区域气象干旱特征多变量Copula分析——以阿克苏河流域为例

doi:10.13249/j.cnki.sgs.2014.012.1480

摘要/Abstract

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(P_a)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。

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 words: drought, copula funcion, return period, drought risk, the Aksu River Basin

中图分类号:

K903

张玉虎, 刘凯利, 陈秋华, 胡欣欣. 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, Xin-xin HU. Bivariate Probability Distribution of Meteorological Drought Characteristics in the Aksu Basin Using Copula[J]. SCIENTIA GEOGRAPHICA SINICA, 2014, 34(12): 1480-1487.

图/表 10

图1

图2

表1

3种常用的Archimedean Copulas"

Copula类型	θ与τ的关系	生成元φ
Gumbel-Hougaard Copula	$τ = 1 - 1 / θ (θ  1$	$(- lnt) θ$
Clayton Copula	$τ = θ / (θ + 2) (θ > 0)$	$1 θ (t - θ - 1$
Frank Copulas	$τ = 1 + 4 θ (1 θ ∫ 0 θ t e t - 1 dt - 1) (θ ≠ 0$	$- ln e - θt - 1 e - θ - 1$

表1

图3

图4

表2

图5

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图7

图8

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