水库调节地区东江流域非一致性水文极值演变特征、成因及影响

叶长青, 陈晓宏, 张家鸣, 张丽娟, 孔兰

Changing Properties, Causes and Impacts of Non-stationary Extreme Stream Flow Under the Changing Environment of Hydraulic Engineering Regulated Basin in Dongjiang River, China

Chang-qing YE, Xiao-hong CHEN, Jia-ming ZHANG, Li-juan ZHANG, Lan KONG

表3 水文频率分析的分布概率密度函数

Table 3 Distributions probability density function of hydrological frequency analysis

分布线型	概率密度函数	参数	特征
PT3	$\begin{matrix} f (x) = \frac{β^{α}}{Γ (α)} (x - a_{0})^{α - 1} \exp [- β (x - a_{0})] \end{matrix}$	尺度: $\begin{matrix} β \end{matrix}$ ;位置: $\begin{matrix} a_{0} \end{matrix}$ ;形状: $\begin{matrix} α \end{matrix}$	薄尾
GLO	$\begin{matrix} f (x) = \frac{1}{α} \frac{\exp [- (1 - k) y]}{[1 + \exp {(- y)]}^{2}} \end{matrix}$ 当 k≠0, y= k^-¹ln{1-k $\begin{matrix} ( \end{matrix}$ x-ξ $\begin{matrix} ) \end{matrix}$ /α}; 当 k=0, y= $\begin{matrix} ( \end{matrix}$ x-ξ $\begin{matrix} ) \end{matrix}$ /α.	尺度: $\begin{matrix} α \end{matrix}$ ;位置: ξ;形状: k	厚尾
GEV	$\begin{matrix} f (x) = \frac{1}{α} {\{1 - \frac{k (x - ξ)}{α}\}}^{(1 / k) - 1} \exp [- {\{1 - \frac{k (x - ξ)}{α}\}}^{\frac{1}{k}}] \end{matrix}$	尺度: $\begin{matrix} α \end{matrix}$ ;位置: ξ;形状:k	混尾
Weibull	$\begin{matrix} f (x) = \frac{k}{α} {(\frac{x - ξ}{α})}^{α - 1} \exp [- {(\frac{x - ξ}{α})}^{k}] \end{matrix}$	尺度: $\begin{matrix} α \end{matrix}$ ;位置: ξ;形状: k	薄尾
Gumbel	$\begin{matrix} f (x) = \frac{1}{α} \exp \{- (\frac{x - ξ}{α}) - \exp [- (\frac{x - ξ}{α})]\} \end{matrix}$	尺度: $\begin{matrix} α \end{matrix}$ ;位置: ξ	混尾
LN3	$\begin{matrix} f (x) = \frac{1}{(x - ξ) σ \sqrt{2 π}} \exp \{\frac{- {[\ln (x - ξ) - μ]}^{2}}{2 σ^{2}}\} \end{matrix}$	尺度: $\begin{matrix} σ \end{matrix}$ ;位置: ξ;形状: $\begin{matrix} μ \end{matrix}$	混尾