[1]刘友存,霍雪丽,郝永红,等.Bayes统计模型在出山月均径流极小值研究中的应用[J].山地学报,2015,(04):425.
　LIU Youcun,HUO Xueli,HAO Yonghong,et al.A Bayesian Analysis of Monthly Average Runoff Minima in Mountain Areas[J].Mountain Research,2015,(04):425.
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Bayes统计模型在出山月均径流极小值研究中的应用()
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《山地学报》[ISSN:1008-2186/CN:51-1516]

卷:
期数:
2015年04期
页码:
425
栏目:
山地环境
出版日期:
2015-08-01

文章信息/Info

Title:
A Bayesian Analysis of Monthly Average Runoff Minima in Mountain Areas
作者:
刘友存;  霍雪丽;  郝永红;  崔玉环;  韩添丁;  沈永平;  王 建
1.天津师范大学 天津市水资源与水环境重点实验室, 天津 300387； 2.天津师范大学 城市与环境科学学院, 天津 300387； 3. 安徽农业大学 理学院, 安徽 合肥 230036; 4.中国科学院 寒区旱区环境与工程研究所, 甘肃 兰州 730000
Author(s):
LIU Youcun;  HUO Xueli;  HAO Yonghong;  CUI Yuhuan;  HAN Tianding;  SHEN Yongping;  WANG Jian
1.Tianjin Key Laboratory of Water Resources and Environment, Tianjin Normal University, Tianjin 300387, China; 2. College of Urban and Environmental Science, Tianjin Normal University, Tianjin 300387, China; 3. School of Science, Anhui Agriculture University,Anhui Hefei 230036, China; 4. Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences,Gansu Lanzhou 730000, China
关键词:
径流极小值; 广义Pareto分布; Markov Chain Monte Carlo (MCMC)方法; 乌鲁木齐河
Keywords:
runoff minima;  GPD model;  MCMC method;  rümqi River
分类号:
P333.3
文献标志码:
A
摘要:
数理统计方法在解决全球气候变化引起的洪水、干旱等极端水文事件中获得了越来越广泛的应用。选取乌鲁木齐河1958—2006年枯水期的月平均出山径流资料，采用广义Pareto极值分布（GPD）模型，并运用Bayes统计模型估计GPD的参数，最后对乌鲁木齐河枯水期月均出山径流极小值变化进行了估算。研究表明：1参数的初始值、先验分布的均值分别取其极大似然估计值，先验分布的标准差取较小值，随机游走项分布的标准差取较大值，这种方法能使Markov链快速收敛；2基于Bayes参数估计值的GPD在拟合月均径流量的极小值时具有很高的精确度，与传统的极大似然估计方法相比，Bayes统计模型的推断效果较好；3乌鲁木齐河重现期为10 a、25 a、50 a和100 a的枯水期月均径流极小值分别约为0.60 m3/s、0.44 m3/s、0.32 m3/s和0.20 m3/s; 4 100 a 重现水平的95%置信区间的下限为－0.238 m3/s，说明当乌鲁木齐河在枯水期遇上百年一遇的极小值时，有可能出现断流的情况。
Abstract:
Global warming has intensified hydrological extreme events and resulted in disasters around the world. For disaster management and adaption of extreme events, it is essential to improve the accuracy of extreme value statistical models. In this study, Bayes’ Theorem is introduced to estimate parameters in the Generalized Pareto Distribution (GPD) model which is applied to simulate the distribution of monthly average runoff minima during dry periods in mountain areas of rümqi River. Bayes’ Theorem treats parameters as random variables and provides machinery way to convert the prior distribution of parameters into a posterior distribution. Statistical inferences based on posterior distribution can provide a more comprehensive representation of the parameters. An improved Markov Chain Monte Carlo (MCMC) method, which can solve highdimensional integral computation in the Bayes equation, is used to generate parameter simulations from the posterior distribution. Model diagnosis plots are made to guarantee the fitted GPD model is appropriate. Then based on the GPD model with Bayesian parameter estimates, monthly average minima corresponding to different return periods can be calculated. The results show that the improved MCMC method is able to make Markov chains converge at a high speed. Compared with the GPD model based on maximum likelihood parameter estimates, the GPD model based on Bayesian parameter estimates obtain more accurate estimations of minimum monthly average runoff. Moreover, the monthly average runoff minima in dry periods corresponding to 10 a, 25 a, 50 a and 100 a return periods are 0.60 m3/s, 0.44 m3/s, 0.32 m3/s and 0.20 m3/s respectively. The lower boundary of 95% confidence interval of 100a return level is -0.238 m3/s, which implies that rümqi River is likely to cease when 100 a return level occurs in dry periods.

参考文献/References:

[1] IPCC. Working Group I Contribution to the IPCC Fifth Assessment Report (WGI AR5), Climate Change 2013: The Physical Science Basis: Summary for Policymakers [R/OL].
[2013-10-28]. http://www.climatechange2013.org/images/report/WG1AR5_SPM_FINAL.pdf
[2] Liu Weilong, Zhao Hui, Wang Xiaodan, et al. Review and evaluation of the effect of the climate change on the high altitude wetland ecosystem in Tibet Plateau [J].Mountain Research, 2014, 32(4):481-487[刘伟龙, 赵慧, 王小丹, 等. 气候变化下西藏高寒湿地生态系统研究的意义和特点[J]. 山地学报, 2014, 32(4): 481- 487 ]
[3] Huziy N O, Sushama L, Khaliq M N, et al. Analysis of streamflow characteristics over Northeastern Canadain a changing climate [J]. Climate Dynamics, 2013, 40: 1879-1901
[4] Dumas P, S. Hallegatte, P. Quintana-Segui,E. Martin. The influence of climate change on flood risks in Francefirst estimates and uncertainty analysis [J]. Natural Hazards and Earth System Sciences, 2013, 13(3), 809-821
[5] Peterson B J, Holmes R M, McClelland J W, et al. Increasing river discharge to the arctic ocean[ J ]. Science, 2002, 298: 2171-2173
[6] Douglas A Burns, Julian Klaus, Michael R McHale. Recent climate trends and implications for water resources in the Catskill Mountain region, New York, USA. Journal of Hydrology, 2007, 336(1), 155-170
[7] Liu Y, Ye B, Metivier F, et al. Preliminary study on reaction of mountain runoff to climate change in Urumqi River, China [A]. International Symposium on Water Resource and Environmental Protection, vol.3: 2350-2354. doi:10.1109/ISWREP.2011. 5893739
[8] Xia J, Du H, Zeng S, et al. Temporal and spatial variations and statistical models of extreme runoff in Huaihe River Basin during 1956—2010 [J]. Journal of Geographical Sciences, 2012, 22(6): 1045-1060
[9] Chen Yaning, Xu Changchun, YangYuhui, et al. Hydrology and water Resources variation and its responses to regional climate change in Xinjiang [J]. Acta Geographica Sinica, 2009, 64(11), 1331-1341 [陈亚宁, 徐长春, 杨余辉, 等. 新疆水文水资源变化及对区域气候变化的响应[J]. 地理学报, 2009, 64(11), 1331-1341]
[10] Wilby R L, Harris I. A framework for assessing uncertainties in climate change impacts: Lowflow scenarios for the River Thames, UK [J]. Water Resource Res, 2006, 42: W02419.
[11] Xv Ruolan, Chen Hua, Guo Jing. Impact of climate change on hydrological extreme events in upper reaches of the hanjiang river basin[J]. Journal of Beijing Normal University:Natural Science, 2010, 46(3): 383-386 [徐若兰, 陈华, 郭靖. 气候变化对汉江流域上游水文极值事件的影响[J]. 北京师范大学学报:自然科学版, 2010, 46(3): 383-386]
[12] Zhou Xudong, Yang Tao, Liang Huidi. Application of generalized extreme value distribution model to low water flow in headwater of Yellow River basin [J]. Water Resources and Power, 2013, 31(2): 12-14, 240 [周旭东, 杨涛, 梁慧迪. 广义极值分布模型在黄河源区枯季径流中的应用[J]. 水电能源科学, 2013, 31(2): 12-14, 240]
[13] Liu Y, Huo X, Liu Y, et al. Analyzing monthly average streamflow extremes in the upper rümqi River based on a GPD model [J]. Environmental Earth Sciences, 2015 (in press) doi:10.1007/s12665-015-4583-4
[14] Liu Y, Wu J, Liu Y, et al. Analyzing effects of climate change on streamflow in a glacier mountain catchment using an ARMA model [J]. Quaternary International, 2015, 358: 137-145. doi:10.1016/j.quaint.2014.10.001
[15] Xu Z X, Zhao F F, Li J Y. Response of streamflow to climate change in the headwater catchment of the Yellow River basin [J]. Quaternary International, 2008, 208( 1 /2) : 62-75
[16] Kumar R, Samaniego L, Attinger S. The effects of spatial discretization and model parameterization on the prediction of extreme runoff characteristics[J]. Journal of Hydrology, 2010, 392(1-2): 54-69
[17] Müller M, Kaspar M. Association between anomalies of moisture flux and extreme runoff events in the southeastern Alps[J]. Natural Hazards and Earth System Sciences, 2011, 11(3): 915-920
[18] Lan Yongchao, ZhongYingjun, Wu Sufen, et al. Sensitivity of mountain runoff of rivers originated from the south slope and the north slope of the Tianshan Mountain to climate change:Taking mountain runoff of Urumqi River and Kaidu River for example [J]. Journal of Mountain Science, 2009, 27(6), 712-718 [蓝永超, 钟英君, 吴素芬, 等. 天山南、北坡河流出山径流对气候变化的敏感性分析——以开都河与乌鲁木齐河出山径流为例 [J]. 山地学报, 2009, 27(6), 712-718]
[19] Paquet E, Garavaglia F, Garon R, et al. The SCHADEX method: a semicontinuous rainfallrunoff simulation for extreme flood estimation [J]. Journal of Hydrology, 2013, 495: 23-37
[20] Wang Yuefeng, Chen Xingwei, Chen Ying. Based on multiple time scales of SPI dry /wet conditions variation and identification of flood and drought events in Minjiang River of Fujian [J]. Mountain Research, 2014, 32(1):52-57 [王跃峰, 陈兴伟, 陈莹. 基于多时间尺度SPI 的闽江流域干湿变化与洪旱事件识别[J]. 山地学报, 2014, 32(1):52-57]
[21] Xia Jun, Liu Chunzhen, Ren Guoyu. Opportunity and Challenge of the Climate Change Impact on the Water Resource of China. Advances in the study of projection of climate change impacts on hydrological extremes [J]. Advances in Earth Science, 2011, 26(1): 1- 12 [夏军, 刘春蓁, 任国玉. 气候变化对我国水资源影响研究面临的机遇与挑战 [J]. 地球科学进展, 2011, 26(1): 1- 12]
[22] Coles S. An Introduction to Statistical Modeling of Extreme Values[M]. London : Springer. 2001.
[23] 史道济. 实用极值统计方法[M]. 天津: 天津科技出版社,2006. [Shi Daoji. Practical Methods of Extreme Value Statistics. Tianjin: Tianjin Science and Technology Press,2006.]
[24] Marshall L, Nott D, Sharma A. A comparative study of Markov chain Monte Carlo methods for conceptual rainfall-runoff modeling [J]. Water Resources Research, 2004, 40(2), W02501.
[25] Haario H, Sakaman E, Tamminem J. An adaptive Metropolis algorithm [J]. Bernoulli, 2001, 7(2): 223-242
[26] Bates BC, Campbell EP. A Markov chain Monte-Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling [J]. Water Resources Research, 2001, 37(4): 937-947
[27] Blasone RS, Vrugt JA, Madsen H, et al. Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling [J]. Advances in Water Resources, 2008, 31(4):630-648
[28] 卫晓蜻, 熊立华, 万民, 等. 融合马尔可夫链-蒙特卡洛算法的改进通用似然不确定性估计方法在流域水文模型中的应用[J]. 水利学报,2009, 40(4):464-480
[29] Xia Jun, Zhai Jinliang, Zhan chesheng. Some reflections on the research and of development water resources in China[J]. Advances in Earth Science, 2011, 26(9): 905- 915 [夏军, 翟金良，占车生. 我国水资源研究与发展的若干思考[J]. 地球科学进展, 2011, 26(9): 905- 915]
[30] Liu Y, Metivier F, Gaillardet J, et al. Erosion rates deduced from seasonal mass balance along the upper Urumqi River in Tianshan [J]. Solid Earth, 2011, 2(2):283-301
[31] Liu Y, Metivier F, Lajeunesse E, et al. Measuring bed load in gravel bed mountain rivers: averaging methods and sampling strategies [J]. Geodinamica Acta, 2008, 21(1-2):81-92
[32] Cowles M K and Carlin BP. Markov Chain Monte Carlo convergence diagnostics:a comparative review [J]. Journal of the American Statistical Association, 1996, 91(434): 883-904

备注/Memo

备注/Memo:
收稿日期(Received date)：2014-03-15；修回日期（Accepted）：2015-05-12。
基金项目（Foundation item）：国家自然科学基金(41471001、41272245、41401022、41001006);中国博士后科学
基金项目(20100480444).\[ The National Nature Science Foundation of China (41471001、41272245、41401022、41001006); China Postdoctoral Science Foundation (20100480444).\]
作者简介（Biography）：刘友存 (1977-), 男, 河北迁安人,理学博士学位, 主要从事寒旱区水文水资源、水文气象等方面的研究工作。 \[Liu Youcun, (1977-), male, Born in Qian'an of Hebei Province, Phd, mainly engaged in hydrology and water resources in cold and arid regions, and hydrometeorology.\] Email: liuyoucun@gmail.com; yliu@ipgp.fr
更新日期/Last Update: 1900-01-01