基于Γ函数的祁连山葫芦沟流域湿季小时降水统计特征

doi:10.11867/j.issn.1001-8166.2016.08.0840.

地球科学进展 ›› 2016, Vol. 31 ›› Issue (8): 840 -848. doi: 10.11867/j.issn.1001-8166.2016.08.0840.

王磊(

), 陈仁升 ^*(

), 宋耀选

1.中国科学院寒区旱区环境与工程研究所黑河上游生态—水文试验研究站,甘肃兰州 730000
2.中国科学院内陆河生态水文重点实验室,甘肃兰州 730000

收稿日期:2016-05-10 修回日期:2016-06-28 出版日期:2016-08-20
通讯作者: 陈仁升 E-mail:sdwanglei@lzb.ac.cn
基金资助:
国家重点基础研究发展计划项目“寒区流域水文过程综合模拟与预估研究”(编号:2013CBA01806);国家自然科学基金项目“黑河流域上游生态水文过程耦合机理及模型研究”(编号:91225302)资助

Study of Statistical Characteristics of wet Season Hourly Rainfall at Hulu Watershed with Γ Function in Qilian Mountains

Lei Wang( ), Rensheng Chen ^*( ), Yaoxuan Song

1.Qilian Alpine Ecology and Hydrology Research Station,Cold and Arid Regions Environmental and Engineering Research Institute, CAS, Lanzhou 730000,China
2.Key Laboratory of Inland Ecohydrology, CAS,LanZhou 730000,China

Received:2016-05-10 Revised:2016-06-28 Online:2016-08-20 Published:2016-08-20
Contact: Rensheng Chen E-mail:sdwanglei@lzb.ac.cn
Supported by:
Project supported by the National Basic Research Program of China “Research on estimation and simulation of hydrological process in region”(No.2013CBA01806);The National Natural Science Foundation of China “Coupling mechanism and model of eco-hydrological processes in the upper of Heihe River Basin”(No.91225302)

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高山区降水主要集中在湿季(5~9月),湿季小时降水的概率分布统计特征是研究山区降水分布的重要基础。选择祁连山中段典型流域为研究区,使用葫芦沟流域6个观测点2015年5~9月半小时降水数据,采用极大似然法对影响Γ分布函数的形状参数α和尺度参数β进行估计,并且对不同强度降水概率密度分布、累计概率密度以及降水概率与海拔和降水量关系进行分析。结果表明:形状参数α和尺度参数β呈明显负相关,形状参数α与小时平均降水量分布大致相同;在葫芦沟流域,除海拔因素外,局地地形也是影响降水再分配和降水概率分布的重要因素;在该流域,除降水事件增加外, 1~3 mm/h强度降水概率随着海拔增加而增加也是降水量随海拔增加而增加的主要原因。

关键词: Γ函数, 高海拔山区, 湿季小时降水, 概率密度

The probability distribution of the wet season hourly precipitation is the important basis for the study of the precipitation distribution, especially in mountainous areas. Hulu watershed is the study area located in the upper reaches of Heihe River, Qilian Mountains. By adopting the maximum likelihood estimation, the shape parameter α and scale parameter β of 6 stations were obtained with observed wet season (May to September) half hourly data, and different intensity precipitation probability density distribution, cumulative probability density and probability of precipitation and elevation and precipitation relationship were analyzed. The shape parameter α and scale parameter β is significantly negatively correlated, shape parameter α and average hourly precipitation distribution is consistent. Local topography is also an important factor to affect the precipitation redistribution and the probability distribution of precipitation in Hulu watershed. In addition to the increase of precipitation events, the probability of 1~3 mm mm/h precipitation increases with the altitude, which is the main reason for the increase of precipitation with altitude.

Key words: Γ function, Alpine mountains, Wet season hourly precipitation, Probability density.

中图分类号:

P426.6

表1 葫芦沟流域降水观测点信息

Table 1 Introduction of precipitation observation points in Hulu watershed

观测站	经度	纬度	海拔/m	雨雪量计
一号点二号点三号点四号点三角洲大本营	99°52.2'E 99°53.4'E 99°53.4'E 99°52.6'E 99°52.6'E 99°52.9'E	38°15.3'N 38°13.9'N 38°13.3'N 38°14.9'N 38°14.9'N 38°16.1'N	3 382 3 711 4 166 4 498 3 232 2 980	TRwS504 TRwS504 TRwS504 TRwS504 TRwS504 TRwS504

表1 葫芦沟流域降水观测点信息

Table 1 Introduction of precipitation observation points in Hulu watershed

观测站	经度	纬度	海拔/m	雨雪量计
一号点二号点三号点四号点三角洲大本营	99°52.2'E 99°53.4'E 99°53.4'E 99°52.6'E 99°52.6'E 99°52.9'E	38°15.3'N 38°13.9'N 38°13.3'N 38°14.9'N 38°14.9'N 38°16.1'N	3 382 3 711 4 166 4 498 3 232 2 980	TRwS504 TRwS504 TRwS504 TRwS504 TRwS504 TRwS504

表2 各观测点参数特征

Table 2 Parameter characteristics of each observation point

观测点	α	β	小时平均降水量/mm	样本总量 (n)
大本营	0.665	1.172	0.780	511
三角洲	0.779	1.242	0.967	514
一号点	0.859	1.178	1.011	491
二号点	0.627	1.534	0.961	616
三号点	0.701	1.527	1.071	622
四号点	0.945	1.137	1.075	632

表2 各观测点参数特征

Table 2 Parameter characteristics of each observation point

观测点	α	β	小时平均降水量/mm	样本总量 (n)
大本营	0.665	1.172	0.780	511
三角洲	0.779	1.242	0.967	514
一号点	0.859	1.178	1.011	491
二号点	0.627	1.534	0.961	616
三号点	0.701	1.527	1.071	622
四号点	0.945	1.137	1.075	632

图1 观测降水量概率密度与概率密度函数拟合对比
(a),(b),(c),(d),(e),(f)分别表示一号点、二号点、三号点、四号点、大本营、三角洲

Fig.1 Comparison of probability of observed precipitation and probability density function
(a),(b),(c),(d),(e),(f) represent the NO.1, NO.2, NO.3, NO.4,Dabenying, Delta

图2 形状参数 α和小时平均降水量

x ?

分布图
(a),(b)分别表示形状参数 α和小时平均降水量

x ?

分布

Fig.2 The distribution of the shape parameter ( α) and average hourly precipitation (

x ?

)
(a),(b)represent the shape parameter ( α) and average hourly precipitation (

x ?

) distribution respectively

图2 形状参数 α和小时平均降水量

x ?

分布图
(a),(b)分别表示形状参数 α和小时平均降水量

x ?

分布

Fig.2 The distribution of the shape parameter ( α) and average hourly precipitation (

x ?

)
(a),(b)represent the shape parameter ( α) and average hourly precipitation (

x ?

) distribution respectively

图3 观测降水量概率累计与概率密度函数累计对比
(a),(b),(c),(d),(e),(f)分别表示一号点、二号点、三号点、四号点、大本营、三角洲

Fig.3 Comparison of probability of observed precipitation and cumulative probability density
(a),(b),(c),(d),(e),(f) represent the NO.1, NO.2, NO.3, NO.4,Dabenying, Delta

图4 各观测点不同累计概率下小时降水阈值折线图

Fig.4 Precipitation threshold line chart of each observation point under different cumulative probability

表3 不同累计概率下降水阈值统计特征(单位:mm)

Table 3 Statistical characteristics of precipitation threshold under different cumulative probability (unit:mm)

观测站	10%	20%	30%	40%	50%	60%	70%	80%	90%
一号点	0.081	0.192	0.317	0.472	0.661	0.899	1.211	1.661	2.446
二号点	0.039	0.113	0.218	0.259	0.544	0.792	1.135	1.654	2.629
三号点	0.056	0.149	0.274	0.434	0.639	0.905	1.226	1.802	2.776
四号点	0.103	0.225	0.367	0.533	0.731	0.975	1.294	1.744	2.524
大本营	0.037	0.101	0.189	0.306	0.456	0.654	0.926	1.333	2.087
三角洲	0.063	0.157	0.276	0.426	0.606	0.839	1.152	1.607	2.417

表3 不同累计概率下降水阈值统计特征(单位:mm)

Table 3 Statistical characteristics of precipitation threshold under different cumulative probability (unit:mm)

观测站	10%	20%	30%	40%	50%	60%	70%	80%	90%
一号点	0.081	0.192	0.317	0.472	0.661	0.899	1.211	1.661	2.446
二号点	0.039	0.113	0.218	0.259	0.544	0.792	1.135	1.654	2.629
三号点	0.056	0.149	0.274	0.434	0.639	0.905	1.226	1.802	2.776
四号点	0.103	0.225	0.367	0.533	0.731	0.975	1.294	1.744	2.524
大本营	0.037	0.101	0.189	0.306	0.456	0.654	0.926	1.333	2.087
三角洲	0.063	0.157	0.276	0.426	0.606	0.839	1.152	1.607	2.417

图5 各观测点不同强度降水概率与海拔、降水量关系

Fig.5 The relationships between the precipitation probability of different observation points and the elevation and precipitation

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