# Multivariate Dam-Site Flood Frequency Analysis of the Three Gorges Reservoir Considering Future Reservoir Regulation and Precipitation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Region and Dataset

^{2}and the river channel length is more than 6300 km. In this study, we focus on the Upper Yangtze basin, which is actually above the Yichang hydrological gauging site and covers a catchment area of about 1 million km

^{2}. Before the operation of the TGR, the dam-site flood of this reservoir can be represented by the flood observed at Yichang gauging site, given that the TGD is located approximately 40 km upstream from the Yichang gauging site and the catchment area between the TGD and the gauging site is negligible compared to the whole catchment area of the Upper Yangtze basin.

## 3. Methods

#### 3.1. Reconstruction of the Dam-Site Floods of the TGR

_{TGR}is the daily dam-site discharge of the TGR; Q

_{C}and Q

_{W}are the daily discharges routed from Cuntan and Wulong gauges, respectively; and Q

_{IW}is the daily runoff generated in the TGR interval watershed. By using Equation (1), the dam-site floods of the TGR for the period from 2003 to 2020, i.e., the period after the operation of the TGR, can be extracted from Q

_{TGR}.

#### 3.2. Time-Varying Multivariate Flood Distribution

_{1}), annual maximum 3-day flood volume (${V}_{3}$), annual maximum 7-day flood volume (${V}_{7}$), annual maximum 15-day flood volume (${V}_{15}$), and annual maximum 30-day flood volume (${V}_{30}$). According to Sklar’s Theorem [33], the probability distribution of the five-dimensional (5-D) flood series $\left({Q}_{1},{V}_{3},{V}_{7},{V}_{15},{V}_{30}\right)$ at time t can be expressed by a copula $C(\cdot )$ as follows:

#### 3.3. Construction of Multivariate Flood Distribution Using Vine Copula

#### 3.4. Multivariate Hydrological Design under Nonstationary Conditions

_{1}to T

_{2}can be calculated by:

## 4. Results and Analysis

#### 4.1. Dam-Site Flood Series

^{3}/s, while after the regulation of the TGR, the observed flood peak at Yichang gauging site downstream the dam was 50,831 m

^{3}/s, indicating a decline of more than 20,000 m

^{3}/s.

#### 4.2. Multivariate Dam-Site Flood Distribution of the TGR

^{3}/s in the mean value of the dam-site flood peak of the TGR.

^{3}(see Table 1). Due to the increasing trend of the predicted SPA under the emission scenario SSP5-8.5, the corresponding flood distribution in the future period will present an upward trend after 2050. The distributions of the dam-site flood volumes of the TGR present the behavior similar to that of the flood peak.

#### 4.3. Multivariate Dam-Site Design Floods for the TGR

^{3}/s. For the emission scenarios of SSP5-8.5, though the precipitation in flooding season is predicted to increase, the design flood peak with the AAR of 0.999 would still present a decrease by about 20,000 m

^{3}/s. Hence in the future, the regulation of reservoirs will be of great benefit in reducing the flood risk of the TGR.

^{3}/s, which is close to the design value (98,000 m

^{3}/s) used in the engineering practice of the TGR. It can be seen that the univariate design flood values are generally smaller than the multivariate design values associated with the OR and Kendall exceedance probabilities, and larger than those associated with the AND exceedance probability.

## 5. Conclusions and Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Observed flood variables at Yichang gauging site and the simulated at-site flood variables of the TGR. Panels (

**a**–

**e**) display the results for the flood variables ${Q}_{1}$,${V}_{3}$, ${V}_{7}$, ${V}_{15}$ and ${V}_{30}$, respectively.

**Figure 5.**Evolution of the distribution of the dam-site flood peak of the TGR considering the reservoir regulation and SPA. Panels (

**a**–

**c**) display the results for emission scenarios SSP1-2.6, SSP2-4.5 and SSP5-8.5, respectively.

**Figure 6.**Dam-site design hydrographs associated with OR exceedance probability for the TGR. Panels (

**a**–

**c**) display the results for design levels with the AARs of 0.9, 0.99 and 0.999, respectively.

**Figure 7.**Dam-site design hydrographs associated with AND exceedance probability for the TGR. Panels (

**a**–

**c**) display the results for design levels with the AARs of 0.9, 0.99 and 0.999, respectively.

**Figure 8.**Dam-site design hydrographs associated with Kendall exceedance probability for the TGR. Panels (

**a**–

**c**) display the results for design levels with the AARs of 0.9, 0.99 and 0.999, respectively.

Reservoir | Catchment Area (10^{6} km^{2}) | Flood control Capacity (10^{9} m^{3}) | Completation Year |
---|---|---|---|

Bikou | 0.026 | 0.083 | 1976 |

Ertan | 0.1164 | 0.9 | 1998 |

Baozhusi | 0.0284 | 0.28 | 1998 |

Zipingpu | 0.0227 | 0.167 | 2006 |

Pubugou | 0.0685 | 0.73 | 2008 |

Silin | 0.0486 | 0.184 | 2009 |

Pengshui | 0.069 | 0.232 | 2009 |

Goupitan | 0.0433 | 0.2 | 2011 |

Shatuo | 0.0545 | 0.209 | 2011 |

Ahai | 0.2354 | 0.215 | 2012 |

Jinanqiao | 0.2374 | 0.158 | 2012 |

Longkaikou | 0.24 | 0.126 | 2013 |

Ludila | 0.2473 | 0.564 | 2013 |

Xiangjiaba | 0.4588 | 0.903 | 2013 |

Jinping I | 0.1026 | 1.6 | 2014 |

Xiluodu | 0.4544 | 4.651 | 2014 |

Tingzikou | 0.0611 | 1.44 | 2014 |

Liyuan | 0.22 | 0.173 | 2015 |

Guanyinyan | 0.2565 | 0.253 | 2015 |

Caojie | 0.1561 | 0.199 | 2015 |

Changheba | 0.0559 | 0.12 | 2017 |

Wudongde | 0.4061 | 2.44 | 2021 |

Baihetan | 0.4303 | 7.5 | 2022 |

Lianghekou | 0.0596 | 0.2 | 2023 |

Shuangjiangkou | 0.0393 | 0.663 | 2024 |

Flood Variable | Distribution Parameters | p-Value of KS Test | ||
---|---|---|---|---|

$\mathit{\mu}$ | $\mathit{\sigma}$ | $\mathit{\nu}$ | ||

Q_{1} (m^{3}/s) | $50215.5+15747.3SPA-6029.2\mathrm{ln}\left(RI+1\right)$ | 0.172 | 0.454 | 0.200 |

V_{3} (10^{9} m^{3}) | $12.51+3.96SPA-1.42\mathrm{ln}\left(RI+1\right)$ | 0.174 | 0.456 | 0.474 |

V_{7} (10^{9} m^{3}) | $26.39+7.87SPA-2.66\mathrm{ln}\left(RI+1\right)$ | 0.175 | 0.456 | 0.407 |

V_{15} (10^{9} m^{3}) | $49.83+14.72SPA-4.84\mathrm{ln}\left(RI+1\right)$ | 0.162 | 0.364 | 0.758 |

V_{30} (10^{9} m^{3}) | $89.36+29.61SPA-7.34\mathrm{ln}\left(RI+1\right)$ | 0.146 | 0.326 | 0.770 |

Bivariate Pair | Copula Parameter | Bivariate Pair | Copula Parameter | Bivariate Pair | Copula Parameter |
---|---|---|---|---|---|

$\left({Q}_{1},{V}_{3}\right)$ | 13.72 | $F\left({Q}_{3}|{Q}_{1}\right),F\left({Q}_{7}|{Q}_{1}\right)$ | 1.77 | $F\left({Q}_{7}|{Q}_{1},{Q}_{3}\right),F\left({Q}_{30}|{Q}_{1},{Q}_{3}\right)$ | 1.45 |

$\left({Q}_{1},{V}_{7}\right)$ | 4.62 | $F\left({Q}_{3}|{Q}_{1}\right),F\left({Q}_{15}|{Q}_{1}\right)$ | 1.30 | $F\left({Q}_{15}|{Q}_{1},{Q}_{3},{Q}_{7}\right),F\left({Q}_{30}|{Q}_{1},{Q}_{3},{Q}_{7}\right)$ | 1.60 |

$\left({Q}_{1},{V}_{15}\right)$ | 2.66 | $F\left({Q}_{3}|{Q}_{1}\right),F\left({Q}_{30}|{Q}_{1}\right)$ | 1.19 | ||

$\left({Q}_{1},{V}_{30}\right)$ | 2.19 | $F\left({Q}_{7}|{Q}_{1},{Q}_{3}\right),F\left({Q}_{15}|{Q}_{1},{Q}_{3}\right)$ | 1.93 |

Flood Variable | AAR = 0.9 | AAR = 0.99 | AAR = 0.999 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | |

Q_{1} (m^{3}/s) | 67,583 | 48,925 | 49,894 | 52,924 | 82,332 | 60,710 | 60,770 | 65,580 | 97,146 | 70,523 | 72,662 | 77,138 |

V_{3} (10^{9} m^{3}) | 16.8 | 12.5 | 12.7 | 13.5 | 20.6 | 15.4 | 15.5 | 16.6 | 24.3 | 18 | 18.6 | 19.7 |

V_{7} (10^{9} m^{3}) | 35.7 | 27.5 | 28.2 | 29.5 | 44 | 33.7 | 33.6 | 36.2 | 51.6 | 39.6 | 39.9 | 42.8 |

V_{15} (10^{9} m^{3}) | 66 | 51 | 52.7 | 54.6 | 80.6 | 61.9 | 62.5 | 67.5 | 93 | 71 | 72.1 | 78.7 |

V_{30} (10^{9} m^{3}) | 115.2 | 93.9 | 93.5 | 99.5 | 137.8 | 111.6 | 113.6 | 122.2 | 158.1 | 126.7 | 128.2 | 141.2 |

**Table 5.**Multivariate dam-site design floods associated with AND exceedance probability for the TGR.

Flood Variable | AAR = 0.9 | AAR = 0.99 | AAR = 0.999 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | |

Q_{1} (m^{3}/s) | 58,617 | 44,196 | 44,401 | 46,578 | 74,561 | 55,696 | 56,423 | 59,444 | 89,647 | 64,802 | 65,967 | 69,347 |

V_{3} (10^{9} m^{3}) | 14.7 | 11.3 | 11.3 | 11.8 | 18.7 | 14.2 | 14.3 | 15.2 | 22.5 | 16.5 | 16.8 | 17.8 |

V_{7} (10^{9} m^{3}) | 31.5 | 25 | 24.8 | 25.9 | 39.6 | 31.4 | 31.4 | 33.1 | 47.7 | 36.1 | 36.7 | 39.0 |

V_{15} (10^{9} m^{3}) | 59.9 | 47.1 | 47.6 | 49.7 | 73.6 | 57.9 | 58.1 | 60.6 | 85.9 | 66.9 | 66.1 | 71.8 |

V_{30} (10^{9} m^{3}) | 106.5 | 85.2 | 86 | 91.6 | 130.2 | 103.8 | 103.3 | 111.8 | 146.2 | 118.9 | 117.9 | 130.6 |

**Table 6.**Multivariate dam-site design floods associated with Kendall exceedance probability for the TGR.

Flood Variable | AAR = 0.9 | AAR = 0.99 | AAR = 0.999 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | |

Q_{1} (m^{3}/s) | 61,929 | 45,502 | 45,911 | 48,982 | 79,589 | 56,674 | 57,897 | 61,405 | 93,683 | 66,561 | 67,838 | 73,077 |

V_{3} (10^{9} m^{3}) | 15.5 | 11.5 | 11.6 | 12.4 | 19.9 | 14.5 | 14.8 | 15.6 | 23.5 | 17 | 17.3 | 18.6 |

V_{7} (10^{9} m^{3}) | 33 | 25.6 | 25.6 | 27.2 | 41.9 | 31.9 | 32.1 | 33.9 | 49.6 | 36.8 | 38.2 | 40.6 |

V_{15} (10^{9} m^{3}) | 61.8 | 48.5 | 48.6 | 51.1 | 76.1 | 58.3 | 59.6 | 62.1 | 88.2 | 66.7 | 69.8 | 74.2 |

V_{30} (10^{9} m^{3}) | 108.2 | 88.1 | 88.5 | 93 | 130.4 | 105.1 | 106.3 | 113.9 | 153.7 | 118.9 | 123.6 | 133.7 |

Flood Variable | AAR = 0.9 | AAR = 0.99 | AAR = 0.999 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | Historical | SSP1-2.6 | SSP2-4.5 | SSP5-8.5 | |

Q_{1} (m^{3}/s) | 64,221 | 47,119 | 47,568 | 50,338 | 80,236 | 58,766 | 59,420 | 63,533 | 94,651 | 69,258 | 70,128 | 75,508 |

V_{3} (10^{9} m^{3}) | 16.0 | 12.0 | 12.1 | 12.8 | 20.1 | 15.0 | 15.1 | 16.2 | 23.7 | 17.7 | 17.9 | 19.2 |

V_{7} (10^{9} m^{3}) | 33.8 | 26.1 | 26.3 | 27.7 | 42.2 | 32.6 | 32.9 | 34.9 | 49.8 | 38.4 | 38.8 | 41.4 |

V_{15} (10^{9} m^{3}) | 62.9 | 49.1 | 49.5 | 52.1 | 76.9 | 59.9 | 60.5 | 64.2 | 89.3 | 69.3 | 70.1 | 74.9 |

V_{30} (10^{9} m^{3}) | 111.8 | 90.5 | 91.3 | 96.6 | 135.1 | 108.7 | 109.9 | 117.6 | 155.2 | 124.4 | 126 | 135.9 |

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**MDPI and ACS Style**

Xiong, L.; Jiang, C.; Guo, S.; Li, S.; Li, R.; Li, W.
Multivariate Dam-Site Flood Frequency Analysis of the Three Gorges Reservoir Considering Future Reservoir Regulation and Precipitation. *Water* **2022**, *14*, 138.
https://doi.org/10.3390/w14020138

**AMA Style**

Xiong L, Jiang C, Guo S, Li S, Li R, Li W.
Multivariate Dam-Site Flood Frequency Analysis of the Three Gorges Reservoir Considering Future Reservoir Regulation and Precipitation. *Water*. 2022; 14(2):138.
https://doi.org/10.3390/w14020138

**Chicago/Turabian Style**

Xiong, Lihua, Cong Jiang, Shenglian Guo, Shuai Li, Rongrong Li, and Wenbin Li.
2022. "Multivariate Dam-Site Flood Frequency Analysis of the Three Gorges Reservoir Considering Future Reservoir Regulation and Precipitation" *Water* 14, no. 2: 138.
https://doi.org/10.3390/w14020138