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基于传递熵方法, 分析Lorenz系统x, y, z三个分量之间的信息传输方向, 并应用温差与垂直速度的再分析资料对Walker环流进行分析. 研究结果表明: 1) 对于Lorenz系统而言, x与y分量之间, y是信息源, x是信息汇; y与z之间, y是信息源, z是信息汇; x与z分量之间的信息传递方向依赖于控制参数r; 且净信息传输的方向不随初值不同而改变; 2)在西太平洋地区, 温差对垂直速度的净信息输送占主导地位, 而赤道东太平洋地区则为垂直速度对温差的净信息输送占主导地位, 这与Walker环流物理机制是一致的, 且海陆热力差异对温差与垂直速度之间的信息输送影响较大; 3)冬季是温差与垂直速度之间的信息输送最强季节, 夏季和秋季次之, 春季最弱, 这可能是存在春季预报障碍的原因之一. 以上结果表明, 传递熵在气象领域有广阔的应用前景, 是测量动力学系统信息传递方向的一种有效方法和工具.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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[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 物理学报 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 物理学报 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 物理学报 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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