Evaluation of critical storm duration rainfall for a typical tributary of the Weihe River: a case study in the Qianhe River Basin
： 2018 - 12 - 07
： 2019 - 05 - 03
： 2019 - 05 - 09
1852 2 0

Abstract & Keywords
Abstract: Background, aim, and scope Climate variability is shown to be an important driver of spatial and temporal changes in hydro-meteorological system. And the influence of climate variability on flood damage has received more attention, especially for larger rivers, in China. The improvement of small and medium-sized river is still an especially important topic in the nation. Flood-prevention project have already implemented in the main stream and their tributaries for the Yellow River. However, extreme flood only occurred in small rivers with less convergence time and lack of flood control works. Upper and middle reaches of the Weihe River is mainly loess hilly-gully region, this can result in large economic losses when the storm has happened. Critical areal rainfall is a crucial indicator for the flood monitoring and forecasting, and also can benefit for river management. Materials and methods Calculation critical areal rainfall of flood are evaluated based on the hourly observed data of hydro-climatic time series for the period of 2006—2013, by using Thiessen Polygons method, power function with three parameters, non-liner regression model and probability distribution simulation, in a typical tributary of the Weihe River Basin. Results The results showed that power function with three parameters can simulate the statistic relationship between water level and discharge. The model can also display strong performance in well demonstrate the process of large typical flood in the Qianhe River. Cumulative precipitation before nine hours has great impact on discharge of monitoring cross section. Critical storm duration rainfall for Qianyang hydrological station increased up to 50 mm when the water level rise from 901m to flood exceeding the designed elevation, and the peak discharge also raised by 1418.51 m3/s. Log-Pearson 3 revealed high performance in simulate probability distribution of peak discharge in the study region. The corresponding critical areal rainfall for different return periods were computed, and water level raised more than 2 m when return period change from 10 years to 100 years. Discussion The power function with three parameters and non-liner regression model showed well performance in this study, however, advanced verification also should be taken when these methods used in other different weather conditions and complex terrains. Cumulative nine hours rainfall corresponding to the peak discharge was adopted in the article, and this time period should be dynamic change under local geographic conditions. Conclusions Disaster early warning information should be given to the public when the cumulative rainfall rose to 16 mm and the corresponding water level for the control hydrological station is 901 mm. Recommendations and perspectives Good knowledge of critical storm duration rainfall under the changing climate can provide great scientific and practical merits for flood simulation and forecast, and also benefit to in the water resource management in the basin scale for the government. More importantly, it can prevent disaster caused great damage to the society.
Keywords: flood; critical storm duration rainfall; stage-discharge relation curve; Weihe River Basin
IPCC第5次评估报告（AR5）根据新的观测事实，更为完善的归因分析和气候模式模拟结果，进一步确认了气候变暖的事实（IPCC，2013）。而气候变暖必然会改变全球和区域的水循环以及时空分布模式，增加水资源系统的复杂性和不确定性，从而导致更多的极端水文事件的发生（Labat et al，2004；Huntington，2006；陈亚宁等，2012；Lu and Guo，2019）。据统计，1949—2005年，我国气候水文事件造成的直接经济损失占灾害总损失的比重达到70%以上（黄崇福，2012）。气候变化导致洪水等极端水文事件的发生及其增加的水灾害风险正成为人类生存所面临的重大挑战（van der Wiel et al，2017）。

1   研究区概况

Fig.1 Basic geographic information for hydrological control station of Qianyang in the Qianhe River Basin
2   数据与方法
2.1   数据

2.2   方法

$P=\frac{1}{A}\sum _{i=1}^{n}pi*ai$

Fig.2 Distribution of Thiessen Polygons and their corresponding area (km2) in the Qianhe River Basin
3   研究结果
3.1   水位流量关系的建立

 年份 次数 日期、涉及区域暴雨规模（等级） 2006 2 最大暴雨过程：7月19—24日，部分地区中到大雨，局地大暴雨；次大暴雨过程：8月27日—9月2日，大部分地区中到大雨，部分地区大暴雨。 2007 2 最大暴雨过程：8月6—9日，部分地区中到大暴雨，局地特大暴雨；次大暴雨过程：7月17—20日，大部分地区中到暴雨，部分地区大暴雨。 2008 3 最大暴雨过程：7月19—21日，大部分地区中到大暴雨；次大暴雨过程：6月13—15日，24 h最大降雨量淳化站达83.8 mm；第3次暴雨过程：6月28—30日，24 h最大降雨量盘安站达72.6 mm。 2009 3 最大暴雨过程：8月2—4日，大部分地区中到特大暴雨；次大暴雨过程：8月28—29日，24 h最大降雨量新贯寺站达116.9 mm；第3次暴雨过程：7月21日前后，渭河下游局部地区中到大暴雨。 2010 1 7月22—24日，大部分地区中到特大暴雨，千河东风站12 h最大降水量达232.6 mm，24 h最大降水量为319.5 mm。 2011 3 最大暴雨过程：7月27—29日，大部分地区中到大暴雨；次大暴雨过程：8月15—25日，大部分地区中到特大暴雨；第3次暴雨过程：9月2—18日，大部分地区中到大暴雨。 2012 2 最大暴雨过程：9月1—20日，大部分地区中到大暴雨，特大暴雨；次大暴雨过程：7月20—21日，部分地区中到大暴雨。 2013 3 最大暴雨过程：6月19—20日，中上游部分地区中到大暴雨，特大暴雨；次大暴雨过程：7月21—25日，大部分地区中到大暴雨，局部特大暴雨；第3次暴雨过程：5月25—28日，中下游大部分地区中到大暴雨。

Fig.3 Statistical relationship between water level and discharge in 2006—2013

Fig.4 Conceptual model between water level and discharge
3.2   降水流量关系的建立

Fig.5 Flood hydrograph occurred from 2：00 AM on 23 rd, July 2010 in the Qianhe River Basin

Fig.6 Correlation coefficient between hourly water level and cumulative areal rainfall h hours before in the Qianyang hydrological station

Fig.7 Regression analysis between discharge and 9 hours cumulative areal rainfall
3.3   致洪临界面雨量阈值的确定

 防洪标准 汛期水位（m） 洪峰流量(m3/s) 致灾临界面雨量 (mm) 一般洪水 <=901 506.96 16.44 设防标准洪水 903.25 1001.55 39.34 撤离洪水 903.75 1287.32 49.69 溃堤洪水 水位上涨，超标准 1925.47 67.20
3.4   不同重现期致洪面雨量阈值的确定

Fig.8 K-S goodness of fit test for probability of peak discharge

 重现期Return period /a 水位Water level /m 洪峰流量Peak discharge /(m3/s) 临界面雨量Critical areal rainfall /mm 10 711.02 850.37 33 15 712.36 920.02 36 20 712.45 993.04 39 30 712.62 1150.94 45 50 712.95 1491.62 56 100 713.88 2730.66 83
4   结论

（1）所选取的三参数幂函数模型对水位与流量的关系模拟经度较高，模型能够模拟典型年份发生的洪水。
（2）洪水发生时，典型控制断面流量主要受前9 h累计降水影响，基于前9 h累计降水与流量建立的一元非线性回归模型具有较高的显著性。
（3）一般、设防标准、撤离以及溃堤等四个不同等级的洪水对应的临界面雨量阈值分别为16.44 mm、39.44 mm、49.69 mm和67.20 mm。
（4）对数皮尔逊Ⅲ型分布能够很好的模拟洪峰流量的概率分布，10年、15年、20年、30年、50年和100年重现期对应的临界面雨量阈值分别为33 mm，36 mm，39 mm，45 mm，56 mm和83 mm。

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CHENG Aifang

SU Xiewei

HUANG Rong

REN Yuanxin

Key Scientific Fund of Baoji University of Arts and Sciences (ZK16062); Program for Mountain Torrent Disaster Risk Survey, Zoning, and Impacts Assessment of Shaanxi Climate Centre; National Natural Science Foundation of China (41771048)

Journal of Earth Environment