基于Copula函数的暴雨要素三维联合分布——以宽甸县为例

doi:10.13249/j.cnki.sgs.2017.04.014

地理科学 ›› 2017, Vol. 37 ›› Issue (4): 603-610.doi: 10.13249/j.cnki.sgs.2017.04.014

基于Copula函数的暴雨要素三维联合分布——以宽甸县为例

张野^1,²(), 王康³, 刘欣铭³, 张苏辰³, 周嘉³(), 王菜林⁴

1. 东北师范大学地理科学学院,吉林长春 130024
2. 齐齐哈尔大学理学院,黑龙江齐齐哈尔 161006
3. 哈尔滨师范大学地理科学学院,黑龙江哈尔滨 150025
4.北京师范大学/民政部/教育部减灾与应急管理研究院,北京 100875

收稿日期:2016-09-22 修回日期:2017-01-09 出版日期:2017-04-25 发布日期:2017-04-25
作者简介:
作者简介：张野(1982-),男,黑龙江海伦人,博士研究生,主要从事区域可持续发展研究。E-mail:zhangy853@nenu.edu.cn
基金资助:
哈尔滨科技局科技创新人才研究专项基金（2016RAXXJ037）,齐齐哈尔软科学项目（RKX-201409）,齐齐哈尔大学青年教师科研启动支持计划项目（2014K-M13）资助

The Three-dimensional Joint Distributions of Rainstorm Factors Based on Copula Function: A Case in Kuandian County, Liaoning Province

Ye Zhang^1,²(), Kang Wang³, Xinming Liu³, Suchen Zhang³, Jia Zhou³(), Cailin Wang⁴

1. College of Geographical Sciences, Northeast Normal University, Changchun 130024, Jilin, China
2. School of Science, QiqiharUniversity, Qiqihar 161006, Heilongjiang, China
3. College of Geographical Sciences, Harbin Normal University, Harbin 150025, Heilongjiang, China
4.Academy of Disaster Reduction and Emergency Management, Ministry of Civil Affairs & Ministry of Education, Beijing Normal University, Beijing 100875,China

Received:2016-09-22 Revised:2017-01-09 Online:2017-04-25 Published:2017-04-25
Supported by:
Harbin Science and Technology Bureau Special Fund for Scientific and Technical Innovation Talents (2016RAXXJ037), Soft Science Project of Qiqihar City(RKX-201409), Young Teachers’ Scientific Research Support Program of Qiqihar University (2014K-M13)

摘要/Abstract

摘要：

以辽宁省宽甸县为例,利用1955~2012年逐日降水数据,提取年暴雨日数（D₅₀）、年暴雨量（P₅₀）、年均暴雨强度（I）和暴雨比（R）共4个暴雨要素,运用K-S法确定各单要素最优概率分布函数;针对暴雨要素多面性,通过引入Copula函数,构建三维联合分布并进行AIC和RMSE优度检验,确定适合暴雨要素的最优Copula函数,分析多要素联合后暴雨的概率和重现期特征。研究表明： ① 单变量拟合仅反映暴雨单个要素本身的信息,无法涉及要素间的联系;三维Copula联合可从3方面呈现暴雨要素间的内在信息,更贴近实际;暴雨本身的多要素性,为Copula函数在暴雨分析上提供了广阔前景; ② 年暴雨日数、年暴雨量和年均暴雨强度的联合适合反映宽甸县暴雨重现期;宽甸县暴雨联合重现期短,多为0~2 a,同现重现期较长,集中于200 a左右;2种重现期变化趋势一致,存在同步效应,反映了暴雨要素的不可分割性。

关键词: Copula函数, 三维联合, 暴雨要素, 重现期

Abstract:

Taking Kuandian County in Liaoning Province as an example, the author extract four rainstorm factors: the annual rainstorm days, annual of rainstorm depth, annual average rainstorm intensity and rainstorm contribution, through the daily precipitation data from 1955 to 2012 and use the Kolmogorov-Smimov method to determine optimal probability distribution for each single factor. For the multifaceted rainstorm factor, we use AIC and RMSE test to confirm the best fitted copulas connect function suitable for rainstorm factor by introducing the copula function and building three-dimensional joint distribution, and analyze the probability of rainstorm and characteristics of return period with many combined factors. Research shows that: 1) The joint of annual rainstorm days, annual of rainstorm depth and annual average rainstorm intensity is suitable for reaction joint return period of rainstorm factor in Kuandian County; In Kuandian County, joint return period is short and distribute on 0-2 years, co-occurrence return period is longer, concentrated in around 200 years; the change trend of two kinds of return period is consistent, it has synchronization effect, this reflect inseparable of rainstorm factor. 2) The univariate reflect just one factor of information in rainstorm and doesn’t involved in the relationship between factors; Three-dimensional copulas joint can present the internal information between heavy elements from three aspects and closer to the actual; Multiple factors of rainstorm, as copulas function on the rainstorm analysis provides a broad prospects.

Key words: Copula function, three-dimensional joint, rainstorm factors, return period

中图分类号:

张野, 王康, 刘欣铭, 张苏辰, 周嘉, 王菜林. 基于Copula函数的暴雨要素三维联合分布——以宽甸县为例[J]. 地理科学, 2017, 37(4): 603-610.

Ye Zhang, Kang Wang, Xinming Liu, Suchen Zhang, Jia Zhou, Cailin Wang. The Three-dimensional Joint Distributions of Rainstorm Factors Based on Copula Function: A Case in Kuandian County, Liaoning Province[J]. SCIENTIA GEOGRAPHICA SINICA, 2017, 37(4): 603-610.

图/表 10

表1

4种三维Copula分布函数及参数范围"

	分布函数	参数范围
Frank	$- 1 θ ln$ {1+ $exp - θ u 1 - 1 exp - θ u 2 - 1 exp - θ u 3 - 1 exp - θ - 1 2$ }	（–∞,∞）\{0}
Clayton	$max u 1 ? θ + u 2 ? θ + u 3 ? θ - 2 - 1 θ$	[-1,∞]\{0}
Gumbel	$exp - ln u 1 θ + - ln u 2 θ + - ln u 3 θ (1 / θ)$	[1,∞]
AMH	$uvw 1 - θ (1 - u) (1 - v) (1 - w)$	[-1,1]

表1

图1

表2

图2

表3

暴雨要素边缘分布函数及参数"

暴雨要素	边缘分布	参数值
D₅₀	$F D d k = ∫ k d d! l n - k dd$	k=4.1579
I	$F D i k, s, m = ∫ 1 - exp - 1 - k i - m s 1 k di$	k=0.0012
		s=1.5709
		m=2.6711
P₅₀	$F D p k, s, m = ∫ 1 - exp - 1 - k p - m s 1 k dp$	k=0.0704
		s=16.964
		m=74.13
R	$F D r k, s, m = ∫ 1 - exp - 1 - k r - m s 1 k dr$	k=-0.296
		s=0.1224
		m=0.3784

表3

表4

图3

表5

表6

图4

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	D₅₀	I	P₅₀	R
GEV	0.1397^*	0.975^*	0.8935^*	0.9985^*
EV	0.0176	0.2135^*	0.088^*	0.7558^*
EXP	0.0313	0.0535^*	0.0000	0.0025
POISS	0.1397^*	0.0000	0.0535^*	0.0000
NORM	0.0006	0.0000	0.0000	0.0001
GP	0.088^*	0.4426^*	0.0006	0.1397^*

分布函数	参数及检验	D₅₀、I& P₅₀	D₅₀、I&R	D₅₀、P₅₀&R	I、P₅₀&R
Frank	参数	2.5117	13.9572	1.9848	5.5522
	RMSE	0.0521	0.0514	0.1658	0.1585
	AIC	-290.88	-292.448	-161.2544	-162.274
Clayton	参数	0.626	5.1859	0.3154	1.0428
	RMSE	0.0558	0.0531	0.1467	0.1430
	AIC	-283.1862	-288.7487	-174.958	-173.87
Gumbel	参数	1.2828	2.995	1.1973	1.8666
	RMSE	0.0572	0.0659	0.1724	0.1646
	AIC	-280.5228	-264.6426	-156.9166	-158.042
AMH	参数	0.379	0.9189	0.5705	0.8541
	RMSE	0.0541	0.0542	0.1752	0.1766
	AIC	-286.5932	-286.5251	-155.0723	-150.187

暴雨要素	年暴雨次数	年暴雨量	强度	站总雨量比
年暴雨次数	1
年暴雨量	0.887^**	1
强度	0.46^**	0.452^**	1
站总雨量比	0.840^**	0.917^**	0.423^**	1

T(a)	D₅₀			P₅₀		I			R			D₅₀,P₅₀,I			D₅₀,I,R
T(a)	(d)		n		(mm)	n		(mm)		n	(%)	n	T_a	T₀	T_a	T₀
2	2.4	39		233.6	40.96	73.4	44.89		0.247	40.67		1.43	3.04		1.39	3.01
5	3.4	28		346	26.19	84.5	27.42		0.337	26.85		3.12	20.45		3.05	20.09
10	4.4	17		421.9	18.71	88	17.85		0.391	21.09		5.06	28.2		4.92	30.1
20	5.3	11		493.6	14.01	99.5	13.49		0.407	12.39		6.81	133.15		6.62	103.27
50	5.6	6.6		544	7.57	109	8.50		0.46	9.42		13.7	214.28		12.56	206.73
100	6.3	6		629.4	6.30	116.6	6.13		0.489	6.57		33.27	547.19		31.4	512.97

基于Copula函数的暴雨要素三维联合分布——以宽甸县为例

The Three-dimensional Joint Distributions of Rainstorm Factors Based on Copula Function: A Case in Kuandian County, Liaoning Province

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