﻿ 基于Copula函数的嘉陵江流域干支流洪水遭遇分析 Flood Coincidence Probability Analysis for Mainstream and Tributaries of the Jialing River Basin Based on Copula Function

Journal of Water Resources Research
Vol.06 No.05(2017), Article ID:21928,9 pages
10.12677/JWRR.2017.65054

Flood Coincidence Probability Analysis for Mainstream and Tributaries of the Jialing River Basin Based on Copula Function

Qixiang Ran, Chang Peng, Xuan Ling

Hydrology and Water Resources Survey Bureau of Upper Yangtze River, Bureau of Hydrology, CWRC, Chongqing

Received: Aug. 15th, 2017; accepted: Aug. 26th, 2017; published: Sep. 5th, 2017

ABSTRACT

Flood coincidence probability is a multivariable hydrologic event. At present, the research is mostly limited to the statistical analysis of observed data. In this study, the annual maximum flood peak data of four hydrological stations in Jialing River and its tributaries, including the Beibei, Xiaoheba, Luoduxi and Wusheng station, are selected for case study. The bivariate copula functions are introduced and used to construct the joint distributions of flood peak. The design flood and flood coincidence probability are computed for different return periods. The result shows that the flood coincidence probability of high return periods is smaller than low return periods. The flood coincidence probability of Jialing River and its tributaries in the same return periods, Qujiang River is greater than Jialing River, and Fujiang River is among the smallest. This study will provide a new approach for Flood encounter analysis.

Keywords:Jialing River Basin, Flood Coincidence Probability, Copula Function, Multivariable

1. 引言

2. Copula函数简述

Copula函数是定义域为均匀分布的多维联合分布函数，它可以将多个变量的边缘分布连接起来构造联合分布，它的表述如下：

(1)

1) Gumbel Copula函数。

(2)

Gumbel Copula函数的相关参数与传统的相关性和一致性测度常有一一对应的关系，Kendall秩相关系数的关系为

2) Clayton Copula函数。

(3)

Clayton Copula函数的相关参数与Kendall秩相关系数的关系为

3) Frank Copula函数。

(4)

Frank Copula函数的相关参数与Kendall秩相关系数的关系为。其中，式中，。函数被称为“Debye”函数。

3. 流域概况

4. 实例研究

4.1. 数据选择

Figure 1. Jialing River basin and hydrological station locations

4.2. 边缘分布

(5)

(6)

4.3. 联合分布

(7)

(a) 小河坝站(Xiaoheba station) (b) 武胜站(Wusheng station)
(c) 罗渡溪站(Luoduxi station) (d) 北碚站(Beibei station)

Figure 2. Fitting-figures of the marginal distributions

Table 1. Parameters and hypothesis test results of the marginal distributions

(8)

4.4. 联合分布重现期

Table 2. Parameters and fitting inspection values of the Copula joint distributions

Figure 3. Joint distribution and empirical probabilities of the observed combinations

4.5. 嘉陵江干支流遭遇分析

Figure 4. The joint (left) and co-occurrence return periods (right) of Jialing River and its tributaries

Table 3. Coincidence risk analysis of flood magnitudes of Jialing River and its tributaries (%)

(9)

5. 结论

Flood Coincidence Probability Analysis for Mainstream and Tributaries of the Jialing River Basin Based on Copula Function[J]. 水资源研究, 2017, 06(05): 459-467. http://dx.doi.org/10.12677/JWRR.2017.65054

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