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。     

MJO随机强迫对CNOP型初始误差演变的影响

用Zebiak-Cane模式和季节内振荡(Madden-Julian Oscillation,MJO)的参数化表述以及条件非线性最优扰动(Conditional Nonlinear Optimal Perturbation,CNOP)方法,分析了以ENSO事件为基态的CNOP型初始误差的空间结构增长规律。结果表明,参数化的MJO对CNOP型初始误差的发展影响较小,其影响主要是使中东太平洋的海表面温度异常增大。CNOP型初始误差比由MJO不确定性产生的模式误差的影响大,前者可能是造成ENSO事件预报不确定性的主要误差来源。由于CNOP型初始误差的局地性,本结论可用来指导ENSO的目标观测和适应性资料同化。     

条件非线性最优扰动法在大气与海洋目标观测研究中的应用

对近年来用条件非线性最优扰动法研究大气与海洋目标观测问题的部分工作进行了总结,主要涉及厄尔尼诺-南方涛动（ENSO）事件、黑潮路径变异事件以及阻塞事件。通过研究这些事件发生的最优前期征兆（OPR）和最快增长初始误差（OGE）,发现这些事件的最优前期征兆和最快增长初始误差分别具有空间的高度相似性及其伴随的局地性特征。理想回报试验表明,如果在ENSO事件和黑潮路径变异事件的最快增长初始误差和最优前期征兆所确定的扰动大值区减小初始场误差,上述事件的预报技巧会大幅度提高;最优前期征兆和最快增长初始误差的空间相似性使得在同一敏感区域增加额外观测,不仅有助于捕捉上述异常事件的前期信号,还可以有效减小初始误差,从而提高对该事件的预报技巧。阻塞事件爆发的最优前期征兆和最快增长初始误差的空间相似性和局地性特征在其目标观测研究中的应用,应该是深入研究的课题。     

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。     

用非线性最优化方法研究El Nio可预报性的进展与前瞻

综述用非线性优化方法研究厄尔尼诺(El Ni~no)南方涛动(ENSO)事件可预报性的进展。针对ENSO可预报性研究中的热点问题———“前期征兆”、“春季可预报性障碍”,以及如何量化研究ENSO可预报性和ENSO的不对称性问题,作者在近年来的工作中先后用理论模式和中等复杂程度ENSO模式研究了ENSO可预报性的动力学,揭示了ENSO的若干重要非线性特征。主要结果如下:(1)条件非线性最优扰动(CNOP)(局部CNOP)比线性奇异向量更易发展成ENSO事件,扮演了ENSO的最优前期征兆。这些ENSO事件关于气候平均态是不对称的。理论分析表明,非线性温度平流过程是造成这种不对称性的重要原因。1980~2002年的海洋再分析资料验证了上述理论结果。(2)ENSO事件CNOP型初始误差的发展有明显的季节依赖性,该误差导致了ENSO事件最显著的春季可预报性障碍(SPB)现象。ENSO事件SPB的发生不仅依赖于气候平均态,而且依赖于ENSO事件本身及其初始误差模态,是三者综合作用的结果。(3)建立了关于ENSO可预报性的最大可预报时间下界、最大预报误差上界和最大允许初始误差下界的三类可预报性问题,分别从三个方面揭示了ENSO事件的春季可预报性障碍现象,比较有效地量化了其可预报性。(4)通过CNOP方法,揭示了非线性温度平流在年代际尺度ENSO不对称性研究中的重要作用,解释了ENSO不对称性的年代际变化,基于所用ENSO模式给出了ENSO不对称性年代际变化的机制。最后,展望了非线性优化方法在ENSO可预报性中应用的前景,并期望该方法能拓展到ENSO第二类可预报性问题的研究中。     

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。     

用非线性最优化方法研究El Ni(n)o可预报性的进展与前瞻

综述用非线性优化方法研究厄尔尼诺(El Ni(n)o)-南方涛动(ENSO)事件可预报性的进展.针对ENSO可预报性研究中的热点问题--"前期征兆"、"春季可预报性障碍",以及如何量化研究ENSO可预报性和ENSO的不对称性问题,作者在近年来的工作中先后用理论模式和中等复杂程度ENSO模式研究了ENSO可预报性的动力学,揭示了ENSO的若干重要非线性特征.主要结果如下:(1)条件非线性最优扰动(CNOP)(局部CNOP)比线性奇异向量更易发展成ENSO事件,扮演了ENSO的最优前期征兆.这些ENSO事件关于气候平均态是不对称的.理论分析表明,非线性温度平流过程是造成这种不对称性的重要原因.1980～2002年的海洋再分析资料验证了上述理论结果.(2)ENSO事件CNOP型初始误差的发展有明显的季节依赖性,该误差导致了ENSO事件最显著的春季可预报性障碍(SPB)现象.ENSO事件SPB的发生不仅依赖于气候平均态,而且依赖于ENSO事件本身及其初始误差模态,是三者综合作用的结果.(3)建立了关于ENSO可预报性的最大可预报时间下界、最大预报误差上界和最大允许初始误差下界的三类可预报性问题,分别从三个方面揭示了ENSO事件的春季可预报性障碍现象,比较有效地量化了其可预报性.(4)通过CNOP方法,揭示了非线性温度平流在年代际尺度ENSO不对称性研究中的重要作用,解释了ENSO不对称性的年代际变化,基于所用ENSO模式给出了ENSO不对称性年代际变化的机制.最后,展望了非线性优化方法在ENSO可预报性中应用的前景,并期望该方法能拓展到ENSO第二类可预报性问题的研究中.     

用非线性最优化方法研究El Niño可预报性的进展与前瞻

综述用非线性优化方法研究厄尔尼诺(El Ni(n)o)-南方涛动(ENSO)事件可预报性的进展.针对ENSO可预报性研究中的热点问题--"前期征兆"、"春季可预报性障碍",以及如何量化研究ENSO可预报性和ENSO的不对称性问题,作者在近年来的工作中先后用理论模式和中等复杂程度ENSO模式研究了ENSO可预报性的动力学,揭示了ENSO的若干重要非线性特征.主要结果如下:(1)条件非线性最优扰动(CNOP)(局部CNOP)比线性奇异向量更易发展成ENSO事件,扮演了ENSO的最优前期征兆.这些ENSO事件关于气候平均态是不对称的.理论分析表明,非线性温度平流过程是造成这种不对称性的重要原因.1980～2002年的海洋再分析资料验证了上述理论结果.(2)ENSO事件CNOP型初始误差的发展有明显的季节依赖性,该误差导致了ENSO事件最显著的春季可预报性障碍(SPB)现象.ENSO事件SPB的发生不仅依赖于气候平均态,而且依赖于ENSO事件本身及其初始误差模态,是三者综合作用的结果.(3)建立了关于ENSO可预报性的最大可预报时间下界、最大预报误差上界和最大允许初始误差下界的三类可预报性问题,分别从三个方面揭示了ENSO事件的春季可预报性障碍现象,比较有效地量化了其可预报性.(4)通过CNOP方法,揭示了非线性温度平流在年代际尺度ENSO不对称性研究中的重要作用,解释了ENSO不对称性的年代际变化,基于所用ENSO模式给出了ENSO不对称性年代际变化的机制.最后,展望了非线性优化方法在ENSO可预报性中应用的前景,并期望该方法能拓展到ENSO第二类可预报性问题的研究中.     

从Nio-3指数看MJO不确定性对ENSO可预报性的影响北大核心CSCD

通过在Zebiak Cane数值模式中引入参数化MJO随机外强迫,着重从Nio 3指数的演变发展探讨了MJO不确定性对ENSO可预报性的影响。结果表明,对Zebiak Cane模式而言,MJO不确定性对由条件非线性最优扰动(CNOP)导致的ENSO事件最大预报误差影响较小;与初始误差相比,由MJO不确定性产生的模式误差在ENSO预报不确定性的产生中具有较小作用,对ENSO可预报性的影响不显著。该结果强调了初始误差在ENSO预报不确定性中的主要作用,从而为ENSO预测的资料同化提供了理论基础。     

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。      

Optimal Precursors Triggering the Kuroshio Extension State Transition Obtained by the Conditional Nonlinear Optimal Perturbation Approach

In this study, the initial perturbations that are the easiest to trigger the Kuroshio Extension(KE) transition connecting a basic weak jet state and a strong, fairly stable meandering state, are investigated using a reduced-gravity shallow water ocean model and the CNOP(Conditional Nonlinear Optimal Perturbation) approach. This kind of initial perturbation is called an optimal precursor(OPR). The spatial structures and evolutionary processes of the OPRs are analyzed in detail. The results show that most of the OPRs are in the form of negative sea surface height(SSH) anomalies mainly located in a narrow band region south of the KE jet, in basic agreement with altimetric observations. These negative SSH anomalies reduce the meridional SSH gradient within the KE, thus weakening the strength of the jet. The KE jet then becomes more convoluted, with a high-frequency and large-amplitude variability corresponding to a high eddy kinetic energy level; this gradually strengthens the KE jet through an inverse energy cascade. Eventually, the KE reaches a high-energy state characterized by two well defined and fairly stable anticyclonic meanders. Moreover, sensitivity experiments indicate that the spatial structures of the OPRs are not sensitive to the model parameters and to the optimization times used in the analysis.     

Initial Error-induced Optimal Perturbations in ENSO Predictions,as Derived from an Intermediate Coupled Model

The initial errors constitute one of the main limiting factors in the ability to predict the El Nio–Southern Oscillation(ENSO) in ocean–atmosphere coupled models. The conditional nonlinear optimal perturbation(CNOP) approach was employed to study the largest initial error growth in the El Nio predictions of an intermediate coupled model(ICM). The optimal initial errors(as represented by CNOPs) in sea surface temperature anomalies(SSTAs) and sea level anomalies(SLAs) were obtained with seasonal variation. The CNOP-induced perturbations, which tend to evolve into the La Nia mode, were found to have the same dynamics as ENSO itself. This indicates that, if CNOP-type errors are present in the initial conditions used to make a prediction of El Nio, the El Nio event tends to be under-predicted. In particular, compared with other seasonal CNOPs, the CNOPs in winter can induce the largest error growth, which gives rise to an ENSO amplitude that is hardly ever predicted accurately. Additionally, it was found that the CNOP-induced perturbations exhibit a strong spring predictability barrier(SPB) phenomenon for ENSO prediction. These results offer a way to enhance ICM prediction skill and, particularly,weaken the SPB phenomenon by filtering the CNOP-type errors in the initial state. The characteristic distributions of the CNOPs derived from the ICM also provide useful information for targeted observations through data assimilation. Given the fact that the derived CNOPs are season-dependent, it is suggested that seasonally varying targeted observations should be implemented to accurately predict ENSO events.     

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.     

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.     

伴随敏感性方法、第一奇异向量方法以及条件非线性最优扰动方法在台风目标观测敏感区识别中的比较研究

本文通过深入分析伴随敏感性（ADS）方法、第一奇异向量（LSV）方法、以及条件非线性最优扰动（CNOP）方法在目标观测敏感区识别方面的原理,提出了非线性程度的概念和计算方法,考察了转向型和直线型台风的非线性程度,分析了上述三种方法在不同非线性程度下识别的敏感区的异同,同时对比了转向型和直线型台风的敏感区的差异,并通过敏感性试验探讨了在不同非线性程度下以及在转向型与直线型台风中,预报对敏感区内初值的敏感性程度,进而探讨台风目标观测在不同情况下的有效性。结果表明,转向型台风的非线性程度差别比较大,或者特别强,或者特别弱;而直线型台风非线性程度居中,不同台风个例之间的非线性程度差别较小。对于非线性较弱的台风,三种方法识别的敏感区较为相似,而对于非线性较强的台风,LSV方法与ADS方法识别的敏感区较为相似,但是与CNOP方法识别的敏感区具有较大的差别。对于转向型台风,敏感区主要位于行进路径的右前方,而对于直线型台风,敏感区主要位于初始台风位置的后方。敏感性试验表明,不论台风非线性强弱,转向还是直行,CNOP敏感区内的随机扰动发展最大,而LSV敏感区内叠加的随机扰动发展次之,ADS敏感区内叠加的扰动发展最小;此外,非线性弱的台风,扰动的发展大于非线性强的台风的扰动的发展,表明非线性弱的台风预报受初值影响更大,目标观测的效果可能会更明显。     

The Optimal Precursors for ENSO Events Depicted Using the Gradientdefinition-based Method in an Intermediate Coupled Model

The predictability of El Ni?o?Southern Oscillation (ENSO) has been an important area of study for years. Searching for the optimal precursor (OPR) of ENSO occurrence is an effective way to understand its predictability. The CNOP (conditional nonlinear optimal perturbation), one of the most effective ways to depict the predictability of ENSO, is adopted to study the optimal sea surface temperature (SST) precursors (SST-OPRs) of ENSO in the IOCAS ICM (intermediate coupled model developed at the Institute of Oceanology, Chinese Academy of Sciences). To seek the SST-OPRs of ENSO in the ICM, non-ENSO events simulated by the ICM are chosen as the basic state. Then, the gradient-definition-based method (GD method) is employed to solve the CNOP for different initial months of the basic years to obtain the SST-OPRs. The experimental results show that the obtained SST-OPRs present a positive anomaly signal in the western-central equatorial Pacific, and obvious differences exist in the patterns between the different seasonal SST-OPRs along the equatorial western-central Pacific, showing seasonal dependence to some extent. Furthermore, the non-El Ni?o events can eventually evolve into El Ni?o events when the SST-OPRs are superimposed on the corresponding seasons; the peaks of the Ni?o3.4 index occur at the ends of the years, which is consistent with the evolution of the real El Ni?o. These results show that the GD method is an effective way to obtain SST-OPRs for ENSO events in the ICM. Moreover, the OPRs for ENSO depicted using the GD method provide useful information for finding the early signal of ENSO in the ICM.     

Application of Conditional Nonlinear Optimal Perturbation to Targeted Observation Studies of the Atmosphere and Ocean

This paper reviews progress in the application of conditional nonlinear optimal perturbation to targeted observation studies of the atmosphere and ocean in recent years, with a focus on the E1 Nifio-Southern Oscillation （ENSO）, Kuroshio path variations, and blocking events. Through studying the optimal precursor （OPR） and optimally growing initial error （OGE） of the occurrence of the above events, the similarity and localization features of OPR and OGE spatial structures have been found for each event. Ideal hindcasting experiments have shown that, if initial errors are reduced in the areas with the largest amplitude for the OPR and OGE for ENSO and Kuroshio path variations, the forecast skill of the model for these events is significantly improved. Due to the similarity between patterns of the OPR and OGE, additional observations implemented in the same sensitive region would help to not only capture the precursors, but also reduce the initial errors in the predictions, greatly increasing the forecast abilities. The similarity and localization of the spatial structures of the OPR and OGE during the onset of blocking events have also been investigated, but their application to targeted observation requires further study.     

Is Model Parameter Error Related to a Significant Spring Predictability Barrier for El Nio events？ Results from a Theoretical Model

Within a theoretical ENSO model, the authors investigated whether or not the errors superimposed on model parameters could cause a significant ``spring predictability barrier' (SPB) for El Nino events. First, sensitivity experiments were respectively performed to the air--sea coupling parameter, α and the thermocline effect coefficient μ. The results showed that the uncertainties superimposed on each of the two parameters did not exhibit an obvious season-dependent evolution; furthermore, the uncertainties caused a very small prediction error and consequently failed to yield a significant SPB. Subsequently, the conditional nonlinear optimal perturbation (CNOP) approach was used to study the effect of the optimal mode (CNOP-P) of the uncertainties of the two parameters on the SPB and to demonstrate that the CNOP-P errors neither presented a unified season-dependent evolution for different El Nino events nor caused a large prediction error, and therefore did not cause a significant SPB. The parameter errors played only a trivial role in yielding a significant SPB. To further validate this conclusion, the authors investigated the effect of the optimal combined mode (i.e. CNOP error) of initial and model errors on SPB. The results illustrated that the CNOP errors tended to have a significant season-dependent evolution, with the largest error growth rate in the spring, and yielded a large prediction error, inducing a significant SPB. The inference, therefore, is that initial errors, rather than model parameter errors, may be the dominant source of uncertainties that cause a significant SPB for El Nino events. These results indicate that the ability to forecast ENSO could be greatly increased by improving the initialization of the forecast model.     

Similarities between optimal precursors for ENSO events and optimally growing initial errors in El Niño predictions

With the Zebiak–Cane model, the relationship between the optimal precursors (OPR) for triggering the El Niño/Southern Oscillation (ENSO) events and the optimally growing initial errors (OGE) to the uncertainty in El Niño predictions is investigated using an approach based on the conditional nonlinear optimal perturbation. The computed OPR for El Niño events possesses sea surface temperature anomalies (SSTA) dipole over the equatorial central and eastern Pacific, plus positive thermocline depth anomalies in the entire equatorial Pacific. Based on the El Niño events triggered by the obtained OPRs, the OGE which cause the largest prediction errors are computed. It is found that the OPR and OGE share great similarities in terms of localization and spatial structure of the SSTA dipole pattern over the central and eastern Pacific and the relatively uniform thermocline depth anomalies in the equatorial Pacific. The resemblances are possibly caused by the same mechanism of the Bjerknes positive feedback. It implies that if additional observation instruments are deployed to the targeted observations with limited coverage, they should preferentially be deployed in the equatorial central and eastern Pacific, which has been determined as the sensitive area for ENSO prediction, to better detect the early signals for ENSO events and reduce the initial errors so as to improve the forecast skill.