A new approach to studying ENSO predictability： Conditional nonlinear optimal perturbation

A new approach, the conditional nonlinear optimal perturbation (CNOP) is introduced to study the predictability of El Nifio-Southern Oscillation (ENSO) using a theoretical coupled ocean-atmosphere model. The differences between CNOP and linear singular vector (LSV) are demonstrated. The results suggest that the nonlinear model and CNOP are superior in determining error growth for studying predictability of the ENSO. In particular, the CNOP approach is used to explore the nature of the ‘spring predictability barrier‘ in ENSO prediction.     

粒子群优化算法在可预报性问题中的应用

为了评价在强非线性影响下粒子群优化(PSO)算法解决可预报性问题的性能,借助二维Ikeda模式,基于传统伴随(ADJ)方法和PSO求取的条件非线性最优扰动(CNOP)方法,即ADJ-CNOP和PSOCNOP方法,研究了最大预报误差的上界和最大允许初始误差的下界的精度问题。数值试验的统计分析结果显示:不论在初始误差较大还是预报时间较长的情况下,PSO-CNOP方法都能有效捕捉全局CNOP,给出最大预报误差的上界和最大允许初始误差的下界的精确估计;由于强非线性的影响,ADJ-CNOP方法会以较大概率获得局部CNOP,从而影响可预报性问题研究中相关估计的精度。实验结果表明,PSO算法具有优良的性能,能有效克服动力模式的强非线性特征带来的影响,值得在可预报性问题中进一步研究和应用。     

Applications of nonlinear optimization methods to quantifying the predictability of a numerical model for El Nino-Southern Oscillation

The nonlinear optimization methods are applied to quantify the predictability of a numerical model for El Nino-Southern Oscillation (ENSO). We establish a lower bound of maximum predictability time for the model ENSO events (i.e. ENSO events in the numerical model), an upper bound of maximum prediction error, and a lower bound of maximum allowable initial error, all of which potentially quantify the predictability of model ENSO. Numerical results reveal the phenomenon of “spring predictability barrier” (SPB) for ENSO event and support the previous views on SPB. Additionally, we also explore the differences between the linear evolution of prediction error and its nonlinear counterpart. The results demonstrate the limitation of linear estimation of prediction error. All these above results suggest that the nonlinear optimization method is one of the useful tools of quantifying the predictability of the numerical model for ENSO.     

非线性动力系统非定常态的最快增长扰动

计算了洛伦兹模式随时间变化的非定常态的条件非线性最优扰动．在比较条件非线性最优扰动和线性奇异向量模态的基础上进一步探讨了它们随时间的演变．结果表明，线性奇异向量代表初始扰动最优增长的方向，条件非线性最优扰动，由于受非线性的影响不能代表扰动最优增长方向，它代表在预报时刻有最大非线性发展的一类初始扰动．另外，条件非线性最优扰动代表了最敏感或最不稳定的扰动模态，从而揭示了非线性对洛伦兹模式敏感性的影响．     

A new approach to the generation of initial perturbations for ensemble prediction: Conditional nonlinear optimal perturbation

Conditional nonlinear optimal perturbation （CNOP）, which is a natural extension of singular vector （SV） into the nonlinear regime, is applied to ensemble prediction study by using a quasi-geostrophic model under the perfect model assumption. SVs and CNOPs have been utilized to generate the initial perturbations for ensemble prediction experiments. The results are compared for forecast lengths of up to 14 d. It is found that the forecast skill of samples, in which the first SV is replaced by CNOP, is comparatively higher than that of samples composed of only SVs in the medium range （day 6-day 14）. This conclusion is valid under the condition that analysis error is a kind of fast-growing ones regardless of its magnitude, whose nonlinear growth is faster than that of SV in the later part of the forecast. Furthermore, similarity Index and empirical orthogonal function （EOF） analysis are performed to explain the above numerical results.     

非线性气候系统扰动发展线性估计的局限性

采用Lorenz方程组研究了非线性系统扰动发展的线性估计和非线性估计,基于扰动的非线性发展计算了系统扰动线性发展的相对误差和绝对误差。结果表明,非线性系统扰动发展的线性估计只适用于小扰动短时间的发展;对于较长的时间跨度,Lorenz系统扰动的线性发展和非线性发展有较大差别,线性化方程组不能刻划非线性对扰动发展的影响。因此,在研究大气和海洋非线性系统扰动的发展时,应采用非线性模式。     

ENSO ensemble prediction: Initial error perturbations vs. model error perturbations

Based on our developed ENSO （El Nino-Southern Oscillation） ensemble prediction system （EPS）, the impacts of stochastic initial-error and model-error perturbations on ENSO ensemble predictions are examined and discussed by performing four sets of 14-a retrospective forecast experiments in both a deterministic and probabilistic sense, These forecast schemes are differentiated by whether they con- sidered the initial or model stochastic perturbations, The comparison results suggest that the sto- chastic model-error perturbations, which are added into the modeled physical fields to mainly represent the uncertainties of the physical model, have significant, positive impacts on improving the ensemble prediction skills during the entire 12-month forecast process, However, the stochastic initial-error perturbations have relatively small impacts on the ensemble prediction system, and its impacts are mainly focusing on the first 3-month predictions.     

Application of nonlinear optimization method to sensitivity analysis of numerical model

A nonlinear optimization method is applied to sensitivity analysis of a numerical model. Theoretical analysis and numerical experiments indicate that this method can give not only a quantitative assessment whether the numerical model is able to simulate the observations or not, but also the initial field that yields the optimal simulation. In particular, when the simulation results are apparently satisfactory, and sometimes both model error and initial error are considerably large, the nonlinear optimization method, under some conditions, can identify the error that plays a dominant role.     

二阶有限元浅水模式的伴随变分资料同化

应用二阶有限元浅水方程的伴随模式作资料同化场的数值试验,并利用极小化方法对具有随机扰动的初始场进行优化处理．通过该极小化算法,使所定义的目标函数达到最小,从而得到最优的气象要素初始场．数值试验结果表明：二阶有限元模式的变分资料同化对具有随机扰动的初始场的处理是很有效的．     

一种新的遗传策略在含“开关”过程的集合预报中的有效应用

针对初值及模式的不确定性,进行了初值扰动集合预报和模式扰动集合预报。在初值扰动集合预报中,将一种新的遗传策略用于四维变分资料同化生成集合预报的分析场,求解条件非线-}生最优扰动,并结合第二、第三主奇异向量（SVs）生成集合预报的初始扰动。为了检验该方法的有效性,采用一个含“开关”过程的偏微分方程的预报模式,设计了3种比较数值试验方案。结果表明：采用第3方案的集合预报在预报技巧上明显高于其他两种方案。第2方案和第1方案相比,由于“开关”的影响,集合预报技巧提高并不明显。在模式扰动集合预报数值实验中,为了模拟模式的不确定性,在控制方程右端添加6个随机的误差项模拟由于物理参数化方案的不同而带来的模式扰动,采用新的遗传策略在扰动模式中同化出6个对应于扰动模式的分析场后进行集合预报,并与基于伴随技术的方法进行比较。结果表明,基于遗传算法的扰动模式集合预报的预报技巧明显优于伴随方法,且这种优势随着预报时间的增加愈发明显。     

Effect of initial perturbations on the simulation capability of numerical models

The effect of an initial perturbation on simulation is studied in a series of numerical experiments using a one-dimensional nonlinear advection equation model. It is shown that the capability of the model tends to decline with an increase in initial perturbation. The error in the initial perturbation grows in a nonlinear manner, indicating that the simulating results can be improved only to a limited degree by increasing the accuracy of the initial data.     

汉语元音的非线性预测

最近研究表明非线性的局部模型是最精确的混沌时间序列预测方法之一．同时有研究表明汉语的产生过程包含非线性．传统的语音处理技术忽视了语音中可能存在的非线性结构，因而限制了处理能力的进一步提高．对汉语元音／a／和／u／的细致相空间分析结果表明，汉语元音的重构相空间有类似于混沌吸引子的结构．根据汉语元音发声过程的非线性特性，进一步对其进行相空间的局部线性预测分析，计算了预测误差随预测步长的关系曲线，讨论了嵌入维数对预测性能的影响，并且与传统的线性方法作了比较．结果表明，尽管非线性的局域线性预测法存在计算开销大的问题，但其预测视野要远大于线性预测法，总体预测性能明显优于线性预测法．     

初始场对暴雨数值预报影响的敏感性试验

为了研究初始场不确定性对暴雨预报的影响,利用尺度分离的方法,在AREM模式分析场上构造了初值扰动,并通过在模式初始物理量上叠加或扣除这些扰动,设计了不同的敏感性试验.试验结果表明,暴雨预报结果对模式的初始相对湿度、温度和风场是敏感的,而对初始位势高度的敏感性较弱.由于各物理量是相互联系和制约的,单独改变某个物理量对暴雨...     

基于相空间重构预测方法预测能力的评估

为了客观地评估基于相空间重构预测方法的预测能力,使用非线性局部Lyapunov指数来替代均方根误差。根据误差平均相对增长的饱和性质,可以确定预测方法的最大预测期限。通过计算得到重构Lorenz相空间和原始Lorenz相空间的最大预测期限分别是12,13s,k-近邻方法(k=1,2,3,4,5)的最大预测期限分别是12.0,9.8,9.7,9.2,8.8s,多变量预测方法的最大预测期限是12.8s,单变量预测方法的最大预测期限是12.0s。研究表明,重构的Lorenz系统的相空间可预报性与原始Lorenz相空间相当。此外,对于重构的Lorenz相空间,由于k-近邻方法集合了预测能力参差不齐的成员,导致其预测能力逊色于零级近似预测,多变量预测方法的预测能力与单变量预测方法几乎相当。     

Predictability of El Niño over the past 148 years

Forecasts of El Ni?o climate events are routinely provided and distributed, but the limits of El Ni?o predictability are still the subject of debate. Some recent studies suggest that the predictability is largely limited by the effects of high-frequency atmospheric 'noise', whereas others emphasize limitations arising from the growth of initial errors in model simulations. Here we present retrospective forecasts of the interannual climate fluctuations in the tropical Pacific Ocean for the period 1857 to 2003, using a coupled ocean-atmosphere model. The model successfully predicts all prominent El Ni?o events within this period at lead times of up to two years. Our analysis suggests that the evolution of El Ni?o is controlled to a larger degree by self-sustaining internal dynamics than by stochastic forcing. Model-based prediction of El Ni?o therefore depends more on the initial conditions than on unpredictable atmospheric noise. We conclude that throughout the past century, El Ni?o has been more predictable than previously envisaged.     

基于 HABC-RBF 神经网络的蒸汽驱预测方法

为解决蒸汽驱开发效果预测精度低和时间长的问题, 提出了一种改进人工蜂群算法和 RBF(Radial Basis Function)神经网络相融合的预测方法。 该方法应用种群最优解修改雇佣蜂解和观察蜂解的搜索方程, 借鉴差 分进化算法思想, 完成对种群最优解和个体搜索解随机扰动, 采用混合编码优化 RBF 神经网络参数。 以辽河 油田齐 40 块为例进行了试算, 结果表明, 该方法对蒸汽驱开发效果预测具有较好的非线性拟合能力和较高的 预测精度。     

基于小波分解和支持向量机的ENSO预测试验

为了改善ENSO的预测效果,基于Nino综合区的海温距平时间序列,采用小波分解和最小二乘支持向量机结合的方法,引入多步递阶预测的思想,建立ENSO的预测模型.试验结果表明:基于小波分解和最小二乘支持向量机结合的多步预测方法,可以有效提高ENSO的预报精度.同时,该模型具有同时得到不同时效的预测结果,建模方便,计算效率高...     

Spatiotemporal distribution and decadal change of the monthly temperature predictability limit in China

Based on the nonlinear Lyapunov exponent and nonlinear error growth dynamics, the spatiotemporal distribution and decadal change of the monthly temperature predictability limit （MTPL） in China is quantitatively analyzed. Data used are daily temperature of 518 stations from 1960 to 2011 in China. The results are summarized as follows： （1） The spatial distribution of MTPL varies regionally. MTPL is higher in most areas of Northeast China, southwest Yunnan Province, and the eastern part of Northwest China. MTPL is lower in the middle and lower reaches of the Yangtze River and Huang-huai Basin. （2） The spatial distribution of MTPL varies distinctly with seasons. MTPL is higher in boreal summer than in boreal winter. （3） MTPL has had distinct decadal changes in China, with increase since the 1970s and decrease since 2000. Especially in the northeast part of the country, MTPL has significantly increased since 1986. Decadal change of MTPL in Northwest China, Northeast China and the Huang-huai Basin may have a close relationship with the persistence of temperature anomaly. Since the beginning of the 21st century, MTPL has decreased slowly in most of the country, except for the south. The research provides a scientific foundation to understand the mechanism of monthly temperature anomalies and an important reference for improvement of monthly temperature prediction.     

基于LQR-IMCS算法的智能结构振动主动控制

为了解决最小控制综合（MCS）算法在快速扰动下缺乏鲁棒性和线性二次调节器（LQR）在非线性扰动下容易失稳的问题,构造了一种自适应增益补偿函数,对标准的MCS算法进行改进.提出了基于LQR-IMCS（改进的最小控制综合）算法的新策略,并通过波波夫准则验证了该系统的稳定性.以实验室压电壁板结构的第1阶振动模态为研究对象,分别施加随机扰动和高次谐波扰动.仿真和实验结果表明：该方法相对于标准的MCS算法具有更快的收敛速度和更小的跟踪误差,对壁板的第1阶模态抑制具有良好的控制效果和鲁棒性.     

粒子群算法优化BP神经网络

现实生活中绝大数系统都是非线性的,BP神经网络通过训练能否达到局部最优值、能否收敛以及训练的时间长短与初始值和阈值的选取关系密切.为此采用了具有动态惯性权重的粒子群算法对BP神经网络初始值进行优化.实验表明具有动态惯性权重的粒子群算法优化BP神经网络预测误差很小,能够跳出局部极小值,得到更优的结果.