采样间隔和插值对混沌系统可预报期限估计的影响

Impacts of sampling interval and interpolation on the estimatimation of the predictability of chaotic systems

利用非线性局部Lyapunov指数的方法研究了采样间隔和插值对混沌系统可预报性的影响,结果表明:在一定范围内,采样间隔对系统可预报期限估计的影响基本是随采样间隔的增大而逐渐减小。但当采样间隔超过一定大小时,所得序列已不能找到真实的局地动力相似,无法得到其真实的误差增长情况,也无法得到系统准确的可预报期限的估计。本文通过插值的方法试图还原同样长度的时间序列,结果表明不论是在采样间隔较大还是较小的情况下,插值都不能有效地改善对系统可预报期限的估计。此外,在采样间隔固定的情况下,随着插值个数的增多,系统的可预报期限的估计反而更低。以上结果提示我们在利用实际海洋观测资料估计其可预报期限时,选用较高分辨率较长时间序列的资料可以得到更接近真实的可预报期限。

Based on the nonlinear local Lyapunov exponent(NLLE) approach, the influences of sampling interval and interpolation on the predictability of the Lorenz system are studied. The results show that the impacts of the sampling interval on the predictability of the chaotic system can be reduced gradually with the increase of the sampling interval in certain extent. But when the sampling interval exceeds a certain value, the real local dynamical similarity cannot be found in the resultant sequence. Thus the real error growth and the accurate estimate of the predictability limit of the chaotic system cannot be obtained. The present study also attempts to reconstruct the time series by using the interpolation method. However, the findings indicate that interpolation cannot effectively improve the estimate of the predictability limit of chaotic systems whether in larger or smaller sampling interval. In addition, with the increase of the number of interpolation, the estimate of the predictability limit of chaotic systems can be lower. These results suggest that data with higher resolution and longer time series can be obtained more close to the real predictability limit.