中国西南地区干旱Copula函数模型对样本量的敏感性分析

左冬冬; 侯威; 王文祥

doi:10.7498/aps.64.100203

摘要

基于中国西南地区(四川省、云南省、贵州省和重庆市) 89个站点1961-2010年的逐月标准化降水指数序列, 利用游程理论和Copula函数建立干旱历时和干旱强度的概率模型, 基于该模型讨论了干旱事件样本量对分布参数、干旱类型的出现概率及联合重现期的影响. 结果表明: 分布参数稳定对样本量的要求较大, 部分区域样本量要求大于50, 并且各参数对样本量的要求不一致, 又以干旱强度分布的参数对样本量的要求最大; 干旱事件样本量为10个左右求得的干旱类型出现概率和联合重现期与样本量为40求得的结果已无明显差异, 以计算结果作为标准可大幅降低统计模型建立对样本量的要求, 进而表明起止时间不一致和具有缺测数据的站点仍可建立干旱历时和干旱强度的分布函数; 气候变暖对模型建立所需的最少样本量影响不大, 样本量波动在± 5之间, 即统计模型具有一定的稳定性, 同时气候态的划分降低了分布检验对样本量的需求, 易于模型的建立.

关键词:

Abstract

Based on the standardized precipitation index data of 89 meteorological stations in southwest China (Sichuan Province, Yunnan Province, Guizhou Province, Chongqing) during 1961-2010, probability model containing drought duration and drought severity is established by using the theory of run and the Copula function. The influences of the drought sample number on the distribution parameters, the probability and drought return period are discussed. The result shows that the stability of distribution parameters needs larger sample number. The sample number is greater than 50 in some regions and the requirements for sample number of each parameter is not consistent. The sample number of severity distribution parameters is largest. The probability and return period obtained in the case where the sample number is about 10 have no significant difference (the significant level is 0.05) from those in the case where the sample number is 40 in most of region. With the results used as the standard, statistical model can greatly reduce the requirements for the sample number. And then it demonstrates that the distribution function of drought duration and drought severity can still be established in the lack of measurement data and the inconsistency between starting and ending time. Climate warming has no influence on the minimum of sample number. The fluctuation is mostly between -5 to 5. Statistical model has a certain stability. Meanwhile, the division of climate state reduces the need for distribution test sample number and makes it easier to build model.

Keywords:

作者及机构信息

1.
扬州大学物理科学与技术学院, 扬州 225002;

2.
国家气候中心, 气候研究开放实验室, 北京 100081

基金项目: 国家自然科学基金(批准号: 41305056, 41175067)和国家重点基础研究发展计划(批准号: 2012CB955901)资助的课题.

Authors and contacts

1.
Department of Physics, Yangzhou University, Yangzhou 225002, China;

2.
Laboratory for Climate Studies, National Climate Center, China Meteorological Administration, Beijing 100081, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41305056, 41175067) and the National Basic Research Program of China (Grant No. 2012CB955901).

参考文献

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施引文献

[1]	Cui D L 2010 M. S. Dissertation (Lanzhou: Lanzhou University) (in Chinese) [崔冬林 2010 硕士学位论文 (兰州: 兰州大学)]
[2]	Liu J G, Wan J H, Tan X M, Ma J M, Zhang N Q 2011 J. Disaster Preven. Miti. Eng. 31 196 (in Chinese) [刘建刚, 万金红, 谭徐明, 马建明, 张念强 2011 防灾减灾工程学报 31 196]
[3]	Yin H, Li Y H 2013 J.Arid Meteor. 31 182 (in Chinese) [尹晗, 李耀辉 2013 干旱气象 31 182]
[4]	Huang R H, Liu Y, Wang L, Wang L 2012 Chin. J. Atmos. Sci. 36 443 (in Chinese) [黄荣辉, 刘永, 王林, 王磊 2012 大气科学 36 443]
[5]	Huang J P, Wang S W 1992 Sci. China 35 207
[6]	Li J P, Ding R Q 2008 Chin. J. Atmos. Sci. 32 975 (in Chinese) [李建平, 丁瑞强 2008 大气科学 32 975]
[7]	Huang J P, Yi Y H, Wang S W, Chou J F 1993 Q. J. R. Meteorol. Soc. 119 547
[8]	Li J P, Ding R Q 2009 Chin. J. Atmos. Sci. 33 551 (in Chinese) [李建平, 丁瑞强 2009 大气科学 33 551]
[9]	Jia X L, Chen L J, Gao H, Wang Y G, Ke Z J, Liu C Z, Song W L, Wu T W, Feng G L, Zhao Z G, Li W J 2013 J. Appl. Meteor. Science 24 641 (in Chinese) [贾小龙, 陈丽娟, 高辉, 王永光, 柯宗建, 刘长征, 宋文玲, 吴统文, 封国林, 赵振国, 李维京 2013 应用气象学报 24 641]
[10]	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]
[11]	Zhao J H, Feng G L, Wang Q G, Yang J, Gong Z Q 2011 Chin. J. Atmos. Sci. 35 1069 (in Chinese) [赵俊虎, 封国林, 王启光, 杨杰, 龚志强 2011 大气科学 35 1069]
[12]	Zhao J H, Zhi R, Shen Q, Yang J, Feng G L 2014 Chin. J. Atmos. Sci. 38 237 (in Chinese) [赵俊虎, 支蓉, 申茜, 杨杰, 封国林 2014 大气科学 38 237]
[13]	Sklar A 1959 Fonctions de Répartitionán Dimensions et Leurs Marges (France: Publications de l’Institut de Statistique de L’Université de Paris) pp229-231
[14]	Wan Z W Z, Abdul A J, Kamarulzaman I 2013 Theor. Appl. Climatol. 111 559
[15]	Shiau J T, Modarres R 2009 Meteorol. Appl. 16 481
[16]	Zhang Q, Xiao M Z, Singh V P, Chen X H 2013 Theor. Appl. Climatol. 111 119
[17]	Xu L Y, Wang H M, Chen J F 2013 J. Appl. Statis and Manage 32 284 (in Chinese) [许玲燕, 王慧敏, 陈军飞 2013 数理统计与管理 32 284]
[18]	Liu C L, Qiang Z, Vijay P S, Cui Y 2011 Nat. Hazards 59 1533
[19]	Ummul F A R, Panlop Z 2014 Theor. Appl. Climatol. 115 153
[20]	Rasoul M, Ahmad F F, Yagob D 2012 Theor. Appl. Climatol. 108 191
[21]	Kao S C, Rao S G 2010 J. Hydrol. 380 121
[22]	Li J, Li Y, Song S B, Cui C F 2012 J. China Hydrol. 32 43 (in Chinese) [李计, 李毅, 宋松柏, 崔晨风 2012 水文 32 43]
[23]	Shiau J T, Reza M, Saralees N 2012 Environ. Model. Assess. 17 469
[24]	Shiau J T 2006 Water Resour. Manage 20 795
[25]	Bahram S, Hossein M 2014 Nat. Hazards 72 1391
[26]	Ganguli P, Reddy M J 2012 Water Resour. Manage 26 3301
[27]	Hao Z C, Amir A 2013 Adv. Water Resour. 57 12
[28]	Herbst P H, Bredenkamp D B, Barker H M G 1966 J. Hydrol. 4 264
[29]	Zuo D D, Hou W, Yan P C, Feng T C 2014 Acta Phys. Sin. 63 230204 (in Chinese) [左冬冬, 侯威, 颜鹏程, 封泰晨 2014 63 230204]
[30]	Zelenhasic E, Salvai A 1987 Water Resour. Res. 23 156
[31]	Shiau J T, Hsieh W S 2001 J. Water Resour. Plann. Manage. 127 30
[32]	Yan B W, Guo S L, Xiao Y, Fang B 2007 Arid Zone Res. 24 537 (in Chinese) [闫宝伟, 郭生练, 肖义, 方彬 2007 干旱区研究 24 537]
[33]	Zhang L, Singh V P 2006 J. Hydrol. Eng. 11 150
[34]	Wei F Y 2007 Modern Climatic Statistical Diagnosis and Prediction Technology (Beijing: China Meteorological Press) pp63-64 (in Chinese) [魏凤英 2007 现代气候统计诊断与预测技术(北京: 气象出版社) 第63-64页]
[35]	Wei F Y 2007 Modern Climatic Statistical Diagnosis and Prediction Technology (Beijing: Meteorological Press) p26 (in Chinese) [魏凤英 2007 现代气候统计诊断与预测技术(北京: 气象出版社) 第26页]
[36]	Liu Y, Zhao E X, Huang W, Zhou J Q, Ju J H 2010 J. Catastrophol. 25 39 (in Chinese) [刘瑜, 赵尔旭, 黄玮, 周建琴,琚建华 2010 灾害学 25 39]
[37]	Ding Y H, Zhang L 2008 Chin. J. Atmos. Sci. 32 794 (in Chinese) [丁一汇, 张莉 2008 大气科学 32 794]
[38]	Xiao D, Li J P 2007 Chin. J. Atmos. Sci. 31 839 (in Chinese) [肖栋, 李建平 2007 大气科学 31 839]
[39]	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]

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