Sensitivity analysis of sample number on the drought descriptive model built by Copula function in southwest China

Zuo Dong-Dong; Hou Wei; Wang Wen-Xiang

doi:10.7498/aps.64.100203

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:

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).

References

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[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 物理学报 63 230204]
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[31]	Shiau J T, Hsieh W S 2001 J. Water Resour. Plann. Manage. 127 30
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[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 物理学报 62 039206]

Cited By

[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 物理学报 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 物理学报 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 物理学报 62 039206]

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