# Comparison of Long Short Term Memory Networks and the Hydrological Model in Runoff Simulation

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## Abstract

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## 1. Introduction

## 2. Study Area and Data Source

#### 2.1. Study Area

#### 2.2. Data Source

#### 2.3. Data Pre-Processing

## 3. Methodology

#### 3.1. Long Short Term Memory Network

#### 3.2. LSTM Setup

#### 3.3. ANN Setup

#### 3.4. Tuning Procedure for LSTM

#### 3.4.1. Tuning for Window Size

#### 3.4.2. Tuning for Hyperparameters

#### 3.5. Evaluation Metrics

#### 3.6. Hydrological Model

## 4. Results

#### 4.1. Effect of the Window Size

#### 4.2. Overall Performance of LSTMs

#### 4.3. Comparison of Simulation Capability with Other Models

## 5. Discussion

#### 5.1. Potential Factors that Influence Runoff Simulation

#### 5.2. Limitations and Uncertainties of Neural Network

#### 5.3. Implications for Regional Water Resources Management

## 6. Conclusions

- The performance of the proposed LSTM model is strongly affected by the widow size. A window in improper large size will dramatically deteriorate the model performance. In terms of PYLB, better model performance can be achieved by increasing the window size when it is less than 15 days. When the window size is between 15 and 60 days, the model performance will remain stable as the window size increase. A window size of 15 days might be appropriate for both accuracy and computational efficiency.
- The proposed LSTM model can achieve desirable results (where the NSE ranged from 0.60 to 0.92 for the test period) with precipitation data as the only input. And the performance can be improved simply by feeding the model with more meteorological variables (where NSE ranged from 0.74 to 0.94 for the test period). In addition, the LSTM model with more meteorological variables is able to capture the peak values of runoff more precisely.
- The comparison results with the ANN and the SWAT showed that the the proposed LSTM model scored the best in most cases even in regions with sparse meteorological stations. The application of LSTMs and its further development have therefore a high potential to extend data-based modeling approaches in the field of hydrology.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LSTM | Long Short Term Memory |

ANN | Artificial Neural Network |

PYLB | Poyang Lake Basin |

RMSE | root mean square error |

NSE | Nash-Sutcliffe Efficiency |

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**Figure 1.**Topography and river networks of Poyang Lake Basin (

**A**). Location of 7 hydrological stations and 13 meteorological stations are presented with red triangles and blue dots, respectively (

**B**).

**Figure 5.**Characteristics of the Poyang Lake Basin: (

**A**) Soil types; (

**B**) Land use and (

**C**) the hydrological response units.

**Figure 6.**Model performance with different window size ((

**A**) root mean square error; (

**B**) Nash-Sutcliffe Efficiency).

**Figure 9.**Performances of LSTMs, ANN and Soil & Water Assessment Tool (SWAT) model in simulating the runoff.

Hydrological Station | Location | Coordinates | Gauged Area (km${}^{2}$) |
---|---|---|---|

Qiujin | Xiushui | 115.41${}^{\xb0}$ E, 29.10${}^{\xb0}$ N | 9914 |

Wanjiabu | Xiushui (Liaohe tributary) | 115.65${}^{\xb0}$ E, 28.85${}^{\xb0}$ N | 3548 |

Waizhou | Ganjiang | 115.83${}^{\xb0}$ E, 28.63${}^{\xb0}$ N | 80,948 |

Lijiadu | Fuhe | 116.17${}^{\xb0}$ E, 28.22${}^{\xb0}$ N | 15,811 |

Meigang | Xinjiang | 116.82${}^{\xb0}$ E, 28.43${}^{\xb0}$ N | 15,535 |

Hushan | Raohe (Le’an tributary) | 117.27${}^{\xb0}$ E, 28.92${}^{\xb0}$ N | 6374 |

Dufengken | Raohe (Changjiang tributary) | 117.12${}^{\xb0}$ E, 29.16${}^{\xb0}$ N | 5013 |

Model | LSTM1 | LSTM2 | ||||||
---|---|---|---|---|---|---|---|---|

Period | Calibration Period | Validation Period | Calibration Period | Validation Period | ||||

Metrics | NSE | RMSE | NSE | RMSE | NSE | RMSE | NSE | RMSE |

Ganjiang | 0.86 | 834.63 | 0.84 | 888.09 | 0.91 | 667.71 | 0.89 | 729.95 |

Fuhe | 0.91 | 192.26 | 0.91 | 221.60 | 0.92 | 177.87 | 0.91 | 213.89 |

Xinjiang | 0.92 | 258.20 | 0.92 | 276.36 | 0.94 | 230.78 | 0.94 | 240.18 |

Raohe | 0.86 | 264.37 | 0.87 | 278.77 | 0.91 | 212.95 | 0.93 | 204.10 |

Xiushui | 0.73 | 293.72 | 0.60 | 240.41 | 0.83 | 230.79 | 0.74 | 192.16 |

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**MDPI and ACS Style**

Fan, H.; Jiang, M.; Xu, L.; Zhu, H.; Cheng, J.; Jiang, J.
Comparison of Long Short Term Memory Networks and the Hydrological Model in Runoff Simulation. *Water* **2020**, *12*, 175.
https://doi.org/10.3390/w12010175

**AMA Style**

Fan H, Jiang M, Xu L, Zhu H, Cheng J, Jiang J.
Comparison of Long Short Term Memory Networks and the Hydrological Model in Runoff Simulation. *Water*. 2020; 12(1):175.
https://doi.org/10.3390/w12010175

**Chicago/Turabian Style**

Fan, Hongxiang, Mingliang Jiang, Ligang Xu, Hua Zhu, Junxiang Cheng, and Jiahu Jiang.
2020. "Comparison of Long Short Term Memory Networks and the Hydrological Model in Runoff Simulation" *Water* 12, no. 1: 175.
https://doi.org/10.3390/w12010175