# A New Flash Flood Warning Scheme Based on Hydrodynamic Modelling

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Hydrodynamic Model

## 3. Materials and Methods

#### 3.1. Hazard Index

#### 3.2. Building Database of Critical Threshold Rainfalls

#### 3.2.1. Modelling Scenarios

#### 3.2.2. Calculation of Critical Rainfall

#### 3.3. Flood Warning Operation Flow

- (1)
- Determine the rainfall duration time according to the rainfall forecast.
- (2)
- Determine the antecedent soil moisture type according to the 5-day accumulated rainfall (Table 2).
- (3)
- Based on the rainfall duration and antecedent soil type determination, determine the corresponding critical rainfall from the database.
- (4)
- Calculate the accumulated rainfall at the decision moment, ${r}_{d}={\displaystyle \sum _{t=0}^{t={t}_{d}}{r}_{o}}$. Calculate the accumulated rainfall at the warning moment, ${r}_{w}={r}_{p}+{r}_{d}$. The calculation time steps for both ${r}_{d}$ and ${r}_{w}$ are 15 min for a 1-h rainfall duration, while they are 30 min for both 3-h and 6-h rainfall durations.
- (5)
- Compare the rainfall at the warning time, ${r}_{w}$, and the critical rainfall, ${r}_{c}$; if ${r}_{w}$ > ${r}_{c}$, send the warning information to the target community.

#### 3.4. Comparison with Existing Systems and Limitations

## 4. Case Study

#### 4.1. Introduction of Lengkou Catchment

^{2}, the main channel upstream of the outlet cross section (Lengkouxiang) is 17 km long, and the average longitudinal bed slope of the main channel is 1/400. There are three types of land cover in the Lengkou catchment: bust wood (14.1 km

^{2}), forest (61.4 km

^{2}), and loess (0.5 km

^{2}), and these values correspond to Manning roughness values of 0.075, 0.12, and 0.05 m

^{1/3}/s, respectively. The resolution of the DEM adopted for hydrodynamic modelling was 30 m × 30 m.

#### 4.2. Results

#### 4.2.1. Impact of Critical Hazard Index

#### 4.2.2. Impact of Rainfall Duration

#### 4.2.3. Impact of Antecedent Rainfall

#### 4.3. Example of Flood Warning Operation

- (1)
- According to the rainfall forecast (Table 3), the rainfall duration can be determined to be 3 h.
- (2)
- As the flood season of the Lengkou catchment occurs in the growing season and the antecedent rainfall is 30 mm, the initial soil saturation is classified as dry (Table 2).
- (3)
- Choose the critical rainfall for the catchment in relation to a 3-h rainfall duration and initial dry soil conditions from the critical rainfall database.
- (4)
- Compute the accumulative rainfall at the warning moment, such as the last row of Table 3.
- (5)
- Taking location P
_{a}as an example, the critical rainfalls are 35 mm and 40 mm for PE and IE, respectively. At decision time ${t}_{d}={t}_{3}$ = 1.0 h, the cumulative rainfall is 25 mm, and the rainfall forecasted for the next 30 min is 15 mm. Therefore, the cumulative rainfall at the warning time is 40 mm. If the rainfall intensity is assumed to be uniform during the next 30 min (i.e., from t = 1.0 to 1.5 h), the cumulative rainfall will reach 35 mm at t = 1.17 h (as shown in Figure 11). Thus, a PE warning will be sent to the people at P_{a}. The cumulative rainfall will reach 40 mm at ${t}_{w}$ = 1.5 h (as shown in Figure 12). Therefore, an IE warning should be sent to people at both locations P_{a}and P_{b}.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Graph of the Lengkou catchment. (

**a**) Location in Shanxi Province, (

**b**) digital elevation model (DEM), and (

**c**) topography with villages.

**Figure 3.**Distribution of critical rainfall of “Preparing Evacuation” (PE) for the case of initial dry soil condition (for the 1-h rainfall duration).

**Figure 4.**Distribution of critical rainfall of “immediate evacuation” (IE) for the case of initial dry soil condition (for the 1-h rainfall duration).

**Figure 5.**Critical rainfall distribution for “immediate evacuation” (IE) under initial wet soil conditions (for the 1-h rainfall duration).

**Figure 6.**Critical rainfall distribution for “immediate evacuation” (IE) under initial wet soil conditions (for the 3-h rainfall duration).

**Figure 7.**Critical rainfall distribution for “immediate evacuation” (IE) under initial wet soil conditions (for the 6-h rainfall duration).

**Figure 8.**Critical rainfall distribution for “preparing evacuation” (PE) under initial dry soil conditions (for the 3-h rainfall duration).

**Figure 9.**Critical rainfall distribution for “preparing evacuation” (PE) under initial medium wet soil conditions (for the 3-h rainfall duration).

**Figure 10.**Critical rainfall distribution for “preparing evacuation” (PE) under initial wet soil conditions (for the 3-h rainfall duration).

**Figure 11.**Critical rainfall distribution for “preparing evacuation” (PE) under initial dry soil conditions (zoomed in from Figure 8).

**Figure 12.**Critical rainfall distribution for “immediate evacuation” (IE) under initial dry soil conditions (for the 3-h rainfall duration).

Rainfall Duration (h) | Total Rainfall (mm) | Modelling Duration (h) | Number of Scenarios | Notes |
---|---|---|---|---|

1 | 10, 20, 30, 40, 50, 60, 70, 80 | 3 | 8 | Initial soil moistures are dry, medium, and saturated. |

3 | 10, 25, 40, 55, 70, 85, 100 | 6 | 7 | |

6 | 10, 30, 50, 70, 90, 110, 130, 150, 170 | 12 | 9 |

**Table 2.**Antecedent soil moisture classes according to the 5-day accumulated rainfall [45].

Antecedent Moisture Classes (AMC) | Total 5-day Antecedent Accumulated Rainfall (mm) | ${\mathit{\theta}}_{\mathit{i}}/{\mathit{\theta}}_{\mathit{s}}$ Ratio | |
---|---|---|---|

Dormant Season | Growing Season | ||

Dry | <12.7 | <35.5 | 1.0/3.0 |

Medium | 12.7~28.0 | 35.5~53.3 | 2.0/3.0 |

Saturated | >28 | >53.3 | 1.0 |

Time | ${\mathit{t}}_{1}$ | ${\mathit{t}}_{2}$ | ${\mathit{t}}_{3}$ | ${\mathit{t}}_{4}$ | ${\mathit{t}}_{5}$ | ${\mathit{t}}_{6}$ | ${\mathit{t}}_{7}$ |
---|---|---|---|---|---|---|---|

$\mathrm{Decision}\text{}\mathrm{time}\text{}{t}_{d}$ (h) | 0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 |

$\mathrm{Warning}\text{}\mathrm{time}\text{}{t}_{w}$ (h) | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 |

$\mathrm{Forecasted}\text{}\mathrm{rainfall}\text{}{r}_{p}$$\text{}\left(\mathrm{mm}\right)\text{}({t}_{k}$$~{t}_{k+1}$) | 10 | 10 | 15 | 10 | 15 | 5 | 0 |

$\mathrm{Observed}\text{}\mathrm{rainfall}\text{}{r}_{o}$$\text{}\left(\mathrm{mm}\right)\text{}({t}_{k-1}$$~{t}_{k}$) | 0 | 15 | 10 | 10 | 15 | 8 | 2 |

$\mathrm{Cumulative}\text{}\mathrm{rainfall}\text{}\mathrm{at}\text{}\mathrm{decision}\text{}\mathrm{time}\text{}{r}_{w}$ (mm) | 0 | 15 | 25 | 35 | 50 | 58 | 60 |

Cumulative rainfall at warning time: ${r}_{w}={r}_{p}+{r}_{d}$ | 10 | 25 | 40 | 45 | 65 | 63 | 60 |

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**MDPI and ACS Style**

Huang, W.; Cao, Z.; Huang, M.; Duan, W.; Ni, Y.; Yang, W.
A New Flash Flood Warning Scheme Based on Hydrodynamic Modelling. *Water* **2019**, *11*, 1221.
https://doi.org/10.3390/w11061221

**AMA Style**

Huang W, Cao Z, Huang M, Duan W, Ni Y, Yang W.
A New Flash Flood Warning Scheme Based on Hydrodynamic Modelling. *Water*. 2019; 11(6):1221.
https://doi.org/10.3390/w11061221

**Chicago/Turabian Style**

Huang, Wei, Zhixian Cao, Minghai Huang, Wengang Duan, Yufang Ni, and Wenjun Yang.
2019. "A New Flash Flood Warning Scheme Based on Hydrodynamic Modelling" *Water* 11, no. 6: 1221.
https://doi.org/10.3390/w11061221