耦合Lorenz模型的吸引子特性及其可预报性分析

通过改变耦合Lorenz模型中控制快、慢子系统之间耦合强度的参数,本文探究了耦合强度对该系统的混沌吸引子特性及可预报性的影响。结果表明:随着耦合增强,快系统中显示出与慢系统类似的低频变化特征,其吸引子也随之变大;而慢系统高频分量变大,导致其变率增强,吸引子轨道变得更加密集。在此基础上,利用非线性局部Lyapunov指数方法定量分析了耦合强度对耦合Lorenz系统可预报性的影响。具体来说,在耦合之后,耦合系统的对数误差增长曲线包含前后两段不同的误差增长率,分别代表快速和慢速误差增长过程。此外,各子系统的可预报性对耦合强度变化响应并不一致,随着对快系统的耦合强度增加,快/慢两个不同尺度系统的可预报上限均减少。然而,增加对慢系统的耦合强度却只能提高快系统的可预报上限,对慢系统的可预报性改变不大。

随机误差对混沌系统可预报性的影响

根据非线性局部Lyapunov指数的方法,以Logistic映射和Lorenz系统的试验数据序列为例,研究了在初始误差存在的情况下,随机误差对混沌系统可预报性的影响。结果表明:初始误差和随机误差对可预报期限影响所起的作用大小主要取决于两者的相对大小。当初始误差远大于随机误差时,系统的可预报期限主要由初始误差决定,可以不考虑随机误差对预报模式可预报性的影响;反之,当随机误差远大于初始误差时,系统的可预报期限主要由随机误差决定;当初始误差和随机误差量级相当时,两者都对系统的可预报期限起重要作用。在后两种情况下,在考虑初始误差对可预报性影响的同时还必须考虑随机误差的作用。此外,我们在已知系统精确的控制方程和误差演化方程的条件下,研究了随机误差对可预报性的影响,理论所得结果与试验数据所得结果相似。这表明在随机误差较小的情况下,对系统可预报期限的估计相对准确,但在随机误差较大的情况下,可预报期限的估计误差也较大。本文利用三种不同的滤波方法对序列进行了试验,结果表明,Lanczos高通滤波得到的高频序列与原始加入的噪声序列无论是在强度上还是在演变趋势上都表现得相当一致,其能有效地去除高频噪音继而提高对系统的可预报期限的估计,这对实际气象观测资料如何有效地去除噪音具有一定的启发意义。

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。

Estimating the Predictability of the Quasi-Biweekly Oscillation Using the Nonlinear Local Lyapunov Exponent Approach

The quasi-biweekly oscillation (QBWO) is a major intraseasonal variability (ISV) in the tropics. Based on bandpass-filtered outgoing longwave radiation (OLR) and wind field data, the predictability limits of the QBWO in boreal summer and boreal winter are investigated using the nonlinear local Lyapunov exponent (NLLE) approach The analysis shows that the evolution of the mean error growth of the QBWO in boreal summer and the evolution of the mean error growth in boreal winter are comparable Both curves exhibit rapid growth in the initial stage followed by a slowly fluctuating, ascending trend before saturation is reached. As a result, the potential predictability limits for the boreal summer QBWO are very close to those for the boreal winter QBWO, with a lead time of approximately three weeks. Given the current limitations in the simulation and prediction of ISV, including the QBWO, the results of this study provide a useful reference for assessing the predictability of the QBWO using model simulations.

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 approx- imately 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 calcu- lated 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.

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 1970 s and decrease since2000. 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 21 st 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.