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。      

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。     

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。     

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。     

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。     

关于线性奇异向量和条件非线性最优扰动差别的一个注记

奇异向量(singular vectors,SVs)和条件非线性最优扰动(conditional nonlinear optimal perturbation,CNOP)已广泛应用于研究大气—海洋系统的不稳定性以及与其相关的可预报性、集合预报和目标观测问题研究。本文首先回顾了SVs和CNOP的发展历史,并简单描述了它们的基本原理;然后针对二维正压准地转模式,使用不同的范数组合,分析了第一线性奇异向量(first singular vector,FSV)和CNOP之间的异同。结果表明,当优化时间较短时,度量SVs和CNOP大小的范数不同也将导致FSV和CNOP相差很大,而当度量SVs和CNOP大小的范数相同时,FSV和CNOP之间的差别则主要是由非线性物理过程作用的结果。因此,针对不同的物理问题,应该选取合适的度量范数研究FSV和CNOP以及其所引起的大气或海洋动力学的异同,从而揭示非线性物理过程的影响机理。     

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。      

Impact of Different Guidances on Sensitive Areas of Targeting Observations Based on the CNOP Method

The conditional nonlinear optimal perturbations(CNOPs) obtained by a fast algorithm are applied to determining the sensitive area for the targeting observation of Typhoon Matsa in 2005 using an operational regional prediction model-the Global/Regional Assimilation and PrEdiction System(GRAPES).Through a series of sensitivity experiments,several issues on targeting strategy design are discussed,including the effectivity of different guidances to determine the sensitive area(or targeting area) and the impa...     

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.     

应用奇异向量方法的适应性观测实例研究

近年来,通过适应性观测技术来减小预报误差已成为国际上数值预报中的一项关键技术,然而实施适应性观测对减小预报误差的影响评估是一个需要深入讨论的问题。文中利用奇异向量方法以2007年3月4日东北地区暴风雪天气过程为研究对象,考察了预报误差对不同观测区域观测资料的敏感性,在确定能量范数的基础上,分析了奇异向量的水平分和特征和垂直分布特征,利用奇异向量的空间结构确定了敏感区域。通过伪逆初始扰动场作为分析误差,研究验证区域的预报误差对不同区域增加观测的敏感性,试验结果表明,在敏感区域内进行补充观测来改善分析误差,能够最有效地提高验证区域内的预报水平;而减小非敏感区域内的分析误差对减小预报误差的贡献相对较小。这些结果表明,利用奇异向量法定义敏感区进行适应性观测,能够和有限的观测资源和计算资源的条件下,最大程度地减小验证区域的预报误差,从而达到提高验证区域预报准确率的目的。     

A Comparison Study of the Contributions of Additional Observations in the Sensitive Regions Identified by CNOP and FSV to Reducing Forecast Error Variance for the Typhoon Morakot

The sensitive regions of conditional nonlinear optimal perturbations (CNOPs) and the first singular vector (FSV) for a northwest Pacific typhoon case are reported in this paper. A large number of probes have been designed in the above regions and the ensemble transform Kalman filter (ETKF) techniques are utilized to examine which approach can locate more appropriate regions for typhoon adaptive observations. The results show that, in general, the majority of the probes in the sensitive regions of CNOPs can reduce more forecast error variance than the probes in the sensitive regions of FSV. This implies that adaptive observations in the sensitive regions of CNOPs are more effective than in the sensitive regions of FSV. Furthermore, the reduction of the forecast error variance obtained by the best probe identified by CNOPs is twice the reduction of the forecast error variance obtained by FSV. This implies that dropping sondes, which is the best probe identified by CNOPs, can improve the forecast more than the best probe identified by FSV. These results indicate that the sensitive regions identified by CNOPs are more appropriate for adaptive observations than those identified by FSV.     

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.     

The Impact of Horizontal Resolution on the CNOP and on Its Identified Sensitive Areas for Tropical Cyclone Predictions

In this study,the impacts of horizontal resolution on the conditional nonlinear optimal perturbation (CNOP) and on its identified sensitive areas were investigated for tropical cyclone predictions.Three resolutions,30 km,60 km,and 120 km,were studied for three tropical cyclones,TC Mindulle (2004),TC Meari (2004),and TC Matsa (2005).Results show that CNOP may present different structures with different resolutions,and the major parts of CNOP become increasingly localized with increased horizontal resolution.CNOP produces spiral and baroclinic structures,which partially account for its rapid amplification.The differences in CNOP structures result in different sensitive areas,but there are common areas for the CNOP-identified sensitive areas at various resolutions,and the size of the common areas is different from case to case.Generally,the forecasts benefit more from the reduction of the initial errors in the sensitive areas identified using higher resolutions than those using lower resolutions.However,the largest improvement of the forecast can be obtained at the resolution that is not the highest for some cases.In addition,the sensitive areas identified at lower resolutions are also helpful for improving the forecast with a finer resolution,but the sensitive areas identified at the same resolution as the forecast would be the most beneficial.     

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。     

Effects of Dropsonde Data in Field Campaigns on Forecasts of Tropical Cyclones over the Western North Pacific in 2020 and the Role of CNOP Sensitivity

Valuable dropsonde data were obtained from multiple field campaigns targeting tropical cyclones, namely Higos,Nangka, Saudel, and Atsani, over the western North Pacific by the Hong Kong Observatory and Taiwan Central Weather Bureau in 2020. The conditional nonlinear optimal perturbation(CNOP) method has been utilized in real-time to identify the sensitive regions for targeting observations adhering to the procedure of real-time field campaigns for the first time. The observing system experiments...