区域气象干旱特征多变量Copula分析——以阿克苏河流域为例" /> 区域气象干旱特征多变量Copula分析——以阿克苏河流域为例" /> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1000-0690-34-12-1480/img_2.jpg"/>区域气象干旱特征多变量Copula分析——以阿克苏河流域为例
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地理科学    2014, Vol. 34 Issue (12): 1480-1487     DOI: 10.13249/j.cnki.sgs.2014.012.1480
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区域气象干旱特征多变量Copula分析——以阿克苏河流域为例
张玉虎1(),刘凯利2,陈秋华2,胡欣欣1
1.首都师范大学资源环境与旅游学院,北京 100048
2.首都师范大学数学科学学院,北京 100048
Bivariate Probability Distribution of Meteorological Drought Characteristics in the Aksu Basin Using Copula
Yu-hu ZHANG1(),Kai-li LIU2,Qiu-hua CHEN2,Xin-xin HU1
1. College of Resources Environment&Tourism, Capital Normal University, Beijing 100048, China
2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
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摘要 

根据阿克苏河流域及其周边区域9个站点1960~2010年日降水资料,以降水距平百分率(Pa)指数表征气象干旱状况,构建了3种Archimedean Copula函数,通过4种方法(RMSE、AIC、BIC、Bayes)的检验,选出GH Copula作为最合适多变量干旱特征联合分布函数,并开展了研究区干旱特征两变量联合分布及重现期研究。结果表明:① 3种Archimedean Copula函数中GH Copula函数对研究区域干旱联合重现期分布的拟合效果最优;② 研究区整体上干旱风险较大,东部比西部干旱风险高,南部高于北部;③ 发生中等干旱和严重干旱时,阿拉尔和柯坪干旱风险增大,整体上“且”与“或”联合重现期的分布大体一致,发生长历时干旱时,干旱的严重程度也大,说明此区域的干旱特征对开展风险管理及应对很不利。

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张玉虎
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关键词 干旱Copula重现期干旱风险阿克苏河流域 
Abstract

Based on the daily precipitation data of 9 meteorological stations within and around the Aksu River Basin from 1960 to 2010, the distribution function of drought duration and drought severity were analyzed using Pa index by Curve fitting method and the Run theory. Though 4 statistical methods(eg.RMSE、AIC、BIC and Bayes), 3 kinds of Archimedean Copula were respectively employed to describe the joint distribution of the two drought characteristics variables. Finally, the spatial distribution status of the drought return periods of the 9 meteorologic stations were analyzed. The results are shown as follows. 1) To describe the joint distribution , the fitting effect of GH Copula is the best, Frank Copula’s is following. When using the curve fitting method to get the distribution function of drought duration, we can define the empirical frequency formula as experience frequency of the two-dimensional Copula function edge distribution. It can make the analysis based on the frequency of Copula function's result more objective and reliable. 2) The drought risk across the Aksu River Basin is very high. The estern and southern drought risk are higher than the western and northern. 3) The results also show that long-lasting droughts are highly probably the severe droughts. The results can provide theoretical support for the basin drought risk response and mitigation.

Key wordsdrought    copula funcion    return period    drought risk    the Aksu River Basin
收稿日期: 2013-10-27      出版日期: 2016-05-28
基金资助:国家十二五科技支撑计划课题 (No.2013BAC10B01、2012BAC19B0305) 资助
作者简介: 张玉虎(1975-), 男, 江苏徐州人, 博士, 讲师.主要从事区域水资源水环境评价与灾害风险研究.E-mail:zhang_yuhu@163.com
引用本文:   
张玉虎, 刘凯利, 陈秋华等 . 区域气象干旱特征多变量Copula分析——以阿克苏河流域为例[J]. 地理科学, 2014, 34(12): 1480-1487.
Yu-hu ZHANG, Kai-li LIU, Qiu-hua CHEN et al . Bivariate Probability Distribution of Meteorological Drought Characteristics in the Aksu Basin Using Copula[J]. SCIENTIA GEOGRAPHICA SINICA, 2014, 34(12): 1480-1487.
链接本文:  
http://geoscien.neigae.ac.cn/CN/10.13249/j.cnki.sgs.2014.012.1480      或      http://geoscien.neigae.ac.cn/CN/Y2014/V34/I12/1480
Fig. 1  研究区域和气象站位置
Fig.2  给定阈值时利用游程理论确定的干旱特征变量
Copula类型 θτ的关系 生成元φ
Gumbel-Hougaard Copula τ=1-1/θ(θ1 (-lnt)θ
Clayton Copula τ=θ/(θ+2)(θ&gt;0) 1θ(t-θ-1
Frank Copulas τ=1+4θ(1θ0θtet-1dt-1)(θ0 -lne-θt-1e-θ-1
Table 1  3种常用的Archimedean Copulas
Fig.3  各站点1960~2010年干旱历时与干旱严重程度
Fig. 4  阿克苏市干旱历时和干旱严重程度的分布曲线
GH Copula Clayton Copula Frank Copula
RMSE 44.40% 0 55.60%
AIC 66.70% 0 33.30%
BIC 100% 0 0
Bayes 100% 0 0
Table 2  Copula 拟合度评价
Fig.5  适线前后GH Copula检验参数值
Fig.6  干旱历时为3个月,单月降水量距平百分率为-70%对应的干旱严重程度时阿克苏河流域联合重现期空间分布
Fig.7  干旱历时为6个月,单月降水量距平百分率为-87.5%对应的干旱严重程度时阿克苏河流域联合重现期
Fig. 8  平均干旱水平下阿克苏河流域“且”和“或”联合重现期
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