# Estimation of Flood Travel Time in River Network of the Middle Yellow River, China

## Abstract

**:**

^{3}/s) were estimated with calibrated parameters. Thirdly, an empirical formula based on simulated results was fitted. This empirical formula could be used to describe the relation between discharges, distances to Tongguan Hydrology Station, and the FTT. Analyses showed that the discharges with minimum FTT were different for different tributaries. For the river reach between Wubu Hydrology Station and the Wuding River, the discharge and corresponding minimum FTT were 6000 m

^{3}/s and approximately 30.4–34 h, respectively. For the river reach between the Zhouchuan and Qingjian Rivers, the discharge and FTT were 3000–3500 m

^{3}/s and 21–26.8 h, respectively. The formula can be used to estimate the FTT of flood events, which would be cost-saving and time-saving for river management. Sensitivity analyses indicated that the FTT were sensitive to the Tongguan elevation and Manning’s roughness coefficient in the main channel.

## 1. Introduction

^{3}/s along the LT reach is 15.2 h, and it increases after 1986 and reaches its maximum value in 2003. Then, the average FTT is shortened to 20 h in recent year [15]. The forecasting requirement of the Tongguan Hydrology Station proposed by the River Management Institute is 30 h. As the FTT along the LT reach has is shorter than 30 h, the investigation of FTT along an extended river reach than the LT reach, namely the reach of Wubu-Tongguan (WT Reach), is necessary [16,17]. As the FTT is related to the magnitude of flood, it would be necessary to establish a relationship between discharge and FTT.

## 2. Drainage Area

## 3. Methodology and Data

#### 3.1. Hydraulic Models

^{3}/(s × m)) and velocity of tributary, respectively, ${C}_{l}$ and ${\rho}_{l}$ are the volumetric suspended sediment concentration and density of the tributary, respectively, ${C}_{\ast j}$ and ${\mathsf{\omega}}_{s,j}$ are the volumetric carrying capacity and settling velocity of the $j$th-sized sediment group, respectively, $E$ and $D$ are the entrainment rate and deposition rate at the interface between the bed load and suspended load, respectively, and $E={{\displaystyle \sum}}^{\text{}}{E}_{j}$, $D={{\displaystyle \sum}}^{\text{}}{D}_{j}$. $C$, $E$, and $D$ are summations of all sized sediment groups and $p$ denotes the porosity of the bed material.

#### 3.2. FTT of Floods with Different Peak Discharges

#### 3.3. Data

#### 3.3.1. Geometry Data of the Main Channel

^{−1/3}× s) in the floodplain of the YR [27,36]. According to the measured water stage ($z$) and discharge ($Q$) at each hydrology station, the stage-versus-discharge curves at hydrology stations could be determined. Adding the geometry data of each hydrology station, the Manning’s roughness coefficients ($n$) of the main channel were back-calculated with $\mathrm{Q}\text{}=\text{}\mathrm{Bh}\raisebox{1ex}{$\left({R}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{J}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)$}\!\left/ \!\raisebox{-1ex}{$n$}\right.$, where hydraulic radius $R=\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$\left(B+2h\right)$}\right.$ and $J$ is the measured slope [27]. According to these estimated Manning’s roughness coefficients at hydrology stations, the coefficients at sections between two adjacent hydrology stations were linearly interpolated [27]. For example, the Manning’s roughness coefficients at Wubu, Longmen and Tongguan Hydrology Stations were back-calculated, while coefficients at the other cross-sections were linearly interpolated.

#### 3.3.2. Geometry Data of Tributaries

^{4}km

^{2}, and it accounts for approximately 2.2% of the area of the Longmen Hydrology Station [20].

#### 3.3.3. Boundary Condition

## 4. Results and Discussion

#### 4.1. Calibration of Physical Parameters by Selected Flood Event

^{−1/3}× s, 0.035 m

^{−1/3}× s, and 0.04 m

^{−1/3}× s, respectively. Manning’s roughness coefficients of the main channel used in simulating the 1977 flood event, 2007 flood event, and 2009 flood event varied between 0.009–0.011 [16,28]. Thus, the Manning’s roughness coefficients in this model are reasonable.

#### 4.2. FTT of Floods with Different Discharges

^{3}/s, with an interval of 500 m

^{3}/s. The geometry data of the LT Reach were measured in 2010, and could represent the up-to-date geometry of this river reach. The concentration and related geometry changes were not considered during the estimation of the FTT.

^{3}/s, the FTT may decrease with the increased discharge. When discharges are larger than 3000 m

^{3}/s, the FTT may increase with the increased discharge.

^{3}/s, and the corresponding FTT of floods running to Tongguan was approximately 30.4–34 h. For the river reach of tributaries with IDs of 13 (Yanshui River) and 16 (Qinjian River), the discharge with minimum FTT was approximately 3500 m

^{3}/s, and the corresponding FTT of floods running to Tongguan was approximately 23.4–26.8 h. For the river reach of tributaries with IDs of 10 (Zhouchuan River) and 12 (Fenchuan River), the discharge with minimum FTT was approximately 3000–3500 m

^{3}/s, and the corresponding FTT of floods running to Tongguan was approximately 21–22 h. The FTT of floods running through the LT Reach was approximately 17.4 h, and the discharge was approximately 3000 m

^{3}/s. The bankfull discharge of the LT Reach was approximately 2600 m

^{3}/s [42]. Thus, the larger FTT of a larger discharge may be affected by over-flooding in the LT Reach. One important item that should be pointed out is that the minimum FTT and the corresponding discharge may have some inaccuracies, as the interval of the analyzed discharge was 500 m

^{3}/s.

#### 4.3. Fitted Formula for FTT

^{3}/s). The coefficients are listed in Table 3.

^{3}/s was less than 30 h, and the FTT of discharges ranging from 4500–7800 m

^{3}/s was longer than 30 h. The FTT was approximately 30–35 h for discharges ranging from 3300–9000 m

^{3}/s. Thus, real-time measured hydrographs in tributaries with ID ≥ 18 (Quchan River) and forecasting of tributaries with ID ≤ 17 (Wuding River) are necessary for the forecasting requirements of Tongguan Hydrology Station.

^{3}/s, the FTT of flood events along the LT Reach may be longer than 20 h. Otherwise, the FTT of flood events along the LT Reach is shorter than 20 h. The FTT for floods with peak discharge larger than 6000 m

^{3}/s is almost the maximum one.

#### 4.4. Sensitivity Analysis of Model Parameters

^{3}/s) changed dramatically during 1960–1974 due to the impoundment of the Sanmenxia Reservoir [43]. After 1975, the Tongguan elevation increased at an almost constant rate, and the annual changed elevation was approximately 0.086 m/yr [43]. Two scenarios (TE1 and TE2) were simulated to explore the effect of increased Tongguan elevation.

## 5. Conclusions

- (1)
- The selected dynamic model can be used to simulate the traveling of flood along the Wubu-Tongguan (WT) Reach. This dynamic model could also be used to simulate the flood propagation and estimate the FTT in other drainage areas.
- (2)
- For different river reaches, discharges with minimum FTT are different. For the river reach between Wubu and tributary 17 (Wuding River), the discharge with minimum FTT was approximately 6000 m
^{3}/s, and the corresponding FTT was approximately 30.4–34 h. For the river reach between tributaries 10 (Zhouchuan River) and 16 (Qingjian River), the discharge with minimum FTT and the corresponding FTT were 3000–3500 m^{3}/s and 21–26.8 h, respectively. For the Longmen-Tongguan (LT) Reach, the discharge with minimum FTT and the corresponding FTT were 3000 m^{3}/s and 17.4 h, respectively. - (3)
- The sensitivity analyses indicate that the FTT simulated by the numerical model are sensitive to the Tongguan elevation, roughness in the main channel, and the Weihe River.

## Funding

## Conflicts of Interest

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**Figure 1.**The Yellow River (YR) basin (

**a**); and sketch map of tributaries of the Wubu-Tongguan (WT) Reach (

**b**).

**Figure 2.**Cross sections of the Wubu (

**a**); Longmen (

**b**); and Tongguan (

**c**) Hydrology Stations; and one typical interpolated cross-section in the WL Reach (

**d**).

**Figure 3.**Cross sections of hydrology stations of typical tributaries, (

**a**) tributary with ID = 17, the Wuding River; (

**b**) tributary with ID = 13, the Yanshui River; (

**c**) tributary with ID = 6, the Lower Weihe River; and (

**d**) tributary with ID = 8, the Fenhe River.

**Figure 4.**Measured and simulated hydrographs of the discharge and concentration of the flood event that occurred in 1986 at the Longmen (

**a**) and Tongguan (

**b**) Hydrology Stations.

**Figure 5.**Comparison between estimated and measured flood travel times (FTTs) of floods in 1986 along the Wubu-Longmen (WL) reach.

**Figure 6.**Comparison between estimated and measured flood travel times (FTTs) of floods along the Wubu-Longmen (WL) Reach, based on geometry data measured in 2010.

**Figure 7.**FTT of floods with different discharges along the Wubu-Tongguan (WT) reach. (

**a**) The Wubu-Tongguan (WT) Reach; (

**b**) The Wubu-Longmen (WL) Reach; (

**c**) The Longmen-Tongguan (LT) Reach.

**Figure 9.**FTT of floods from tributaries in the Wubu-Tongguan (WT) Reach (based on Equations (12) and (13)).

Tributary | ID | Drainage Area (km^{2}) | Hydrology Station | |||
---|---|---|---|---|---|---|

Area ^{a} | Area ^{b} | Name | Distance ^{c} (km) | Distance ^{d} (km) | ||

Sanchuan River | 19 | 4161 | 4075 | Houdacheng | 24.5 | 1528.9 |

Quchan River | 18 | 1220 | 1023 | Peigou | 17.7 | 1509.7 |

Wuding River | 17 | 30,261 | 29,662 | Baijiachuan | 58.5 | 1476.5 |

Qingjian River | 16 | 4080 | 3468 | Yanchuan | 37.9 | 1415.7 |

Zhi River | 15 | - | - | - | - | - |

Xinshui River | 14 | 4326 | 3992 | Daning | 36.6 | 1368.7 |

Yanshui River | 13 | 7687 | 5891 | Ganguyi | 112 | 1360 |

Fenchuang River | 12 | 1785 | 1720 | Xinshihe | 23.4 | 1335.8 |

Shiwangchuang River | 11 | 2356 | 2141 | Dacun | 28.7 | 1320.7 |

Zhouchuang River | 10 | 647 | 436 | Jixian | 22.8 | 1314.1 |

**is the total drainage area of the tributary, area above the river mouth of the tributary;**

^{a}**is the drainage area of the upper area of the hydrology station;**

^{b}^{c}is the distance between the hydrology station and the conjunction point of the tributary with the stem channel;

**is the distance between the conjunction point of the tributary and the mouth of the stem channel (YR).**

^{d}Indicator | Longmen | Tongguan | Note | ||
---|---|---|---|---|---|

Discharge | Concentration | Discharge | Concentration | ||

NSE Equation(8) | 0.92 | 0.45 | 0.68 | −0.56 | Daily |

MARE Equation (9) | 0.10 | 0.4 | 0.18 | 0.86 | Daily |

PEP Equation (10) | 0.09 | 0.22 | 0.09 | 0.55 | Flood event |

$\mathsf{\Delta}\mathrm{T}$(H) Equation (11) | 3.0 | 3.0 | 7.5 | 3.0 | Flood event |

${\mathit{d}}_{\mathbf{1}}$ | ${\mathit{\beta}}_{\mathbf{1}}$ | ${\mathit{d}}_{\mathbf{2}}$ | ${\mathit{\beta}}_{\mathbf{2}}$ | - | - | |

Equation (12) | 0.5945 | 0.2804 | 76.872 | 0.2883 | - | - |

${\mathit{a}}_{\mathbf{1}}$ | ${\mathit{b}}_{\mathbf{1}}$ | ${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{a}}_{\mathbf{2}}$ | ${\mathit{b}}_{\mathbf{2}}$ | ${\mathit{c}}_{\mathbf{2}}$ | |

Equation (13) | 1 × 10^{−9} | −8 × 10^{−6} | 0.1484 | −4 × 10^{−8} | 3 × 10^{−4} | −0.8285 |

Randomly Selected Parameters | Calibrated Parameters | |||
---|---|---|---|---|

Case | Scenario | Physical Variable | Mean | |

1 | D5 | Drop of the Hukou Waterfall | 5 m | 30 m |

2 | D10 | 10 m | ||

3 | D20 | 20 m | ||

4 | W477 | Width of cross-sections upstream and downstream the Hukou Waterfall are the same as that of Wubu Station | 477 m | With of cross-sections upstream and downstream the Hukou Waterfall are 300 m and 50 m, respectively |

5 | TE1 | Tongguan elevation | Increased by 0.86 m | Tongguan Elevation estimated by stage-versus-discharge rating curve at Tongguan (2010) |

6 | TE2 | Increased by 1.72 m | ||

7 | W1 | Roughness of the main channel of the LT reach | 0.014 | Back-calculated using the measured stage-versus-discharge rating curve at reach hydrology station |

8 | W2 | 0.018 |

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**MDPI and ACS Style**

He, L. Estimation of Flood Travel Time in River Network of the Middle Yellow River, China. *Water* **2020**, *12*, 1550.
https://doi.org/10.3390/w12061550

**AMA Style**

He L. Estimation of Flood Travel Time in River Network of the Middle Yellow River, China. *Water*. 2020; 12(6):1550.
https://doi.org/10.3390/w12061550

**Chicago/Turabian Style**

He, Li. 2020. "Estimation of Flood Travel Time in River Network of the Middle Yellow River, China" *Water* 12, no. 6: 1550.
https://doi.org/10.3390/w12061550