# Dongting Lake Water Level Forecast and Its Relationship with the Three Gorges Dam Based on a Long Short-Term Memory Network

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## Abstract

**:**

^{2}). The test shows the LSTM model has better accuracy compared to the support vector machine (SVM) model. Furthermore, the model is adjusted to simulate the situation where the TGD does not exist to explore the dam’s impact. The experiment shows that the water level of Dongting Lake drops conspicuously every year from September to November during the TGD impounding period, and the water level increases mildly during dry seasons due to TGD replenishment. Additionally, the impact of the TGD results in a water level decline in Dongting Lake during flood peaks and a subsequent lagged rise. This research provides a tool for flood forecasting and offers a reference for TGD water regulation.

## 1. Introduction

^{3}[5]. Like any other hydraulic project in the world, the TGD has a large impact on the surrounding geological and environmental systems. Its function of flood control and hydroelectric generation can alter the downstream hydrologic regime by affecting the streamflow of the Yangtze River, the total runoff quantity, water quality, and duration of extreme runoff [6,7]. Additionally, as one of the most controversial projects in the world, the TGD has impacted the landscape, wildlife, agriculture, and other areas [8]. For Dongting Lake, the river–lake relationship becomes increasingly complicated [9], which makes it increasingly challenging to determine how the water level of Dongting Lake is affected by the TGD; however, this relationship is worthy of study.

## 2. Materials and Methods

#### 2.1. Study Area and Data

#### 2.2. Methodology

_{t}refers to the vector at time step t, which is the input vector, and h

_{t}is the output hidden vector. h

_{t}contains information from h

_{t−}

_{1}, and together with the input vector at time t (x

_{t}), the information is passed on to the next time step t + 1, ensuring the information will persist.

_{t}, i

_{t}, o

_{t}, and C

_{t}refer to the forget gate, input gate, output gate, and memory cell vectors, respectively, and W

_{f}, W

_{i}, W

_{o}, and W

_{C}are the weighted parameter matrices. σ and tanh are the activation functions computed as Equations (7) and (8).

#### 2.3. LSTM Model Establishment

#### 2.3.1. Variable Selection

- A series of various units must be transformed to be dimensionless using a normalization method. For instance, a comparability sequence ${x}_{i}\left(k\right)$ is transformed as follows:$${x}_{i}^{\ast}\left(\mathrm{k}\right)=\frac{{x}_{i}\left(\mathrm{k}\right)-\mathrm{min}\left({x}_{i}\left(\mathrm{k}\right)\right)}{\mathrm{max}\left({x}_{i}\left(\mathrm{k}\right)\right)-\mathrm{min}\left({x}_{i}\left(\mathrm{k}\right)\right)}$$
- Calculate the Grey relational coefficients using the preprocessed sequences. The Grey relational coefficient is defined as below:$${\gamma}_{i}\left(k\right)=\frac{\underset{\forall j\in i}{\mathrm{min}}\underset{\forall k}{\mathrm{min}}\left|{x}_{o}^{\ast}\left(k\right)-{x}_{i}^{\ast}\left(k\right)\right|+\rho \underset{\forall j\in i}{\mathrm{max}}\underset{\forall k}{\mathrm{max}}\left|{x}_{o}^{\ast}\left(k\right)-{x}_{i}^{\ast}\left(k\right)\right|}{\left|{x}_{o}^{\ast}\left(k\right)-{x}_{i}^{\ast}\left(k\right)\right|+\rho \underset{\forall j\in i}{\mathrm{max}}\underset{\forall k}{\mathrm{max}}\left|{x}_{o}^{\ast}\left(k\right)-{x}_{i}^{\ast}\left(k\right)\right|}$$
- Calculate the Grey relational grade ${r}_{i}$, which is the mean value of each Grey relational coefficient and is defined as follows:$${r}_{i}=\frac{1}{n}{\displaystyle \sum}_{k=1}^{n}{\gamma}_{i}\left(k\right)$$

#### 2.3.2. Data Processing

#### 2.3.3. LSTM Network Design

#### Base Model Design

#### Model Evaluation

^{2}) is used to measure prediction performance. These two indexes are calculated using Equations (13) and (14) as follows:

^{2}is 1, it indicates that the predictions perfectly fit the data. That is, the closer R

^{2}is to 1, the better the prediction model.

#### Model Optimization

^{−6}). Also, a good default value for the learning rate η is 0.001.

## 3. Results

^{2}) were calculated to evaluate the model. The result showed the RMSE was 0.083, and the coefficient of determination was 0.999, which showed high precision. Because one of the main characteristics of deep learning is that it is stochastic, the model is very likely to obtain a different result every time we run the network. However, after a great deal of tests, the RMSE was always within the range of 0.080–0.100. The coefficient of determination stayed at 0.999, which showed the robustness of the LSTM network. Table 4 shows the results of running the model 10 times on the test dataset. The test results suggest that this deep learning network is a sound prediction model and capable of portraying the relationship between the TGD and Dongting Lake water level.

## 4. Discussion

#### 4.1. Support Vector Machine Comparison Experiment

^{2}was 0.873, which was well under the 0.999 LSTM model performance.

#### 4.2. TGD’s Impact on Dongting Lake Water Level

^{3}flow per second [50]. Nevertheless, the water level of Dongting Lake did not increase much as a result. In fact, the lake level dropped 0.22 m after the TGD discharge was reduced to 30000 m

^{3}/s (maximum outflow), as opposed to 70000 m

^{3}/s (maximum inflow) if the TGD does not exist. The water level increased substantially in August after the flood, which was when the TGD opened sluices to release the flood water. By doing so, the TGD managed to stagger the flood peak to alleviate the rise in water level in Dongting Lake. Then, the water level showed a moderate decline in September and November due to the impoundment of the TGD.

## 5. Conclusions

- The water level of Dongting Lake dropped conspicuously when the TGD is being impounded, which occurred annually from September to November. The drop was approximately 0.3 m on average and could be as large as 1.2 m in a single day.
- The water level increased mildly during dry seasons because of the TGD water replenishment strategy, which demonstrated the water conservancy effects of the dam.
- There was a decline in the water level of Dongting Lake during flood seasons (mostly July during flood peaks) and a lagged increase occurred later, proving that the dam’s effects on flood control and staggering the flood peak.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 10.**Water level difference between reality and simulation every year with (

**a**–

**k**) showing years 2003–2013, respectively.

Variables | TGD discharge | Xiangtan discharge | Taojiang discharge | Taoyuan discharge | Jinshi discharge | Precipitation |

Grey relational grade | 0.7242 | 0.6699 | 0.6798 | 0.6570 | 0.6140 | 0.6197 |

Var 1 | Var 2 | Var 3 | Var 4 | Var 5 | Var 6 | Var 7 |
---|---|---|---|---|---|---|

Water level | TGD discharge | Xiangtan discharge | Taojiang discharge | Taoyuan discharge | Jinshi discharge | Precipitation |

Var1 (t − 1) ^{1} | Var2 (t − 1) | Var3 (t − 1) | Var4 (t − 1) | Var5 (t − 1) | Var6 (t − 1) | Var7 (t − 1) | Var1 (t) |
---|---|---|---|---|---|---|---|

Water level | TGD discharge | Xiangtan discharge | Taojiang discharge | Taoyuan discharge | Jinshi discharge | Precipitation | Water level |

^{1}Var1 (t

**−**1) refers to variable 1 at time t

**−**1, and the same is true for the other variables.

No. | RMSE | R^{2} |
---|---|---|

1 | 0.083 | 0.999 |

2 | 0.091 | 0.999 |

3 | 0.099 | 0.999 |

4 | 0.090 | 0.999 |

5 | 0.086 | 0.999 |

6 | 0.086 | 0.999 |

7 | 0.085 | 0.999 |

8 | 0.085 | 0.999 |

9 | 0.088 | 0.999 |

10 | 0.087 | 0.999 |

Input | Output | |||||
---|---|---|---|---|---|---|

Var1 | Var2 | Var3 | Var4 | Var5 | Var6 | Target variable |

TGD discharge | Xiangtan discharge | Taojiang discharge | Taoyuan discharge | Jinshi discharge | Precipitation | Water level |

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**MDPI and ACS Style**

Liang, C.; Li, H.; Lei, M.; Du, Q.
Dongting Lake Water Level Forecast and Its Relationship with the Three Gorges Dam Based on a Long Short-Term Memory Network. *Water* **2018**, *10*, 1389.
https://doi.org/10.3390/w10101389

**AMA Style**

Liang C, Li H, Lei M, Du Q.
Dongting Lake Water Level Forecast and Its Relationship with the Three Gorges Dam Based on a Long Short-Term Memory Network. *Water*. 2018; 10(10):1389.
https://doi.org/10.3390/w10101389

**Chicago/Turabian Style**

Liang, Chen, Hongqing Li, Mingjun Lei, and Qingyun Du.
2018. "Dongting Lake Water Level Forecast and Its Relationship with the Three Gorges Dam Based on a Long Short-Term Memory Network" *Water* 10, no. 10: 1389.
https://doi.org/10.3390/w10101389