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。     

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。      

几种约束优化算法求解含“开关”过程的条件非线性最优扰动的比较

求解条件非线性最优扰动(Conditional Nonlinear Optimal Perturbation,CNOP)属约束最优化问题,一般采用基于伴随模式提供梯度信息的约束优化算法(简称ADJ)进行求解。当优化问题涉及不连续的"开关"过程时,传统优化算法的寻优能力会受到较大的影响。近年来遗传算法(Genetic Algorithm,GA)因其在非光滑优化问题中的鲁棒性备受关注,但GA的性能不仅与优化问题有关,还取决于遗传算子的配置。本文将一种新的约束GA(GA1)用于求解CNOP,并对GA1,ADJ及具有不同遗传算子配置的约束GA(GA2)求解含"开关"过程的CNOP时的性能进行了比较。数值试验结果显示,GA1和GA2的全局寻优能力明显优于ADJ,后者易于陷入局部最优;对于不同的初猜值(不同的初始种群),GA1求解的CNOP能够保持一个较为一致的空间结构,ADJ求解的CNOP呈现了明显的两种结构,一种代表的是全局CNOP,一种是局部CNOP。通过验证不同遗传策略对优化结果的影响发现,对不同的优化问题,采用合适的遗传策略以及合适的参数设置是获取更好优化结果的一种有效途径。     

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。      

集合预报多尺度奇异向量初值扰动方法研究

目前国际上采用的奇异向量集合预报初值扰动法对于初值不确定性的描述存在一定的不足,为了更有效地反映初始误差的时空多尺度特性,基于GRAPES全球奇异向量计算技术,计算了不同空间分辨率及不同最优时间间隔的多个尺度的奇异向量,并采用基于高斯分布的线性组合法来构造多尺度奇异向量的扰动初值,以代表在相空间中增长最快的多尺度初值误差模态。通过2019年1月19日的初值扰动集合预报试验,对比分析了单一尺度奇异向量初值扰动法与多尺度初值扰动法的扰动特征及集合预报效果。结果表明,多尺度奇异向量初值扰动法为区域集合预报提供的初始扰动场是合理的,扰动的大小随时间增长,且在空间分布上较好地反映了当前大气的斜压不稳定特征。此外,多尺度奇异向量扰动可以描述一定的大尺度以及中小尺度运动误差特征,较单一尺度奇异向量扰动能反映出更多初始场的不确定性信息。检验分析表明,GRAPES多尺度奇异向量集合预报在集合一致性、连续等级概率评分、离群值等方面有一定的优势,相比于单一尺度奇异向量法有较好的预报技巧。因此,基于GRAPES的多尺度奇异向量初值扰动法对于集合预报的预报效果有一定的提高,能为构建一套完善的GRAPES区域奇异向量集合预报系统提供一定的科学依据和应用基础。      

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。     

基于条件非线性最优扰动的目标观测中瞄准区 不同引导性变量的影响试验研究

基于GRAPES区域业务预报模式,采用一种快速算法计算出来的条件非线性最优扰动对实际台风个例麦莎(No.0509)开展了目标观测研究,应用数值模式,进行一系列的敏感性试验,讨论了与目标观测设计相关的一些问题,包括确定瞄准区时使用不同的引导性变量对目标观测效果的影响、及瞄准区范围变化对预报效果的影响。文中分别以提高麦莎在检验区(20.125°—35.3125°N,116.8125°—129.75°E)内的24 h海平面气压预报和24 h累积降水量预报为目的,基于条件非线性最优扰动使用了3种不同的引导性变量寻找敏感区(又称瞄准区),对这些敏感区的分布特点和有效性进行了比较和讨论。试验结果表明,在使用的3种引导性变量中,用不同的引导性变量识别的敏感区是有差别的,总体上说,文中使用的3种引导性变量识别的瞄准区对提高预报都是有效的,特别是第2和第3种的效果更好些,且两者识别的瞄准区常显示出类似的特点。文中进一步针对检验区内24 h累积降水量预报误差问题,将前面确定的瞄准区范围扩大相同的幅度,讨论瞄准区范围变化对改进预报的影响。试验结果表明,增加瞄准格点数,有可能使预报效果得到改善,但是试验结果同时也暗示了单纯靠扩大瞄准...     

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.     

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.     

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.     

Application of the Conditional Nonlinear Optimal Perturbation Method to the Predictability Study of the Kuroshio Large Meander

A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations.The results show that the model was able to capture the essential features of these path variations.We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander (KLM) state using the conditional nonlinear optimal parameter perturbation (CNOP-P) method.Because of their relatively large uncertainties,three model parameters were considered:the interfacial friction coefficient,the wind-stress amplitude,and the lateral friction coefficient.We determined the CNOP-Ps optimized for each of these three parameters independently,and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 (SPG2) algorithm.Similarly,the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation (CNOP-I) method.Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days.But the prediction error caused by CNOP-I is greater than that caused by CNOP-P.The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored.Hence,to enhance the forecast skill of the KLM in this model,the initial conditions should first be improved,the model parameters should use the best possible estimates.     

Ensemble Forecasts of Tropical Cyclone Track with Orthogonal Conditional Nonlinear Optimal Perturbations

This paper preliminarily investigates the application of the orthogonal conditional nonlinear optimal perturbations(CNOPs)–based ensemble forecast technique in MM5(Fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model). The results show that the ensemble forecast members generated by the orthogonal CNOPs present large spreads but tend to be located on the two sides of real tropical cyclone(TC) tracks and have good agreements between ensemble spreads and ensemble-mean forecast errors for TC tracks. Subsequently, these members reflect more reasonable forecast uncertainties and enhance the orthogonal CNOPs–based ensemble-mean forecasts to obtain higher skill for TC tracks than the orthogonal SVs(singular vectors)–, BVs(bred vectors)– and RPs(random perturbations)–based ones. The results indicate that orthogonal CNOPs of smaller magnitudes should be adopted to construct the initial ensemble perturbations for short lead–time forecasts, but those of larger magnitudes should be used for longer lead–time forecasts due to the effects of nonlinearities. The performance of the orthogonal CNOPs–based ensemble-mean forecasts is case-dependent,which encourages evaluating statistically the forecast skill with more TC cases. Finally, the results show that the ensemble forecasts with only initial perturbations in this work do not increase the forecast skill of TC intensity, which may be related with both the coarse model horizontal resolution and the model error.     

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.     

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.     

Three-Dimensional Structure of Optimal Nonlinear Excitation for Decadal Variability of the Thermohaline Circulation

The decadal variability of the North Atlantic thermohaline circulation（THC） is investigated within a three-dimensional ocean circulation model using the conditional nonlinear optimal perturbation method. The results show that the optimal initial perturbations of temperature and salinity exciting the strongest decadal THC variations have similar structures： the perturbations are mainly in the northwestern basin at a depth ranging from 1500 to 3000 m. These temperature and salinity perturbations act as the optimal precursors for future modifications of the THC, highlighting the importance of observations in the northwestern basin to monitor the variations of temperature and salinity at depth. The decadal THC variation in the nonlinear model initialized by the optimal salinity perturbations is much stronger than that caused by the optimal temperature perturbations, indicating that salinity variations might play a relatively important role in exciting the decadal THC variability. Moreover, the decadal THC variations in the tangent linear and nonlinear models show remarkably different characteristics, suggesting the importance of nonlinear processes in the decadal variability of the THC.     

Inducing Unstable Grassland Equilibrium States Due to Nonlinear Optimal Patterns of Initial and Parameter Perturbations: Theoretical Models

Due to uncertainties in initial conditions and parameters,the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern.Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models.We used a nonlinear optimization approach,i.e.,a conditional nonlinear optimal perturbation related to initial and parameter perturbations (CNOP) approach,in our work.Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously.A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes.We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects:abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously.We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter.The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations,especially for more parameters or when special parameters are involved,plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.     

Time-Dependent Nonlinear Forcing Singular Vector-Type Tendency Error of the Zebiak-Cane Model

Based on the Zebiak-Cane model, the timedependent nonlinear forcing singular vector （NFSV）-type tendency errors with components of 4 and 12 （denoted by NFSV-4 and NFSV-12） are calculated for predetermined El Nifio events and compared with the constant NFSV （denoted by NFSV-1） from their patterns and resultant prediction errors. Specifically, NFSV-1 has a zonal dipolar sea surface temperature anomaly （SSTA） pattern with negative anomalies in the equatorial eastern Pacific and positive anomalies in the equatorial central-western Pa- cific. Although the first few components in NFSV-4 and NFSV-12 present patterns similar to NFSV-1, they tend to extend their dipoles farther westward; meanwhile, the positive anomalies gradually cover much smaller regions with the lag times. In addition, the authors calculate the predic- tion errors caused by the three kinds of NFSVs, and the results indicate that the prediction error induced by NFSV-12 is the largest, followed by the NFSV-4. However, when compared with the prediction errors caused by random tendency errors, the NFSVs generate significantly larger prediction errors. It is therefore shown that the spatial structure of tendency errors is important for producing large prediction errors. Furthermore, in exploring the tendency errors that cause the largest prediction error for E1 Nifio events, the timedependent NFSV should be evaluated.