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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。     

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。     

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.     

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.     

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.     

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。     

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。     

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。     

模式含有开关时遗传算法求解条件非线性最优扰动的有效性研究

在基于条件非线性最优扰动(CNOP)的台风适应性观测研究中,针对预报模式的湿物理参数化产生的“on-off”开关导致传统伴随方法不能为最优化过程提供正确梯度这一现象,将模式含有“on-off”开关时求解CNOP的问题视为非光滑最优化问题,引入遗传算法,在给出详细的算法流程后,以一个在强迫项中含“on-off”开关的理想模式,分析了“on-off”开关对求解CNOP的影响,三个数值试验检验了模式含有“on-off”开关时遗传算法求解CNOP的有效性,并分析了不同初始种群对最优化结果的影响。结果显示,所采用的含有“on-off”开关的理想模式下,遗传算法能有效求解CNOP,最后对遗传算法求解CNOP的优缺点进行了详细讨论。     

Nonlinearity and Finite-Time Instability in a T21L3 Quasigeostrophic Model

In this paper,a nonlinear optimization method is used to explore the finite-time instability of the atmospheric circulation with a three-level quasigeostrophic model under the framework of the conditional nonlinear optimal perturbation (CNOP).As a natural generalization of linear singular vector (SV),CNOP is defined as an initial perturbation that makes the cost function the maximum at a prescribed forecast time under certain physical constraint conditions.Special attentions are paid to the different structures and energy evolutions of the optimal perturbations.The results show that the most instable region of the global atmospheric circulation lies in the midlatitude Eurasian continent.More specially,SV and CNOP in the total energy norm with an optimization time of 2 days both present localness:they are mainly located in the midlatitude Asian continent and its east coast.With extension of the optimization time,SVs are more upstream and less localized in the zonal direction,and CNOPs differ essentially from SVs with broader zonal and meridional coverages; as a result,CNOPs acquire larger kinetic and available potential energy amplifications than SVs in the nonlinear model at the corresponding optimization time.For the climatological wintertime flow,it is seen that the baroclinic terms remain small over the entire time evolution,and the energy production comes essentially from the eddy kinetic energy,which is induced by the horizontal shear of the basic flow.In addition,the effects of SVs and CNOPs on the Eurasian atmospheric circulation are explored.The results show that the weather systems over the Eurasian continent in the perturbed fields by CNOPs are stronger than those by SVs at the optimization time.This reveals that the CNOP method is better in evaluating the instability of the atmospheric circulation while the SV method underestimates the possibility of extreme weather events.     

Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.     

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.     

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.     

Nonlinearity and finite-time instability in a T21L3 quasigeostrophic model

In this paper, a nonlinear optimization method is used to explore the finite-time instability of the atmospheric circulation with a three-level quasigeostrophic model under the framework of the conditional nonlinear optimal perturbation (CNOP). As a natural generalization of linear singular vector (SV), CNOP is defined as an initial perturbation that makes the cost function the maximum at a prescribed forecast time under certain physical constraint conditions. Special attentions are paid to the different structures and energy evolutions of the optimal perturbations.     

Optimal Initial Error Growth in the Prediction of the Kuroshio Large Meander Based on a High-resolution Regional Ocean Model

Based on the high-resolution Regional Ocean Modeling System(ROMS) and the conditional nonlinear optimal perturbation(CNOP) method, this study explored the effects of optimal initial errors on the prediction of the Kuroshio large meander(LM) path, and the growth mechanism of optimal initial errors was revealed. For each LM event, two types of initial error(denoted as CNOP1 and CNOP2) were obtained. Their large amplitudes were found located mainly in the upper 2500 m in the upstream region of the LM, i.e., southeast of Kyushu. Furthermore, we analyzed the patterns and nonlinear evolution of the two types of CNOP. We found CNOP1 tends to strengthen the LM path through southwestward extension. Conversely,CNOP2 has almost the opposite pattern to CNOP1, and it tends to weaken the LM path through northeastward contraction.The growth mechanism of optimal initial errors was clarified through eddy-energetics analysis. The results indicated that energy from the background field is transferred to the error field because of barotropic and baroclinic instabilities. Thus, it is inferred that both barotropic and baroclinic processes play important roles in the growth of CNOP-type optimal initial errors.     

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 Roles of Spatial Locations and Patterns of Initial Errors in the Uncertainties of Tropical Cyclone Forecasts

In this study,a series of sensitivity experiments were performed for two tropical cyclones (TCs),TC Longwang (2005) and TC Sinlaku (2008),to explore the roles of locations and patterns of initial errors in uncertainties of TC forecasts.Specifically,three types of initial errors were generated and three types of sensitive areas were determined using conditional nonlinear optimal perturbation (CNOP),first singular vector (FSV),and composite singular vector (CSV) methods.Additionally,random initial errors in randomly selected areas were considered.Based on these four types of initial errors and areas,we designed and performed 16 experiments to investigate the impacts of locations and patterns of initial errors on the nonlinear developments of the errors,and to determine which type of initial errors and areas has the greatest impact on TC forecasts.Overall,results from the experiments indicate the following:(1) The impact of random errors introduced into the sensitive areas was greater than that of errors themselves fixed in the randomly selected areas.From the perspective of statistical analysis,and by comparison,the impact of random errors introduced into the CNOP target area was greatest.(2) The initial errors with CNOP,CSV,or FSV patterns were likely to grow faster than random errors.(3) The initial errors with CNOP patterns in the CNOP target areas had the greatest impacts on the final verification forecasts.     

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION "ON-OFF" SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the on-off switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedur...     

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.