# Computing River Discharge Using Water Surface Elevation Based on Deep Learning Networks

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}/s, 0.9973, 207 m

^{3}/s, and 0.0336, respectively. With this data-driven based technology, it will be more convenient to obtain river discharge time series directly from local water surface elevation time series accurately in natural rivers, which is of practical value to water resources management and flood protection.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

#### 2.1.1. Study Area

^{2}, are located above Yichang and hold a strategic position in China’s water resource management and regulation. Figure 1 shows the location of the Yangtze River basin and the hydrologic observation stations used in this paper.

#### 2.1.2. Data Description

#### 2.2. Deep Learning Networks

#### 2.3. Computation Procedure Design

#### 2.3.1. Computation Procedure

#### 2.3.2. Evaluation Metrics

_{o}is the observed data, y

_{p}is the estimated, and ${\overline{y}}_{o}$ is the average value of the observed data.

## 3. Results

#### 3.1. Comparison of the Effect of Different Deep Learning Networks

#### 3.2. Estimated Results in Different Parameters

#### 3.3. Estimated Results in Different Datasets

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of the Yangtze River basin and hydrologic observation stations located within the basin.

**Figure 4.**Basic structure of deep learning networks. (

**a**) Workflow of RNN, (

**b**) the basic unit of LSTM, (

**c**) the basic unit of GRU, (

**d**) the typical structure of Bi-direction networks, (

**e**) the typical structure of Seq2eq, and (

**f**) the typical structure of Seq2eq attention.

**Figure 6.**Computation results of eight deep learning networks in Zhutuo (the red bar in these figures represent relative error at different times and the value is determined by the right vertical axis). (

**a**,

**b**) BiGRU’s performances on the training dataset and testing dataset respectively; (

**c**,

**d**) BiLSTM’s performances on the training dataset and testing dataset, respectively; (

**e**,

**f**) BiRNN’s performances on the training dataset and testing dataset, respectively; (

**g**,

**h**) GRU’s performances on the training dataset and testing dataset, respectively; (

**i**,

**j**) LSTM’s performances on the training dataset and testing dataset, respectively; (

**k**,

**l**) RNN’s performances on the training dataset and testing dataset, respectively; (

**m**,

**n**) Seq2Seq’s performances on the training dataset and testing dataset, respectively; (

**o**,

**p**) Sq2Seq attention’s performances on the training dataset and testing dataset, respectively.

**Figure 9.**Relation between estimated discharge and observed discharge in six stations. (

**a**) Gaochang, (

**b**) Fushun, (

**c**) Panzhihua, (

**d**) Sanduizi, (

**e**) Wudongde, and (

**f**) Zhutuo.

**Figure 10.**White noise examination of six stations. (

**a**) Gaochang, (

**b**) Fushun, (

**c**) Panzhihua, (

**d**) Sanduizi, (

**e**) Wudongde, and (

**f**) Zhutuo.

Hyperparameters | a | b | c | d | e | f | g | h | i |
---|---|---|---|---|---|---|---|---|---|

Batch size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 12 | 24 |

Time step | 72 | 72 | 48 | 72 | 72 | 96 | 72 | 72 | 72 |

Number of neurons | 128 | 64 | 128 | 128 | 128 | 128 | 256 | 128 | 128 |

Number of layers | 2 | 2 | 2 | 4 | 6 | 2 | 2 | 2 | 2 |

Evaluation Metrics | a | b | c | d | e | f | g | h | i |
---|---|---|---|---|---|---|---|---|---|

RMSE | 266.008 | 258.448 | 268.750 | 267.236 | 269.780 | 266.016 | 256.950 | 261.046 | 256.058 |

NSE | 0.9971 | 0.9973 | 0.9971 | 0.9971 | 0.9970 | 0.9971 | 0.9973 | 0.9972 | 0.9973 |

MAE | 216.089 | 210.169 | 219.553 | 210.205 | 213.596 | 215.500 | 207.430 | 213.075 | 207.624 |

MAPE | 0.0369 | 0.0355 | 0.0355 | 0.0352 | 0.0336 | 0.0369 | 0.0360 | 0.0357 | 0.0355 |

Evaluation Metrics | a | b | c | d | e | f | g | h | i |
---|---|---|---|---|---|---|---|---|---|

RMSE | 5 | 3 | 8 | 7 | 9 | 6 | 2 | 4 | 1 |

NSE | 5 | 1 | 5 | 5 | 9 | 5 | 1 | 4 | 1 |

MAE | 8 | 3 | 9 | 4 | 6 | 7 | 1 | 5 | 2 |

MAPE | 8 | 3 | 3 | 2 | 1 | 8 | 7 | 6 | 3 |

Total scores | 26 | 10 | 25 | 18 | 25 | 26 | 11 | 19 | 7 |

Evaluation Metrics | Gaochang | Fushun | Panzhihua | Sanduizi | Wudongde | Zhutuo |
---|---|---|---|---|---|---|

RMSE | 154.084 | 77.161 | 214.67 | 16.257 | 98.836 | 266.009 |

NSE | 0.9898 | 0.9800 | 0.9678 | 0.9999 | 0.9984 | 0.9971 |

MAE | 70.546 | 47.760 | 94.089 | 12.443 | 80.534 | 216.089 |

MAPE | 0.0536 | 0.1272 | 0.0548 | 0.004 | 0.0276 | 0.0370 |

Evaluation Metrics | Gaochang | Fushun | Panzhihua | Sanduizi | Wudongde | Zhutuo |
---|---|---|---|---|---|---|

RMSE | 4 | 2 | 5 | 1 | 3 | 6 |

NSE | 4 | 5 | 6 | 1 | 2 | 3 |

MAE | 3 | 2 | 5 | 1 | 4 | 6 |

MAPE | 4 | 6 | 5 | 1 | 2 | 3 |

Total scores | 15 | 15 | 21 | 4 | 11 | 18 |

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## Share and Cite

**MDPI and ACS Style**

Liu, W.; Zou, P.; Jiang, D.; Quan, X.; Dai, H.
Computing River Discharge Using Water Surface Elevation Based on Deep Learning Networks. *Water* **2023**, *15*, 3759.
https://doi.org/10.3390/w15213759

**AMA Style**

Liu W, Zou P, Jiang D, Quan X, Dai H.
Computing River Discharge Using Water Surface Elevation Based on Deep Learning Networks. *Water*. 2023; 15(21):3759.
https://doi.org/10.3390/w15213759

**Chicago/Turabian Style**

Liu, Wei, Peng Zou, Dingguo Jiang, Xiufeng Quan, and Huichao Dai.
2023. "Computing River Discharge Using Water Surface Elevation Based on Deep Learning Networks" *Water* 15, no. 21: 3759.
https://doi.org/10.3390/w15213759