数值天气预报和气候预测可预报性研究的若干动力学方法

简要回顾了数值天气预报和气候预测可预报性研究的若干动力学方法,包括用于研究第一类可预报性问题的线性奇异向量（LSV）和条件非线性最优初始扰动（CNOP-I）方法,以及Lyapunov指数和非线性局部Lyapunov指数方法。前两种方法用于研究预报或预测的预报误差问题,可以用于估计天气预报和气候预测的最大预报误差,而且根据导致最大预报误差的初始误差结构的信息,这两种方法可以用于确定预报或预测的初值敏感区。应该指出的是,LSV是基于线性化模式,对于描述非线性大气和海洋的运动具有局限性。因而,对于非线性模式,应该选择使用CNOP-I估计最大预报误差。Lyapunov指数和非线性局部Lyapunov指数可以用于研究第一类可预报性问题中的预报时限问题,前者是基于线性模式,不能解释非线性对预报时限的影响,而非线性局部Lyapunov指数方法则考虑了非线性的影响,能够较好地估计实际天气和气候的预报时限。第二类可预报性问题的研究方法相对较少,本文仅介绍了由我国科学家提出的关于模式参数扰动的条件非线性最优参数扰动（CNOP-P）方法,该方法可以用于寻找到对预报有最大影响的参数扰动,并可以进一步确定哪些参数最应该利用观测资料进行校准。另一方面,通过对比CNOP-I和CNOP-P对预报误差的影响,可以判断导致预报不确定性的主要误差因子,进而指导人们着力改进模式或者初始场。     

天气和气候的可预报性

从理论和实际角度描述了天气和气候可预报性的认识过程.天气和气候的可预报性,特别是10～30天预报依赖于空间和时间尺度,预报包含了可预报分量和混沌分量.可预报性研究的最大挑战,来自气象极端事件的可预报性问题.     

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。     

降水气候噪声和可预报性问题的初步研究

从气候噪声和可预报性的定义出发，讨论了气候噪声产生的原因，提出一种消除气候噪声的函数，讨论该函数的参数设置，并在此基础上进行了实例分析，结果表明利用该函数作用于气候预测样本，可以部分消除气候噪声，提高可预报性。     

单站气温信息传递及其可预报性研究

采用信息传递量作为度量气候可预报性的指标，分别讨论了我国各大气候区的１０个代表测站平均气温的可预报性。数值计算表明，各种不同时间尺度信息传递量具有不同的衰减特征，其差异反映出实际气候背景的差异，信息传递量较好地代表了可预报性特征。由于实测的信息衰减与模式信息衰减具有一致性，因此，信息传递可作为检验模式可预报性的有益工具。     

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。     

长期天气过程的可预报性研究的进展

在数值天气预报中,大气可预报性问题是一个重要的研究课题。它们有的是从数值预报模式初值场误差探讨,即讨论计算过程中的误差增长使得预报与实况差异太大的时间。这段时间一般为两周,它称为大气可预报的时间。这是短期天气过程可预报性问题。长期天气过程的可预报性,大多是从天气变化稳定性进行探讨。短期天气过程与长期天气过程的关系以及长期天气过程的可预报性问题一直是近十余年来气象学者十分关心的研究课题,本文将着重介绍有关长期天气过程可预报性研究的进展。     

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。      

气候系统可预报性理论研究

介绍了作者近年来关于气候系统可预报性理论研究的一些工作,包括:非线性最快增长扰动理论以及在气候预测的可预报性研究中的应用;从一个新的角度研究了2类可预报性问题,并提出可预报性的3类子问题;根据计算不确定性原理,讨论了模式可预报性与机器精度的关系;探讨了可预报性与时空尺度的关系,建立了可预报性的相对观.     

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.     

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.     

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。     

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.     

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.     

Predictability of the 500 hPa Height Field

The dimensions of attractors and predictability are estimated from phase space trajectories of observed 500 hPa height over the Northern Hemisphere. As a first estimate the dimensions of attractors are about 11.5 and the doubling time of the initial error is 6 to 7 days for original data. But the former is shorter and the latter is longer for low frequency data set.To verify if the predictability estimated by this method and by general circulation model is identical, the doubling time of the initial error of a model data set by both methods is estimated. It is shown that the predictability obtained from phase space trajectories is overestimated to sufficient small initial error. But it is underestimated to the time being equal to the climatological RMS error.     

Analysis Study on Perturbation Energy and Predictability of Heavy Precipitation in South China

The AREMv2.3 mesoscale numerical model is used to explore storm processes in South China during the pre-rainy season in 2006 by imposing perturbations on the initial fields of physical variables (temperature, humidity, and wind fields). Sensitivity experiments are performed to examine the impacts of initial uncertainties on precipitation, on the error growth, and on the predictability of mesoscale precipitation in South China. The primary conclusion is that inherent initial condition uncertainties can signi...