Calculation of Early Warning Index of Mountain Torrent Disaster in Yushe County

Conference paper
Part of the Environmental Earth Sciences book series (EESCI)


According to the investigation of the disaster of mountain torrents in Yushe County, the disaster water level of the flood disaster prevention objective is determined with regard to the disaster situation of the village and the historical flood investigation of the small watershed. According to the “Shanxi Hydrological Calculation Manual” analysis of a design storm, combined with the actual situation in Shanxi, analysis determined the warning period and soil moisture content. Based on the hypothesis of rainstorm and flood of the same frequency, the same frequency anti-push method is used to reverse the disaster flow from the designed storm flood. The designed rainfall is the early warning rainfall in the early warning period, that is, the small rainfall warning index (immediate transfer of indicators). Through the analysis and calculation, the rainfall warning index of 0.5, 1 and 1.5 h of Yuhong County flood disaster prevention objective is determined, and the rationality of an early warning index is analyzed. The results show that the early warning index of the mountain flood disaster in Yuqi County is reasonable and reliable.


Mountain torrent disaster Critical rainfall Rainfall warning index Yushe County 

1 Introduction

A mountain torrents disaster is caused by floods and flash floods induced debris flow and landslides in the hilly area, which cause loss of the national economy and people’s lives and property [1]. The formation of mountain torrents is the result of the combination of various factors such as climate, topography, rainfall and underlying surface conditions [2]. A flash flood warning is an important part of the prevention of system flood disasters, which is an effective means of reducing casualties and property losses. The mountain flood disaster warning is based on weather, hydrological and other forecast information to predict the occurrence of flash floods that occur and to release the emergency instructions or signals. In the method of judging the critical flow or water level method and critical rainfall method, the critical rainfall method is the most widely used one at home and abroad [3, 4]. The concept of critical rainfall is widely found in the study of generalized mountain flood disaster prediction [4, 5, 6, 7], including landslide and debris flow, which is the key index of the forecast of mountain flood disaster and directly affects the rate of omission and empty reporting rate, which is the center of the work of mountain flood disaster prevention and control work.

The warning index of mountain flood disaster plays a key role in the operability of the flood protection plan and determines whether sufficient time is required when flash floods or debris flows occur. The general situation is based on historical rainfall and flash flood disaster data, terrain, topography, vegetation, and soil type to determine the revised and improved practical application. For the more abundant areas, it is usually measured by the actual rainfall statistics, storm critical curve method [8], water level or flow reversal method [7, 9] and comprehensive analysis and other calculations. For less data or no data areas, interpolation [5, 6], comparison [5, 6], disaster and rainfall frequency analyses were used [7, 10, 11]. Due to the scarcity of rain stations in Yushe County, many areas are monitoring the blank area, and the construction time is relatively late. The observation series is short and the observation means is backward, which is because of the severe shortage of rainstorms. In this paper, the critical rainfall is calculated by using the watershed model method.

2 Overview of Mountain Torrent Disaster in Yushe County

A mountain flood disaster is the highest frequency, the greatest harm to natural disasters in Yushe County, which are affected by the climate and the underlying surface. The main source of floods in Yushe County is the formation of rainfall, the convergence of the mountain slope steep, more rivers, ferocious flash floods convergence. In a few hours or less it can form a torrential flood, resulting in flash floods. Yushe County flood season is in early May to the end of September; the main flood season is concentrated in June–August. This time is also the Yushe County torrential disasters of the multiple period, the regional heavy rain intensity, steep mountains, quick convergence, flood steep rise and fall, with obvious mountain river characteristics. In the county since the founding of the disaster occurred in the year 1963, 1976, 1989, 1991, 1992, 1996, 1998, 2004, 2008, 2009, 2012, 2013, torrential disasters directly caused major casualties and property damage.

According to the investigation, there are 49 mountain flood disaster prevention objects that need to be heavily guarded by the threat of mountain torrent disaster in Yushe County to carry out analysis of early warning indicators. This paper lists the calculation of analyzed results as a typical example of early warning index analysis for Luo Xiu Village, Yushe County and Simma township.

3 Research Methods

3.1 Calculating Designed Flood

Calculation of the Design of Rainstorm. The statistical parameters of villages threatened by mountain torrential floods are read on the isoline map of statistical parameters of point rainstorm in Shanxi Hydrology Manual. The design point rainfall of various diachronic periods is calculated according to the parameters, and the design area rainfall is calculated according to the point surface reduction coefficient. Time history distribution is according to the design rain pattern. It mainly includes three steps: design point rainfall, design area rainfall and design rainstorm time distribution. According to the design rain pattern and the design rainfall results of the time period, the time history distribution of the time period design rainfall of each frequency is carried out by using the method of precipitation sequence of the time period.

Calculating Designed Flood. Design floods were the design of heavy rain by the production flow and the convergence calculation derived. In the calculation of the runoff yield of the watershed model, the design of net rainfall depth is calculated by using the hyperbolic tangent model. The net rain process is calculated by the variable loss rate deduction method. The integrated instantaneous unit hydrograph is used to calculate the confluence of the watershed model. In the design flood analysis, the river cross section along the river village is taken as the control section, and the calculation and analysis of the different frequency design floods are carried out. Each frequency designed flood result of Luo Xiu village control section is shown in Table 1.
Table 1

Luo Xiu village control section of the frequency design of the flood results

Flood elements

Reproduced flood element values

100 years

50 years

20 years

10 years

5 years

Peak flow (m3/s)






Flood volume (million m3)






Flood hydrograph (H)






Flood duration (h)






Peak water level (m)

3.2 Calculation of Rainfall Early Warning Index

Determination of Disaster Water Level and Control Section. According to the actual situation of the village section along the river, the hydraulic method is used to calculate the water surface line. The river section of the village along the river in Yushe County did not investigate the highest flood level in history, so the scope of design flood inundation once in 100 years is now defined as the dangerous area. It is determined that there are 49 dangerous river villages in Yushe county from the range of dangerous areas. The design flood water surface line is designed for 50 years, 20 years, 10 years and 5 years, respectively. According to the results of design flood surface line of each frequency, combined with the topography of villages along the river and the elevation of residential households, the flood inundation range of each frequency is drawn.

A comparison of the elevation of the residents on the side of the river and the water surface level of the river reach were used to determine flood level, and the specific method is:
  1. (1)

    According to the frequency design flood, the flooding range was used to determine the minimum design flooding period that can threaten households.

  2. (2)
    The residential households on the side of the river submerged by the design flood during the recurrence period are projected onto the vertical section, and the comparison between the elevation of the residential household and the design flood surface line during the recurrence period is drawn. The comparison between the elevation of residents and the line of water surface in Luo Xiu Village is shown in Fig. 1. Residential households below the water line represent the submerged.
    Fig. 1

    Luo Xiu village residents’ elevation and water line comparison diagram

  3. (3)

    The residential household height farthest from the water surface line determined in the last step is the flood level, and the nearest cross section from the household is the control section.

The water level-flow relationship of the control section is derived from the analysis of the frequency of the water surface line. The results are shown in Fig. 2.
Fig. 2

Luo Xiu village control section water level-discharge curve

According to the above water level-flow curve (Fig. 2), it can be seen that Luo Xiu village control sections of the water level flow relations are gentle. There are no bifurcations and tributaries of the river along the river control section, and they are relatively straightforward, with good representation; therefore, there is no need to correct the relationship diagram.

According to the above-mentioned water level-flow curve, the peak flow rate corresponding to the flood water level is deduced; at the same time, it refers to the flow frequency curve, and the disaster water level of the flood flow corresponds to the peak flow, which is determined by the interpolation method. The flood return period is then obtained as the river flood control capacity. The table of the flood level and its corresponding flood frequency in Yushi County is given in Table 2.
Table 2

Achievements of flood water level and corresponding flood frequency in Yushe County

Name of administrative division

Administrative division code

Disaster water level (m)

Peak flow (m3/s)

Frequency (%)

Luo Xiu village





According to the water level flow curve, as well as the disaster water level, the frequency of the design of the flood level of population and household statistics for Luo Xiu village, the flood control status evaluation is shown in Fig. 3.
Fig. 3

Luo Xiu village flood control status evaluation chart

Warning Period to Determine. The warning period is related to the confluence time of the river basin and is determined according to the following principles:
  1. (1)

    According to Yushe County characteristics of a rainstorm, the size of the basin area, the average ratio, the shape factor and the underlying surface, the basic warning period is 0.5, 1, 2, 3 and 6 h;

  2. (2)

    If the confluence time is not less than 6 h, the warning period is 0.5, 1, 2, 3 and 6 h as well as the confluence time. If the confluence time is less than 6 h, the warning period is set as the confluence time and the basic warning period is less than the confluence time.


Watershed soil water content: the use of “hydrological manual” in the basin before the water holding capacity \( B_{0} \) is an indirect indicator of soil moisture or soil moisture. \( B_{0} \) values of 0, 0.3 and 0.6, respectively, on behalf of the soil moisture is more dry, generally and more wet in three cases.

Calculation of Critical Rainfall. After determining the disaster water level, the warning period and the production and confluence analysis method, it is possible to calculate the water-holding capacity of different watersheds (\( B_{0} \)) for each typical period of the critical area of the critical rainfall. The specific calculation steps are as follows:
  1. (1)

    A maximum value is assumed in the second hours to maximum value in the sixth hours of the total rainfall initial value H. According to the design hyetograph, respectively, the maximum value in the second hours to maximum value in sixth hours the corresponding rainfall is P2′–P6′.

  2. (2)
    Calculation of the rainstorm parameters: The total rainfall value H1–H6 and rainfall value P2–P6 of the maximum value in the second hours to maximum value in sixth hours of different rainstorm parameters are calculated from the formulas (1) and (2). According to the range of rainstorm parameters in Table 3, it is possible to obtain multiple sets of P2–P6, and each group P2–P6 is compared with P2′–P6′. The parameter of P2–P6 with the smallest sum of squares is the required. The rainstorm parameters are as follows:
    Table 3

    Range of rainstorm parameters

    Rainstorm parameters












    $$ H_{p} \left( t \right) = \left\{ \begin{aligned} S_{p} \cdot t^{1 - n} ,\lambda \ne 0 \hfill \\ S_{p} \cdot t^{{1 - n_{s} }} ,\lambda = 0 \hfill \\ \end{aligned} \right.\begin{array}{*{20}l} \quad{ 0\le \lambda < 0.12} \hfill \\ {} \hfill \\ \end{array} $$
    $$ n = n_{S} \frac{{t^{\lambda } - 1}}{\lambda \,\ln t} $$
    In the formula, \( n \), \( n_{S} \), respectively, the slope of the curve between rainstorm duration and rainstorm intensity and the slope at \( t \) = 1 h in double logarithmic coordinate system; \( s_{p} \) for the design of rain force, that is, 1 h design rainfall, mm/h; \( t \) for the storm lasted, h; \( \lambda \) for empirical parameters.
  1. (3)

    For the value of the rainstorm parameter calculated from (2), the rainfall value of the maximum value in the second hours to maximum value in the sixth hours can be calculated by the Eqs. (1) and (2). According to the design hyetograph, a typical period of time per hour of rainfall Hp1, Hp2, …, Hp6 must be obtained.

  2. (4)

    The hyperbolic tangent flow model and the unit line basin convergence model were used to calculate the peak flow rate Qm formed by the rainfall in the typical period.

  3. (5)

    If 丨Qm − Q丨 > 1 m3/s, then with dichotomy to re-assume H, where Q is the flood level corresponding to the peak flow.

  4. (6)

    Repeat steps (2)–(5) until the丨Qm − Q丨is less than 1 m/s. the total amount of rainfall in each hour in a typical period is the critical rainfall.

According to the above calculation steps, the dynamic critical rainfall of 49 dangerous villages along the river village is obtained, and the dynamic critical rainfall results of Luo Xiu village are shown in Table 4. The warning of critical rainfall is drawn from the dynamic critical rainfall. The warning of critical rainfall curve is shown in Fig. 4.
Table 4

Results of dynamic critical rainfall in Yushe County

Name of administrative division

Administrative division code


Time period (h)

Rainfall (mm)

Luo Xiu village





1 (τ)





1 (τ)





1 (τ)


Fig. 4

Luo Xiu village warning rainfall critical curve

Estimation of Rainfall Early Warning Indicators.
  1. (1)

    Immediate transfer of indicators

Since the critical rainfall is calculated from the flood of the corresponding disaster water level, in the numerical form the critical rainfall is considered to be an immediate transfer of indicators.
  1. (2)

    Prepare transfer indicators


When the warning period is 0.5 h, prepare the transfer index = immediate transfer index × 0.7.

When the warning period is 1, 2, 3 and 6 h and the confluence time, the immediate transfer index of the first 0.5 h is the preparation index of the warning period.

Calculation results can be seen from Table 5.
Table 5

Yushe County early warning indicators results table

Name of administrative division



Time period (h)

Early warning indicator (mm)

Rainfall (mm)

Prepare for transport

Immediate transfer

Water level (m)

Luo Xiu cun

Rainfall amount






1 (τ)









1 (τ)




Analysis of Rationality of Rainfall Early Warning Index. Because of the limitations of the data conditions with only three years of data of Yushe County village along the river floods, the data series is shorter, and should not be used as a basis for comparison of design flood results. However, the field investigation of two historical floods in 2006, Shecheng town of Xiyadi river section of the catchment area is 51.7 km2 with peak flow of 35.6 m3/s, the watershed model method was used to calculate the design of floods in 100 years. The catching area of Shawang village in the town is 23.16 km2 and the peak flow rate is 44.8 m3/s in 5 years. Through the area ratio method, it can be seen that with the historical flood marks close; and the recurrence period is 3 years. The calculation result is reasonable. In 1970, Qicheng town of Shizhandao river section of the catchment area is 702 km2, the peak flow is 1190 m3/s, the catchment area of Wangjing Village in Qicheng town is 55.25 km2, and the peak flow rate is 137.15 m3/s in 5 years. Through the area ratio method, it can be seen that with the historical flood marks close and the recurrence period of 4 years, the calculation results are reasonable.

Based on the analysis, the calculation results of Shawang and Wang Jing Village are reasonable. The data and methods used in the calculation of the torrential floods in the villages threatened by the torrential floods, which are derived from the Handbook of Hydrology in Shanxi Province and Detailed verification, the design of the storm flood calculation results is reasonable.

4 Conclusion

In view of the complexity of the mountain channel, such as more wading buildings and serious river siltation, part of the river is occupied by man-made buildings, channel irregularity, bank slope low easy floodplain. In addition, there are factors such as measurement error, soil moisture content, roughness, specific drop error, design error, etc. The early warning index of a mountain flood disaster in a small watershed of Yushe County is not completely accurate, but through the analysis the results are more reasonable. According to the actual situation of Yushe County, the following suggestions are put forward: (1) The early warning index of a mountain flood disaster in Yushuan County can be placed on the early warning platform after the accumulation of hydrological data and rainfall data over a certain period of time. In the application process, there must be step-by-step optimization, in order to more accurately guide the mountain flood disaster prevention. (2) For the objects of defense in the same river basin, in order to facilitate management and application, if the current flood control capacity is basically the same, the same early warning index may be used; for a river basin, the villages along the upper and lower rivers must be linked up and down, and the information should be shared which is common defense.


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Authors and Affiliations

  1. 1.College of Water Conservancy and HydroelectricHebei University of EngineeringHandanChina

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