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By the transfer entropy method, in this article we analyze the transfer of information between x, y, z component of Lorenz system and Walker circulation with temperature difference and vertical velocity. It is found that y is the information source and x is the information sink between x and y component of Lorenz system, also y is the information source and z is the information sink between x and z component. But the direction of information transfer depends on the control parameter r between x and z component, even if the direction of information transfer between x, y and z component of Lorenz system does not vary when the initial value changes. In western Pacific, the information transfers from the temperature difference to the vertical velocity, while the information transfers from the vertical velocity to the temperature difference in the eastern equatorial Pacific, which is consistent with the physical mechanism of Walker circulation. And land-sea thermal plays an important role in the information transfer between temperature difference and vertical velocity. In winter, the information transfer between temperature difference and vertical velocity is strongest, in summer and autumn it is weaker, and in spring it is weakest, which may be the reasons of spring predictability barrier. These results suggest that transfer entropy is proved to be an effective method and tool of measuring the transfer direction of the kinetic system information, and has broad application prospects in the field of meteorology.
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Keywords:
- transfer entropy /
- information transfer /
- Lorenz system /
- walker circulation
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[2] Feng G L, Dong W J 2003 Chin. Phys. 13 413
[3] Feng G L, Gong Z Q, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5494 (in Chinese) [封国林, 龚志强, 董文杰, 李建平 2005 54 5494]
[4] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear Theories and Methods on Spatial-Temporal Distribution of the Observational Data (Beijing: Metrological Press) p86 (in Chinese) [封国林, 董文杰, 龚志强, 侯威, 万仕全, 支蓉 2006 观测数据非线性时空分布理论和方法(北京: 气象出版社) 第86页]
[5] Feng G L, Gao X Q, Dong W J, Li J P 2008 Chaos Soliton. Fract. 37 487
[6] Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745
[7] Li J P, Gao L 2006 J. Atmos. Sci. 30 834 (in Chinese) [李建平, 高丽 2006 大气科学 30 834]
[8] Li J P, Wang X L 2003 Adv. Atmos. Sci. 20 661
[9] Li J P, Chou J F 1997 Acta Meteor. Sin. 11 57
[10] Li J P, Zeng Q C, Chou J F 2000 Sci. China E 30 550 (in Chinese) [李建平, 曾庆存, 丑纪范 2000 中国科学 (E辑) 30 550]
[11] Dai X G, Wang P, Chou J F 2004 Proc. Nat. Sci. 14 73
[12] Gong Z Q, Zhou L, Zhi R, Feng G L 2008 Acta Pyhs. Sin. 57 5351 (in Chinese) [龚志强, 周磊, 支蓉, 封国林2008 57 5351]
[13] Kullback S 1959 Information Theory and Statistics (New York: Wiley) p126
[14] Schreiber T 2000 Phys. Rev. Lett. 85 461
[15] Verdes P F 2005 Phys. Rev. E 72 026222
[16] Liang X S, Kleeman R 2005 Phys. Rev. Lett. 95 244101
[17] Andrew J M, John H 2007 Proc. Natl. Acad. Sci. 104 9558
[18] Kleeman R 2007 J. Atmos. Sci. 64 1005
[19] Materassi M, Wernik A, Yordanova E 2007 NPG 14 153
[20] Lorenz E N 1963 J. Atmos. 20 130
[21] Li A B, Zhang L F, Xiang J 2012 Acta Phys. Sin. 61 119202 (in Chinese) [黎爱兵, 张立凤, 项杰 2012 61 119202]
[22] Sikka D R, Gadgil S 1980 Mon. Wea. Rev. 108 1840
[23] Christiansen B 2003 J. Clim. 16 3681
[24] Walker G T 1923 Mem. Indian Meteor. Dept. 24 75
[25] Walker G T 1924 Mem. Indian Meteor. Dept. 24 275
[26] Walker G T, Bliss E W 1932 V. Mem. Roy Met. Soc. 4 53
[27] Bjerknes J 1969 Mon. Wea. Rev. 97 163
[28] Rasmusson E M, Carpenter T H 1982 Mon. Wea. Rev. 110 354
[29] Bo Y Q, Wu H B 2008 Science and Technology Innovation Herald 31 5 (in Chinese) [薄燕青, 吴洪宝 2008 科技创新导报 31 5]
[30] Lorenz E N 1976 Quart. Res. 6 495
[31] Li C H, Wang D X, Liang J Y 2006 Chin. Sci. Bull. 51 596 (in Chinese) [李春晖, 王东晓, 梁建茵2006 科学通报 51 596]
[32] Zhang Q Y, Wang Y 2006 Clim. Environ. Res. 11 487 (in Chinese) [张庆云, 王媛 2006 气候与环境研究 11 487]
[33] Xu W C, Ma J S, Wang W 2005 Scientia Meteorol. Sin. 25 212 (in Chinese) [许武成, 马劲松, 王文 2005 气象科学 25 212]
[34] Chan J C L 1985 Mon. Wea. Rev. 113 599
[35] Ge X Y, Zhou X Q, Jiang S C 2002 J. Tropical Meteorol. 18 182 (in Chinese) [葛旭阳, 周霞琼, 蒋尚城 2002 热带气象学报 18 182]
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[1] Chou J F 1997 Bull. Chin. Acad. Sci. 5 325 (in Chinese) [丑纪范 1997 中国科学院院刊 5 325]
[2] Feng G L, Dong W J 2003 Chin. Phys. 13 413
[3] Feng G L, Gong Z Q, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5494 (in Chinese) [封国林, 龚志强, 董文杰, 李建平 2005 54 5494]
[4] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear Theories and Methods on Spatial-Temporal Distribution of the Observational Data (Beijing: Metrological Press) p86 (in Chinese) [封国林, 董文杰, 龚志强, 侯威, 万仕全, 支蓉 2006 观测数据非线性时空分布理论和方法(北京: 气象出版社) 第86页]
[5] Feng G L, Gao X Q, Dong W J, Li J P 2008 Chaos Soliton. Fract. 37 487
[6] Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745
[7] Li J P, Gao L 2006 J. Atmos. Sci. 30 834 (in Chinese) [李建平, 高丽 2006 大气科学 30 834]
[8] Li J P, Wang X L 2003 Adv. Atmos. Sci. 20 661
[9] Li J P, Chou J F 1997 Acta Meteor. Sin. 11 57
[10] Li J P, Zeng Q C, Chou J F 2000 Sci. China E 30 550 (in Chinese) [李建平, 曾庆存, 丑纪范 2000 中国科学 (E辑) 30 550]
[11] Dai X G, Wang P, Chou J F 2004 Proc. Nat. Sci. 14 73
[12] Gong Z Q, Zhou L, Zhi R, Feng G L 2008 Acta Pyhs. Sin. 57 5351 (in Chinese) [龚志强, 周磊, 支蓉, 封国林2008 57 5351]
[13] Kullback S 1959 Information Theory and Statistics (New York: Wiley) p126
[14] Schreiber T 2000 Phys. Rev. Lett. 85 461
[15] Verdes P F 2005 Phys. Rev. E 72 026222
[16] Liang X S, Kleeman R 2005 Phys. Rev. Lett. 95 244101
[17] Andrew J M, John H 2007 Proc. Natl. Acad. Sci. 104 9558
[18] Kleeman R 2007 J. Atmos. Sci. 64 1005
[19] Materassi M, Wernik A, Yordanova E 2007 NPG 14 153
[20] Lorenz E N 1963 J. Atmos. 20 130
[21] Li A B, Zhang L F, Xiang J 2012 Acta Phys. Sin. 61 119202 (in Chinese) [黎爱兵, 张立凤, 项杰 2012 61 119202]
[22] Sikka D R, Gadgil S 1980 Mon. Wea. Rev. 108 1840
[23] Christiansen B 2003 J. Clim. 16 3681
[24] Walker G T 1923 Mem. Indian Meteor. Dept. 24 75
[25] Walker G T 1924 Mem. Indian Meteor. Dept. 24 275
[26] Walker G T, Bliss E W 1932 V. Mem. Roy Met. Soc. 4 53
[27] Bjerknes J 1969 Mon. Wea. Rev. 97 163
[28] Rasmusson E M, Carpenter T H 1982 Mon. Wea. Rev. 110 354
[29] Bo Y Q, Wu H B 2008 Science and Technology Innovation Herald 31 5 (in Chinese) [薄燕青, 吴洪宝 2008 科技创新导报 31 5]
[30] Lorenz E N 1976 Quart. Res. 6 495
[31] Li C H, Wang D X, Liang J Y 2006 Chin. Sci. Bull. 51 596 (in Chinese) [李春晖, 王东晓, 梁建茵2006 科学通报 51 596]
[32] Zhang Q Y, Wang Y 2006 Clim. Environ. Res. 11 487 (in Chinese) [张庆云, 王媛 2006 气候与环境研究 11 487]
[33] Xu W C, Ma J S, Wang W 2005 Scientia Meteorol. Sin. 25 212 (in Chinese) [许武成, 马劲松, 王文 2005 气象科学 25 212]
[34] Chan J C L 1985 Mon. Wea. Rev. 113 599
[35] Ge X Y, Zhou X Q, Jiang S C 2002 J. Tropical Meteorol. 18 182 (in Chinese) [葛旭阳, 周霞琼, 蒋尚城 2002 热带气象学报 18 182]
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