# Application of Long Short-Term Memory (LSTM) Neural Network for Flood Forecasting

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}), the Nash–Sutcliffe efficiency (NSE), and the root mean square error (RMSE). The study revealed that it could predict discharge for two days with reliable performance and the ANN model could be used to fill data gaps in a disrupted discharge on a time series scale. Elsafi [5] suggested an ANN model for one-day flowrate forecasting at the Dongola station in the Nile River basin (Sudan) based on upstream flow data. The author concluded that the ANN model provided a reliable means of detecting the flood hazard on the river with an accuracy (R

^{2}value) of about 97%. This acts as a precursor to the establishment of a flood warning system for certain sections of the Nile River. Khan et al. [6] established an ANN model that exploited daily information data of discharge and water level at the stations along the river as the inputs to forecast one-day streamflow ahead for the Ramgama River in India. The results of this research demonstrated that the selected model could be useful for predicting discharge and water level for the Ramganga River with an accuracy of about 93.4% for monsoon flow pattern. Sung et al. [7] constructed an ANN model for hourly water level forecasting at Anyangcheon Stream, Korea with a lead-time of one to three hours. The model’s accuracy was validated by three statistical methods: RMSE, R

^{2}, and NSE. They concluded that the model provided good results when forecasting a one-hour to two-hour water levels.

## 2. Methodology

#### 2.1. Study Area and Data

^{2}, in which approximately 50% (26,800 km

^{2}) of the basin area is in Vietnam. It flows through the high mountain area in Vietnam and has an abundant flow, which yields substantial hydroelectric power. In addition, due to the topographical characteristics of the area, the distribution of rainfall on the basin is uneven in spatial and temporal. Rainfall concentrates mainly from May to September, accounting for 85–88% of the total annual rainfall. Information on the maximum daily precipitation and peak flood discharge in this area are summarized in Table 1. Currently, there are three large hydroelectric plants on the Da River, namely: The Hoa Binh Dam (1994), the Son La Dam (2012), and the Lai Chau Dam (2016) with the total combined power capacity of about 5520 MW.

^{3}/s).

#### 2.2. Artificial Neural Network (ANN)

^{n}is the n-dimensional input vector consisting of variables X

_{1}, …, X

_{i}, …, X

_{n}; Y is the output vector. The functional form of f(.) in Equation (1) is not revealed explicitly by the model; rather, the network parameters will represent it.

#### 2.3. Recurrent Neural Network (RNN)

_{t}is the input at time step t and h

_{t}is the output at time step t. During the training process, RNN uses a backpropagation algorithm, a prevalent algorithm applied in calculating gradients and adjusting weight matrices in ANN. However, it will adjust and update the weights following the modification of the feedback process. Therefore, it is commonly referred to as the backpropagation through time (BPTT). The BPTT process uses a working-backward approach, layer by layer, from the network’s final output, tweaking the weights of each unit according to the unit’s calculated portion of the total output error. The information loops repeat resulting in huge updates to neural network model weights and lead to an unstable network due to the accumulation of error gradients during the updating process. Therefore, BPTT is not sufficiently efficient to learn a pattern from long-term dependency because of the gradient vanishing and the exploding gradient problems [29]. This would be one of the crucial reasons leading to difficulties in the training of recurrent neural networks [34,35,36].

#### 2.4. Long Short-Term Memory (LSTM) Neural Network

_{t−1}) at time t − 1 and the current input (X

_{t}) at time t. Additionally, the sigmoid function determines which part from the old output should be eliminated. This gate is called the forget gate (or f

_{t}); where f

_{t}is a vector with values ranging from 0 to 1, corresponding to each number in the cell state, C

_{t−1}.

_{f}and b

_{f}are the weight matrices and bias, respectively, of the forget gate.

_{t}) in the cell state as well as to update the cell state. This step contains two parts, the sigmoid layer and second the tanh layer. First, the sigmoid layer decides whether the new information should be updated or ignored (0 or 1), and second, the tanh function gives weight to the values which passed by, deciding their level of importance (−1 to 1). The two values are multiplied to update the new cell state. This new memory is then added to old memory C

_{t−1}resulting in C

_{t}.

_{t−1}and C

_{t}are the cell states at time t − 1 and t, while W and b are the weight matrices and bias, respectively, of the cell state.

_{t}) is based on the output cell state (O

_{t}) but is a filtered version. First, a sigmoid layer decides which parts of the cell state make it to the output. Next, the output of the sigmoid gate (O

_{t}) is multiplied by the new values created by the tanh layer from the cell state (C

_{t}), with a value ranging between −1 and 1.

_{o}and b

_{o}are the weight matrices and bias, respectively, of the output gate.

#### 2.5. Model Evaluation Criteria

_{i}and P

_{i}are observed discharges and simulated discharges at time t, respectively; $\overline{{O}_{i}}$ is the mean of observed discharges; and n is the total number of observations.

## 3. Model Structure

#### 3.1. Scenarios

^{3}/s) at the Hoa Binh Station occurred on 15 July 1984.

#### 3.2. Model Design

## 4. Results and Discussion

#### 4.1. Validation Results

^{3}/s (RMSE value). For the two-day and three-day flow forecast, the NSE values are approximately 95% and 87% respectively.

#### 4.2. Test Results

^{3}/s. The performance of the models was determined using the NSE and RMSE metrics when comparisons between the measured data and forecasted values were made.

#### 4.2.1. Results for Testing Phase

^{3}/s.

#### 4.2.2. Results for Flood Peak Forecasts

^{3}/s on July 15th. Base on the optimal parameters selected for the scenarios, the prediction results of the one-day, two-day, and three-day flood peaks are depicted in Table 5.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Location of the study area and the gauge stations. (

**a**) Description of Da River basin in provinces of Vietnam; (

**b**) Description of provinces in Vietnam; (

**c**) Description of location of gauge stations on the Da River basin.

**Figure 3.**Sequential processing in a Recurrent Neural Network (RNN) [33].

**Figure 4.**The structure of the Long Short-Term Memory (LSTM) neural network. Reproduced from Yan [38].

**Figure 5.**Comparison between the observed and predicted one-day flow values for the first scenario (case S1_1d_2) in the validation phase.

**Figure 6.**Scatter plot for one-day flow forecasting in the validation phase corresponding to the first scenario (

**a**) and the second scenario (

**b**).

**Figure 7.**Comparison between the observed and predicted one-day flow values for the second scenario (case S2_1d_2) in the testing phase.

**Figure 8.**Scatter plot for one-day flow forecasting in testing phase corresponding to the first scenario (

**a**) and the second scenario (

**b**).

**Figure 9.**Scatter plot for two-day flow forecasting in the testing phase corresponding to the first scenario (

**a**) and the second scenario (

**b**).

**Figure 10.**Scatter plot for three-day flow forecasting in the testing phase corresponding to the first scenario (

**a**) and the second scenario (

**b**).

No. | Stations | Items | Value | Unit | Period (24 years) | Time |
---|---|---|---|---|---|---|

1 | Muong Te | Maximum Daily Precipitation | 197.4 | mm | 1961–1984 | 14 July1970 |

2 | Lai Chau | Maximum Daily Precipitation | 197.5 | mm | 1961–1984 | 13 June 1961 |

3 | Quynh Nhai | Maximum Daily Precipitation | 169.9 | mm | 1961–1984 | 13 June 1980 |

4 | Son La | Maximum Daily Precipitation | 198 | mm | 1961–1984 | 29 June 1980 |

5 | Yen Chau | Maximum Daily Precipitation | 172 | mm | 1961–1984 | 16 July 1965 |

6 | Moc Chau | Maximum Daily Precipitation | 166.7 | mm | 1961–1984 | 13 June 1965 |

7 | Hoa Binh | Maximum Daily Precipitation | 176.2 | mm | 1961–1984 | 9 July 1973 |

8 | Ta Gia | Peak Flood Discharge | 3320 | m^{3}/s | 1961–1984 | 15 July 1970 |

9 | Nam Muc | Peak Flood Discharge | 1680 | m^{3}/s | 1961–1984 | 8 July 1964 |

10 | Lai Chau | Peak Flood Discharge | 10,200 | m^{3}/s | 1961–1984 | 18 August 1971 |

11 | Ta Bu | Peak Flood Discharge | 15,300 | m^{3}/s | 1961–1984 | 8 July 1964 |

12 | Hoa Binh ^{1} | Peak Flood Discharge | 16,900 | m^{3}/s | 1961–1984 | 9 July 1964 |

^{1}denotes the target station.

No | Stations | Items | Latitude | Longitude | Period (24 Years) | Correlation Coefficient of Data | Location (Province) |
---|---|---|---|---|---|---|---|

1 | Muong Te | R | 22°22′ | 102°50′ | 1961–1984 | 0.30 | Lai Chau |

2 | Lai Chau | R | 22°04′ | 103°09′ | 1961–1984 | 0.24 | Dien Bien |

3 | Quynh Nhai | R | 21°51′ | 103°34′ | 1961–1984 | 0.18 | Son La |

4 | Son La | R | 21°20′ | 103°54′ | 1961–1984 | 0.23 | Son La |

5 | Yen Chau | R | 21°03′ | 104°18′ | 1961–1984 | 0.24 | Son La |

6 | Moc Chau | R | 20°50′ | 104°41′ | 1961–1984 | 0.25 | Son La |

7 | Hoa Binh | R | 20°49′ | 105°20′ | 1961–1984 | 0.21 | Hoa Binh |

8 | Ta Gia | Q | 21°47′ | 103°48′ | 1961–1984 | 0.77 | Lai Chau |

9 | Nam Muc | Q | 21°52′ | 103°17′ | 1961–1984 | 0.83 | Dien Bien |

10 | Lai Chau | Q | 22°04′ | 103°09′ | 1961–1984 | 0.95 | Dien Bien |

11 | Ta Bu | Q | 21°26′ | 104°03′ | 1961–1984 | 0.97 | Son La |

12 | Hoa Binh ^{1} | Q | 20°49′ | 105°19′ | 1961–1984 | 1.00 | Hoa Binh |

^{1}denotes the target station. R = Rain; Q = Discharge.

Items | Detail |
---|---|

Prediction Target | Discharge forecasting at Hoa Binh Station for: - Day one - Day two - Day three |

Input Variable | Observed daily rainfall and flow data include: - Rainfall data at seven meteorological stations - Flow rate data at five hydrological stations |

Training Parameters | - Learning rate: 0.0001 - Number of units: 20; 30; 50 - Number of epochs: 100,000 |

Forecast for | Case | Input Variable | Number of Units | Number of Epochs | RMSE (m^{3}/s) | NSE (%) | |
---|---|---|---|---|---|---|---|

One day | 1st scenario | S1_1d_1 | 12 | 20 | 6500 | 149.6 | 99.1 |

S1_1d_2 | 12 | 30 | 8628 | 149.0 | 99.2 | ||

S1_1d_3 | 12 | 50 | 6971 | 151.3 | 99.1 | ||

2nd scenario | S2_1d_1 | 5 | 20 | 7887 | 165.0 | 99.0 | |

S2_1d_2 | 5 | 30 | 8474 | 163.4 | 99.0 | ||

S2_1d_3 | 5 | 50 | 10,132 | 164.0 | 99.0 | ||

Two days | 1st scenario | S1_2d_1 | 12 | 20 | 3636 | 366.1 | 94.9 |

S1_2d_2 | 12 | 30 | 5494 | 367.7 | 94.9 | ||

S1_2d_3 | 12 | 50 | 4772 | 367.4 | 94.9 | ||

2nd scenario | S2_2d_1 | 5 | 20 | 7683 | 374.2 | 94.7 | |

S2_2d_2 | 5 | 30 | 7361 | 370.9 | 94.8 | ||

S2_2d_3 | 5 | 50 | 7438 | 373.7 | 94.7 | ||

Three days | 1st scenario | S1_3d_1 | 12 | 20 | 2654 | 567.3 | 87.8 |

S1_3d_2 | 12 | 30 | 3075 | 573.1 | 87.5 | ||

S1_3d_3 | 12 | 50 | 2296 | 584.8 | 87.0 | ||

2nd scenario | S2_3d_1 | 5 | 20 | 3655 | 589.7 | 86.8 | |

S2_3d_2 | 5 | 30 | 4620 | 589.0 | 86.8 | ||

S2_3d_3 | 5 | 50 | 4864 | 590.3 | 86.8 |

Predict for | Case | RMSE Test (m^{3}/s) | NSE Test (%) | Forecasted Peak (m^{3}/s) | Observed Peak (m^{3}/s) | Relative Error (%) |
---|---|---|---|---|---|---|

One day | S1_1d_2 | 152.4 | 99.1 | 9340 | 10,000 | 6.6 |

S2_1d_2 | 151.5 | 99.1 | 9510 | 10,000 | 4.9 | |

Two days | S1_2d_1 | 360.7 | 94.9 | 8477 | 10,000 | 15.2 |

S2_2d_2 | 373.3 | 94.5 | 8632 | 10,000 | 13.7 | |

Three days | S1_3d_1 | 571.4 | 87.2 | 7181 | 10,000 | 28.2 |

S2_3d_2 | 594.0 | 86.2 | 7527 | 10,000 | 24.7 |

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**MDPI and ACS Style**

Le, X.-H.; Ho, H.V.; Lee, G.; Jung, S.
Application of Long Short-Term Memory (LSTM) Neural Network for Flood Forecasting. *Water* **2019**, *11*, 1387.
https://doi.org/10.3390/w11071387

**AMA Style**

Le X-H, Ho HV, Lee G, Jung S.
Application of Long Short-Term Memory (LSTM) Neural Network for Flood Forecasting. *Water*. 2019; 11(7):1387.
https://doi.org/10.3390/w11071387

**Chicago/Turabian Style**

Le, Xuan-Hien, Hung Viet Ho, Giha Lee, and Sungho Jung.
2019. "Application of Long Short-Term Memory (LSTM) Neural Network for Flood Forecasting" *Water* 11, no. 7: 1387.
https://doi.org/10.3390/w11071387