随机误差对混沌系统可预报性的影响  

Impacts of Random Error on the Predictability of Chaotic Systems

作　　者：史珍[1,2] 丁瑞强[1] 李建平[1] 

机构地区：[1]中国科学院大气物理研究所大气科学和流体力学数值模拟国家重点实验室,北京100029 [2]中国科学院研究生院,北京100049

出　　处：《大气科学》2012年第3期458-470,共13页Chinese Journal of Atmospheric Sciences

基　　金：国家重点基础研究发展计划项目2010CB950400;国家自然科学基金资助项目41030961;40821092

摘　　要：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。Based on the nonlinear local Lyapunov exponent （NLLE） approach, the influences of random error and initial error on the predictability of the Logistic map and the Lorenz system are studied. The influences of initial error and random error on the predictability mainly depend on their relative magnitudes. When the magnitude of initial error is much greater than that of random error, the predictability limit of two systems is mainly determined by the initial error. On the contrary, when the magnitude of random error is much greater than that of initial error, the predictability limit of two systems is mainly determined by the random error. When the magnitude of initial error is close to that of random error, both of them contribute to the predictability limit of two systems. In addition, the au- thors have investigated the influences of random error on the predictability by integrating the error growth equa- tions. The results are similar to those obtained using experimental data. This finding indicates that due to the im- pacts of random error, only an approximation of the true predictability of chaotic systems can be obtained when the random error is sufficiently small. It is impossible to obtain the true predictability for large random errors. The present study also attempts to use the filtering method to reduce the impact of random error on the estimates of the predictability limit of chaotic systems. The results show that by using the high-pass Lanczos filter, both the high- frequency sequence and the noise sequence perform conformably either in intensity or in the evolution of trends. This method can effectively remove the random noise and then improve the estimate of the predictability limit of chaotic systems, which also gives some enlightenment to the removal of the noise contained in observational data.

关 键 词：非线性局部 LYAPUNOV指数 初始误差 随机误差 可预报性 

分 类 号：P456[天文地球—大气科学及气象学]