基于Lorenz系统的数值天气转折期预报理论探索
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摘要
以Lorenz系统为研究对象,对数值天气转折期预报中的动力学特征进行了理论研究,通过对Lorenz系统平衡点稳定性的讨论,得到了区分准稳定区域和准不稳定区域的分界曲面,由此标定出准稳定区域和准不稳定区域.在准稳定区域,Lorenz曲线保持相对稳定,能够在该平衡点周围周期运动;在准不稳定区域,Lorenz曲线可能会从这个平衡点周围跃过分界曲面而进入另外一个平衡点周围,即发生突变,这是Lorenz系统的一个重要动力学特征;对数值天气转折期预报与气候突变检测、预测给出一种新理论和新方法.
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.
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.
引文
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[25]Yan P C,Hou W,Hu J G 2012 Acta Phys.Sin.61189202(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]
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[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 21109201
[33]Wang Q G,Zhi R,Zhang Z P 2008 Acta Phys.Sin.575343(in Chinese)[王启光,支蓉,张增平2008物理学报575343]
[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 Bifurc ation 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]
1 Nereus,希腊神话中的海神,他值得信赖、和蔼可亲、公正善良.
2 Proteus,希腊神话中的海神,他能随意变成各种形状,变化多端.
[2]Richardson 1922 The Weather Prediction by Numerical Process(London:Cambridge University Press)
[3]Charney J G,Fjrtoft R,von Neumann J 1950 Tellus 2237
[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.29249(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.66892(in Chinese)[封国林,龚志强,支蓉2008气象学报66892]
[25]Yan P C,Hou W,Hu J G 2012 Acta Phys.Sin.61189202(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 21109201
[33]Wang Q G,Zhi R,Zhang Z P 2008 Acta Phys.Sin.575343(in Chinese)[王启光,支蓉,张增平2008物理学报575343]
[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 Bifurc ation 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]
1 Nereus,希腊神话中的海神,他值得信赖、和蔼可亲、公正善良.
2 Proteus,希腊神话中的海神,他能随意变成各种形状,变化多端.