Study On Driving Force Extraction Based On Slow Feature Analysis

The gradual external forcing is one of the important factors to non-stationary system,and how to extract hidden forcing information from a chaotic system becomes the key to study the dynamic characteristics of this system.Slow Feature Analysis(SFA)is a method for extracting external forcing information from complex chaotic systems.It has certain ability to extract the hidden information from the climate system,and may be a new way to discuss the influence factors of climate change and to analyze the causal relationship.The work of this study is divided into two parts: the first is to further test the ability of the slow feature analysis to extract external forcing information in a continuous chaotic model;and the other is to apply SFA to the actual data(the 500 hPa geopotential height data)to find the possible physical factors in the SFA extraction signal.In the theoretical model experiment,we have discussed the ability of SFA to extract externally forcing signals based on the modified Lorenz system under conditions of periodic forcing,weakened periodic forcing,exponentially decay forcing,and periodic forcing with exponential decay.The results show that the SFA method can extract the external forcing information in the Lorenz continuous system,and the extraction ability is affected by the embedded dimension m,the strength of the external forcing signal and the noise: as the embedding dimension m increases,its extraction ability can be improved.The weaken forcing signal or the existence of noise interference can lead to a worse extraction results,and a large number of high frequency fluctuations appears in the extracted signal.The experiment also shows that the external forcing acting on a single variable embeds its driving information in the whole system,therefore,SFA can be used to extract the original external forcing signal from the time series of other variables.When there are two independent forcing signals with different periods acting on the Lorenz model,to some extent,SFA can reconstruct the original forcing signal,its extraction effect is related to the embedding dimension m,the analyzed variables,the position of the forcing signal acting on the system.And combined with wavelet analysis,the two original forcing signals can be separated from the SFA extraction signals respectively.Besides,the results show when time delay parameter is 1,the extraction can be stable and effective.In the study,slow feature analysis and wavelet analysis are applied to the 500 hPa geopotential height data in the mid-high latitudes of the northern hemisphere.The results show that the long-wave trough and ridge in the northern hemisphere may be a significant factor in the interannual variation of the 500 hPa geopotential height,which provides a signal for an about 4-years period.In order to further determine whether the SFA extraction signal can reflect the periodic variation characteristics of the trough and ridge,we take the East Asian large groove as an example to analyze the correlation between the East Asian large groove index and the SFA extraction signal.The results show that only in the region where the East Asian trough is located,the maximum correlation coefficient has exceeded 0.4 and passed the 99% significance level test,which indicates that this 4-years periodic characteristic of the East Asian trough can reflect in the SFA extraction signal in this region,and this oscillation cycle may be an important factor acting in climate system.