复杂系统中的层次结构提取与分析

Extraction and analysis of hierarchy in complex system

气候系统是一个非平稳复杂系统的事实已经得到了广泛认同,产生这种非平稳性质的根本原因在于气候系统存在的层次结构,处于高层系统中的外强迫信号随时间发生变化,造成了大气运动的非平稳现象.慢特征分析法可以从快变的非平稳信号中提取慢变的外强迫信号,并已应用于气候系统的归因分析中.本文利用慢特征分析法提取改进的Henon映射模型构造的非平稳时间序列以及北京月平均气温的外强迫信号,并且使用小波变换方法对外强迫信号的尺度特征及物理背景机理进行分析.结果表明,气候系统受到长周期的外强迫信号与短周期外强迫信号的共同作用.同时,长周期的外强迫信号影响短周期外强迫信号.该工作有助于理解气候系统的层次结构特征.

The non-stationary characteristics of the climate system have been widely recognized.The occurrence of this non-stationary phenomenon is caused by the hierarchical structure of the climate system.As a high-level system,the external driving forcing changes with time,which leads to the non-stationary phenomenon of atmospheric movement.Slow feature analysis(SFA)method can extract the slow-changing features from fast-changing non-stationary signal.The SFA has been applied to attribution analysis of the climate system.In this paper,we use the SFA method to extract the driving force signal from the non-stationary time series obtained by the Henon mapping model to test its extraction capability.Then we extract the external driving force signal from Beijing monthly average temperature time series,and analyze the scale characteristics and physical mechanism of external driving forcing signals combined with wavelet transform.The results show that the long-period external driving forcing signal and the short-period external driving forcing signal jointly work on the climate system.At the same time,the long-period external driving forcing signal also works on short-period external driving forcing signal.This work contributes to understanding the hierarchical characteristics of the climate system.