基于Lorenz系统的数值天气转折期预报理论探索

达朝究; 穆帅; 马德山; 于海鹏; 侯威; 龚志强

doi:10.7498/aps.63.029201

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.

关键词:

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:

作者及机构信息

1.
西北民族大学数学与计算机科学学院, 兰州 730030;

2.
兰州大学大气科学学院, 兰州 730000;

3.
国家气候中心气候研究开放实验室, 北京 100081

基金项目: 国家科技支撑计划（批准号：2009BAC51B04）、公益性行业（气象）科研专项（批准号：GYHY201206009，GYHY201106016）、全球变化研究国家重大科学研究计划（批准号：2012CB955902）、国家自然科学基金（批准号：40930952，41175067，61162021）和中央高校基本科研业务费专项资金（批准号：zyz2012079）资助的课题.

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).

参考文献

[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 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 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 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 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 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 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 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 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]

施引文献

[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 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 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 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 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 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 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 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 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]

[1]	李保生, 丁瑞强, 李建平, 钟权加. 强迫Lorenz系统的可预报性研究. , 2017, 66(6): 060503. doi: 10.7498/aps.66.060503
[2]	官国荣, 吴成茂, 贾倩. 一种改进的高性能Lorenz系统构造及其应用. , 2015, 64(2): 020501. doi: 10.7498/aps.64.020501
[3]	刘群群, 何文平, 顾斌. 非线性动力学方法在气候突变检测中的应用. , 2015, 64(17): 179201. doi: 10.7498/aps.64.179201
[4]	张志森, 龚志强, 支蓉. 利用传递熵对Lorenz系统和Walker环流信息传输方向的分析. , 2013, 62(12): 129203. doi: 10.7498/aps.62.129203
[5]	贾红艳, 陈增强, 薛薇. 分数阶Lorenz系统的分析及电路实现. , 2013, 62(14): 140503. doi: 10.7498/aps.62.140503
[6]	吴浩, 侯威, 王文祥, 颜鹏程. 试用Lyapunov指数探讨气候突变及其前兆信号. , 2013, 62(12): 129204. doi: 10.7498/aps.62.129204
[7]	吴浩, 侯威, 颜鹏程. 试用临界慢化原理探讨气候突变. , 2013, 62(3): 039206. doi: 10.7498/aps.62.039206
[8]	吴浩, 封国林, 侯威, 颜鹏程. 中国不同区域气候突变的前兆信号. , 2013, 62(5): 059202. doi: 10.7498/aps.62.059202
[9]	黎爱兵, 张立凤, 项杰. 外强迫对Lorenz系统初值可预报性的影响. , 2012, 61(11): 119202. doi: 10.7498/aps.61.119202
[10]	吴浩, 侯威, 颜鹏程, 封国林. 基于临界慢化现象的气候突变前兆信号的初步研究. , 2012, 61(20): 209202. doi: 10.7498/aps.61.209202
[11]	李清都, 谭宇玲, 杨芳艳. 连续时间系统二维不稳定流形的异构算法. , 2011, 60(3): 030206. doi: 10.7498/aps.60.030206
[12]	李小娟, 徐振源, 谢青春, 王兵. 单向耦合下两个不同Lorenz系统的广义同步. , 2010, 59(3): 1532-1539. doi: 10.7498/aps.59.1532
[13]	孙克辉, 杨静利, 丁家峰, 盛利元. 单参数Lorenz混沌系统的电路设计与实现. , 2010, 59(12): 8385-8392. doi: 10.7498/aps.59.8385
[14]	李清都, 杨晓松. 一种二维不稳定流形的新算法及其应用. , 2010, 59(3): 1416-1422. doi: 10.7498/aps.59.1416
[15]	王启光, 支蓉, 张增平. Lorenz系统长程相关性研究. , 2008, 57(8): 5343-5350. doi: 10.7498/aps.57.5343
[16]	王启光, 张增平. 近似熵检测气候突变的研究. , 2008, 57(3): 1976-1983. doi: 10.7498/aps.57.1976
[17]	王兴元, 王明军. 超混沌Lorenz系统. , 2007, 56(9): 5136-5141. doi: 10.7498/aps.56.5136
[18]	何文平, 封国林, 高新全, 丑纪范. 准周期外力驱动下Lorenz系统的动力学行为. , 2006, 55(6): 3175-3179. doi: 10.7498/aps.55.3175
[19]	封国林, 龚志强, 董文杰, 李建平. 基于启发式分割算法的气候突变检测研究. , 2005, 54(11): 5494-5499. doi: 10.7498/aps.54.5494
[20]	郭会军, 刘君华. 基于径向基函数神经网络的Lorenz混沌系统滑模控制. , 2004, 53(12): 4080-4086. doi: 10.7498/aps.53.4080

计量

文章访问数: 6545
PDF下载量: 531
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板