征,这些事件的OGR刻画的局地性区域可能也代表了初值敏感区.     

基于CNOP方法的台风目标观测中三种敏感区 确定方案的比较研究

在目标观测中,敏感区的确定是个关键性的问题。本文详细研究了如何用条件非线性最优扰动（CNOP）方法确定敏感区。提出了三种确定敏感区的方案:水平投影方案、单点能量投影方案以及垂直积分能量方案。比较了三种方案确定的敏感区的差异,分析了它们所阐释的物理意义,讨论了它们的优缺点,并通过理想回报试验考查了不同方案确定的敏感区的有效性。对六个台风个例的应用结果显示,单点能量投影方案与垂直积分能量方案下识别的敏感区较为相似,二者与水平投影方案确定的敏感区则有较大的区别。两种能量方案确定的敏感区更多地反映了环境场对台风的影响,而水平投影方案则反映了台风自身对流不对称性结构对台风发展变化的影响。理想回报试验结果表明,由两种能量方案确定的敏感区对预报误差能量的减小程度以及路径预报的改善程度都要大于水平投影方案确定的敏感区的效果,且垂直积分能量方案确定的敏感区的有效性最高。而在强度预报方面,三种方案对预报效果的改善程度相当。因此,总的说在台风目标观测研究中,利用CNOP方法确定敏感区时,垂直积分能量方案是较佳的方案。     

台风强度模拟的海温目标观测研究

根据非线性强迫奇异向量(NFSV)型海温(SST)强迫误差识别的敏感性特征,通过观测系统模拟试验(OSSE)确定了12个热带气旋(TC)的强度模拟的海温目标观测最优布局.NFSV型SST强迫误差敏感区一般沿着台风移动路径,主要位于台风快速增强阶段.结果 表明,在NFSV型SST强迫目标观测敏感区内以90 km间隔加密海...     

Lorenz 96模式中三种目标观测方法的有效性比较

目标观测是有效提升观测效能和观测质量的一种观测策略,其核心部分是敏感区的识别。本文在Lorenz-96模式上比较了奇异向量法(SVs)、集合变换卡尔曼滤波法(ETKF)和条件非线性最优扰动法(CNOP)识别敏感区的优劣,并尝试揭示ETKF方法性能不稳定的原因与机制。试验结果表明:在312h内的不同预报时刻,CNOP方法识别的敏感区范围较小且对预报效果的提升率最高;SVs方法识别的敏感区对72h内的预报有较好的改进,但72h后改进程度急剧下降,到120h后基本失效;ETKF方法识别的敏感区在72h内不如其他方法的效果好。此外,在ETKF方法识别的敏感区与随机选取的敏感区对比中发现,由于ETKF方法操作时采用顺序观测资料处理方案搜寻敏感区,本质上忽略了观测资料间的相关性,导致ETKF方法识别出的敏感区并不一定是全局信号方差最大的区域,对预报效果的改善有限,这也说明了如何优化敏感区搜寻方案是提高ETKF方法效能的关键。     

条件非线性最优扰动在长江中下游地区冬季暴雨中的应用研究

为了提高长江中下游地区高影响天气的数值预报,利用条件非线性最优扰动(CNOP)方法,对一次长江中下游地区冬季降水个例(高影响天气事件)进行目标观测研究,并通过观测系统模拟试验(OSSE)检验了该方法确定敏感区的有效性和可行性。试验结果表明,CNOP方法可有效识别对应于高影响天气事件的敏感区。通过对敏感区进行初始场修正后,可明显改善验证区内24 h累积降水预报误差和总能量预报误差。进一步分析发现,通过改善敏感区内的初始场信息(如水汽通量场和低层冷空气活动等),使得数值模式不仅能更真实刻画该天气系统的初始结构,还能更好模拟出该天气系统随时间的演变特征,因而减少了验证区内对该天气系统的预报误差。这一结果表明可以把CNOP方法应用于长江中下游地区高影响天气事件的目标观测研究或实践中。      

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.     

THE APPLICATION OF CONDITIONAL NONLINEAR OPTIMAL PERTURBATION TO THE BINARY TYPHOONS INTERACTION —FENGSHEN AND FUNG-WONG

The interaction between the typhoons Fengshen and Fung-wong over the Western Pacific in 2002 is studied with the Conditional Nonlinear Optimal Perturbation (CNOP) method. The study discovered that the CNOP method reveals the process of one-way interaction between Fengshen and Fung-wong. Moreover, if the region of Fung-wong was selected for verification, the sensitivity area was mainly located in the region of Fengshen and presented a half-ring structure; if the region of Fengshen was selected for verification, most of the sensitivity areas were located in the region between the Fengshen and the subtropical high, far away from Fung-wong. This indicated that Fung-wong is mainly steered by Fengshen, but Fengshen is mainly affected by the subtropical high. The sensitivity experiment showed that the initial errors in the CNOP-identified sensitive areas have larger impacts on the verification-area prediction than those near the typhoon center and their developments take a large proportion in the whole domain. This suggests that the CNOP-identified sensitive areas do have large influence on the verification-area prediction.     

A Fast Algorithm for Solving CNOP and Associated Target Observation Tests

Conditional Nonlinear Optimal Perturbation （CNOP） is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector （LSV） to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest developing perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function （EOF）. The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System （GRAPES）, an operational regional forecast model of China. The effectivity and feasibility of the algorithm to determine the sensitivity （target） area is evaluated through two observing system simulation experiments （OSSEs）. The results, as expected, show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. The sensitivity area is effectively identified with the CNOP from the new algorithm, using 24 h as the prediction time window. The 24-h accumulated rainfall prediction errors （ARPEs） in the verification region are reduced significantly compared with the ＂true state,＂ when the initial conditions （ICs） in the sensitivity area are replaced with the ＂observations.＂ The decrease of the ARPEs can be achieved for even longer prediction times （e.g., 72 h）. Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the typhoon＇s initial warm-core, upper level relative vorticity, water vapor conditions, etc., as a result of the updated ICs in the sensitivity area.     

Applications of Conditional Nonlinear Optimal Perturbation in Predictability Study and Sensitivity Analysis of Weather and Climate

Considering the limitation of the linear theory of singular vector (SV), the authors and their collaborators proposed conditional nonlinear optimal perturbation (CNOP) and then applied it in the predictability study and the sensitivity analysis of weather and climate system. To celebrate the 20th anniversary of Chinese National Committee for World Climate Research Programme (WCRP), this paper is devoted to reviewing the main results of these studies. First, CNOP represents the initial perturbation that has largest nonlinear evolution at prediction time, which is different from linear singular vector (LSV) for the large magnitude of initial perturbation or/and the long optimization time interval. Second, CNOP, rather than linear singular vector (LSV), represents the initial anomaly that evolves into ENSO events most probably. It is also the CNOP that induces the most prominent seasonal variation of error growth for ENSO predictability; furthermore, CNOP was applied to investigate the decadal variability of ENSO asymmetry. It is demonstrated that the changing nonlinearity causes the change of ENSO asymmetry. Third, in the studies of the sensitivity and stability of ocean’s thermohaline circulation (THC), the nonlinear asymmetric response of THC to finite amplitude of initial perturbations was revealed by CNOP. Through this approach the passive mechanism of decadal variation of THC was demonstrated; Also the authors studies the instability and sensitivity analysis of grassland ecosystem by using CNOP and show the mechanism of the transitions between the grassland and desert states. Finally, a detailed discussion on the results obtained by CNOP suggests the applicability of CNOP in predictability studies and sensitivity analysis.     

The Time and Regime Dependencies of Sensitive Areas for Tropical Cyclone Prediction Using the CNOP Method

This study examines the time and regime dependencies of sensitive areas identified by the conditional nonlinear optimal perturbation(CNOP) method for forecasts of two typhoons.Typhoon Meari(2004) was weakly nonlinear and is herein referred to as the linear case,while Typhoon Matsa(2005) was strongly nonlinear and is herein referred to as the nonlinear case.In the linear case,the sensitive areas identified for special forecast times when the initial time was fixed resembled those identified for other forecast times.Targeted observations deployed to improve a special time forecast would thus also benefit forecasts at other times.In the nonlinear case,the similarities among the sensitive areas identified for different forecast times were more limited.The deployment of targeted observations in the nonlinear case would therefore need to be adapted to achieve large improvements for different targeted forecasts.For both cases,the closer the forecast time,the higher the similarities of the sensitive areas.When the forecast time was fixed,the sensitive areas in the linear case diverged continuously from the verification area as the forecast period lengthened,while those in the nonlinear case were always located around the initial cyclones.The deployment of targeted observations to improve a special forecast depends strongly on the time of deployment.An examination of the efficiency gained by reducing initial errors within the identified sensitive areas confirmed these results.In general,the greatest improvement in a special time forecast was obtained by identifying the sensitive areas for the corresponding forecast time period.     

Observation System Experiments for Typhoon Nida (2004) Using the CNOP Method and DOTSTAR Data

This study investigated the influence of dropwindsonde observations on typhoon forecasts. The study also evaluated the feasibility of the conditional nonlinear optimal perturbation (CNOP) method as a basis for sensitivity analysis of such forecasts. This sensitivity analysis could furnish guidance in the selection of targeted observations. The study was performed by conducting observation system experiments (OSEs). This research used the fifth-generation Mesoscale Model (MM5), the Weather Research and Forecasting (WRF) model, and dropsonde observations of Typhoon Nida at 1200 UTC 17 May 2004. The dropsondes were collected under the operational Dropsonde Observations for Typhoon Surveillance near the Taiwan Region (DOTSTAR) program. In this research, five kinds of experiments were designed and conducted:(1) no observations were assimilated; (2) all observations were assimilated;(3) observations in the sensitive area revealed by the CNOP method were assimilated;(4) the same as in (3), but for the region revealed by the first singular vector (FSV) method;and (5) observations within a randomly selected area were assimilated. The OSEs showed that (1) the DOTSTAR data had a positive impact on the forecast of Nida’s track;(2) dropsondes in the sensitive areas identified by the MM5 CNOP and FSV remained effective for improving the track forecast for Nida on the WRF platform;and (3) the greatest improvement in the track forecast resulted from the CNOP-based (third) simulation, which indicated that the CNOP method would be useful in decision making about dropsonde deployments.     

The Impact of Verification Area Design on Tropical Cyclone Targeted Observations Based on the CNOP Method

This study investigated the impact of different verification-area designs on the sensitive areas identified using the conditional nonlinear optimal perturbation (CNOP) method for tropical cyclone targeted observations.The sensitive areas identified using the first singular vector (FSV) method,which is the linear approximation of CNOP,were also investigated for comparison.By analyzing the validity of the sensitive areas,the proper design of a verification area was developed.Tropical cyclone Rananim,which occurred in August 2004 in the northwest Pacific Ocean,was studied.Two sets of verification areas were designed;one changed position,and the other changed both size and position.The CNOP and its identified sensitive areas were found to be less sensitive to small variations of the verification areas than those of the FSV and its sensitive areas.With larger variations of the verification area,the CNOP and the FSV as well as their identified sensitive areas changed substantially.In terms of reducing forecast errors in the verification area,the CNOP-identified sensitive areas were more beneficial than those identified using FSV.The design of the verification area is important for cyclone prediction.The verification area should be designed with a proper size according to the possible locations of the cyclone obtained from the ensemble forecast results.In addition,the development trend of the cyclone analyzed from its dynamic mechanisms was another reference.When the general position of the verification area was determined,a small variation in size or position had little influence on the results of CNOP.