基于Copula函数的千米尺度综合干旱指数构建与应用—

基于Copula函数的千米尺度综合干旱指数构建与应用——以重庆市为例

杨辰飞, 吴田军, 王长鹏, 杨丽娟, 骆剑承, 张新

Construction and application of a comprehensive drought index based on Copula function on a kilometer scale: A case study of Chongqing, China

YANG Chenfei, WU Tianjun, WANG Changpeng, YANG Lijuan, LUO Jiancheng, ZHANG Xin

表1 二维Copula函数形式

Tab.1 Two-dimensional Copula function form

Copula类型		函数形式^①
Gaussian-copula	$p = C_{G a u s s i a n} (u, v) = Φ_{2} (Φ^{- 1} (u), Φ^{- 1} (v))$
t-copula	$p = C_{t} (u, v) = T_{2} (T^{- 1} (u), T^{- 1} (v))$
Gumbel-copula	$\begin{array}{l} p = C_{G u m b e l} (u, v) = \\ e x p {- [{(- l n u)}^{θ} + {(- l n v)}^{θ}]^{1 / θ}} \end{array}$
Clayton-copula	$p = C_{C l a y t o n} (u, v) = (u^{- θ} + v^{- θ} {- 1)}^{- 1 / θ}$
Frank-copula	$\begin{array}{l} p = C_{F r a n k} (u, v) = \\ - \frac{1}{θ} l n [1 + \frac{(e^{- θ u} - 1) (e^{- θ v} - 1)}{e^{- θ} - 1}] \end{array}$