The Applicability of Several Distribution Functions Which used to Describe the Characteristics of Cumulative Precipitation in China

  • WU Zijun ,
  • ZHANG Qiang ,
  • SHI Yanjun ,
  • JIN Shiqiang ,
  • ZHANG Hongli
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  • School of AtmosphericSciences, Lanzhou University, Lanzhou 730000, China;Lanzhou Institute of Arid Meteorology of Chinese Meteorological Administration, Lanzhou 730020, China;Lanzhou Institute of Arid Meteorology of Chinese Meteorological Administration, Lanzhou/Key Laboratory of Arid Climatic Changing and Reducing Disaster of Gansu Province/Open Laboratory of Arid Climatic Changing and Disaster of Chinese Meteorological Administration/Gansu Metrological Bureau, Lanzhou 730020, China;School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China;Department of Statistics, Kansas State University, Kansas State 66502, USA

Received date: 2015-12-28

  Online published: 2017-10-28

Abstract

In order to find out the best distribution to describe the characteristics of cumulative precipitation on multiple time scales in China, Gamma distribution, Generalized Extreme Value distribution (GEV distribution), Log-normal distribution, Weibull distribution, Normal distribution and Rayleigh distribution were chosen.On the six time scales of one, three, six, nine, twelve, twenty-four months, a nationwide K-S test was taken on these six distributions with the 1961-2013 monthly precipitation datas of 760 meteorological stations in China.The results show that among the six distributions, the GEV distribution is the most suitable function for describing the cumulative precipitation characteristics on every timescale in China, followed by Gamma distribution, Rayleigh distribution is the least suitable one.After a detailed discuss for every season and different part of China on one month time scale and three month time scale, it turned out that on the one month time scale, GEV distribution is better than Gamma distribution in spring, summer and autumn, while Gamma distribution is better than GEV distribution in winter, however, there are some exceptions in different climatic region of China in every season.On the three month time scale, GEV distribution is better than Gamma distribution in both summer and winter, as well as in all regions of China.

Cite this article

WU Zijun , ZHANG Qiang , SHI Yanjun , JIN Shiqiang , ZHANG Hongli . The Applicability of Several Distribution Functions Which used to Describe the Characteristics of Cumulative Precipitation in China[J]. Plateau Meteorology, 2017 , 36(5) : 1221 -1233 . DOI: 10.7522/j.issn.1000-0534.2016.00079

References

[1]Aksoy H. 2000. Use of Gamma Distribution in hydrological analysis[J]. Turkish Journal of Engineering and Environmental Sciences, 24(6):419-428.
[2]Guegan D, Hassani B. 2014. A Mathematical resurgence of risk management:an extreme modeling of expert opinions[J]. Frontiers in Finance and Economics, 11(1):25-45.
[3]Guttman N B. 1999. Accepting the standardized precipitation index:A calculation algorithm1[J]. Journal of the American Water Resources Association, 311-322.
[4]Kolmogorov А Н. 1933. Sulla determinazione empirica di una leggi di distribuzione[J]. Giorn Ist Ital Attuari, 4:83-91.
[5]Lukacs E. 1942. A characterization of the normal distribution[J]. The Annals of Mathematical Statistics, 13(1):91-93.
[6]McKee T B, Doesken N J, Kleist J. 1995. Drought monitoring with multiple time scales[C] Proceedings of the 9th Conference on Applied Climatology. Dallas, Boston, MA:American Meteorological Society, 233-236.
[7]McKee T B, Doesken N J, Kleist J. 1993. The relationship of drought frequency and duration to time scales[C] Proceedings of the 8th Conference on Applied Climatology. Boston, MA:American Meteorological Society, 17(22):179-183.
[8]Muraleedharan G, Guedes C, Lucas C. 2011. Characteristic and moment Generating Functions of Generalized Extreme Value Distribution(GEV), sea level rise, coastal engineering, shorelines and tides[J]. Nova Science Publishers. Chapter-14, pp. 269-276.
[9]Robert W, Freeman D H, Johnson M F. 1979. Justification for the lognormal distribution as a model for blood pressure[J]. Journal of Chronic Diseases, 32(3):245-250.
[10]Sharif M N, Islam M N. 1980. The Weibull distribution as a general model for forecasting technological change[J]. Technological Forecasting and Social Change, 18(3):247-256.
[11]Siddiqui M M. 1962. Some problems connected with rayleigh distributions[J]. Journal of Research of the National Bureau of Standards, 66(2):167-174.
[12]Smirnov N V. 1939. Estimate of deviation between empirical distribution functions in two independent samples[J]. Bulletin Moscow University, 2(2):3-16.
[13]Xu Chongyu, Widden E, Halldin S. 2005. Modeling Hydrological Consequences of Climate Change-progress and Challenge[J]. Adv Atmos Sci, 22(6):789-797.
[14]Zhang Qiang, Xu Chongyu, Chen Yongqin, et al. 2009. Spatial assessment of hydrologic alteration across the Pearl River Delta, China, and possible underlying causes[J]. Hydrological Processes, 23:1565-1574.
[15]John K, John A D, Zhou Yaowu, et al. 2005. The quantification of drought:an evaluation of drought indices[J]. Arid Meteor, 2:85-94.<br/>John K, John A D, 周跃武, 等. 2005.干旱的定量化:干旱指数的评价[J].干旱气象, 2:85-94.
[16]Chen Yuying, Chen Nan, Wang Shigong, et al. 2010. Temporal and spatial change features of precipitation over China-Mongolia Arid-and Semiarid-Areas(Ⅰ):Annual rainfall feature and May~September on REOF analyses[J]. Plateau Meteor, 29(1):33-43.<br/>陈豫英, 陈楠, 王式功, 等. 2010.中蒙干旱半干旱区降水的时空变化特征(Ⅰ):年降水特征及5~9月降水的REOF分析[J].高原气象, 29(1):33-43.
[17]Cheng Zhi. 2011. Statistical models for predicting summer rainfall and its extremes in China[D]. Lanzhou:Lanzhou University, 1-43.<br/>程智. 2011. 中国汛期降水及其极端值的统计推断模型研究[D]. 兰州: 兰州大学, 1-43.
[18]Ding Yuguo. 1994. Research of Universality for Γ distribution model of precipitation[J]. Chinese J Atmos Sci, 18(5):552-560.<br/>丁裕国. 1994.降水量Γ分布模式的普适性研究[J].大气科学, 18(5):552-560.
[19]Duan Ying, Wang Wen, Cai Xiaojun. 2013. Applied analyses on palmer, SPEI and CI Indices of drought process in Yangtze-Huaihe River basins during winter of 2010/spring of 2011[J]. Plateau Meteor, 33(4):1126-1139. DOI:10. 7522/j. issn. 1000-0534. 2012. 00106.<br/>段莹, 王文, 蔡晓军. 2013. PDSI、SPEI及CI指数在2010/2011年冬、春季江淮流域干旱过程的应用分析[J].高原气象, 32(4):1126-1139.
[20]Huang Ronghui, Liu Yong, Wang Lin, et al. 2012. Analyses of the causes of severe drought occurring in Southwest China from the fall of 2009 to the spring of 2010[J]. Chinese J Atmos Sci, 36(3):443-457.<br/>黄荣辉, 刘永, 王林, 等. 2012. 2009年秋至2010年春我国西南地区严重干旱的成因分析[J].大气科学, 36(3):443-457.
[21]Huang Wanhua, Sui Yue, Yang Xiaoguang, et al. 2013. Characteristics and adaptation of seasonal drought in southern China under the background of climate change. Ⅴ. seasonal drought characteristics division and assessment in southern China[J]. Chinese Journal of Applied Ecology, 24(10):2917-2925.<br/>黄晚华, 隋月, 杨晓光, 等. 2013.气候变化背景下中国南方地区季节性干旱特征与适应Ⅴ.南方地区季节性干旱特征分区和评述[J].应用生态学报, 24(10):2917-2925.
[22]Huang Wanhuan, Yang Xiaoguang, Li Maosong, et al. 2010. Evolution characteristics of seasonal drought in the south of China during the past 58 years based on standardized precipitation index[J]. Transactions of the Chinese Society of Agricultural Engineering, 26(7):50-59.<br/>黄晚华, 杨晓光, 李茂松, 等. 2010.基于标准化降水指数的中国南方季节性干旱近58a演变特征[J].农业工程报, 26(7):50-59.
[23]Li Hongying, Zhang Xiaoyu, Wang Jing, et al. 2014. Analysis of drought disasters-causing factors in Ningxia Based on CI Index[J]. Plateau Meteor, 33(4):995-1001. DOI:10. 7522/j. issn. 1000-0534. 2013. 00043.<br/>李红英, 张晓煜, 王静, 等. 2014.基于CI指数的宁夏干旱致灾因子特征指标分析[J].高原气象, 33(4):995-1001.
[24]Luan Chen, Song Minhong, Cai Ying, et al. 2012. Distribution and change feature of intense precipitation in the west part of Northwestern China during summer half years[J]. Plateau Meteor, 31(3):629-637.<br/>栾晨, 宋敏红, 蔡英, 等. 2012.西北区西部夏半年强降水分布与变化特征[J].高原气象, 31(3):629-637.
[25]Ma Zhuguo, Fu Congbin. 2005. Decadal variations of arid and semi-arid boundary in China[J]. Chinese J Geophys, 48(3):519-525.<br/>马柱国, 符淙斌. 2005.中国干旱和半干旱带的10年际演变特征[J].地球物理学报, 48(3):519-525.
[26]Nan Bo. 2012. Statistical analysis of snow load based on K-S inspection method[J]. Journal of Lanzhou University of Technology, 38(1):115-119.<br/>南波. 2012.基于K-S检验法的雪荷载统计分析[J].兰州理工大学学报, 38(1):115-119.
[27]Qian Zheng'an, Song Minhong, Li Wanyuan, et al. 2011. Global, China-Mongolia Arid-and Semiarid-Areas (CMASA) and the details of precipitation distribution in part regions of CMASA[J]. Plateau Meteor, 30(1):1-12.<br/>钱正安, 宋敏红, 李万源, 等. 2011.全球、中蒙干旱区及其部分地区降水分布细节[J].高原气象, 30(1):1-12.
[28]Ran Jinjiang. 2014. The spatial and temporal characteristics of temperature and precipitation in arid and semi-arid regions of China[D]. Lanzhou:Lanzhou University, 1-60.<br/>冉津江. 2014. 我国干旱半干旱区温度和降水的时空分布特征[D]. 兰州: 兰州大学, 1-60.
[29]Shi Yanjun. 2014. Research on regional extreme drought events and their numerical simulation and prediction in Xinjiang area[D]. Lanzhou:Lanzhou University, 1-97.<br/>石彦军. 2014. 新疆区域性极端干旱事件及其数值模拟和预测研究[D]. 兰州: 兰州大学, 1-97.
[30]Shi Fangxin, HaoZhenchun, Yang Chuanguo, et al. 2014. Analysis of probability distribution of precipitation in Yellow HuaihaiRegion[J]. Water Resources and Power, (9):1-5.<br/>时芳欣, 郝振纯, 杨传国, 等. 2014.黄淮海地区降水概率分布类型分析[J].水电能源科学, (9):1-5.
[31]Wang Bin, Fu Qiang, Wang Min, et al. 2011. Comparative analysis on three distribution functions simulating daily rainfall[J]. Mathematics in Practice and Theory, 41(9):128-133.<br/>王斌, 付强, 王敏, 等. 2011.几种模拟逐日降水的分布函数比较分析[J].数学的实践与认识, 41(9):128-133.
[32]Wang Chenghai, Wang Zhilan, Guo Yipeng. 2012. Application and verification of drought index in meteorology drought monitor and prediction[J]. Adv Earth Sci, 27(9):957-968.<br/>王澄海, 王芝兰, 郭毅鹏. 2012. GEV干旱指数及其在气象干旱预测和监测中的应用和检验[J].地球科学进展, 27(9):957-968.
[33]Wang Suping, Wang Jingsong, Zhang Qiang, et al. 2015. Applicability evaluation of drought indices in monthly scale drought monitoring in southwestern and southern China[J]. Plateau Meteor, 34(6):1616-1624. DOI:10. 7522/j. issn. 1000-0534. 2014. 00089.<br/>王素萍, 王劲松, 张强, 等. 2015.几种干旱指标对西南和华南区域月尺度干旱监测的适用性评价[J].高原气象, 34(6):1616-1624.
[34]Wang Zhilan, Wang Chenghai, Li Yaohui, et al. 2013. Comparison of application between generalized extreme value index and standardized precipitation index in northwest China[J]. Plateau Meteor, 32(3):839-847. DOI:10. 7522/j. issn. 1000-0534. 2012. 00077.<br/>王芝兰, 王劲松, 李耀辉, 等. 2013.标准化降水指数与广义极值分布干旱指数在西北地区应用的对比分析[J].高原气象, 32(3):839-847.
[35]Xiong Guangjie, Wang Shigong, Li Chongyin, et al. 2014. Analysis of applicability of three drought indices for drought events in southwest China[J]. Plateau Meteor, 33(3):686-697. DOI:10. 7522/j. issn. 1000-0534. 2013. 00007.<br/>熊光洁, 王式功, 李崇银, 等. 2014.三种干旱指数对西南地区适用性分析[J].高原气象, 33(3):686-697.
[36]Xu Erhao. 1950. On the normality of annual rainfall[J]. Acta Meteor Sinica, 21(1):17-34.<br/>徐尔灏. 1950.论年雨量之常态性[J].气象学报, 21(1):17-34.
[37]Yang Xuan, Li Dongliang. 2008. Precipitation variation characteristics and arid climate division in China[J]. Arid Meteor, 26(2):17-24.<br/>杨绚, 李栋梁. 2008.中国干旱气候分区及其降水量变化特征[J].干旱气象, 26(2):17-24.
[38]Yuan Wenping, Zhou Guangsheng. 2004. Comparison between standardized precipitation index and Z-Index in China[J]. Chinese J Plant Ecology, 28(4):523-529.<br/>袁文平, 周广胜. 2004.标准化降水指标与Z指数在我国应用的对比分析[J].植物生态学报, 28(4):523-529.
[39]Zhang Lei, Pan Jie, Tao Shengcai, et al. 2013. Spatial and temporal characteristics of drought/flood in linyi based on Standard Precipitation Index (SPI) in recent 51 years[J]. Arid Meteor, 31(4):695-701.<br/>张磊, 潘婕, 陶生才, 等. 2013.基于标准化降水指数的近51a山东临沂市旱涝时空特征[J].干旱气象, 31(4):695-701.
[40]Zhang Yuxing. 1998. Distribution of climatic type of Chinese desertification[J]. Arid Zone Res, 15(2):46-50.<br/>张煜星. 1998.中国荒漠化气候类型的分布[J].干旱区研究, 15(2):46-50.
[41]Zhong Jun. 2013. Temporal-spatial and probability of distribution of precipitation in China[D]. Nanjing:Nanjing University of Information Science% Technology, 1-57.<br/>钟军. 2013. 中国降水的时空和概率分布特征[D]. 南京: 南京信息工程大学, 1-57.
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