非线性误差增长理论在大气可预报性中的应用

为了能从非线性误差增长动力学的角度来研究大气的可预报性问题,在非线性动力系统的理论和方法基础上,文中引入了可预报性研究的新方法--非线性局部Lyapunov指数.非线性局部Lyapunov指数及其相关统计量能够用来定量地确定混沌系统可预报性的大小,真正地实现了对可预报性的定量化研究.首先给出了利用大气单个变量的实际观测资料获得其可预报期限估计的计算方法,因而解决了将非线性误差增长理论应用到大气实际的可预报性研究中的问题.然后,以位势高度场为例,详细讨论了逐日时间尺度上全球可预报性的时空分布,得到的主要结论为:(1)在水平方向上,全球位势高度场可预报性表现为一定的南北纬向带状分布,赤道地区和南极地区的可预报期限最长,可以达到两周左右;北极地区次之,可预报期限大约为9-12 d;北半球中高纬度地区可预报期限相对较短,可预报期限大约为6-9 d;而在南半球的中纬度地区最短,可预报期限仅为4-6 d.此外,500 hPa位势高度场可预报性分市随季节有明显变化,季节不同一些可预报期限的高值区和低值区所在的纬度和经度也会不同,总体来说,全球大部分地区的可预报性冬季都大于夏季,尤其在南极地区、热带印度洋以及北太平洋地区.(2)在垂直方向上,位势高度场可预报期限随高度升商而增加,可预报期限从对流层下层的两周以下增加到平流层下层的1个月左右,对流层和平流层天气尺度运动的可预报期限与其时间尺度是十分一致的.     

新疆气温长期变化可预报性的初步研究(二)──分维、可预报期限分析

利用新疆区域50个站30年气温资料，计算了新疆地区逐日气温、逐候气温、逐月气温的分维和平均可预报期限，研究了新疆气温不同时间层次的可预报期限的分布特征，得到一些有意义的结果。     

新疆气温长期变化可预报性的初步研究(一)──气候噪音、潜在可预报性分析

利用新疆50个站的30年逐日气温资料分析了新疆气温的气候噪音、替在可预报性、信噪比的时空分布特征，研究了新疆气温长期变化的预报精度问题。结果表明新疆气温的气候噪音、信噪比、潜在可预报性具有较强的地域性和季节性。     

短期气候预测的评估问题

该文系统地介绍了国内外评估月、季尺度短期气候预测结果的方法 ,比较了相关系数(R)、预报技巧分 (S)和准确率 (P)的特点 ,并对当前国内外气候预测业务水平进行了分析 ,着重对大气环流、气温、降水及 ENSO的预测水平进行了评估 ,指出国内外月、季尺度的降水预报的水平目前在 55%～ 60 %左右 ,对 ENSO的发生、结束和强度的预报水平有限 .文中探讨了短期气候预测的可预报性问题 ,提出月、季尺度气候预测的可预报性的理论上限可能为 6～ 1 2月 ,准确率在 80 %～ 85%之间 .     

中国区域月气候预测方法和预测能力评估

利用我国台站降水和温度观测资料,评估了BCC_AGCM1.0月动力延伸预报的回算和预测、国家气候中心月气候预测业务统计方法、持续性预报以及业务发布预报对中国区域月气候要素的预测能力。结果表明,业务发布月平均温度和降水预测的技巧平均低于动力方法和统计方法的预测结果。温度的持续性预报和最优气候值统计方法预报技巧高于其它统计预报方法,考虑了综合相似特征的统计方法对降水预测有相对的优势。动力延伸预报的三种超前预报时间的预测结果总体高于统计方法,在月气候预测能力上具有明显优势。月尺度预测动力和统计方法评估的年际变化特征表明月降水和温度的可预报性一般在El Nio状态下较高,而在La Nia发生时偏低。     

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。     

天气可预报性的时空分布

为了能从非线件误差增长动力学的角度研究大气的可预报性问题,文章引入了可预报性研究的新方法--非线性局部Lyapunov指数.非线性局部Lyapunov指数及其相关统计量能够被用来定量地确定混沌系统可预报性的大小,真正地实现对可预报性的定量化研究.为了把非线性局部Lyapunov指数方法应用到实际的大气可预报性研究中,给出了一种利用大气的实际观测资料估计非线性局部Lyapunov指数的计算方法.存非线性局部Lyapunov指数方法的基础上,文中利用NCEP/NCAR再分析资料,对大气位势高度场、温度场、纬向风场、经向风场等要素场可预报性的时空分布进行了研究,结果表明:(1)在500 hPa高度层上,对于不同的要素场,其可预报期限的大小以及时空分布规律都不一样;全球大部分地区位势高度场可预报期限最大,温度场和纬向风场次之,而经向风场的可预报期限最小.(2)在500 hPa高度层七,位势高度场和温度场的纬向平均可预报期限基本上表现为一定的南北纬向带状分布,热带地区和南极地区的可预报期限最大,北极地区次之,南北半球中高纬度地区可预报期限相对较小.纬向风场可预报期限在热带地区最高,但是南北极地区可预报期限与邻近的中高纬度地区差别不大.经向风场可预报期限在南北两极地区最高,南北半球的中纬度和赤道附近地区可预报期限最小.(3)在垂直方向上,纬向平均高度场、温度场以及纬向风场可预报期限基本上都是随高度升高而增加,高层的可预报期限明显大于低层;经向风场可预报期限随高度的变化比较复杂,不同的纬度有所不同.(4)可预报性有明显的季节变化,不同要素场可预报期限高低值区的位置和强度随季节鄙有明显变化,对于全球大部分地区来说,冬季可预报性都大于夏季的.     

青海省月降水、气温的动力模式解释应用及其效果检验

利用月动力延伸预报500hPa高度场资料、青海省36站实况降水、气温等资料,研究对不同月份及不同季节降水分别有重大影响的大尺度预测因子。并选取稳定高相关、物理意义明确、彼此间独立的影响因子,通过多次试验选择适合的统计降尺度方法,建立青海省月降水、气温的动力降尺度解释应用预测模型。按国家气候中心业务评分标准,用独立样本对模型预测效果进行检验,通过与近6年实际预报评分比较,模式降尺度应用后预测评分大部分超过业务评分,其中降水预测评分最高达84％,最低为67％。月平均气温降尺度解释应用评分最高达84％,最低也达到67％,平均评分虽不及业务评分高,仍是比较客观的预报方法,在短期气候预测中有实用价值。     

气候系统可预报性的全局研究

胞映射方法是对非线性系统进行全局分析的强有力工具。文中基于一个最大简化的地－气耦合模式,引入胞映射全局分析方法,对气候系统的可预报性进行了全局的研究。气候系统存在最大可预报期限,对于超过逐日预报可预报期限后的预报,用胞映射思想证明了平均值的可预报性,并得到了定量的结果。研究表明,耦合机制具有延长可预报期限的作用,观测精度的提高亦可延长可预报期限     

我国华东地区月尺度气候动力预测的研究:(Ⅱ) 嵌套模式的回报评估

采用数值模式方法对我国华东地区进行月尺度短期气候预测。预测框架由改进的低分辨率全球环流模式T63 L9嵌套并入了水文模型VXM的区域气候模式RegCM3构成,根据嵌套气候模式的积分结果,经剔除系统误差后制作短期气候预报。本文利用国家气候中心的评分方法对2003、2004两年的降水和地表气温回报结果作了评估;还将本系统的预报结果与CMAP降水资料、NMC温度资料及全国160站的观测资料进行了对比。结果表明,该系统可以比较稳定地对我国华东地区的降水和温度进行月尺度预测。     

Estimation of the monthly precipitation predictability limit in China using the nonlinear local Lyapunov exponent

By using the nonlinear local Lyapunov exponent and nonlinear error growth dynamics, the predictability limit of monthly precipitation is quantitatively estimated based on daily observations collected from approximately 500 stations in China for the period 1960–2012. As daily precipitation data are not continuous in space and time, a transformation is first applied and a monthly standardized precipitation index (SPI) with Gaussian distribution is constructed. The monthly SPI predictability limit (MSPL) is quantitatively calculated for SPI dry, wet, and neutral phases. The results show that the annual mean MSPL varies regionally for both wet and dry phases: the MSPL in the wet (dry) phase is relatively higher (lower) in southern China than in other regions. Further, the pattern of the MSPL for the wet phase is almost opposite to that for the dry phase in both autumn and winter. The MSPL in the dry phase is higher in winter and lower in spring and autumn in southern China, while the MSPL values in the wet phase are higher in summer and winter than those in spring and autumn in southern China. The spatial distribution of the MSPL resembles that of the prediction skill of monthly precipitation from a dynamic extended-range forecast system.     

Progress in Predictability Studies in China （2003-2006）

Since the last International Union of Geodesy and Geophysics General Assembly(2003),predictability studies in China have made significant progress.For dynamic forecasts,two novel approaches of conditional nonlinear optimal perturbation and nonlinear local Lyapunov exponents were proposed to cope with the predictability problems of weather and climate,which are superior to the corresponding linear theory.A possible mechanism for the"spring predictability barrier"phenomenon for the El Ni(?)o-Southern Oscillation (ENSO)was provided based on a theoretical model.To improve the forecast skill of an intermediate coupled ENSO model,a new initialization scheme was developed,and its applicability was illustrated by hindcast experiments.Using the reconstruction phase space theory and the spatio-temporal series predictive method, Chinese scientists also proposed a new approach to improve dynamical extended range(monthly)prediction and successfully applied it to the monthly-scale predictability of short-term climate variations.In statistical forecasts,it was found that the effects of sea surface temperature on precipitation in China have obvious spatial and temporal distribution features,and that summer precipitation patterns over east China are closely related to the northern atmospheric circulation.For ensemble forecasts,a new initial perturbation method was used to forecast heavy rain in Guangdong and Fujian Provinces on 8 June 1998.Additionally, the ensemble forecast approach was also used for the prediction of a tropical typhoons.A new downscaling model consisting of dynamical and statistical methods was provided to improve the prediction of the monthly mean precipitation.This new downsealing model showed a relatively higher score than the issued operational forecast.     

季节内印度洋-西太平洋对流涛动对次季节-季节尺度大气可预报性的影响

利用非线性局部Lyapunov指数和条件非线性局部Lyapunov指数定量估计了季节内印度洋-西太平洋对流涛动（IPCO）和实时多变量Madden-Julian指数（RMM指数）可预报期限,量化了季节内IPCO对S2S尺度大气可预报性的贡献,深入研究了季节内IPCO演变下S2S尺度可预报期限空间分布的变化规律。结果表明：（1）与RMM指数相比,季节内IPCO指数可预报性更强,可预报期限达到31天左右,比RMM指数高出2周以上;（2）印度洋-西太平洋区域S2S尺度大气可预报性最强,可预报期限达到30天以上,其中季节内IPCO是该地区的主要可预报性来源之一,其贡献达到6天,占总可预报期限的25%以上;（3）随着季节内IPCO的演变,印度洋-西太平洋地区S2S尺度大气可预报性有空间结构变化,表现为可预报期限异常的传播和振荡。S2S尺度大气可预报期限正负异常沿季节内IPCO传播路径,一支以赤道中西印度洋为起点北传至印度半岛,一支向东传播,经过海洋性大陆到赤道西太平洋后向北传播,到达日本南部。同时,可预报性异常的传播在在东印度洋和西太平洋表现出反向变化的特征,形成东西两极振荡,当季节内IPCO向正位相发展时,东印度洋具有更强的可预报性,西太平洋具有更弱的可预报性,反之亦然。季节内IPCO的发展（衰退）可使东印度洋（西太平洋）S2S尺度大气可预报性更强,表明模式预报技巧对此具有更大的提升空间。     

用复数自回归模式预报月平均气温

在复数域最小二乘法的基础上, 建立了复数自回归模式。数学推导和实例应用表明:这一复数自回归模式不同于将复数序列中的实部和虚部分开来计算的结果, 将实部和虚部分开来计算的方法不是真正意义的最小二乘法。应用包括一个任意给定的复数序列和全国160个基本气象台站上历年7月月平均气温。采用距平相关系数和均方根误差两种检验标准, 对独立预报结果进行检验, 并与其他3种常用统计模型作比较。结果显示:该复数自回归模式确实具有较好的预报效果。     

A Regression-based Assessment of the Predictability of New Zealand Climate Anomalies

Summary Estimates of the predictability of New Zealand monthly and seasonal temperature and rainfall anomalies are calculated using a cross-validated linear regression procedure. Predictors are indices of the large scale circulation, sea-surface temperatures, the Southern Oscillation Index and persistence. Statistical significance is estimated through a series of Monte Carlo trials. No significant forecast relationships are found for rainfall anomalies at either the monthly or seasonal time scale. Temperature forecasts are however considered to exhibit significant skill, with variance reductions of the order of 10–20% in independent trials. Temperature anomalies are most skilfully predicted over the North Island, and skill is greatest in Spring and Summer in most areas. At the monthly time scale, predictors local to the New Zealand region account for most of the forecast skill, while at the seasonal time scale, skill depends strongly upon “remote” predictors defined over regions of the southern hemisphere distant from New Zealand. Indices of meridional flow over the Tasman Sea/New Zealand region are found to be useful predictors, especially for monthly forecasts, perhaps as a proxy for atmospherically-forced sea surface temperature anomalies. Sea surface temperature anomalies to the west of New Zealand and in the tropical Indian Ocean are also useful, especially for seasonal predictions. Forecast skill is more reliably estimated at the monthly time scale than at the seasonal time scale, as a result of the larger sample size of monthly mean data. While long-term mean levels of skill may be estimated reliably over the whole data set, statistically significant decadal-scale variations are found in the predictability of temperature anomalies. Therefore, even if long-term forecast skill levels are reliably estimated, it may be impossible to predict the short-term skill of operational seasonal climate forecasts. Implications for operational climate predictions in mid-latitudes are discussed. Received July 18, 1997 Revised April 2, 1998     

Recent Advances in Predictability Studies in China （1999-2002）

Since the last International Union of Geodesy and Geophysics (IUGG) General Assembly (1999), the predictability studies in China have made further progress during the period of 1999-2002. Firstly, three predictability sub-problems in numerical weather and climate prediction are classified, which are concerned with the maximum predictability time, the maximum prediction error, and the maximum allowable initial error, and then they are reduced into three nonlinear optimization problems. Secondly, the concepts of the nonlinear singular vector (NSV) and conditional nonlinear optimal perturbation (CNOP) are proposed,which have been utilized to study the predictability of numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be revealedby NSV and CNOP. Thirdly, attention has also been paid to the relations between the predictability and spatial-temporal scale, and between the model predictability and the machine precision, of which the investigations disclose the importance of the spatial-temporal scale and machine precision in the study of predictability. Also the cell-to-cell mapping is adopted to analyze globally the predictability of climate,which could provide a new subject to the research workers. Furthermore, the predictability of the summer rainfall in China is investigated by using the method of correlation coefficients. The results demonstrate that the predictability of summer rainfall is different in different areas of China. Analysis of variance, which is one of the statistical methods applicable to the study of predictability, is also used to study the potential predictability of monthly mean temperature in China, of which the conclusion is that the monthly mean temperature over China is potentially predictable at a statistical significance level of 0.10. In addition,in the analysis of the predictability of the T106 objective analysis/forecasting field, the variance and the correlation coefficient are calculated to explore the distribution characteristics of the mean-square errors.Finally, the predictability of short-term climate prediction is investigated by using statistical methods or numerical simulation methods. It is demonstrated that the predictability of short-term climate in China depends not only on the region of China being investigated, but also on the time scale and the atmospheric internal dynamical process.     

Progress in the Study of Nonlinear Atmospheric Dynamics and Predictability of Weather and Climate in China (2007--2011)

Recent progress in the study of nonlinear atmospheric dynamics and related predictability of weather and climate in China (2007-2011) are briefly introduced in this article. Major achievements in the study of nonlinear atmospheric dynamics have been classified into two types:(1) progress based on the analysis of solutions of simplified control equations, such as the dynamics of NAO, the optimal precursors for blocking onset, and the behavior of nonlinear waves, and (2) progress based on data analyses, such as the nonlinear analyses of fluctuations and recording-breaking temperature events, the long-range correlation of extreme events, and new methods of detecting abrupt dynamical change. Major achievements in the study of predictability include the following:(1) the application of nonlinear local Lyapunov exponents (NLLE) to weather and climate predictability; (2) the application of condition nonlinear optimal perturbation (CNOP) to the studies of El Nin o-Southern Oscillation (ENSO) predictions, ensemble forecasting, targeted observation, and sensitivity analysis of the ecosystem; and (3) new strategies proposed for predictability studies. The results of these studies have provided greater understanding of the dynamics and nonlinear mechanisms of atmospheric motion, and they represent new ideas for developing numerical models and improving the forecast skill of weather and climate events.     

Decreasing predictability as a precursor indicator for abrupt climate change

Abrupt climate change has an important impact on sustainable economic and social development, as well as ecosystem. However, it is very difficult to predict abrupt climate changes because the climate system is a complex and nonlinear system. In the present paper, the nonlinear local Lyapunov exponent (NLLE) is proposed as a new early warning signal for an abrupt climate change. The performance of NLLE as an early warning signal is first verified by those simulated abrupt changes based on four folding models. That is, NLLE in all experiments showed an almost monotonous increasing trend as a dynamic system approached its tipping point. For a well-studied abrupt climate change in North Pacific in 1976/1977, it is also found that NLLE shows an almost monotonous increasing trend since 1970 which give up to 6 years warning before the abrupt climate change. The limit of the predictability for a nonlinear dynamic system can be quantitatively estimated by NLLE, and lager NLLE of the system means less predictability. Therefore, the decreasing predictability may be an effective precursor indicator for abrupt climate change.