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Volume 8 Issue 2

Mar.  1991

Article Contents

Determination of Kolmogorov Entropy of Chaotic Attractor Included in One-Dimensional Time Series of Meteorological Data


doi: 10.1007/BF02658098

  • The 1970-1985 day to day averaged pressure dataset of Shanghai and the extension method in phase space are used to calculate the correlation dimension D and the second-order Renyi entropy K2 of the approximation of Kolmogorov’s entropy, the fractional dimension D = 7.7~7.9 and the positive value K2 ≈ 0.1 are obtained. This shows that the attractor for the short-term weather evolution in the monsoon region of China exhibits a chaotic mo-tion. The estimate of K2 yields a predictable time scale of about ten days. This result is in agreement with that ob-tained earlier by the dynamic-statistical approach.The effects of the lag time τ on the estimate of D and K2 are investigated. The results show that D and K2 are convergent with respect to τ. The day to day averaged pressure series used in this paper are treated for the extensive phase space with τ = 5, the coordinate components are independent of each other; therefore, the dynamical character quantities of the system are stable and reliable.
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    [6] WANG Geli, YANG Peicai, ZHOU Xiuji, 2013: Nonstationary Time Series Prediction by Incorporating External Forces, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1601-1607.  doi: 10.1007/s00376-013-2134-z
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    [9] Li Jun, Zhou Fengxian, Gao Qinghuai, 1991: Satellite Data Reduction Using Entropy-preserved Image Compression Technique, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 237-242.  doi: 10.1007/BF02658097
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Manuscript History

Manuscript received: 10 March 1991
Manuscript revised: 10 March 1991
通讯作者: 陈斌, bchen63@163.com
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Determination of Kolmogorov Entropy of Chaotic Attractor Included in One-Dimensional Time Series of Meteorological Data

  • 1. Nanjing Institute of Meteorology, Nanjing 210044, China,Nanjing Institute of Meteorology, Nanjing 210044, China,Nanjing Institute of Meteorology, Nanjing 210044, China

Abstract: The 1970-1985 day to day averaged pressure dataset of Shanghai and the extension method in phase space are used to calculate the correlation dimension D and the second-order Renyi entropy K2 of the approximation of Kolmogorov’s entropy, the fractional dimension D = 7.7~7.9 and the positive value K2 ≈ 0.1 are obtained. This shows that the attractor for the short-term weather evolution in the monsoon region of China exhibits a chaotic mo-tion. The estimate of K2 yields a predictable time scale of about ten days. This result is in agreement with that ob-tained earlier by the dynamic-statistical approach.The effects of the lag time τ on the estimate of D and K2 are investigated. The results show that D and K2 are convergent with respect to τ. The day to day averaged pressure series used in this paper are treated for the extensive phase space with τ = 5, the coordinate components are independent of each other; therefore, the dynamical character quantities of the system are stable and reliable.

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