# Transformer Based Water Level Prediction in Poyang Lake, China

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}during the dry season to around 3000 km

^{2}in the wet season [38]. The lake bottom elevation increases from north to south, and there are five hydrological gauging stations: Hukou, Xingzi, Duchang, Tangyin, and Kangshan stations.

#### 2.2. Research Data

#### 2.3. Transformer-Based Water Level Prediction

#### 2.3.1. Modelling

#### 2.3.2. Training and Testing

_{i}is the observation value, $x$

_{max}and $x$

_{min}are the maximum and minimum of the data set, respectively.

^{0}, we then input them into several transformer layers to conduct feature representation learning according to the following formulas:

#### 2.4. LSTM-Based Water Level Prediction

#### 2.5. Implementation Details

^{−5}. The batch size is 32 and we train the model up to 150 epochs. We evaluate the model every one epoch and select the model that performs best on the validation set for producing the final results. All the training and testing operations are conducted on a GeForce RTX 3090 GPU card with 24 G memory.

#### 2.6. Performance Evaluation

^{2}), Nash–Sutcliffe efficiency coefficient (NSE). and the root mean square error (RMSE). The value of R

^{2}is from 0 to 1, and the larger the value, the better the model simulation effect. NSE is a parameter that determines the relative importance of the residual variance compared to the observed variance. It takes a value from negative infinity to 1. The closer to 1, the better the simulation effect and the higher the credibility of the model; close to 0, the simulation result is close to the mean values of the observations, the root mean square error (RMSE), but the process simulation error is large. An RMSE value of 0 indicates that the observed value is in perfect agreement with the predicted value.

^{2}, RMSE, and NSE are listed as follows:

## 3. Results and Discussion

#### 3.1. Model Performance at Lake Water Level Simulation

^{2}of 0.84–0.91 at four hydrological stations in training stage and an R

^{2}of 0.76–0.84 in testing stage. The RMSE is 1.12 m, 1.02 m, 0.96 m, and 0.94 m in training stage and 1.60 m, 1.63 m, 1.66 m, and 1.28 m in testing stage in Xingzi, Duchang, Tanyin, and Kangshan stations, respectively. The NSE of S1 is 0.83–0.91 and 0.69–0.79 in training stage and testing stages, respectively. Scenario 2 (S2) produced a much better simulation at all four stations. R

^{2}values increased from 0.76–0.91 for S1 to 0.97–1.0 for S2, which showed the highest fit between observations and simulations. The RMSE values of S2 are 0.16 m, 0.15 m, 0.14 m, and 0.14 m for four stations in the training stage respectively, and this is much lower than that of S1 (0.94–1.12 m) at the same stage. Similarly, in the testing stage, the RMSE values decreased from 1.28–1.66 m in S1 to 0.26–0.70 m in S2. NSE values of S2 are higher than 0.94 in both training and testing stages at all four stations, and are higher than that of S1. Moriasi [44] showed that NSE values around 0.75 mean the model simulation is effective. Therefore, the simulation accuracy of S2 is high and can reflect the temporal water level variation characteristics in Poyang Lake. The better performance of S2 indicated that the discharge of the Yangtze River has non-negligible effects on the Poyang Lake water level variations. Li [37] found similar results using the back-propagation neural network, and Yu 2022 [45] also found that the Yangtze River plays the most important role in lake water level variations, followed by five rivers inflowing, and lake rainfall effects were the weakest.

#### 3.2. The Contribution of the Yangtze River on Simulation Performance in Different Stages

#### 3.3. Effects of Window Size, Model Layers, and Lead Time on Model Performance

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Poyang Lake area (

**A**) and rivers, hydrological stations and gauging stations in Poyang Lake (

**B**).

**Figure 2.**The Transformer Model architecture [29].

**Figure 9.**Effects of lead time on model accuracy in Xingzi Station. The red vertical line split the results into two groups to indicate the reason why the difference gap suddenly increased from day 7 to day 15: the left group are the prediction results for the coming 1 day to 7 days correspondingly; the right group are the prediction results for day 15 and day 30 respectively.

Data Description | Gauging Station | Duration | Application |
---|---|---|---|

Meteorological data | 14 national meteorological stations | 1960–2013 | Input |

Catchment inflow | Waizhou (Ganjiang River) | 1960–2013 | Input |

Lijiadu (Fuhe River) | 1960–2013 | Input | |

Meigang (Xinjiang River) | 1960–2013 | Input | |

Dufengkeng (Raohe River) Hushan (Raohe River) | 1960–2013 1960–2013 | Input Input | |

Wanjiabu (Xiushui River) | 1960–2013 | Input | |

Yangtze River water level | Hukou | 1960–2013 | Input |

Poyang lake water level | Xingzi | 1960–2013 | Output |

Duchang | 1960–2013 | Output | |

Tangyin | 1960–2013 | Output | |

Kangshan | 1960–2013 | Output |

Stage | Index | Xingzi | Duchang | Tangyin | Kangshan |
---|---|---|---|---|---|

Scenario 1 | |||||

Training | R^{2} | 0.91 | 0.91 | 0.89 | 0.84 |

RMSE | 1.12 | 1.02 | 0.96 | 0.94 | |

NSE | 0.91 | 0.91 | 0.89 | 0.83 | |

Testing | R^{2} | 0.84 | 0.84 | 0.81 | 0.76 |

RMSE | 1.60 | 1.63 | 1.66 | 1.28 | |

NSE | 0.79 | 0.76 | 0.69 | 0.66 | |

Scenario 2 | |||||

Training | R^{2} | 1.00 | 1.00 | 1.00 | 1.00 |

RMSE | 0.16 | 0.15 | 0.14 | 0.14 | |

NSE | 1.00 | 1.00 | 1.00 | 1.00 | |

Testing | R^{2} | 0.99 | 0.97 | 0.97 | 0.98 |

RMSE | 0.40 | 0.70 | 0.43 | 0.26 | |

NSE | 0.99 | 0.94 | 0.96 | 0.98 |

Study Area | Temporal Scale | Model Input | Training Period | Testing Period | Performance Evaluation Criteria | Reference | |
---|---|---|---|---|---|---|---|

LSTM | Poyang Lake | Daily | River flows | 1956–1980 | 1981–2000 | R^{2}, RMSE, NSE | Guo and Lai 2020 [32] |

LSTM, SVM | Dongting Lake | Daily | Water level, water inflow, rainfall | 2003–2012 | 2011–2013 | R^{2}, RMSE | Liang 2018 [30] |

FFNN, LSTM | Vrana Lake | Monthly | Water level | 1978–2016 | 12 months | R, RMSE | Hrnjica and Bonacci 2019 [31] |

FFNN, DL | 69 lakes in Poland | Monthly | Water level | 1984–2014 (2/3rd) | 1984–2014 (1/3rd) | R, RMSE | Zhu 2020 [46] |

Transformer | Poyang Lake | Daily and monthly | Water level, meteorological factors | 1960–2000 | 2001–2013 | R^{2}, RMSE, NSE | This study |

Station | Model | Training Stage | Testing Stage | ||||
---|---|---|---|---|---|---|---|

R_{2} | RMSE/m | NSE | R_{2} | RMSE/m | NSE | ||

Xingzi | LSTM | 0.98 | 0.81 | 0.94 | 0.98 | 0.55 | 0.97 |

Transformer | 1.00 | 0.16 | 1.00 | 0.99 | 0.40 | 0.99 | |

Duchang | LSTM | 0.92 | 0.91 | 0.85 | 0.97 | 0.79 | 0.93 |

Transformer | 1.00 | 0.15 | 1.00 | 0.97 | 0.70 | 0.94 | |

Tangyin | LSTM | 0.99 | 0.76 | 0.95 | 0.96 | 0.48 | 0.95 |

Transformer | 1.00 | 0.14 | 1.00 | 0.97 | 0.43 | 0.96 | |

LSTM | 0.97 | 0.77 | 0.89 | 0.96 | 0.37 | 0.95 | |

Kangshang | Transformer | 1.00 | 0.14 | 1.00 | 0.98 | 0.26 | 0.98 |

Period | RMSE Contribution Rate (%) | NSE Contribution Rate (%) | ||||||
---|---|---|---|---|---|---|---|---|

Xingzi | Duchang | Tangyin | Kangshan | Xingzi | Duchang | Tangyin | Kangshan | |

Dry period | 38.0 | 2.8 | 58.8 | 65.0 | 50.1 | 8.6 | 223.5 | 81.4 |

Rising period | 70.8 | 62.4 | 79.3 | 72.5 | 19.1 | 24.8 | 36.9 | 23.7 |

Flood period | 85.2 | 84.8 | 79.7 | 83.9 | 514.6 | 506.6 | 507.8 | 803.1 |

Receding period | 92.0 | 80.3 | 82.6 | 86.4 | 505.5 | 550.6 | 477.0 | 274.1 |

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**MDPI and ACS Style**

Xu, J.; Fan, H.; Luo, M.; Li, P.; Jeong, T.; Xu, L.
Transformer Based Water Level Prediction in Poyang Lake, China. *Water* **2023**, *15*, 576.
https://doi.org/10.3390/w15030576

**AMA Style**

Xu J, Fan H, Luo M, Li P, Jeong T, Xu L.
Transformer Based Water Level Prediction in Poyang Lake, China. *Water*. 2023; 15(3):576.
https://doi.org/10.3390/w15030576

**Chicago/Turabian Style**

Xu, Jiaxing, Hongxiang Fan, Minghan Luo, Piji Li, Taeseop Jeong, and Ligang Xu.
2023. "Transformer Based Water Level Prediction in Poyang Lake, China" *Water* 15, no. 3: 576.
https://doi.org/10.3390/w15030576