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目录 contents

    摘要

    从初始误差、模式误差以及两者综合影响的角度,综述了天气、气候集合预报方法的研究进展,指出了传统方法的优势,同时也评论了这些方法的局限性,提出了对未来先进集合预报方法的一些思考,以及需要解决的挑战性问题和可能的应用。

    Abstract

    This article reviews the research progress of ensemble forecast methods for weather and climate from the perspective of initial errors, model errors, and the combined effects of the above two. The authors clarify the advantages of traditional methods; meanwhile, they comment on the limitations of these methods. Finally, the authors propose some ideas on developing more advanced ensemble forecast methods, raise some challenging problems that need to be resolved, and address possible applications of the ensemble methods.

  • 1 引言

    大气、海洋及其耦合系统的异常变化是地球环境天气、气候异常的始作俑者,它们的运动呈现了非线性不稳定性系统的解对初值极端敏感性的特征。在数值预报和预测中,这种非线性不稳定性将导致初始观测资料误差快速增长,在预报时刻导致天气、气候事件较大的预报误差 (Lorenz,1969Kalnay,2003Kirtman et al.,2013);另外,目前的数值模式尚不能很好地刻画大气、海洋及其耦合系统等地球要素运动的规律和特征,从而存在模式误差。初始误差、模式误差以及非线性系统的不稳定性共同导致了大气、海洋及其耦合系统,尤其是与之相关的天气和气候事件预报的预报误差 (Mu et al.,2010Palmer et al.,2014)。关于预报误差的研究属于可预报性研究 (Mu et al.,2004)。可预报性研究对于提高天气预报和气候预测的预报技巧具有重要作用,而关于预报误差的估计则有助于人们很好地判断预报产品的可靠性,正如 Tennekes(1991)指出,没有进行预报误差估计的预报产品不是一个完整的预报产品[亦见 Thompson(1957)Palmer et al.(1994)]。因此,预报误差的估计是数值天气预报和气候预测中必不可少的环节。集合预报常常被用来估计预报误差。经典的集合预报是用来估计未来状态的概率密度分布。 Epstein(1969)建议显式积分Liouville方程估计大气状态的概率密度分布。然而,数值天气预报和气候预测系统的自由度多达数百万,甚至数千万,从而导致这种方法在计算上是不可行的 (Epstein,1969)。随后, Leith(1974)提出了蒙特卡洛(Monte Carlo Forecasting,MCF)方法,该方法的思路是将多组随机初始扰动叠加在初始分析场上,产生一组预报成员来估计预报状态的概率密度分布,从而得到预报结果的不确定性。这就是集合预报的思想。蒙特卡洛方法实现了集合预报从理论研究转向实际。 Epstein(1969)Leith(1974)认为,在完美模式情况下,如果一组初始扰动能够很好地反映初始状态的不确定性,那么将这些初始扰动叠加到模式初值进行预报,则可得到多个扰动的预报结果,这些扰动的预报结果能较好地反映预报结果的不确定性,而其集合平均则滤掉了不可预报的成分,保留了各预报成员最可能发生的共同成分,得到了更可信的预报结果,从而可以改善单一确定性(或控制)预报的预报技巧 (Leutbecher and Palmer,2008);通过计算集合预报成员关于集合平均的离散度,集合预报可以给出集合平均预报产品的不确定性。理论上,一个可靠集合预报系统的集合平均预报误差与其离散度度量的预报不确定性是相等的 (Branković et al.,1990Eckel and Mass,2005)。因此,集合预报系统可以通过集合离散度预报集合平均预报的预报误差 (Bowler,2006Buckingham et al.,2010)。同时,集合预报也可以通过集合成员,利用度量概率预报技巧的方法,给出我们所关心的事件发生的概率信息 (Buizza et al.,2005Leutbecher and Palmer,2008)。可见,集合预报不仅可以提供确定性的集合平均的预报结果,而且可以对该结果的预报误差做出估计,同时也能够通过概率预报给出我们所关心事件发生的可能性。

    集合预报可以提供给人们所关心的天气或气候事件的预报结果、预报误差,以及所关心事件发生的可能性的预报产品,这些产品足以让人们判断在未来的天气和气候状态下如何安排必要的生产、生活和各项国民经济活动,或者帮助决策者判断未来时间应采取何种防灾减灾措施,避免大的损失。集合预报产品的丰富性和有用性决定了其在数值预报预测中具有无可替代的重要作用。世界气象组织(World Meteorological Organization,WMO)已将集合预报列为未来数值预报的主要发展战略之一。所以,集合预报的发展在现代业务数值预报体系中正呈现着巨大潜力,关于集合预报的研究在气象和气候学研究中具有重要的战略意义和实际应用价值。

    本文将从理论上阐明集合预报的基本思路,并综述国际上已发展的主要的集合预报方法;通过分析这些方法各自的优势和不足,展望未来亟须加强的先进集合预报方法,及其可能遇到的挑战性问题。

  • 2 减小初值不确定性影响的集合预报方法

    经典的集合预报是一个初值问题,即采用一些相关性不大的初值,积分数值模式而估计预报状态概率密度分布的方法(Leith,1974)。具体地,集合预报是在控制预报存在较大不确定性的情形下,在其初始分析场上叠加初始扰动,形成一次扰动预报,不同的初始扰动可以得到不同的扰动预报,这些扰动预报形成集合预报的集合成员样本。根据集合成员样本,集合预报可以估计未来状态的概率密度分布。那么,何种初始扰动有利于更高的集合预报技巧呢?作者认为,集合预报在控制预报上叠加初始扰动形成集合成员的主要目的是使其能够描述真值,是对真值的估计。既然控制预报与真值存在较大差别,那么我们只有在控制预报上叠加随时间发展而增长的初始扰动才能使集合成员更接近真值,从而更好地刻画真值(图1)。所以,只有在控制预报上叠加增长型初始扰动,才能使集合预报具有更高预报技巧。

    图1
                            控制预报、集合预报成员以及增长型初始扰动演变的示意图

    图1 控制预报、集合预报成员以及增长型初始扰动演变的示意图

    Fig. 1 Schematic diagram showing the control forecast, the ensemble forecast members, and temporal evolution of the fast-growing initial perturbation

    国际上已发展了多种产生集合预报初始扰动的方法,并且这些方法在不同国家和地区的业务部门得到了较为成功的应用。如引言所述, Leith (1974)提出了蒙特卡洛方法(Monte Carlo method,MCF)并将其应用于数值模式中进行集合预报,使得集合预报从理论研究转向实际应用。该方法将真实大气的初始分析误差看作是随机分布的,其优点是能产生大量的集合成员,缺点是不能反映初始分析误差的空间分布,不能描述不稳定增长的初始扰动。为了在集合预报中刻画增长型初始扰动,欧洲中期天气预报中心(European Centre for Medium-Range Weather Forecasts,ECMWF)使用奇异向量法(Singular Vectors,SVs; Lorenz,1965Mureau et al.,1993Leutbecher and Palmer,2008)产生集合预报成员。SVs代表了线性化模式中相互独立的相空间中的最快增长扰动,代表了相空间最不稳定的方向 (Lorenz,1965)。将这些相互独立的SVs作为相空间的一组正交基,通过线性组合形成不同的扰动向量描述初始分析误差的不确定性,将这些向量作为集合预报的初始扰动产生集合预报成员。该方法的优点是具有明确的动力学意义,容易抓住初始分析误差的不稳定增长性质,但该方法的一个致命缺点是在产生SVs正交基时对非线性模式采取了线性近似,致使上述初始扰动不能充分反应非线性物理过程的影响,不能给出极端扰动可能性的相关信息,因而影响集合预报的预报技巧 (Anderson,1997Hamill et al.,2000Mu and Jiang,2008Jiang and Mu,2009Duan and Huo,2016)。为了克服SVs的局限性, Mu et al. (2003)提出了条件非线性最优扰动(conditional nonlinear optimal perturbation,CNOP)方法,该方法描述了非线性模式中增长最快的初始扰动,充分考虑了非线性的影响。 Duan and Huo (2016)将该方法拓展到数值模式相互独立的相空间中产生正交CNOPs,并将其作为集合预报初始扰动应用于登陆我国的台风的路径预报,得到了较SVs等方法更高的集合平均预报技巧 (Huo and Duan,2019Huo et al.,2019),给出了更合理的预报不确定性估计,但该方法的计算代价是昂贵的,期待未来能够发展更为有效的算法应用于正交CNOPs,从而拓展其在数值天气预报和气候预测中的应用。为了考虑非线性物理过程对集合预报初始扰动的影响,NCEP在时滞集合预报的基础上,发展了繁殖向量法(Breeding vectors,BVs; Toth and Kalnay,1997)用于产生集合预报初始扰动,并投入到实际业务中。该方法借鉴了资料同化技术,通过模式的繁殖循环计算快速增长初始误差模态,然后把得到的误差模态作为集合预报的初始扰动。该方法的优点是扰动结构与模式大气结构的协调性较好,计算量小,但该方法刻画的是预报初始时刻之前时间段的快速增长扰动。若将其应用于集合预报产生初始扰动,所得初始扰动在描述控制预报的初始分析误差发展方面动力学意义不明确,而且由该方法产生的集合初始扰动是非独立的,集合成员具有较高的相似性,不利于有效估计预报结果的不确定性。尽管 Feng et al.(2014)Magnusson et al.(2008)等考虑了BVs的正交性,分别使用正交的非线性局部Lyapunov向量和正交BVs进行集合预报研究,但仍然不能克服BVs刻画预报初始时刻之前时间段快速增长扰动的局限性。事实上, Huo et al. (2019)将CNOPs集合预报与BVs对比后发现,BVs倾向于产生更小的集合离散度,且集合样本主要分布在控制预报周围,因而具有较小的集合平均预报技巧。BVs刻画过去时间的最优扰动可能是其集合预报具有较小离散度的主要原因之一。一种基于集合技术的资料同化方法也被应用到集合预报中。如集合卡曼滤波(Ensemble Kalman filter,EnKF; Evensen,1994Houtekarner et al.,2007)、集合转换卡曼滤波(Ensemble transform Kalman filter,ETKF; Houtekamer and Derome,1994Bishop and Toth,1999)等。这些方法利用集合成员估计预报误差的协方差矩阵,然后利用观测资料,通过同化方法对预报误差的协方差矩阵进行更新,得到分析集合成员,这些分析集合成员构成了集合预报成员的初始场。该类方法在集合预报试验中取得了较好的效果,但需要指出的是,EnKF方法通常对非线性观测算子做简单的线性化处理,对观测误差采用高斯分布假设,从而使得对于非高斯分布的观测误差,EnKF方法不能很好地抓住系统状态的变化特征 (Von Leeuwen,2009)。另外,EnKF方法存在使用有限集合样本数的局限性,该局限性常常使得在估计背景误差协方差矩阵时引入伪相关,从而造成协方差被低估和滤波发散(即产生很大的取样误差)的现象,最终导致分析值不能较好地反映系统的真实状态,影响集合预报的效果。EnKF方法的计算量巨大,限制了其广泛被使用。虽然针对EnKF方法计算量巨大,前人提出了ETKF方法 (Bishop and Toth,1999),但该方法的预报误差协方差采用线性近似,对于非线性系统预报误差协方差的估计具有线性局限性。而且,与BVs类似,EnKF和ETKF的集合扰动主要刻画预报时刻之前时间段的初始扰动,动力学意义不明确,这可能是EnKF和ETKF集合离散度相对较小,而不得不采用人工干预或考虑模式误差的方式增加其离散度的原因 (Yang et al.,2015Zheng and Zhu,2016),尤其这些方法在具体的业务应用中仍处于发展尝试阶段。

    综上可见,目前关于初值的集合预报方法各自尚存在优缺点,但可以看到,气象学家们是在不断地探索和尝试,并努力给出一个具有更高预报技巧且理论上更合理的集合预报方法。那么,如何考虑上述各种方法的局限性,进而给出一个各方面更完备的集合预报方法呢?另外,从上述方法可以看出,一些局限性在不同方法之间可以相互克服,那么,如果未能给出更完备的集合预报方法时,我们是否可以退而求其次,考虑将不同集合预报方法的结果进行集合而减小单一集合预报方法局限性带来的负面影响呢?无论如何,这些思路都值得去尝试,并期望未来能够给出一个理论上更合理,且具有更高预报技巧的初值集合预报方法。

  • 3 减小模式不确定性影响的集合预报方法

    从第2节可知,经典的集合预报方法仅考虑初始不确定性,即假定模式是完美的。然而,越来越多的研究表明,模式误差也在很大程度上影响着天气和气候的预报精度,尤其是地球环境经历了气候变化后,有关的天气和气候事件发生了变异,而目前的数值模式不能很好地抓住引起天气和气候事件变异的物理过程,从而存在较大的模式误差。模式误差引起的天气预报和气候预测不确定性也越来越受到气象学家们的重视 (Kirtman et al.,2013Duan et al.,2014Mu et al.,2015)。如IPCC-AR5在考虑初始不确定性的基础上,进一步考虑模式误差的影响,给出了气候可预报性新的定义,即他们认为“气候可预报性”度量了当前状态或系统的微小误差对未来状态的影响程度:如果初始误差随时间发展迅速放大或概率密度分布迅速变宽,那么系统的可预报性较低;相反,系统的可预报性较高 (Kirtman et al.,2013)。另外, Wang et al.(2018)表明,天气集合预报效果不好的主要原因是模式系统误差的存在。可见,天气、气候集合预报需要考虑模式误差的影响。然而,模式误差导致的预报不确定性,与初始误差类似,也包含在数值预报的不确定性中,而且与初始误差导致的预报误差相互作用,难以区分。上述关于初始误差的集合预报未能充分考虑模式误差及其与初始误差的相互作用,从而可能使得预报产品的不确定性被错误估计,误导人们依据预报产品对未来天气和气候走向的判断。

    模式误差来源广泛,不仅涉及次网格物理过程的参数化,而且数值模式的离散格式,以及计算机的计算误差也引入了不可避免的模式误差,因此要通过集合的方法描述模式误差及其与初始误差的相互作用,要远比单独描述初始误差难度更大 (Barkmeijer et al.,2003Moore et al.,2006Duan and Zhou,2013Qi et al.,2017)。尽管这样,国际学者也不断尝试新的集合预报方法估计模式误差导致的预报不确定性。如Houtekamer et al.(1996)在加拿大环境局的全球集合预报系统中使用不同的对流、水平扩散、重力波拖曳、辐射和地形处理方案,采用了多物理过程组合来减小物理过程不确定性引起的模式误差的集合预报方法 (Stensrud et al.,2000Jankov et al.,2005); McCabe et al. (2016)则通过随机扰动数值模式中的参数进行集合预报,从而减小参数误差引起的模式误差;除此之外,ECMWF在1998年集合预报系统中的模式倾向方程引入了随机物理过程法 (Buizza et al.,1999)。该方法假定模式的不确定性主要来自于参数化过程的不准确和数值模式的截断误差,通过产生不同的随机误差扰动模式某些敏感参数或在模式的相关项上引入一个随机过程或因子对其进行扰动,进行集合预报 (Shutts and Palmer,2004)。显然,这些集合预报方法仅考虑了部分模式误差的影响。为克服该局限性,Evans et al.(2000)Goerss(2000)等将多个模式的预报结果进行集合,进行多模式集合预报 (Harrison et al.,1999),这种方法考虑了不同模式误差的综合影响,与其他方法相比具有一定的优势。多模式集合预报方法也被应用于气候预测的集合预报中,并取得了一定的成功 (Kirtman and Min,2009)。然而,上述集合预报方法仅考虑模式误差的影响,那么如何在集合预报中同时考虑模式误差和初始误差,及其相互作用对预报结果的影响呢?

  • 4 同时减小初值和模式不确定性影响的集合预报方法

    以上介绍的集合预报方法要么仅考虑初始不确定性产生初始扰动,要么仅考虑模式不确定性采用多物理过程参数化方案,或者多模式集合,或者随机扰动物理参数化方案。事实上,如引言所述,数值预报同时存在初值和模式的不确定性,而且一个复杂的数值模式是由很多个物理参数化方案组成的,其下又包含了大量的参数(很多为不具物理意义的经验参数)。在集合预报中,若要全部考虑这些物理参数化过程及其所包含的参数的不确定性,及其与初始误差的相互作用,并逐个扰动进行集合预报是一项相当困难的工作。那么,能否跳出这些微观细节、从宏观的角度刻画模式误差并考虑其与初始误差的相互作用呢?目前国际上采用的多模式—多初值集合预报可以同时考虑不同物理过程和初值不确定性对集合预报的影响 (Hou et al.,2001)。所谓多模式—多初值集合预报,即是指将多个模式对应的子集合预报系统的所有预报构成集合成员,进行集合预报。该方法同时考虑了初始误差和模式不确定的影响,但受模式数量所限,多模式集合可能在统计上不显著,预报成员之间也可能由于模式之间较大的差异而存在较大的非等同性,从而会造成集合预报结果较大的系统偏差。那么是否可以找到一种方法避免该问题呢?

    NCEP从2010年开始使用随机全倾向扰动法(stochastic total tendency perturbation,STTP; Hou et al.,20062008),即在模式方程的倾向中加入随机强迫项来描述数值模式所有模式误差的综合影响,通过多次实现随机强迫来产生集合预报成员。事实上,该方法是在数值模式倾向方程叠加随机强迫扰动,通过多次实现该随机扰动产生集合成员进行集合预报。随机倾向扰动意味着该扰动叠加在模式积分的每一步,包括预报的起始时刻。所以,该随机强迫既扰动了初值,也扰动了模式(倾向),从而既考虑了初始误差,又充分考虑了模式误差的影响。所以,STTP方法可以认为是多初值—多模式的集合预报方法的一种简化形式。STTP方法基于同一个数值模式,因而能够避免不同模式间的非等同性;由于STTP方法可以多次实现随机倾向扰动产生集合预报成员,因而可以通过产生大量随机扰动避免集合预报结果在统计上不显著的现象;而且 Hou et al.(20062008)表明,STTP方法可以增加集合离散度,减少集合平均预报中的系统误差。但STTP与蒙特卡洛初值集合预报方法类似,随机外强迫不能充分反映模式误差的空间分布,不能很好地刻画模式误差的不稳定空间结构,从而不能充分反映模式误差导致的预报误差的不稳定增长。因而,STTP方法在充分刻画初始误差和模式误差共同导致的预报不确定性方面具有局限性。如前所述,由增长型扰动产生的集合预报成员能够使集合预报具有更高的预报技巧。因此,如果能够通过一种有效的方法产生刻画不稳定增长的倾向扰动,并形成集合预报成员,那么该集合预报方法不仅同时考虑了初始误差和模式误差影响,而且考虑了扰动的不稳定增长,因而会具有更高的预报技巧,从而避免了多模式—多初值集合预报统计上可能不显著的局限性,而且克服了STTP未能充分刻画不稳定增长扰动的不足之处。那么,如何产生该类倾向扰动呢?

  • 5 讨论和展望

    为了刻画数值模式全倾向扰动的不稳定增长, Barkmeijer et al. (2003)参照SVs方法,通过考虑数值预报模式全倾向扰动导致的预报误差与倾向扰动本身的最大比率,定义了强迫奇异向量(forcing singular vector,FSV)。 Barkmeijer et al. (2003)表明,FSV描述了最优全倾向扰动的线性增长[亦见 Moore et al. (2006)]。可见,FSV未能充分考虑大气、海洋运动中的非线性物理过程的影响,而且由其定义可知,FSV考虑的预报误差与其本身的比率,动力学意义不明确。为了克服该局限性, Duan and Zhou (2013)提出了非线性强迫奇异向量(nonlinear forcing singular vector,NFSV)方法。该方法直接使用非线性模式,考虑了倾向扰动导致的最大预报误差,强调了具有特定空间结构的全倾向扰动的非线性不稳定增长,能够揭示导致天气和气候事件最大预报误差的倾向误差。所以,NFSV克服了FSV未能充分考虑非线性影响的局限性,具有明确的动力学意义,而且对于上述讨论的随机全倾向扰动来说,NFSV也避免了其不能反映模式误差空间分布及其未能刻画预报误差不稳定增长的局限性 (Duan and Zhao,2015),且NFSV作为全倾向扰动,与STTP类似,同时考虑了初始误差和模式误差,及其相互作用的影响,尤其NFSV所包含的初始误差和模式误差在动力上是协调发展的。所以,如果将NFSV应用于集合预报,它将是一个极具潜力,且理论上更可靠的先进集合预报方法。那么,如何将NFSV应用于集合预报呢?

    从NFSV的定义可知,NFSV只能揭示整个相空间的最快增长全倾向扰动。然而,同时考虑初始误差和模式误差的集合预报方法要求产生相关性不大的多个集合预报成员,因而需要在数值模式相互独立的相空间中产生相互正交的NFSVs。因此,要将NFSV方法应用于集合预报,必须考虑相互独立的相空间的正交NSFVs。NFSV的计算需求解一个非线性优化问题,而对于计算相互独立的正交NFSVs来说,需要考虑在相互独立的相空间,根据所关心的天气和气候事件的物理过程建立相应的非线性优化问题,而这无论在理论上还是实际计算上都是一个具有挑战性的问题,但对于集合预报却是亟须探讨的一个具有重要科学和战略意义的问题。因此,要获得能够同时考虑初始误差和模式误差不稳定增长的相互独立相空间的NFSVs,作者认为需大力开展非线性最优全倾向扰动及其算法的研究,该研究无疑将成为集合预报研究中的一个重要的开放课题,且在大气、海洋运动的预报中将具有重要的应用前景。

    众所周知,ENSO事件是影响我国天气和气候异常的极端气候事件之一,ENSO预测也是目前国际上短期气候预测最为成功的领域 (Chen et al.,19952004Lopez and Kirtman,2014郑飞等,2016),但其预报技巧仍不能满足人们防灾减灾的需求 (Qi et al.,2017Duan and Mu,2018)。尤其是20世纪90年代后,随着全球气候的变化,一种区别于传统东太平洋型El Niño事件的新型事件,即中太平洋型El Niño事件开始频繁发生,更增加了ENSO预测的不确定性 (Kirtman et al.,2013Duan et al.,20142018),从而也使得ENSO的预测多了一项内容,即关于El Niño类型的预测。 Hendon et al. (2009)指出对于两类El Niño事件的预测,尤其是准确区分未来发生的El Niño事件属于何种类型有很大困难,有效的预报时效最多为1个月; Jeong et al.(2012)表明,即使采用初值集合预报,区分两类El Niño事件的预报技巧也最多仅为4个月。可见,新类型El Niño事件的频繁发生使ENSO预测又重新面临严峻的挑战。国际上许多文献强调初始误差对东太平洋型El Niño的预测具有重要影响 (Moore and Kleeman,1996Chen et al.,2004Duan et al.,20092018),而模式误差在中太平洋型El Niño的预测不确定性中发挥了重要作用 (Duan et al.,20142018)。即是说,目前的数值模式对于ENSO事件空间模态变化的物理过程的描述尚存在缺陷,即存在模式误差,使得人们在预测中无法较好区分El Niño类型。这可能是 Jeong et al. (2012)关于El Niño类型的初值集合预报无法取得较高预报技巧的原因之一。因此,在El Niño类型的集合预报中,如果能通过恰当的方法既考虑初始误差,又考虑模式误差,同时也考虑两者相互作用影响的话,El Niño类型的预报技巧会大大提高。上述正交NFSVs集合预报方法,综合考虑了初始误差和模式误差的不稳定增长,因此我们有理由相信它在提高El Niño类型的预报技巧中将发挥重要作用。

    台风是影响我国国家公共安全的主要自然灾害之一,台风预报对于我国防灾减灾具有重要意义。近年来,随着人们对台风认识的深入以及数值预报水平的提高,对台风移动路径的预报技巧有了显著提高,而对台风强度预报技巧的提高则显得非常缓慢 (DeMaria et al.,2014Emanuel and Zhang,2016),尤其是近10多年来,台风强度的预报技巧几乎没有得到改善。而且,气候变化引起的台风变化也更增加了台风预报的不确定性。数值预报是目前台风预报的主要手段。研究表明,初值的不确定性对台风路径的影响较大 (Yamaguchi and Majumdar,2010Munsell et al.,2015Dong and Zhang,2016),改进数值模式的初始场,可以较大程度地提高台风的路径预报,尤其一些学者通过考察初始场的不确定性信息,应用集合预报来改善台风的预报技巧,并估计其预报不确定性。 Zhang and Krishnamurti(19971999)通过扰动初始台风的位置、结构和环境场产生集合预报成员,并对大西洋的台风个例进行集合预报试验,结果表明集合预报可以较大程度地减小台风的路径预报误差。 Weber(2003)也表明集合预报可以使大西洋台风的72 h路径预报误差减小20%以上。此外,也有学者通过扰动初值构造集合预报成员,对台风进行集合预报试验,并成功地提高了台风的登陆、转向等方面的预报技巧 (Munsell et al.,2015智协飞等,2015Dong and Zhang,2016)。可见,初值不确定性的准确估计在提高台风集合预报技巧中具有重要作用。然而,初值的改进对台风强度预报的改进并不显著 (Xue et al.,2013Munsell et al.,2015Emanuel and Zhang,2016)。近来, Emanuel and Zhang (2016)指出,改善模式对提高热带气旋的强度预报是极其重要的 (Li and Pu,2008Green and Zhang,2013Li et al.,2014Zhang and Marks,2015Chen et al.,2018a2018b),而且 Torn (2016)表明在考虑台风的集合预报时,应充分考虑模式的各种不确定性信息 (Vukicevic and Posselt,2008Rios-Berrios et al.,2014)。从上述讨论可见,台风路径预报的准确程度主要取决于初值的准确程度,而台风强度预报的准确程度更多地取决于模式物理过程、边界条件、外强迫等的准确程度。因此,为了综合提高台风的路径和强度的集合预报技巧,需要同时考虑初值和模式的不确定性,而采用综合考虑初始误差和模式误差及其相互影响的正交NFSVs集合预报方法则能够满足上述台风预报的需求,因而将会在提高台风预报技巧中发挥重要作用。

    上述讨论将ENSO和台风高影响事件作为例子,强调了数值天气预报和气候预测在集合预报中同时考虑初始误差和模式误差及其相互作用的重要性,展望了正交NFSVs集合预报方法及其可能的有用性。当然,尚有其他高影响天气、气候事件的预报、预测也同时受到初始误差和模式误差的影响,也需采用能够同时考虑初始误差和模式误差的集合预报方法,这里就不一一赘述。总之,随着全球气候的变化,天气和气候异常也发生了变化,模式误差逐渐成为与初始误差同样重要的影响天气和气候事件预报、预测不确定性的主要因子。所以,在天气预报和气候预测中,除了加大力度增加观测、改进数值模式的初始场之外,也需对已有数值模式适当改进;而在预报预测方法的研究中,则需发展综合考虑初始误差和模式误差的预报预测方法,而作者建议的正交NFSVs集合预报方法无疑适应了该需求。期望在未来研究的基础上,我们能够将其发展成为具有明确动力和物理意义的有用的集合预报方法。

  • 6 总结

    本文在前人研究的基础上对集合预报的定义、性质,以及作用进行了详细介绍,强调了集合预报方法是无可替代的一种预报方法。通过分析,作者对采用何种集合样本能够获得集合预报的较高技巧进行了思考,指出了快速增长型扰动在控制预报与真值有较大差别的条件下,能够使得集合预报具有较高技巧,从而说明了集合预报有较高技巧的先决条件,也阐明了集合预报的适用范围。然后,作者对传统的集合预报方法进行了评述,指出了各种方法的优势,同时分析了它们的局限性。考虑到目前高影响天气、气候事件的预报、预测同时受到初始误差和模式误差的影响,作者综述了国际上目前正在探讨或尝试在业务预报中使用的关于模式参数和物理过程不确定性的集合预报方法,以及随机倾向扰动(STTP)集合预报方法。虽然STTP方法综合考虑了初始误差和模式误差,克服了国际上一些传统方法的局限性,但其未能充分考虑扰动的非线性不稳定增长性质,从而限制了集合预报的技巧。作者针对STTP方法的局限性,讨论了非线性强迫奇异向量(NFSV)在集合预报中的可能应用,并以ENSO和台风作为例子,展望了NFSV集合预报的可能应用及其有用性。

    集合预报方法及其应用的研究具有明显的数理交叉特色。因此,希望在未来的数值天气预报和气候预测研究中,气象学家们能够积极与数学家们通力合作,在大力研究和探讨的基础上提出一个理论上可靠,预报技巧高的集合预报方法。

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段晚锁

机 构:

1. 中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室(LASG),北京100029

2. 中国科学院大学,北京100049

Affiliation:

1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

2. University of Chinese Academy of Sciences, Beijing 100049

邮 箱:duanws@lasg.iap.ac.cn

作者简介:段晚锁,男,1973年出生,研究员,主要从事可预报性研究。E-mail: duanws@lasg.iap.ac.cn

汪叶

机 构:

1. 中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室(LASG),北京100029

2. 中国科学院大学,北京100049

3. 河南大学数学与统计学院,河南开封475004

Affiliation:

1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

2. University of Chinese Academy of Sciences, Beijing 100049

3. School of Mathematics and Statistics, Henan University, Kaifeng, Henan Province 475004

霍振华

机 构:中国气象局国家气象中心,北京 100081

Affiliation:National Meteorological Center, China Meteorological Administration, Beijing 100081

周菲凡

机 构:中国科学院大气物理研究所云降水物理与强风暴重点实验室(LACS),北京100029

Affiliation:Key Laboratory of Cloud-Precipitation Physics and Severe Storm (LACS), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

/html/qhhj/18133/alternativeImage/960cee9f-22da-4b03-bd1e-ddce3c28acd0-F001.jpg

图1 控制预报、集合预报成员以及增长型初始扰动演变的示意图

Fig. 1 Schematic diagram showing the control forecast, the ensemble forecast members, and temporal evolution of the fast-growing initial perturbation

image /

无注解

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