# Optimizing the Flood Limit Water Level of Reservoirs in Sediment-Laden Rivers under Changing Water and Sediment Conditions: A Case Study of the Xiaolangdi Reservoir

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}/s than the operation mode of raising the FLWL at one time. However, with enhanced benefits of sediment blocking and siltation reduction, other benefits such as water resources supply, hydropower generation, and ecological improvement are reduced. The average annual number of days that do not meet the downstream water resources supply requirements, irrigation, and ecological improvement was increased by 0.64–2.16 days, and 91–197 million kW·h reduced average annual hydropower generation. The critical amount of incoming sediment was 350 million for conversion between the two FLWL operation modes, and it will increase to 450 million tons if the incoming runoff of the Yellow River increases by 20%. After constructing the Guxian Reservoir in the middle of the Yellow River, the critical amount of incoming sediment will increase to 600 million tons. This study is of great significance for improving the utilization efficiency of water resources and promoting the socio-economic development of river basins.

## 1. Introduction

^{3}and 240 million tons, which were 27.3% and 77.8% less than those from 1960 to 2000, respectively. The siltation rate of the reservoir has also decreased significantly. Water and sediment changes affect FLWL in reservoirs. Therefore, to improve the comprehensive benefits of a reservoir, it is essential to optimize the operation mode of FLWL according to the conditions of incoming water and sediment. However, under the changing water and sediment conditions, there is still a lack of relevant research on optimizing the FLWL operation mode of reservoirs in sediment-laden rivers to improve the comprehensive utilization efficiency.

## 2. Methodology

#### 2.1. Water–Sediment Mathematical Model

#### 2.1.1. Model Principles and Control Equations

- Water flow movement control equation$$B\frac{\partial z}{\partial t}+\frac{\partial Q}{\partial x}={q}_{l}$$$$\frac{\partial Q}{\partial t}+2\frac{Q}{A}\frac{\partial Q}{\partial x}-\frac{B{Q}^{2}}{{A}^{2}}\frac{\partial z}{\partial x}-\frac{{Q}^{2}}{{A}^{2}}\frac{\partial A}{\partial x}{\left(\right|}_{z}=-gA\frac{\partial z}{\partial x}-\frac{g{n}^{2}\left|Q\right|Q}{A{\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$B$}\right.\right)}^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}$$
^{3}/s); $z$ is the water level (m); $A$ denotes the cross-sectional overflow area (m^{2}); $B$ is the river width (m); ${q}_{l}$ is the inflow (or outflow) per unit time and per unit length (m^{2}/s^{2}); $n$ is the Manning roughness coefficient; and $g$ denotes the gravitational acceleration (m/s^{2}). - Non-equilibrium sediment transport equation

^{3}); ${S}_{*k}$ is the sediment carrying capacity of group $k$ (kg/m

^{3}); $\alpha $ is the recovery saturation coefficient; ${\omega}_{k}$ is the settling velocity of group k (m/s); ${q}_{ls}$ is the sediment inflow (or outflow) per unit time and unit length (kg/(m

^{.}s)); ${S}_{V}$ is the volumetric sediment concentration (kg/m

^{3}); u represents the flow velocity (m/s); h denotes the water depth (m); $\kappa $ is the Karman constant affected by the sediment concentration; ${\rho}_{S}$ and ${\rho}_{m}$ are the densities of solid particles and muddy water, respectively (kg/m

^{3}); ${\omega}_{m}$ is the representative settling velocity of mixed sediment (m/s); and ${D}_{50}$ is the median diameter of bed sediment (mm).

- 3.
- Riverbed deformation equation$${\gamma}^{\prime}\frac{\partial A}{\partial t}={\displaystyle \sum _{k=1}^{M}\alpha {\omega}_{k}B\left({S}_{k}-{S}_{*k}\right)}-\frac{\partial B{q}_{b}}{\partial x}$$
^{3}). - 4.
- Power generation equation$$N=9.81\eta {Q}_{p}{H}_{n}$$
^{.}h); $\eta $ is the hydropower station efficiency obtained by verification from the measured data; ${Q}_{p}$ is the discharge flowing through the hydropower station turbine (m^{3}/s); and ${H}_{n}$ is the net head of the hydropower station (m).

#### 2.1.2. Solution Method

#### 2.1.3. Constraining Conditions

_{ut}) is the maximum outflow of reservoir; ${Q}_{fc}$ is the outflow of flood control; Q

_{out}(Z

_{i}) is the outflow under the Z

_{i}level; ${Q}_{\mathrm{max}}\left({Z}_{i}\right)$ is the maximum outflow capacity of reservoir under the Z

_{i}level; min(Q

_{out}) is the minimum outflow of reservoir; ${Q}_{wi}$ is the outflow required for water resources supply and irrigation; $\mathrm{m}\mathrm{i}\mathrm{n}\left({Q}_{p}\right)$ is the minimum outflow of a single turbine in a hydropower station; and $\mathrm{m}\mathrm{i}\mathrm{n}\left({Q}_{e}\right)$ is the minimum outflow for the ecological requirement of the downstream river.

#### 2.1.4. Model Verification

^{3}and calculated as 3.336 billion m

^{3}, with a relative error of 4.2%. The cumulative siltation amount from 1976 to 2021 in the LYR was measured as 735 million tons and calculated as 665 million tons, with a relative error of 9.6%. The model verification results are shown in Figure 3, which indicate that the mathematical model could accurately simulate the erosion and deposition characteristics of reservoirs and river channels in sediment-laden rivers.

#### 2.2. Comprehensive Benefit Evaluation Model

#### 2.2.1. Evaluation Indices

#### 2.2.2. Evaluation Model

## 3. Case Study

#### 3.1. Research Area and Data

#### 3.1.1. Research Area

^{2}, accounting for about 92.3% of the Yellow River basin area. The design storage capacity of the XLDR is 12.65 billion m

^{3}, of which 4.1 billion m

^{3}is for controlling flood, 7.55 billion m

^{3}is for retaining sediment, and 1.0 billion m

^{3}is for regulating flow and sediment [40]. Moreover, the designed FLWL of the XLDR is 254 m during regular operation. During the design stage of the XLDR, based on the assumption that the sediment amount in the Yellow River is 1.275 billion tons, it was proposed that the FLWL should be gradually raised during the pre-flood (from July to August) and post-flood (from September to October) periods to slow down the siltation of the reservoir as much as possible, with a predicted sediment retention period of just 15 years. However, during 23 years of the XLDR operation, the sediment amount decreased to less than 300 million tons, and the siltation rate of the reservoir has slowed down significantly. The XLDR came into operation in October 1999, and until April 2022, its cumulative siltation amount was 3.392 billion m

^{3}, accounting for 45% of the design sediment retention capacity. The reservoir was operated by gradually raising the FLWL (Figure 5). The current FLWLs of 235 m and 248 m during the pre-flood and post-flood periods are still 19 m and 6 m lower than the designed FLWL of 254 m during normal operation, respectively.

^{3}/s in 2002 to 4600 m

^{3}/s, significantly reducing flood prevention pressure in the LYR.

#### 3.1.2. Datasets

^{3}and 240 million tons, decreasing by 27.3% and 77.8%, respectively, compared with those from 1960 to 2000. The future amounts of incoming flow and sediment are influenced by natural climatic factors and human activities, such as water conservancy projects, soil and water conservation projects, and economic and social development [43]. Generally, the water and sediment amount in the future will be significantly reduced. The current perception of future sediment amounts in the Yellow River ranges from approximately 300 to 800 million tons.

#### 3.1.3. Minimum Discharge from the XLDR

_{out}) should be greater than or equal to the maximum of the three minimum discharge requirements (Table 2). The greater the number of days that do not meet the minimum discharge requirements for the reservoir, the worse the benefits of water resources supply, irrigation, electricity generation, and ecological improvements are.

#### 3.2. Scenario Conditions

#### 3.2.1. Scenario Conditions of Incoming Water and Sediment

^{3}, respectively. The incoming flow and sediment processes of each scenario are shown in Figure 6. Industrial and agricultural water use was considered in the incoming water processes.

#### 3.2.2. Scenario Conditions of FLWL Operation Modes for the XLDR

^{3}, the reservoir started discharging. It released a large outflow with a value larger than 3700 m

^{3}/s into the LYR at the Huayuankou station for at least five days. The corresponding highest water level was the FLWL during that flood season. When the reservoir’s adjustable water amount was more than 600 million m

^{3}and the forecasted inflow was greater than or equal to 2600 m

^{3}/s, it started discharging when gathering the flow and released a large outflow with the value of more than 3700 m

^{3}/s at the Huayuankou station for at least five days. When the forecasted inflow was greater than or equal to 2600 m

^{3}/s and the sediment concentration was greater than or equal to 200 kg/m

^{3}, the reservoir activated a high-sediment concentration dispatch, pre-discharging two days in advance or storing 300 million m

^{3}of water and then making the outflow equal to the inflow. After the reservoir entered the second stage of sediment retention (when the siltation amount exceeds 4.2 billion m

^{3}) and the forecasted inflow was greater than or equal to 2600 m

^{3}/s, the reservoir started to lower the water level, thereby scouring the sediment in the reservoir area. For the mode in which the FLWL was raised at one time, the reservoir started discharging when the water level of the XLDR reached the designed FLWL of 254 m from 11 July to 31 August. The reservoir continued discharging when gathering the flow, but the high-sediment concentration dispatch and lowering of the water level to scour the reservoir area were no longer operated to maintain a suitable channel scale of the downstream river channel.

#### 3.3. Results

#### 3.3.1. Analysis of Single Objective Effect

_{SRP_XLDR}).

_{bmin_}

_{LYR}) was smaller. Under the incoming sediment amount scenarios of 400–800 million tons, for the mode of gradually raising the FLWL, the average annual siltation of the LYR (W

_{S}

_{_LYR}) was smaller by 10–19 million tons, and the minimum bank-full discharge was larger by 150–260 m

^{3}/s at the end of the calculation period. After 50 years, the downstream channel of the two modes will still be in a state of erosion under the incoming sediment amount scenario of 300 million tons. The smaller the incoming sediment amount, the smaller the differences in the average annual siltation in the LYR and the minimum bank-full discharge are.

_{d}) was greater by 0.64–2.16 days. The smaller the incoming sediment amount, the smaller the corresponding incoming runoff amount, and the larger this difference will be.

_{XLDR}) was 6.79–8.35 m lower, and the hydropower generation (N

_{XLDR}) was 91–197 million kW

^{.}h smaller for the operation mode of gradually raising the FLWL, with the differences between the two modes increasing with decreasing incoming sediment amount in the Yellow River.

#### 3.3.2. Analysis of Comprehensive Effects

_{1}= (0.923, 0.974, 0.976, 0.971, 0.993, 0.996), m

_{2}= (0.846, 0.948, 0.953, 0.942, 0.986, 0.992), and m

_{3}= (0.769, 0.922, 0.929, 0.912, 0.980, 0.989), and the relative membership values to the optimal scheme were set to 0.75, 0.50, and 0.25, respectively. Thus, five training samples were obtained for the BP-ANN. The sample outputs were the expected model parameter training output values of 1.00, 0.75, 0.50, 0.25, and 0.00, while the computed outputs were the actual output values (Table 5). The relative membership weights were obtained via network training. The simulation errors in the table show that the trained BP-ANN network has a good simulation ability of relative membership values to the optimum scheme for different schemes. The multi-objective relative membership of the schemes to be optimized was substituted into the trained ANN network to obtain the corresponding membership values (Figure 6). Via optimal sorting, the relative membership value to the optimal scheme of 0.804 for the operation mode of gradually raising the FLWL was higher than the value of 0.494 for the operation mode of raising the FLWL at one time. It indicates that the comprehensive utilization benefits obtained by gradually raising the FLWL of the XLDR during the flood season are higher, with 800 million tons of incoming sediment in the Yellow River.

#### 3.3.3. Suggestions for Optimizing the FLWL of the XLDR during Flood Seasons

^{3}/s, for at least five days to maintain the size of the downstream river channel.

#### 3.4. Discussion

^{3}is transferred, 6 billion m

^{3}is used for socio-economic development, and 2 billion m

^{3}is diverted to the Middle Yellow River. Under the six incoming sediment amount scenarios of 800, 700, 600, 500, 400, and 300 million tons in the Middle Yellow River and the corresponding annual runoff increase of 2 billion m

^{3}, the critical amount of incoming sediment for conversion of the two modes of raising the FLWL gradually or at one time was calculated to be ~450 million tons (see Figure 9).

^{3}, which includes 9.342 billion m

^{3}for retaining sediment and 2.00 billion m

^{3}for regulating the incoming flow and sediment. After completion, the project will be operated with the XLDR, significantly reducing the LYR sediment. Under the incoming sediment amount scenarios of 600 million tons and below, the LYR will be in a state of erosion in the next 50 years. After the Guxian project takes effect, the critical amount of incoming sediment for conversion of the two FLWL operation modes in the XLDR is ~600 million tons (see Figure 10).

## 4. Conclusions

- A mathematical model of water and sediment was established to simulate the water level, outflow, siltation, sediment retention period, and hydropower generation in the reservoir and siltation and minimum bank-full discharge in the river channel to study the FLWL operation modes of the reservoirs in sediment-laden rivers under changing water and sediment conditions. Considering the objectives of flood control, silt reduction, water resources supply, irrigation, hydropower generation, and ecological improvement, an index system for evaluating the comprehensive benefit of the FLWL was proposed. Furthermore, a comprehensive benefit evaluation model of the FLWL was established based on the fuzzy optimization theory and BP-ANN to evaluate the various FLWL operation modes’ effects.
- Considering six scenarios of the incoming sediment amounts, which include 800, 700, 600, 500, 400, and 300 million tons, the water–sediment mathematical model was used to estimate the effect of the operation modes of raising the FLWL gradually or at one time during the XLDR’s sediment retention period. The former mode provided more sediment discharge opportunities and slowed XLDR’s sedimentation rate. Furthermore, the sediment retention period was 4–13 years longer, the average annual siltation in the LYR was lower, and the minimum bank-full discharge of the main channel after 50 years was larger by 150–260 m
^{3}/s. However, the mean annual number of days that did not meet the requirements for the downstream water resources supply, irrigation, and ecological improvement was larger by 0.64–2.16 days, average annual water level from July to August during the main flood period was lower by 6.79–8.35 m, and average annual hydropower generation was lower by 91–197 million kW^{.}h. The above results indicated that the regulation mode of gradually raising the FLWL is good for sediment retention and siltation reduction but poor for economic and ecological improvements. - The reservoir’s comprehensive benefit by raising the FLWL gradually decreases with the reduction in incoming sediment amounts in the Yellow River, while that of the reservoir with raising the FLWL at one time increases. The critical amount of incoming sediment for conversion of the two FLWL operation modes in the XLDR is about 350 million tons. It is suggested that the reservoir be operated in the current mode and gradually raise the FLWL during the flood season when the incoming sediment amount exceeds 350 million tons. However, the FLWL can be raised from the current level of 235 m during the pre-flood season and 248 m during the post-flood season to the designed FLWL of 254 m when the incoming sediment amount is <350 million tons. It is feasible to increase the water amount of the Yellow River by transferring water from the outer basin or reducing sediment into the downstream river channel by constructing large-scale water conservancy projects to improve the flexibility of reservoir operation. When the average annual incoming water volume increases by 2 billion m
^{3}, the critical amount of incoming sediment for converting the two FLWL operation modes will be ~450 million tons. This will increase to ~600 million tons after the Guxian Water Conservancy Project takes effect.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Comparison of calculated and measured cumulative siltation amounts in (

**a**) the XLDR and (

**b**) the LYR.

**Figure 6.**Processes of (

**a**) incoming water and (

**b**) sediment in the Middle Yellow River under different water and sediment scenarios.

**Figure 7.**Comparison of the regulation effects of two FLWL modes for the XLDR in the next 50 years under changing sediment conditions. (

**a**) T

_{SRP_XLDR}. (

**b**) W

_{S}_

_{LYR}. (

**c**) Q

_{bmin_}

_{LYR}after 50 years. (

**d**) T

_{d}. (

**e**) WL

_{XLDR}. (

**f**) N

_{XLDR}. Mode A: gradually raising the FLWL; Mode B: raising the FLWL at one time; A-B: difference between Mode A and Mode B. The data next to the bars in each figure panel reflect the differences.

**Figure 8.**Comparison of the relative membership values to the optimal scheme of the two FLWL operation modes for the XLDR in the next 50 years under different incoming sediment amount scenarios. Mode A: gradually raising the FLWL; Mode B: raising the FLWL at one time.

**Figure 9.**Comparison of the relative membership values to the optimal scheme of the two FLWL operation modes for the XLDR in the next 50 years under a 20% increase in the incoming water. Mode A: gradually raising the FLWL; Mode B: raising the FLWL at one time.

**Figure 10.**Comparison of the relative membership values to the optimal scheme of the two FLWL operation modes for the XLDR in the next 50 years after constructing the Guxian Water Conservancy Project in the upstream section. Mode A: gradually raising the FLWL; Mode B: raising the FLWL at one time.

Overall Objective | Primary Indices | Secondary Indices | Tertiary Indices | Types |
---|---|---|---|---|

The optimal regulation effect of comprehensive utilization of the reservoir | Flood control | Reservoir | Maximum water level for flood control | Cost |

Downstream river channel | Cross-section flow capacity | Benefit | ||

Siltation reduction | Reservoir | Sediment retention period | Benefit | |

Downstream river channel | Siltation amount | Cost | ||

Minimum bank-full discharge of main channel | Benefit | |||

Water resources supply, Irrigation, ecological improvement | Downstream river channel | Number of days that do not meet the minimum discharge requirement | Cost | |

Hydropower generation | Reservoir | Water level in front of the dam | Benefit (within the water level limit) | |

Power Station | Hydropower generation | Benefit |

**Table 2.**Minimum discharge requirements of the Xiaolangdi Reservoir for water supply, irrigation, and ecological improvement in the lower reaches of the Yellow River. Units: m

^{3}/s.

Discharge Requirements | January | February | March | April | May | June | July | August | September | October | November | December |
---|---|---|---|---|---|---|---|---|---|---|---|---|

a. Water resources supply and irrigation | 89 | 307 | 617 | 653 | 509 | 354 | 206 | 151 | 282 | 319 | 130 | 112 |

b. Hydropower generation of a single station | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 |

c. Minimum ecological discharge at sea entry control station | 100 | 100 | 100 | 75 | 75 | 75 | 220 | 220 | 220 | 220 | 100 | 100 |

min(Q_{out}) = max(a,b,c) | 300 | 307 | 617 | 653 | 509 | 354 | 300 | 300 | 300 | 319 | 300 | 300 |

**Table 3.**Operation modes of raising the FLWL gradually and once in the XLDR during the flood season.

Operation Modes | Discharging When Filling Up | Discharging When Gathering Flow | Dispatching with High Sediment Concentration | Lowering the Water Level to Scour the Reservoir Area | |
---|---|---|---|---|---|

Gradually raising the flood limit water level | Starting condition | W_{XLD} ≥ 1.3 billion m^{3} | Q_{in} ≥ 2600 m^{3}/s W _{XLD} ≥ 600 million m^{3} | Q_{in} ≥ 2600 m^{3}/s S _{in} ≥ 200 kg/m^{3} | Q_{in} ≥ 2600 m^{3}/s ΔWs _{XLD} ≥ 4.2 billion m^{3} |

Scheduling command | Q_{HYK} ≥ 3700 m^{3}/s T ≥ 5 d | Q_{HYK} ≥ 3700 m^{3}/s T ≥ 5 d | Pre-discharge or storage water to 300 million m^{3} 2 days in advance,Q _{out} = Q_{in} | Q_{HYK} = 4000 m^{3}/s 2 days in advance until Q_{in} < 2600 m^{3}/s | |

Raising the flood limit water level at one time | Starting condition | Z_{XLD} ≥ 254 m | Same with gradually raising the flood limit water level | / | / |

Scheduling command | Q_{HYK} ≥ 3700 m^{3}/s T ≥ 5 d | Same with gradually raising the flood limit water level | Q_{out} = min(Q_{out}) | Q_{out} = min(Q_{out}) |

_{XLD}is the adjustable water volume, i.e., the sum of incoming water volume and the storage volume above the dead level of the reservoir; Q

_{in}, Q

_{out,}and Q

_{HYK}are the inflow of the Xiaolangdi Reservoir, an outflow of the Xiaolangdi Reservoir, and the flow at the Huayuankou Station of the LYR, respectively; S

_{in}is the sediment concentration in the inflow; ΔWs

_{XLD}is the accumulated siltation in the Xiaolangdi Reservoir; T is the time; Z

_{XLD}is the water level in front of the dam in the Xiaolangdi Reservoir; min (Q

_{out}) is the minimum flow that the reservoir needs to discharge.

Evaluation Index | T_{SRP_XLDR} | W_{S}_{_LYR} | Q_{bmin_}_{LYR} | T_{d} | WL_{XLDR} | N_{XLDR} |
---|---|---|---|---|---|---|

relative membership weights | 0.19 | 0.20 | 0.24 | 0.16 | 0.12 | 0.09 |

Options | Sample Input | Expected Output | Calculated Output | Simulation Errors |
---|---|---|---|---|

Best | (1.000, 1.000, 1.000, 1.000, 1.000, 1.000) | 1.00 | 1.000408 | 0.000408 |

Intermediate 1 | (0.923, 0.974, 0.976, 0.971, 0.993, 0.996) | 0.75 | 0.750250 | 0.000250 |

Intermediate 2 | (0.846, 0.948, 0.953, 0.942, 0.986, 0.992) | 0.50 | 0.500157 | 0.000157 |

Intermediate 3 | (0.769, 0.922, 0.929, 0.912, 0.980, 0.989) | 0.25 | 0.249994 | −0.000006 |

Worst | (0.692, 0.896, 0.906, 0.883, 0.973, 0.985) | 0.00 | 0.000071 | 0.000071 |

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## Share and Cite

**MDPI and ACS Style**

Chen, C.; Gao, X.; Wu, M.; Zhu, C.; An, C.; Li, D.; Liu, J.
Optimizing the Flood Limit Water Level of Reservoirs in Sediment-Laden Rivers under Changing Water and Sediment Conditions: A Case Study of the Xiaolangdi Reservoir. *Water* **2023**, *15*, 3552.
https://doi.org/10.3390/w15203552

**AMA Style**

Chen C, Gao X, Wu M, Zhu C, An C, Li D, Liu J.
Optimizing the Flood Limit Water Level of Reservoirs in Sediment-Laden Rivers under Changing Water and Sediment Conditions: A Case Study of the Xiaolangdi Reservoir. *Water*. 2023; 15(20):3552.
https://doi.org/10.3390/w15203552

**Chicago/Turabian Style**

Chen, Cuixia, Xing Gao, Moxi Wu, Chenghao Zhu, Cuihua An, Da Li, and Junxiu Liu.
2023. "Optimizing the Flood Limit Water Level of Reservoirs in Sediment-Laden Rivers under Changing Water and Sediment Conditions: A Case Study of the Xiaolangdi Reservoir" *Water* 15, no. 20: 3552.
https://doi.org/10.3390/w15203552