# Optimization of Multi-Reservoir Flood Control Operating Rules: A Case Study for the Chaobai River Basin in China

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods and Materials

#### 2.1. Chaobai River Basin

^{2}and has a diverse topography, with higher elevations in the northern region and a gradual decrease in elevation towards the southeast. It is characterized by two major tributaries, namely the Chao River and the Bai River, which merge at the Miyun Reservoir and form the Chaobai River downstream of the reservoir. The annual precipitation and runoff are around 553 mm (range 500–700) and 1653 million m

^{3}(range 615–4320) [36]. The major flood season is June–August. Over 70% of the annual rainfall occurs during this period, predominantly in the form of intense and localized downpours [37].

^{3}[38] and a drainage area of approximately 90% of the basin’s total area. The Miyun Reservoir has long been the sole surface water resource for Beijing through the Jingmi Canal. Since the introduction of water transfer from the Central Route of the SNWDP in 2015, the reservoir’s role shifted to serving as an emergency strategic water resource reserve.

#### 2.2. Multi-Reservoir Flood Control Operation Model

^{3}/s, exceeding which would result in varying degrees of flooding. Through flood routing simulations, the extent of inundation and damage in the channel can be determined. Figure 2b illustrates the relationship between the total discharge and the downstream losses due to flooding.

^{3}), respectively. Specifically, ${V}_{3}^{t}$ is the ending storage of the Miyun Reservoir. ${V}_{FLWL,3}$ and ${V}_{DFL,3}$ are the storages corresponding to the flood limited water level and designed flood level (m

^{3}), respectively. $I,\text{}R,\text{}Z$ are the natural inflow (m

^{3}/s), reservoir outflow (m

^{3}/s), and reservoir water level (m), respectively. The intermediate flow between reservoirs, i.e., regions between the reservoir and the flood control section, is ignored. The Miyun Reservoir (R3) receives the discharges from the Yaoqiaoyu Reservoir (R1) and the Banchengzi Reservoir (R2). ${R}_{3}^{t}$, ${R}_{4}^{t}$, and ${R}_{5}^{t}$ are the discharges of the Miyun (R3), Shachang (R4), and Huairou (R5) reservoirs (m

^{3}/s), the sum of which is the flow rate at the downstream Suzhuang flood control section. ${Z}_{min,i}$ and ${Z}_{max,i}$ are the lower and upper limits of the reservoir water level (m), respectively, and are typically the dead water level and check flood level (CFL), respectively, during the flood season. ${R}_{min,i}$ and ${R}_{max,i}$ are the boundaries of the outflow constraints and are equal to the ecological flow requirement and the reservoir spillway capacity of the respective reservoir at the check flood level (m

^{3}/s).

#### 2.3. Operating Rules

^{3}/s), which is usually a piecewise parametric function of the reservoir states, i.e., the inflow ${Q}_{in}$ (m

^{3}/s) and water level $Z$ (m). ${Q}_{min,k}$, ${Q}_{max,k}$, ${Z}_{min,k}$, and ${Z}_{max,k}$, k = 1,2,…K, are the hierarchical boundaries of the classified reservoir inflow and water level.

^{3}/s); ${R}_{Fmax,i}$, ${R}_{Dmax,i}$, and ${R}_{max,i}$ are the maximum allowable discharges (m

^{3}/s) under FLWL, DFL, and CFL, respectively. The parameters ${\alpha}_{i=\mathrm{1,2}\dots 5}$, ${\beta}_{i=\mathrm{1,2}\dots 5}$, and ${\gamma}_{i=\mathrm{4,5}}$ are the decision variables that need to be optimized in this study.

#### 2.4. Investigated Floods

#### 2.5. NSGA-II Solving Method

## 3. Results and Discussion

#### 3.1. Impact of Inter-Basin Water Transfer on the Flood Control Situation of the Miyun Reservoir

^{3}). Since then, a combination of factors including reduced rainfall, has led to consistently low reservoir storage (Figure 4). Flood control was not a major consideration during the flood season. Instead, the reservoir intercepted all incoming floodwater for non-flood season water supply.

#### 3.2. Flood Regulation

_{1}). In this case, the water level of the Miyun Reservoir remains relatively stable at the FLWL (Figure 6a). To achieve this, almost all inflow is discharged, leading to high flow rates in the Suzhuang station, and the peak value even surpasses the system’s natural inflow (Figure 6b). As the concern shifts toward prioritizing the downstream flood safety (the trade-off point B on the Pareto front), the reservoir storage gradually increases (orange curve in Figure 6a) from the FLWL (3037 million m

^{3}) to 154.7 m (3422 million m

^{3}) within 72 h. In return, the system release exhibits a noticeable peak attenuation effect (Figure 6b). The goal of red point (curve) C is to minimize downstream flooding by intercepting as much incoming floodwater as possible in the Miyun Reservoir.

#### 3.3. Compariosn to the Current Operating Rules

^{3}spill. Assuming a unit water price of 2.33 CNY for the water transferred to Beijing via the Central Route of the SNWDP [42], the surplus water is worth about around 17 million CNY.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Location of the Chaobai River Basin (

**a**) and the schematic diagram of the mixed five-reservoir flood control system (

**b**).

**Figure 2.**Relationships between inundation loss in the Miyun Reservoir area and the reservoir storage (

**a**), and the downstream losses and discharge in the Suzhuang flood control section (

**b**).

**Figure 4.**Annual available water resources into the Miyun Reservoir (including external transfer), end-of-year reservoir storage, and the historical flood limited water level (FLWL) from 1990 to 2021. The Central Route of the South-to-North Water Diversion Project (SNWDP) commenced water transfer in 2015.

**Figure 5.**The Pareto front for the dual-objective operation model under a 20-year flood and a 1000-year flood. The six points (A, B, C, A’, B’, and C’) represent the six solutions under different flood conditions and distinct objective prioritization.

**Figure 6.**The reservoir operation process in terms of the Miyun Reservoir storage (

**a**,

**c**) and the basin’s downstream total discharge (

**b**,

**d**) corresponding to the points A, B, C, A’, B’, and C’ in Figure 5.

**Figure 7.**Comparison of operation under current rules and optimized rules in terms of the objective values (

**a**), the Miyun Reservoir storage process (

**b**), and the basin’s downstream total discharge (

**c**).

**Table 1.**Characteristic parameters of the Chaobai River flood control system. In the last three rows, the characteristic water level [m

^{3}], and in parentheses the respective storage [10

^{6}m

^{3}], for each reservoir are given.

Characteristic Water Level [m ^{3}] | Yaoqiaoyu Reservoir (R1) | Banchengzi Reservoir (R2) | Miyun Reservoir (R3) | Shachang Reservoir (R4) | Huairou Reservoir (R5) |
---|---|---|---|---|---|

Designed flood control standard [yr] | 100 | 100 | 1000 | 50 | 100 |

Flood limited water level | 463 (12.1) | 255 (5.75) | 152 (3037) | 165.5 (15.65) | 58 (39.4) |

Design flood level | 468.1 (17.37) | 258.5 (8.05) | 157.5 (3964) | 167.95 (19.05) | 64.16 (98.2) |

Check flood level | 469.78 (19.34) | 259.3 (8.63) | 158.5 (4145.4) | 170 (21.2) | 67.73 (144) |

Flood return period [yr] | 1000 | 100 | 50 | 20 | 10 |

Frequency [%] | 0.1 | 1 | 2 | 5 | 10 |

Peak flow [m^{3}/s] | |||||

R1 (Yaoqiaoyu) | 2290 | 1500 | 1280 | 980 | 763 |

R2 (Banchengzi) | 457 | 288 | 195 | 78 | 67.2 |

R3 (Miyun) | 15,800 | 9320 | 7460 | 5120 | 3480 |

R4 (Shachang) | 1510 | 975 | 800 | 590 | 419 |

R5 (Huairou) | 7710 | 5059 | 4270 | 3280 | 2440 |

**Table 3.**The current flood control operating rules for individual reservoirs and the optimized rule parameters for the integrated operation of the five reservoirs on the Chaobai River when confronting a 100-year flood.

Criteria | R1 | R2 | R3 | R4 | R5 | Upstream Damage | Downstream Damage | Release from R3 |
---|---|---|---|---|---|---|---|---|

Release according to the current rules | [economic equivalence] | [10^{6} m^{3}] | ||||||

Z < FLWL | 0 | 0 | 0 | 0 | 0 | 15.91 | 9.1 | 479 |

FLWL $\le $ Z < DFL | ${R}_{Fmax,1}$ | 80 | {600, 1000, 1500} ^{a} | ${Q}_{in,4}^{t}$ | $\frac{{Q}_{in,5}^{t}{R}_{Dmax,5}}{5059}$ ^{a} | |||

DFL $\le $ Z < CFL | ${R}_{Dmax,1}$ | 200 | {${Q}_{in,3}^{t}$, ${R}_{Dmax,3}$} ^{a} | {420, 670} ^{a} | ${R}_{Dmax,5}$ | |||

Z $\ge $ CFL | ${R}_{max,1}$ | ${R}_{max,2}$ | {${Q}_{in,3}^{t}$, ${R}_{max,3}$} ^{a} | ${R}_{max,4}$ | ${R}_{max,5}$ | |||

Rule parameters for the Pareto optimal | ||||||||

${\alpha}_{i}$ | 0.2698 | 0.3616 | 0.3528 | 0.4129 | 0.4032 | 14.4 | 8.9 | 471.6 |

${\beta}_{i}$ | 0.5586 | 0.6210 | 0 | 0.4779 | 0.0114 |

^{a}: the specific determination of how much to release is found in the respective reservoir flood operation scheme.

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**MDPI and ACS Style**

Wan, W.; Liu, Y.; Zheng, H.; Zhao, J.; Zhao, F.; Lu, Y.
Optimization of Multi-Reservoir Flood Control Operating Rules: A Case Study for the Chaobai River Basin in China. *Water* **2023**, *15*, 2817.
https://doi.org/10.3390/w15152817

**AMA Style**

Wan W, Liu Y, Zheng H, Zhao J, Zhao F, Lu Y.
Optimization of Multi-Reservoir Flood Control Operating Rules: A Case Study for the Chaobai River Basin in China. *Water*. 2023; 15(15):2817.
https://doi.org/10.3390/w15152817

**Chicago/Turabian Style**

Wan, Wenhua, Yueyi Liu, Hang Zheng, Jianshi Zhao, Fei Zhao, and Yajing Lu.
2023. "Optimization of Multi-Reservoir Flood Control Operating Rules: A Case Study for the Chaobai River Basin in China" *Water* 15, no. 15: 2817.
https://doi.org/10.3390/w15152817