山西短时强降水概率密度分布及灾害风险评价

doi:10.13866/j.azr.2025.11.03

摘要/Abstract

摘要： 利用山西省109个气象站点1981—2023年短时强降水资料和近12 a 980个区域气象站分钟降水数据及社会经济资料，采用概率密度计算，分析不同历时、不同等级的短时强降水概率密度空间分布特征，并采用模糊层次分析法、半梯形分布模型，对短时强降水概率密度大值区所在的垣曲县和晋城城区进行灾害风险评价,进而完成山西省短时强降水灾害风险区划。结果表明：（1） 1 h和6 h强降水概率密度具有南部大于北部、同纬度东、西山区大于中部盆地的分布特征。（2）垣曲县是40 mm≤R(1 h)<60 mm、80 mm≤R(1 h)<93 mm、110 mm≤R(6 h)<130 mm、130 mm≤R(6 h)<218 mm的概率密度最大值区域，晋城城区是20 mm≤R(1 h)<40 mm、 60 mm≤R(1 h)<80 mm、80 mm≤R(6 h)<110 mm的概率密度最大值区域。（3）将评价区域灾害风险分为低风险、次低风险、中风险、次高风险和高风险5个等级，根据评价区域目标层的权重向量和指标层的模糊综合评价结果，计算获得垣曲县和晋城城区最大隶属度分别为0.3195和0.7005，模糊综合评价结果分别为次高风险和高风险,评价结果与灾情调查结果吻合。（4）山西省灾害风险区划显示：晋城市大部、长治市中东部、运城市中北部、临汾东南部县区、吕梁的柳林县、太原的小店区以及晋中的局部县区和乡镇是短历时强降水灾害的高风险区。

关键词: 短历时强降水, 概率密度分布, 灾害风险, 模糊评价, 风险区划

Abstract:

Utilizing short-duration heavy precipitation data of 109 stations in Shanxi Province (1981-2023), minute precipitation data of 980 regional stations in past 12 years, and socioeconomic data, this study analyzes the spatial distribution characteristics of probability density for short-duration heavy precipitation with different durations and intensity levels through probability density calculations. The fuzzy analytic hierarchy process (FAHP) and semi-trapezoidal distribution model were employed to conduct disaster risk assessments for two high probability density areas: Yuanqu County and Jincheng Urban District. The results show that: (1) The probability density of the short-duration heavy precipitation of 1 hour and 6 hours has the same distribution characteristics: It is higher in the south than in the north, higher in the eastern and western mountainous areas than in the central basin at the same latitude. (2) Yuanqu County is the region with the maximum probability density for 1-hour rainfall in the ranges of 40 mm≤R(1 h)<60 mm, 80 mm≤R(1 h)<93 mm, and for 6-hour rainfall in the ranges of 110 mm≤R(6 h)<130 mm, 130 mm≤R(6 h)<218 mm; Jincheng Urban Area is the region with the maximum probability density for 1-hour rainfall in the ranges of 20 mm≤R(1 h)<40 mm, 60 mm≤R(1 h)<80 mm, and for 6-hour rainfall in the range of 80 mm≤R(6 h)<110 mm. (3) For the evaluated area, disaster risks are classified into five levels: low risk, sub low risk, medium risk, sub high risk, and high risk. Based on the weight vector of the target layer and the fuzzy comprehensive evaluation results of the indicator layer for the evaluated area, the maximum membership degrees of Yuanqu County and Jincheng City are calculated to be 0.3195 and 0.7005, respectively, with fuzzy comprehensive evaluation results indicating secondary high risk and high risk. The evaluation results are consistent with the disaster investigation findings. (4) The provincial disaster risk zoning indicates that the high-risk areas for short-duration heavy precipitation disasters encompass most of Jincheng City, the central and eastern regions of Changzhi City, the north-central sections of Yuncheng City, southeastern counties and districts of Linfen, Liulin County in Luliang, Xiaodian District in Taiyuan, as well as specific counties and townships within Jinzhong.

Key words: short-duration heavy precipitation, probability density distribution, disaster risk, fuzzy assessment, risk zoning

屈志勇, 苗爱梅, 王洪霞. 山西短时强降水概率密度分布及灾害风险评价[J]. 干旱区研究, 2025, 42(11): 1982-1993.

QU Zhiyong, MIAO Aimei, WANG Hongxia. Probability density distribution characteristics of short-duration heavy precipitation and evaluation of disaster risk in Shanxi Province[J]. Arid Zone Research, 2025, 42(11): 1982-1993.

图/表 12

图1

表1

图2

图3

表2

短历时强降水灾害风险评价层次结构模型"

目标层	指标层	基础层
短历时强降水灾害风险评价 $A$	致灾因子危险性 $A 1$	1 h降水量≥20 mm的概率密度 $a 1$
		1 h降水量历史极值 $a 2$ （mm）
		6 h降水量≥50 mm的概率密度 $a 3$
		6 h降水量历史极值 $a 4$ （mm）
		12 h降水量历史极值 $a 5$ (mm)
	孕灾环境敏感性 $A 2$	地质环境因子（地质灾害易发分区） $a 6$ (%)
	孕灾环境敏感性 $A 2$	河网密度 $a 7$ （ $k m$ ·km^-2）
	承灾体易损性 $A 3$	人口密度 $a 8$ （人·km^-2）
		GDP密度 $a 9$ (10⁸元·km^-2)
		公路密度 $a 10$ [km·（100km²）^-1]
		耕地面积比 $a 11$ （%）

表2

表3

评价区域评价因子实际参数"

评价区域	评价因子
评价区域	$a 1$ /10^-5	$a 2$ /mm	$a 3$ /10^-5	$a 4$ /mm	$a 5$ /mm	$a 6$ /%	$a 7$ /( $k m$ ·km^-2)	$a 8$ /(人·km^-2)	$a 9$ /(10⁸元·km^-2)	$a 10$ /[km·（100km²）^-1]	$a 11$ /%
垣曲县	26.9	81.5	21.7	179.4	231.8	66	0.1	119	0.061	65.06	16.23
晋城城区	27.6	78.7	21.7	217.5	223.9	98	0.3	4103	2.3	102.44	31.0

表3

表4

判断矩阵权重系数和一致性检验参数"

矩阵	$w 1$	$w 2$	$w 3$	$w 4$	$w 5$	$λ m a x$	$C I$	$C R$
$A$	0.49	0.312	0.198	-	-	3.070	0.035	0.067
$A 1$	0.326	0.188	0.188	0.188	0.111	5.228	0.057	0.050
$A 2$	0.750	0.250	-	-	-	2.000	0.000	0.000
$A 3$	0.435	0.234	0.234	0.097	-	4.022	0.007	0.008

表4

表5

层次总排序"

评价因子	$A 1$	$A 2$	$A 3$	层次总排序权重	评价因子	$A 1$	$A 2$	$A 3$	层次总排序权重
评价因子	0.490	0.312	0.198	层次总排序权重	评价因子	0.490	0.312	0.198	层次总排序权重
$a 1$	0.326	-	-	0.159740	$a 7$	-	0.250	-	0.078000
$a 2$	0.188	-	-	0.092120	$a 8$	-	-	0.435	0.086130
$a 3$	0.188	-	-	0.092120	$a 9$	-	-	0.234	0.046332
$a 4$	0.188	-	-	0.092120	$a 10$	-	-	0.234	0.046332
$a 5$	0.111	-	-	0.054390	$a 11$	-	-	0.097	0.019206
$a 6$	-	0.750	-	0.234000

表5

表6

短历时强降水灾害评价因子风险等级赋值"

评价因子	$E 1$	$E 2$	$E 3$	$E 4$	$E 5$
$a 1$ /10^-5	<11.0	11.0~13.8	13.9~16.5	16.6~20.3	20.4~27.7
$a 2$ /mm	<20.0	20~39.9	40~59.9	60~79.9	80~99.9
$a 3$ /10^-5	<4.76	4.76~6.79	6.8~8.49	8.5~10.49	10.5~21.8
$a 4$ /mm	<50.0	50~79.9	80~129.9	130~179.9	180~218.5
$a 5$ /mm	<80.0	80~109.9	110~149.9	150~199.9	200~250.0
$a 6$ /%	<3.0	3.0~10.0	10.0~33.9	34~66.9	67~99.9
$a 7$ /（ $k m$ ·km^-2）	0~0.03	0.03~0.09	0.1~0.19	0.2~0.29	0.3~0.39
$a 8$ /（人·km^-2）	1~99	100~999	1000~1999	2000~2999	3000~4200
$a 9$ /（10⁸元·km^-2）	0~0.01	0.011~0.03	0.031~0.05	0.051~1.05	1.051~3.39
$a 10$ /[km·(100 km²)^-1]	0~39.99	40~55.99	56~69.99	70~99.99	100~130.99
$a 11$ /%	1~10.0	10.1~15.0	15.1~20.0	20.1~30.0	30.1~40.0

表6

表7

垣曲县短历时强降水灾害评价因子隶属度"

隶属度	评价因子
隶属度	$a 1$ /10^-5	$a 2$ /mm	$a 3$ /10^-5	$a 4$ /mm	$a 5$ /mm	$a 6$ /%	$a 7$ /( $k m$ ·km^-2)	$a 8$ /(人·km^-2)	$a 9$ /(10⁸元·km^-2)	$a 10$ /[ $k m$ ·(100 km²)^-1]	$a 11$ /%
$E 1$	-	-	-	-	-	-	-	0.999	-	-	-
$E 2$	-	-	-	-	-	-	0.9	0.022	-	0.352	0.754
$E 3$	-	-	-	-	-	-	0.1	-	-	0.648	0.246
$E 4$	-	-	-	0.99	-	0.973	-	-	0.011	-	-
$E 5$	0.892	0.08	0.991	-	0.637	-	-	-	-	-	-

表7

表8

晋城城区短历时强降水灾害评价因子隶属度"

隶属度	评价因子
隶属度	$a 1$ /10^-5	$a 2$ /mm	$a 3$ /10^-5	$a 4$ /mm	$a 5$ /mm	$a 6$ /%	$a 7$ /( $k m$ ·km^-2)	$a 8$ /(人·km^-2)	$a 9$ /(10⁸元·km^-2)	$a 10$ /[ $k m$ ·(100 km²)^-1]	$a 11$ /%
$E 1$	-	-	-	-	-	-	-	-	-	-	-
$E 2$	-	-	-	-	-	-	-	-	-	-	-
$E 3$	-	-	-	-	-	-	-	-	-	-	-
$E 4$	-	0.94	-	-	-	-	-	-	-	-	-
$E 5$	0.986	-	0.991	0.974	0.479	0.942	0.1	0.919	0.534	0.079	0.1

表8

图4

参考文献 23

[1]	Deshpande N R, Kulkarni A, Kumar K Krishna. Characteristic features of hourly rainfall in India[J]. International Journal of Climatology, 2012, 32(11): 1730-1744. doi: 10.1002/joc.v32.11
[2]	Xiao Chan, Yuan Weihua, Yu Rucong. Diurnal cycle of rainfall in amount, frequency, intensity, duration, and the seasonality over the UK[J]. International Journal of Climatology, 2018, 38(13): 4967-4978. doi: 10.1002/joc.2018.38.issue-13
[3]	苗爱梅, 王洪霞, 武捷. 山西不同历时强降水的统计特征及趋势变化[J]. 高原气象, 2020, 39(4): 796-807. doi: 10.7522/j.issn.1000-0534.2019.00069
	[ Miao Aimei, Wang Hongxia, Wu Jie. Statistical characteristics and trend change of different duration short-duration heavy rainfallin Shanxi province[J]. Plateau Meteorology, 2020, 39(4): 796-807. ] doi: 10.7522/j.issn.1000-0534.2019.00069
[4]	袁征, 张志高, 闫瑾, 等. 1960—2020年黄河流域不同等级降水时空特征[J]. 干旱区研究, 2024, 41(8): 1259-1271. doi: 10.13866/j.azr.2024.08.01
	[ Yuan Zheng, Zhang Zhigao, Yan Jin, et al. Spatiotemporal characteristics of different grades of precipitation in Yellow River Basin from 1960 to 2020[J]. Arid Zone Research, 2024, 41(8): 1259-1271. ] doi: 10.13866/j.azr.2024.08.01
[5]	杨霞, 江远安, 张林梅, 等. 哈密市伊吾县峡沟水库集水区汛期降水特征[J]. 干旱区研究, 2024, 41(5): 753-764. doi: 10.13866/j.azr.2024.05.04
	[ Yang Xia, Jiang Yuan’an, Zhang Linmei, et al. Analysis of precipitation characteristics in the Xiagou reservoir watershed in Yiwu County, Hami City, during the rainy season[J]. Arid Zone Research, 2024, 41(5): 753-764. ] doi: 10.13866/j.azr.2024.05.04
[6]	周子涵, 王基鑫, 刘维成, 等. 甘肃省暖季降水日变化特征[J]. 干旱区研究, 2024, 41(8): 1-12.
	[ Zhou Zihan, Wang Jixin, Liu Weicheng, et al. Diurnal variation characteristics of warm season precipitation[J]. Arid Zone Research, 2024, 41(1): 1-12. ] doi: 10.13866/j.azr.2024.01.01
[7]	赵玉娟, 路亚奇, 张洪芬, 等. 基于模糊数学的甘肃河东地区短时暴雨的大气环境参数综合评价研究[J]. 干旱区研究, 2023, 40(4): 543-551. doi: 10.13866/j.azr.2023.04.03
	[ Zhao Yujuan, Lu Yaqi, Zhang Hongfen, et al. Comprehensive evaluation of atmospheric environmental parameters ofshort-duration rainstorm in Hedong region of Gansu Province basedon fuzzy mathematics[J]. Arid Zone Research, 2023, 40(4): 543-551. ] doi: 10.13866/j.azr.2023.04.03
[8]	王娜娜, 韩磊, 柳利利, 等. 银川平原夏半年不同等级降雨水汽输送机制[J]. 干旱区研究, 2023, 40(9): 1404-1413. doi: 10.13866/j.azr.2023.09.04
	[ Wang Nana, Han Lei, Liu Lili, et al. Water vapor transport mechanisms for varied precipitation grades during thesummer half-year in Yinchuan Plain[J]. Arid Zone Research, 2023, 40(9): 1404-1413. ] doi: 10.13866/j.azr.2023.09.04
[9]	谌芸, 孙军, 徐珺, 等. 北京721特大暴雨极端性分析及思考(一)观测分析及思考[J]. 气象, 2012, 38(10): 1255-1266.
	[ Shen Yun, Sun Jun, Xu Jun, et al. Analysis and thinking on the extremes of the 21 July 2012 torrential rain in Beijing Part I: Observation and thinking[J]. Meteorological Monthly, 2012, 38(10): 1255-1266. ]
[10]	崔慧慧, 李荣, 郜彦娜, 等. “7·20”郑州极端特大暴雨降水细节特征和成灾过程研究[J]. 灾害学, 2023, 38(2): 114-120, 149.
	[ Cui Huihui, Li Rong, Gao Yanna, et al. Study on the precipitation details and disaster formation process of “7·20” extreme rainstorm in Zhengzhou[J]. Journal of Catastrophology, 2023, 38(2): 114-120, 149. ]
[11]	苏爱芳, 吕晓娜, 崔丽曼, 等. 郑州“7.20”极端暴雨天气的基本观测分析[J]. 暴雨灾害, 2021, 40(5): 445-454.
	[ Su Aifang, Lyu Xiaona, Cui Liman, et al. The basic observational analysis of “7.20”extreme rainstorm in Zhengzhou[J]. Torrential Rain and Disasters, 2021, 40(5): 445-454. ]
[12]	王洪霞, 苗爱梅, 邱贵强, 等. “0711”山西晋城极端强降水过程的宏微观特征分析[J]. 高原气象, 2023, 42(5): 1232-1246. doi: 10.7522/j.issn.1000-0534.2022.00103
	[ Wang Hongxia, Miao Aimei, Qiu Guiqiang, et al. Macro and micro characteristics of extreme heavy rainfall process in Jincheng of Shanxi Province on 11 July 2021[J]. Plateau Meteorology, 2023, 42(5): 1232-1246. ] doi: 10.7522/j.issn.1000-0534.2022.00103
[13]	邓雪, 李家铭, 曾浩健, 等. 层次分析法权重计算方法分析及其应用研究[J]. 数学的实践与认识, 2012, 42(7): 93-100.
	[ Deng Xue, Li Jiaming, Zeng Haojian, et al. Research on computation methods of AHP wight vector and its applications[J]. Mathematics in Practice and Theory, 2012, 42(7): 93-100. ]
[14]	汪志红, 王斌会. 投影寻踪技术在突发事件风险分类评级中的应用——以广东省雷电灾害风险评价为例[J]. 灾害学, 2011, 26(3): 78-82.
	[ Wang Zhihong, Wang Binhui. Application of projection pursuit technology in emergency risk classification and rating-A case study on assessment of lightning disaster in Guangdong Province[J]. Journal of Catastrophology, 2011, 26(3): 78-82. ]
[15]	徐建新, 闫旖君. 基于变异系数法的灰色关联决策模型在城市供水方案优选中的应用[J]. 水资源与水工程学报, 2007, 18(4): 9-11.
	[ Xu Jianxin, Yan Yijun. Application of gray correlative decision-making model for the optimization of water supply scheme based on the variation coefficient method[J]. Journal of Water Resources & Water Engineering, 2007, 18(4): 9-11. ]
[16]	强欣欢, 高文文, 王博, 等. 基于遥感的土壤盐渍化风险评估及其演变规律[J]. 干旱区研究, 2025, 42(3): 431-444. doi: 10.13866/j.azr.2025.03.04
	[ Qiang Xinhuan, Gao Wenwen, Wang Bo, et al. Remote sensing-based risk assessment of soil salinization and its change over time[J]. Arid Zone Research, 2025, 42(3): 431-444. ] doi: 10.13866/j.azr.2025.03.04
[17]	于月鹏, 刘洋, 赵云鹏. 基于模糊层次分析法的汶川锄头沟泥石流危险性评价研究[J]. 东北水利水电, 2024, 42(10): 22-25, 53.
	[ Yu Yuepeng, Liu Yang, Zhao Yunpeng. Study on mudslide risk assessment in Chutougou Valley of Wenchuan based on fuzzy analytic hierarchy process[J]. Water Resources & Hydropower of Northeast, 2024, 42(10): 22-25, 53. ]
[18]	山西省统计局, 国家统计局山西调查总队. 2021山西统计年鉴[M]. 北京: 中国统计出版社, 2021: 200-279.
	[ Shanxi Provincial Bureau of Statistics, Shanxi Survey Team of National Bureau of Statistics.2021 Shanxi Statistical Yearbook[M]. Beijing: China Statistics Press, 2021: 200-279. ]
[19]	马丽, 苗爱梅, 董春卿, 等. “0713”山西短时强降水天气的潜势及触发条件分析[J]. 大气科学学报, 2020, 43(4): 663-672.
	[ Ma Li, Miao Aimei, Dong Chunqing, et al. Analysis of the potential and triggering characteristics of short-term heavy precipitation in Shanxi on July 13, 2018[J]. Transactions of Atmospheric Sciences, 2020, 43(4): 663-672. ]
[20]	苗爱梅, 郝振荣, 贾利冬, 等. “0702”山西大暴雨过程的多尺度特征[J]. 高原气象, 2014, 33(3): 786-800. doi: 10.7522/j.issn.1000-0534.2013.00014
	[ Miao Aimei, Hao Zhenrong, Jia Lidong, et al. The multi-scale features of “0702” heavy rainstorm process[J]. Plateau Meteorology, 2014, 33(3): 786-800. ] doi: 10.7522/j.issn.1000-0534.2013.00014
[21]	周雅清, 胡桃花, 王弢, 等. 山西省汛期短历时强降水特征[J]. 沙漠与绿洲气象, 2021, 15(6): 40-46.
	[ Zhou Yaqing, Hu Taohua, Wang Tao, et al. Characteristics of short duration heavy rainfall during flood seasonin Shanxi Province[J]. Desert and Oasis Meteorology, 2021, 15(6): 40-46. ]
[22]	金磊. 山西夏季短历时强降水系统配置及关键物理量阈值的研究[D]. 兰州: 兰州大学, 2017.
	[ Jin Lei. Study of Summer Short-duration Heavyprecipitation and Thresholds of Key Physicalvariables in Shanxi province[D]. Lanzhou: Lanzhou University, 2017. ]
[23]	申欣凯, 吕义清, 张静, 等. 基于ArcGIS的山西省暴雨灾害风险评估[J]. 国土资源科技管理, 2020, 37(1): 61-73.
	[ Shen Xinkai, Lyu Yiqing, Zhang Jing, et al. Risk assessment of rainstorm disaster in Shanxi Province based on ArcGIS[J]. Scientific and Technological Management of Land and Resources, 2020, 37(1): 61-73. ]

级序	1 h雨强级界/mm	6 h雨强级界/mm
1	20~39.9	50~79.9
2	40~59.9	80~109.9
3	60~79.9	110~129.9
4	80~93	130~218