# Prediction of Tail Water Level under the Influence of Backwater Effect Based on Deep Learning Models: A Case Study in the Xiangjiaba Hydropower Station

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## Abstract

**:**

^{3}/s and 7000 m

^{3}/s, respectively. Finally, based on the analysis of the time lag and the threshold of the backwater effect, a deep learning model (LSTM)-based TWL forecasting method is established and applied to predict the TWL of the XJB station. The results show that the forecasting model has a good predictive performance, with 98.22% of absolute errors less than 20 cm. The mean absolute error over the validation dataset is 5.27 cm, and the maximum absolute error is 63.35 cm. Compared with the LSTM-based prediction model without considering the backwater effect, the mean absolute error decreased by 31%, and the maximum absolute error decreased by 71%.

## 1. Introduction

## 2. Case Study, Data, and Method

#### 2.1. Case Study

^{3}, the flood control capacity is 903 million m

^{3}, and the total capacity is 5.163 billion m

^{3}. Figure 1 shows that the upstream water level of the XJB is influenced by the operation of the Xiluodu Hydropower Station (XLD), while the downstream water level is affected by the backwater effect of the confluence of the Hengjiang River (HJR) and the Minjiang River (MJR). The complex boundary conditions make the prediction of water level by hydrodynamic method or water balance method prone to large errors [20].

#### 2.2. Data

#### 2.3. Method

_{t}determines which water level influence information of h

_{t−1}and X

_{t}should be discarded at time t. The input gate is used to determine how much X

_{t}and h

_{t−1}water level impact information needs to be passed to C

_{t}at time t in order to update the information stored by C

_{t−1}. LSTM uses the output gate to control the unit state C

_{t}. at the current time t and how much water level influence information in h

_{t−1}and X

_{t}should be output [23,24].

## 3. Analysis of Backwater Effect

#### 3.1. Analysis Method of Backwater Effect

#### 3.2. Time Lag Analysis of Backwater Effect

#### 3.3. Threshold Analysis of Backwater Effect

^{3}/s for HJR run off and 7000 m

^{3}/s for MJR run off). These thresholds divide the scenarios into two types: Scenario 1, where either the HJR flow rate or the MJR flow rate exceeds their respective thresholds, and Scenario 2, where both flow rates are below their thresholds. Additionally, an overall scenario without threshold division is also considered. The 12 h prediction errors for three scenarios are visualized in Figure 7.

^{3}/s as the threshold for the HJR flow rate and 7000 m

^{3}/s as the threshold for the MJR flow rate can effectively differentiate between forecast scenarios. When both flow rates are below the threshold, the maximum absolute prediction error is 55.02 cm, and the average prediction error is 5.93 cm. In comparison, it can be assumed that this scenario is minimally impacted by the backwater effect.

## 4. Analysis of Predictive Performance

#### 4.1. Prediction Result of the WBE Model

#### 4.2. Prediction Result of LSTM Model

#### 4.3. Result Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Mossa, M.; Petrillo, A.; Chanson, H.; Yausda, Y.; Takahashi, M.; Ohtsu, I. Tailwater level effects on flow conditions at an abrupt drop. J. Hydraul. Res.
**2005**, 43, 217–224. [Google Scholar] [CrossRef] - Ahn, J.; Na, Y.; Park, W.S. Development of Two-Dimensional Inundation Modelling Process using MIKE21 Model. KSCE J. Civ. Eng.
**2019**, 23, 3968–3977. [Google Scholar] [CrossRef] - Zhu, S.; Hrnjica, B.; Ptak, M.; Choiński, A.; Sivakumar, B. Forecasting of water level in multiple temperate lakes using machine learning models. J. Hydrol.
**2020**, 585, 124819. [Google Scholar] [CrossRef] - Li, X.; Liu, B.; Wang, Y.; Yang, Y.; Liang, R.; Peng, F.; Xue, S.; Zhu, Z.; Li, K. The hydrodynamic and environmental characteristics of tributary bay influenced by backwater jacking and intrusion of main reservoir. Hydrol. Earth Syst. Sci.
**2020**, 24, 5057–5076. [Google Scholar] [CrossRef] - Liang, Z. Simulate the forecast capacity of a complicated water quality model using the long short-term memory approach. J. Hydrol.
**2020**, 581, 124432. [Google Scholar] [CrossRef] - Choi, C.; Kim, J.; Han, H.; Han, D.; Kim, H.S. Development of water level prediction models using machine learning in wetlands: A case study of Upo wetland in South Korea. Water
**2019**, 12, 93. [Google Scholar] [CrossRef] - Wang, D.; Qi, X.; Wen, S.; Dan, Y. Robust nonlinear control and svm classifier based fault diagnosis for a water level process. ICIC Express Lett.
**2015**, 9, 767–774. [Google Scholar] - Haijiao, D.; Wengang, C. Prediction Model of River Water Level Based on LS-SVM. In Proceedings of the International Conference on Intelligent Computation Technology & Automation, Nanchang, China, 14–15 June 2015; IEEE Computer Society: Los Alamitos, CA, USA, 2015. [Google Scholar] [CrossRef]
- Wang, H.; Song, L. Water Level Prediction of Rainwater Pipe Network Using an SVM-Based Machine Learning Method. Int. J. Pattern Recognit. Artif. Intell.
**2019**, 34, 2051002. [Google Scholar] [CrossRef] - Zhang, J.; Wang, X.; Zhao, C.; Bai, W.; Shen, J.; Li, Y.; Pan, Z.; Duan, Y. Application of cost-sensitive LSTM in water level prediction for nuclear reactor pressurizer—ScienceDirect. Nucl. Eng. Technol.
**2020**, 52, 1429–1435. [Google Scholar] [CrossRef] - Wunsch, A.; Liesch, T.; Broda, S. Groundwater level forecasting with artificial neural networks: A comparison of long short-term memory (LSTM), convolutional neural networks (CNNs), and non-linear autoregressive networks with exogenous input (NARX). Hydrol. Earth Syst. Sci.
**2021**, 25, 1671–1687. [Google Scholar] [CrossRef] - Shuofeng, L.; Puwen, L.; Koyamada, K. LSTM Based Hybrid Method for Basin Water Level Prediction by Using Precipitation Data. J. Adv. Simul. Sci. Eng.
**2021**, 8, 40–52. [Google Scholar] [CrossRef] - Zhang, Z.; Qin, H.; Yao, L.; Liu, Y.; Jiang, Z.; Feng, Z.; Ouyang, S.; Pei, S.; Zhou, J. Downstream Water Level Prediction of Reservoir based on Convolutional Neural Network and Long Short-Term Memory Network. J. Water Resour. Plan. Manag.
**2021**, 147, 04021060. [Google Scholar] [CrossRef] - Nourani, V. Reply to comment on ‘Nourani V, Mogaddam AA, Nadiri AO. An ANN-based model for spatiotemporal groundwater level forecasting. Hydrological Processes 2008, 22, 5054–5066’. Hydrol. Process.
**2010**, 24, 370–371. [Google Scholar] [CrossRef] - Kochhar, A.; Singh, H.; Sahoo, S.; Litoria, P.K.; Pateriya, B. Prediction and forecast of pre-monsoon and post-monsoon groundwater level: Using deep learning and statistical modelling. Model. Earth Syst. Environ.
**2021**, 8, 2317–2329. [Google Scholar] [CrossRef] - Litrico, X.; Belaud, G.; Baume, J.P.; Ribot-Bruno, J. Hydraulic modeling of an automatic upstream water-level control gate. J. Irrig. Drain. Eng.
**2005**, 131, 176–189. [Google Scholar] [CrossRef] - Bazartseren, B.; Hildebrandt, G.; Holz, K.P. Short-term water level prediction using neural networks and neuro-fuzzy approach. Neurocomputing
**2003**, 55, 439–450. [Google Scholar] [CrossRef] - Yan, H.U. Reservoir sediment computation of Xiangjiaba hydropower plant. Yangtze River
**2003**, 4, 36–38+48. [Google Scholar] - Ma, W.; Nie, D.; Cao, Y. Key Technical Schemes for ±800 kV UHVDC Project from Xiangjiaba to Shanghai. Power Syst. Technol.
**2007**, 38, 34–38. [Google Scholar] [CrossRef] - Lu, P.; Zhou, J.; Wang, C.; Qiao, Q.; Mo, L. Short-term hydro generation scheduling of Xiluodu and Xiangjiaba cascade hydropower stations using improved binary-real coded bee colony optimization algorithm. Energy Convers. Manag.
**2015**, 91, 19–31. [Google Scholar] [CrossRef] - Yang, Y.; Zhang, M.; Sun, Z.; Han, J.; Li, H.; You, X. The relationship between water level change and river channel geometry adjustment in the downstream of the Three Gorges Dam. J. Geogr. Sci.
**2018**, 28, 19. [Google Scholar] - Cao, G.; Cai, Z. Research and Application of Optimized Model for Long-term Daily-operation of the Three Gorges & Gezhouba Cascade Power Stations. In Proceedings of the International Symposium on Three Gorges Project and Water Resources Development and Protection of Yangtze River; CTGPC: Wuhan, China, 2010. [Google Scholar]
- Wang, B.; Liu, S.; Wang, B.; Wu, W.; Wang, J.; Shen, D. Multi-step ahead short-term predictions of storm surge level using CNN and LSTM network. Acta Oceanol. Sin.
**2021**, 40, 104–118. [Google Scholar] [CrossRef] - Jung, S.; Cho, H.; Kim, J.; Lee, J. Prediction of water level in a tidal river using a deep-learning based LSTM model. J. Korea Water Resour. Assoc.
**2018**, 51, 1207–1216. [Google Scholar]

**Figure 13.**Comparison of prediction errors depending on whether the model considers the backwater effect.

Data Type | Station | Time Series | Time Step |
---|---|---|---|

Water level | Upstream water level and tail water level of XJB | 2015–2020 | 2 h, 1 h |

Flow rate | XLD and XJB’s outbound flow rate, inbound Flow rate and abandon flow rate, HJR and MJR run off | 2015–2020 | 1 h |

Output | XLD, XJB plant, branch plant, and each unit’s output | 2015–2020 | 2 h, 1 h |

Empirical curve | XLD’s and XJB’s water level–storage curve, head loss curve, unit flow rate curve, tail water level curve, etc. | / | / |

Period | Characteristic Variable |
---|---|

Historical data | XJB upstream and downstream water levels, rainfall among XLD and XJB, Pengshan and MJR rainfall, HJR rainfall, HJR run off, MJR run off, XJB inflow, XJB output, XJB abandon flow |

Future data | Rainfall among XLD and XJB, XLD and XJB output, XLD and Xiangjiaba abandon flow, HJR run off, MJR run off |

Mean Absolute Error | Maximum Absolute Error | |
---|---|---|

LSTM_Model1 | 7.66 | 217.52 |

LSTM_Model2 | 5.27 | 63.35 |

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**MDPI and ACS Style**

Zhang, S.; Xie, S.; Wang, Y.; Xu, Y.; Zhang, Z.; Jia, B.
Prediction of Tail Water Level under the Influence of Backwater Effect Based on Deep Learning Models: A Case Study in the Xiangjiaba Hydropower Station. *Water* **2023**, *15*, 3854.
https://doi.org/10.3390/w15213854

**AMA Style**

Zhang S, Xie S, Wang Y, Xu Y, Zhang Z, Jia B.
Prediction of Tail Water Level under the Influence of Backwater Effect Based on Deep Learning Models: A Case Study in the Xiangjiaba Hydropower Station. *Water*. 2023; 15(21):3854.
https://doi.org/10.3390/w15213854

**Chicago/Turabian Style**

Zhang, Sen, Shuai Xie, Yongqiang Wang, Yang Xu, Zheng Zhang, and Benjun Jia.
2023. "Prediction of Tail Water Level under the Influence of Backwater Effect Based on Deep Learning Models: A Case Study in the Xiangjiaba Hydropower Station" *Water* 15, no. 21: 3854.
https://doi.org/10.3390/w15213854