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

Yan Shaojin; Peng Yongqing; Wang Jianzhong

doi:10.1007/BF02658098

Impact Factor: 5.8

Volume 8 Issue 2

Mar. 1991

Article Contents

Article > ADVANCES IN ATMOSPHERIC SCIENCES > 1991 > 8(2): 243-250

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

doi: 10.1007/BF02658098

Abstract
References
Related papers
PDF

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.
References

[1]	Peng Yongqing, Zhu Yufeng, Yan Shaojin, 1994: Preliminary Study of Reconstruction of a Dynamic System Using an One-Dimensional Time Series, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 277-284. doi: 10.1007/BF02658146
[2]	Xinrong WU, Shaoqing ZHANG, Zhengyu LIU, 2016: Implementation of a One-Dimensional Enthalpy Sea-Ice Model in a Simple Pycnocline Prediction Model for Sea-Ice Data Assimilation Studies, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 193-207. doi: 10.1007/s00376-015-5099-2
[3]	Ji jinjun, 1989: Atmosphere-Ocean Coupling Schemes in a One-Dimensional Climate Model, ADVANCES IN ATMOSPHERIC SCIENCES, 6, 275-288. doi: 10.1007/BF02661534
[4]	JIN Ling, Fanyou KONG, LEI Hengchi, and HU Zhaoxia, 2014: A Methodological Study on Using Weather Research and Forecasting (WRF) Model Outputs to Drive a One-Dimensional Cloud Model, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 230-240. doi: 10.1007/s00376-013-2257-2*
[5]	Qiumeng XUE, Li GUAN, Xiaoning SHI, 2022: One-Dimensional Variational Retrieval of Temperature and Humidity Profiles from the FY4A GIIRS, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 471-486. doi: 10.1007/s00376-021-1032-z
[6]	Wang Guiqin, 1990: Simulation of the Influence of Ion-Produced NOX and HOX Radicals on the Antarctic Ozone Depletion with a One-Dimensional Model, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 98-103. doi: 10.1007/BF02919172
[7]	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
[8]	Zhou Jiabin, 1985: A NEW TYPE OF TIME-SERIES-FORECASTING METHOD, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 385-401. doi: 10.1007/BF02677255
[9]	GUO Yanjun, DING Yihui, 2011: Impacts of Reference Time Series on the Homogenization of Radiosonde Temperature, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 1011-1022. doi: 10.1007/s00376-010-9211-3
[10]	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
[11]	Zhang Banglin, Liu Jie, Sun Zhaobo, 1993: A New Multidimensional Time Series Forecasting Method Based on the EOF Iteration Scheme, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 243-247. doi: 10.1007/BF02919147
[12]	Marek PÓŁROLNICZAK, Leszek KOLENDOWICZ, Bartosz CZERNECKI, Mateusz TASZAREK, Gabriella TÓTH, 2021: Determination of Surface Precipitation Type Based on the Data Fusion Approach, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 387-399. doi: 10.1007/s00376-020-0165-9
[13]	Liao Dongxian, 1985: DETERMINATION OF THE DISTANCE BETWEEN TWO ADJACENT STATIONS, THE OBSERVATIONAL VERTICAL INCREMENT AND THE OBSERVATIONAL TIME INTERVAL IN OPTIMUM SENSE, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 316-324. doi: 10.1007/BF02677247
[14]	YE Liming, YANG Guixia, Eric VAN RANST, TANG Huajun, 2013: Time-Series Modeling and Prediction of Global Monthly Absolute Temperature for Environmental Decision Making, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 382-396. doi: 10.1007/s00376-012-1252-3
[15]	A. Mary Selvam, J. S. Pethkar, M. K. Kulkarni, 1995: Some Unique Characteristics of Atmospheric Interannual Variability in Rainfall Time Series over India and the United Kingdom, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 377-385. doi: 10.1007/BF02656987
[16]	Athanassios A. ARGIRIOU, Zhen LI, Vasileios ARMAOS, Anna MAMARA, Yingling SHI, Zhongwei YAN, 2023: Homogenised Monthly and Daily Temperature and Precipitation Time Series in China and Greece since 1960, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 1326-1336. doi: 10.1007/s00376-022-2246-4
[17]	Qu Xiaobo, Julian Heming, 2002: The Impact of Dropsonde Data on Forecasts of Hurricane Debby by the Meteorological Office Unified Model, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 1029-1044. doi: 10.1007/s00376-002-0062-4
[18]	Peng ZHANG, Qifeng LU, Xiuqing HU, Songyan GU, Lei YANG, Min MIN, Lin CHEN, Na XU, Ling Sun, Wenguang BAI, Gang MA, Di XIAN, 2019: Latest Progress of the Chinese Meteorological Satellite Program and Core Data Processing Technologies, ADVANCES IN ATMOSPHERIC SCIENCES, 36, 1027-1045. doi: 10.1007/s00376-019-8215-x
[19]	Peng ZHANG, Jun YANG, Jinsong WANG, Xinwen YU, 2021: Preface to the Special Issue on Fengyun Meteorological Satellites: Data, Application and Assessment, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1265-1266. doi: 10.1007/s00376-021-1002-5
[20]	Honghua Dai, 1996: Machine Learning of Weather Forecasting Rules from Large Meteorological Data Bases, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 471-488. doi: 10.1007/BF03342038

PDF

Get Citation+

Export:

Article Metrics

Article Views: 1400 Times

PDF downloads: 1134 Times

Cited by: Times

Proportional views

Manuscript History

Manuscript received: 10 March 1991

Manuscript revised: 10 March 1991

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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

Manuscript received: 1991-03-10
Manuscript revised: 1991-03-10

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.