The theoretical study of the turning period in numerical weather prediction models based on the Lorenz equations

Da Chao-Jiu; Mu Shuai; Ma De-Shan; Yu Hai-Peng; Hou Wei; Gong Zhi-Qiang

doi:10.7498/aps.63.029201

Abstract

Based on the Lorenz equations, the dynamics of the weather turning period is studied about numerical weather prediction. Through the analysis of the stability of equilibrium points of the Lorenz equations, we get the surfaces which separate the quasi-stable region and quasi-unstable region. In the quasi-stable region, the path curve of the Lorenz equations can remain relatively stable around the equilibrium points, however in the quasi-unstable region, the path curve of the Lorenz equations can spring from this equilibrium point to another one. This is one of the important dynamic characteristics of the Lorenz system, and the paper give new method and theory for the detection of the abrupt change of climate.

Keywords:

Authors and contacts

1.
School of Mathematics and Computer Science Institute, Northwest University for Nationalities, Lanzhou 730030, China;
2.
College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000, China;
3.
Laboratory for Climate Studies, National Climate Center, China Meteorological Administration, Beijing 100081, China
Funds: Project supported by the Key Technologies R&D Program of China (Grant No. 2009BAC51B04), the Meteorological Special Project of China (Grant Nos. GYHY201206009, GYHY201106016), the National Basic Research Program of China (Grant No. 2012CB955902), the National Natural Science Foundation of China (Grant Nos. 40930952, 41175067, 61162021) and the Fundamental Research Funds for the Central Universities, China (Grant No. zyz2012079).

References

[1]	Bjerknes V 1904 Meteor. Zeit. 21 1
[2]	Richardson 1922 The Weather Prediction by Numerical Process (London: Cambridge University Press)
[3]	Charney J G, Fjörtoft R, von Neumann J 1950 Tellus 2 237
[4]	Gu Z C 1958 Acta Meteor. Sin. 29 176 (in Chinese) [顾震潮 1958 气象学报 29 176]
[5]	Gu Z C 1958 Acta Meteor. Sin. 29 93 (in Chinese) [顾震潮 1958 气象学报 29 93]
[6]	Chou J F 1974 Sci. China D 6 635 (in Chinese) [丑纪范 1974 中国科学 D 6 635]
[7]	Qiu C J, Shao A M, Xu Q, Wei L 2007 J. Geophys. Res. 112 D11105
[8]	Shao A M, Xi S, Qiu C J, Xu Q 2009 J. Geophys. Res. 114 D17114
[9]	Huang J P, Chou J F 1989 Sci. China B 9 1001 (in Chinese) [黄建平, 丑纪范 1989 中国科学 B 9 1001]
[10]	Huang J P, Wang S W 1991 Sci. China B 21 216 (in Chinese) [黄建平, 王绍武 1991 中国科学 B 21 216]
[11]	Huang J P, Yi Y H, Wang S W, Chou J F 1993 Quart. J. Roy Meteor. Soc. 119 547
[12]	Huang J P, Yi Y H 1991 Sci. China B 3 331 (in Chinese) [黄建平, 衣育红 1991 中国科学 B 3 331]
[13]	Huang J P, Yi Y H 1991 Sci. China B 34 1246
[14]	Huang J P, North G R 1996 J. Atmosph. Sci. 53 370
[15]	Feng G L, Cao H X, Wei F Y 1999 J. Appl. Meteor. Sci. 10 470 (in Chinese) [封国林, 曹鸿兴, 魏凤英 1999 应用气象学报 10 470]
[16]	Feng G L, Dong W J 2003 Chin. Phys. 12 1076
[17]	Zheng Z H 2010 Ph. D. Dissertation (Lanzhou: Lanzhou University) (in Chinese) [郑志海 2010 博士学位论文 (兰州: 兰州大学)]
[18]	Da C J 2011 Ph. D. Dissertation (Lanzhou: Lanzhou University) (in Chinese) [达朝究 2011 博士学位论文 (兰州: 兰州大学)]
[19]	Xue H L 2013 Ph. D. Dissertation (Lanzhou: Lanzhou University) (in Chinese) [薛海乐 2013 博士学位论文 (兰州: 兰州大学)]
[20]	Shabbar A, J Huang, K Higuchi 2001 Int. J. Climatol. 21 355
[21]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[22]	Fu Z B, Wang Q 1992 Chin. J. Atmos. Sci. 16 482 (in Chinese) [符淙斌, 王强 1992 大气科学 16 482]
[23]	Ye D Z, Tao S Y, Li M C 1958 Acta Meteor. Sin. 29 249 (in Chinese) [叶笃正, 陶诗言, 李麦村 1958 气象学报 29 249]
[24]	Feng G L, Gong Z Q, Zhi R 2008 Acta Meteor. Sin. 66 892 (in Chinese) [封国林, 龚志强, 支蓉 2008 气象学报 66 892]
[25]	Yan P C, Hou W, Hu J G 2012 Acta Phys. Sin. 61 189202 (in Chinese) [颜鹏程, 侯威, 胡经国 2012 物理学报 61 189202]
[26]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林, 戴新刚, 王爱慧, 丑纪范 2001 物理学报 50 606]
[27]	Wu H, Hou W, Yan P C 2013 Acta Phys. Sin. 62 039206 (in Chinese) [吴浩, 侯威, 颜鹏程 2013 物理学报 62 039206]
[28]	Feng G L, Hou W, Zhi R 2011 Research on Detecting, Diagnosing and Predictability of Extreme Climate Events (Beijing: Science Press) pp350–366 (in Chinese) [封国林, 侯威, 支蓉 2011 极端气候事件的检测、诊断和可预测性研究 (北京: 科学出版社) 第350–366页]
[29]	Zhao J H, Feng G L, Zhang S X, Sun S P 2011 Acta Phys. Sin. 60 099205 (in Chinese) [赵俊虎, 封国林, 张世轩, 孙树鹏 2011 物理学报 60 099205]
[30]	Zhao J H, Yang J, Gong Z Q, Zhi R 2013 Acta Phys. Sin. 62 099206 (in Chinese) [赵俊虎, 杨杰, 龚志强, 支蓉 2013 物理学报 2013 62 099206]
[31]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光, 张增平 2008 物理学报 57 1976]
[32]	Cui H, He H L, Liu X H, Li Y 2012 Chin. Phys. B 21 109201
[33]	Wang Q G, Zhi R, Zhang Z P 2008 Acta Phys. Sin. 57 5343 (in Chinese) [王启光, 支蓉, 张增平 2008 物理学报 57 5343]
[34]	Zheng Z H, Ren H L, Huang J P 2009 Acta Phys. Sin. 58 7359 (in Chinese) [郑志海, 任宏利, 黄建平 2009 物理学报 58 7359]
[35]	Wang Q G, Feng G L, Zheng Z H, Zhi R 2011 Chin. J. Atmos. Sci. 35 287 (in Chinese) [王启光, 封国林, 郑志海, 支蓉 2011 大气科学 35 287]
[36]	Zheng Z H, Huang J P, Feng G L, Chou J F 2012 Sci. China D 43 594 (in Chinese) [郑志海, 黄建平, 封国林, 丑纪范 2013 中国科学 D 43 594]
[37]	Zhang J Y, Feng B Y 2000 The Geometric and Bifurcation Theory of Ordinary Differential Equations (Beijing: Beijing University Press) p36 (in Chinese) [张锦炎, 冯贝叶 2003 常微分方程几何理论与分支问题 (北京: 北京大学出版社) 第36页]
[38]	Gunter Maher, Ke Z Y 1995 Theory of Matrices (Beijing: Higher Education Press) p127 (in Chinese) [甘特马赫尔, 柯召译 1995 矩阵论 (北京: 高等教育出版社) p127]

Cited By

[1]	Bjerknes V 1904 Meteor. Zeit. 21 1
[2]	Richardson 1922 The Weather Prediction by Numerical Process (London: Cambridge University Press)
[3]	Charney J G, Fjörtoft R, von Neumann J 1950 Tellus 2 237
[4]	Gu Z C 1958 Acta Meteor. Sin. 29 176 (in Chinese) [顾震潮 1958 气象学报 29 176]
[5]	Gu Z C 1958 Acta Meteor. Sin. 29 93 (in Chinese) [顾震潮 1958 气象学报 29 93]
[6]	Chou J F 1974 Sci. China D 6 635 (in Chinese) [丑纪范 1974 中国科学 D 6 635]
[7]	Qiu C J, Shao A M, Xu Q, Wei L 2007 J. Geophys. Res. 112 D11105
[8]	Shao A M, Xi S, Qiu C J, Xu Q 2009 J. Geophys. Res. 114 D17114
[9]	Huang J P, Chou J F 1989 Sci. China B 9 1001 (in Chinese) [黄建平, 丑纪范 1989 中国科学 B 9 1001]
[10]	Huang J P, Wang S W 1991 Sci. China B 21 216 (in Chinese) [黄建平, 王绍武 1991 中国科学 B 21 216]
[11]	Huang J P, Yi Y H, Wang S W, Chou J F 1993 Quart. J. Roy Meteor. Soc. 119 547
[12]	Huang J P, Yi Y H 1991 Sci. China B 3 331 (in Chinese) [黄建平, 衣育红 1991 中国科学 B 3 331]
[13]	Huang J P, Yi Y H 1991 Sci. China B 34 1246
[14]	Huang J P, North G R 1996 J. Atmosph. Sci. 53 370
[15]	Feng G L, Cao H X, Wei F Y 1999 J. Appl. Meteor. Sci. 10 470 (in Chinese) [封国林, 曹鸿兴, 魏凤英 1999 应用气象学报 10 470]
[16]	Feng G L, Dong W J 2003 Chin. Phys. 12 1076
[17]	Zheng Z H 2010 Ph. D. Dissertation (Lanzhou: Lanzhou University) (in Chinese) [郑志海 2010 博士学位论文 (兰州: 兰州大学)]
[18]	Da C J 2011 Ph. D. Dissertation (Lanzhou: Lanzhou University) (in Chinese) [达朝究 2011 博士学位论文 (兰州: 兰州大学)]
[19]	Xue H L 2013 Ph. D. Dissertation (Lanzhou: Lanzhou University) (in Chinese) [薛海乐 2013 博士学位论文 (兰州: 兰州大学)]
[20]	Shabbar A, J Huang, K Higuchi 2001 Int. J. Climatol. 21 355
[21]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[22]	Fu Z B, Wang Q 1992 Chin. J. Atmos. Sci. 16 482 (in Chinese) [符淙斌, 王强 1992 大气科学 16 482]
[23]	Ye D Z, Tao S Y, Li M C 1958 Acta Meteor. Sin. 29 249 (in Chinese) [叶笃正, 陶诗言, 李麦村 1958 气象学报 29 249]
[24]	Feng G L, Gong Z Q, Zhi R 2008 Acta Meteor. Sin. 66 892 (in Chinese) [封国林, 龚志强, 支蓉 2008 气象学报 66 892]
[25]	Yan P C, Hou W, Hu J G 2012 Acta Phys. Sin. 61 189202 (in Chinese) [颜鹏程, 侯威, 胡经国 2012 物理学报 61 189202]
[26]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林, 戴新刚, 王爱慧, 丑纪范 2001 物理学报 50 606]
[27]	Wu H, Hou W, Yan P C 2013 Acta Phys. Sin. 62 039206 (in Chinese) [吴浩, 侯威, 颜鹏程 2013 物理学报 62 039206]
[28]	Feng G L, Hou W, Zhi R 2011 Research on Detecting, Diagnosing and Predictability of Extreme Climate Events (Beijing: Science Press) pp350–366 (in Chinese) [封国林, 侯威, 支蓉 2011 极端气候事件的检测、诊断和可预测性研究 (北京: 科学出版社) 第350–366页]
[29]	Zhao J H, Feng G L, Zhang S X, Sun S P 2011 Acta Phys. Sin. 60 099205 (in Chinese) [赵俊虎, 封国林, 张世轩, 孙树鹏 2011 物理学报 60 099205]
[30]	Zhao J H, Yang J, Gong Z Q, Zhi R 2013 Acta Phys. Sin. 62 099206 (in Chinese) [赵俊虎, 杨杰, 龚志强, 支蓉 2013 物理学报 2013 62 099206]
[31]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光, 张增平 2008 物理学报 57 1976]
[32]	Cui H, He H L, Liu X H, Li Y 2012 Chin. Phys. B 21 109201
[33]	Wang Q G, Zhi R, Zhang Z P 2008 Acta Phys. Sin. 57 5343 (in Chinese) [王启光, 支蓉, 张增平 2008 物理学报 57 5343]
[34]	Zheng Z H, Ren H L, Huang J P 2009 Acta Phys. Sin. 58 7359 (in Chinese) [郑志海, 任宏利, 黄建平 2009 物理学报 58 7359]
[35]	Wang Q G, Feng G L, Zheng Z H, Zhi R 2011 Chin. J. Atmos. Sci. 35 287 (in Chinese) [王启光, 封国林, 郑志海, 支蓉 2011 大气科学 35 287]
[36]	Zheng Z H, Huang J P, Feng G L, Chou J F 2012 Sci. China D 43 594 (in Chinese) [郑志海, 黄建平, 封国林, 丑纪范 2013 中国科学 D 43 594]
[37]	Zhang J Y, Feng B Y 2000 The Geometric and Bifurcation Theory of Ordinary Differential Equations (Beijing: Beijing University Press) p36 (in Chinese) [张锦炎, 冯贝叶 2003 常微分方程几何理论与分支问题 (北京: 北京大学出版社) 第36页]
[38]	Gunter Maher, Ke Z Y 1995 Theory of Matrices (Beijing: Higher Education Press) p127 (in Chinese) [甘特马赫尔, 柯召译 1995 矩阵论 (北京: 高等教育出版社) p127]

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Vol. 63, Issue 2 - 2014-01-20

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