# Learning Enhancement Method of Long Short-Term Memory Network and Its Applicability in Hydrological Time Series Prediction

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model

#### 2.1.1. Long Short-Term Memory Network

_{t}) and cell (c

_{t}) state variables and three gates—forget (f), input (i), and output (o) [26]. For more detailed information on internal calculations of LSTM cells and LSTM networks in terms of hydrology, see Kratzert et al. [6].

#### 2.1.2. Benchmark Model

#### 2.2. Study Area and Data

#### 2.3. Experimental Setup

#### 2.3.1. Experiment 1: Combination of Input Data for Learning

#### 2.3.2. Experiment 2: Multi-Basins Integrated Learning

#### 2.4. Model Evaluation

^{2}); (3) Nash-Sutcliffe efficiency (NSE) [33]; (4) Kling-Gupta efficiency (KGE) [9]; and (5) correlation coefficient (c.c). All metrics are reported for the test period. The threshold of R

^{2}and NSE for good performance is between 0.5 and 0.65 [34]. Likewise, if KGE is higher than 0.6, the simulations can be considered a good description of the observations [35]. RMSE close to zero indicates a small error between the simulations and the observations. A strong correlation is assumed when c.c > 0.7 [36,37].

## 3. Results and Discussion

#### 3.1. Best Combination of Input Variables for LSTM Learning

^{2}, and c.c for four applied cases are similar with about 3.28–3.43 mm/day, 0.71–0.73, and 0.84–0.86, respectively, but the performances between basins have some differences for cases. The LSTMs that learned only rainfall (case P in Figure 5) show the most considerable performance bias in most metrics, and the LSTMs that learned rainfall and potential evapotranspiration (case P+E in Figure 5) also show significant differences by basin. When learning rainfall and temperature (case P+T in Figure 5), it cannot be said that it is improved overall compared to case P, but the performance bias decreases compared to case P by adding temperature information.

#### 3.2. One LSTM for Predicting Streamflow in Each Basin

^{2}and c.c decreased by 0.01. The median value of RMSE was improved by about 10%.

#### 3.3. Performance Evaluation for Flow Segments

#### 3.4. Integrated Learning Considering a Basin Characteristic

## 4. Conclusions

- The performance and robustness of the outputs from LSTM can be enhanced by using various meteorological information as an input variable of LSTM;
- The LSTM could reasonably predict streamflow in the basins through the integrated learning method. This result means that the integrated learning method is a possible approach for reducing the data demand, and the concept of regionalization can be applied to LSTM. This regionalization approach may also help the streamflow in ungauged basins through further research;
- In particular, at least in the basins selected in this study, low-flow predictions are improved through the integrated learning;
- The selection of target basins for the integrated learning affects the performance of LSTM. Therefore, further research is needed on this topic.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic diagram of a recurrent neural network. The input data (x

_{t}) for each time step (t) is input to each cell in the first recurrent layer, and the output of each recurrent cell is supplied to the cell of the next time step and the next recurrent layer. The output of the last recurrent layer in the last time step is supplied to the dense layer to calculate the final prediction (y); and (

**b**) the internal operation of an LSTM cell, where f stands for the forget gate, i for the input gate, and o for the output gate. Note that x

_{t}denotes the input at time step t, c

_{t}denotes the cell state, and h

_{t}denotes the hidden state.

**Figure 2.**Locations of study basins. Here, red markers on the map denote the location of meteorological stations, and blue markers denote the dams.

**Figure 4.**Scatterplots of observed and predicted streamflow during the test period, where P is the case where only rainfall is input, P+T is where rainfall and temperature are input, P+E is where rainfall and potential evapotranspiration are input, ALL is where all meteorological information is input, and EHPM is the benchmark model.

**Figure 5.**Summary of streamflow prediction performance during the test period (2012 to 2020). Here, P is the case where only rainfall is input, P+T is where rainfall and temperature are input, P+E is where rainfall and potential evapotranspiration are input, ALL is where all meteorological information is input, and EHPM is the benchmark model. Noted that circle markers are median values, and bars denote the first and third quartiles. Translucent dots are the results for each basin, and curved lines show the kernel density curves.

**Figure 7.**Observed and predicted streamflow time series in Basin 4 for each case. The black dots are the observed streamflow and red solid lines are the streamflow predicted by each case.

**Figure 8.**Boxplots for streamflow prediction performances of the benchmark model (EHPM), the separately learned LSTM (CASE 1), and the integrally learned LSTM (CASE 2). Note that the red lines are median values, the blue boxes represent the first and third quartile, the whiskers represent the range between maximum and minimum values, and the red cross markers are the outlier. The value on the side of a box is its median value.

**Figure 9.**Performance differences between the LSTMs separately learned for each basin (CASE 1) and the LSTM integrally learned for all basins (CASE 2). Note that solid black lines are zero-lines, solid blue lines represent the performance difference (CASE 2 minus CASE 1), and dotted blue lines represent the mean difference.

**Figure 10.**Summary of RMSEs of streamflow predicted from each model for four flow segments. EHPM is the benchmark model, CASE 1 is the separately learned LSTM, and CASE 2 is the integrally learned LSTM. Note that Q1 is the segment for the top 0% to 25% flow magnitude, Q2 is for 25% to 50%, Q3 is for 50% to 75%, and Q4 is for 75% to 100%.

**Figure 11.**Comparison of NSEs for the LSTMs integrally learned considering a basin characteristic (Groups 1 and 2) and the LSTM integrally learned for the entire basins in Section 3.2 (CASE 2). Here, Group 1 is a combination of basins with a relatively lower CN value, and Group 2 is a combination of basins with a relatively higher CN value.

Basin Number | Basin Name | Area (km ^{2}) | Annual Mean Precipitation, P (mm/year) | Annual Mean Streamflow, Q (mm/year) | Runoff Ratio | Curve Number |
---|---|---|---|---|---|---|

1 | Chungju | 6661.5 | 1305.7 | 742.0 | 0.57 | 64.2 |

2 | Soyanggang | 2694.3 | 1276.1 | 803.5 | 0.63 | 53.8 |

3 | Namgang | 2281.7 | 1519.8 | 1027.1 | 0.68 | 65.2 |

4 | Andong | 1590.7 | 1178.0 | 606.0 | 0.51 | 61.4 |

5 | Imha | 1367.7 | 1115.5 | 466.9 | 0.42 | 67.8 |

6 | Yongdam | 930.4 | 1446.6 | 815.9 | 0.56 | 64.3 |

7 | Hapcheon | 928.9 | 1329.0 | 712.5 | 0.54 | 59.5 |

8 | Seomjingang | 763.5 | 1388.2 | 785.6 | 0.57 | 69.6 |

9 | Goesan | 676.7 | 1294.4 | 651.1 | 0.50 | 68.7 |

10 | Woonmoon | 301.9 | 1149.1 | 705.5 | 0.61 | 68.6 |

11 | Hoengseong | 207.9 | 1335.0 | 777.7 | 0.58 | 54.1 |

12 | Boryeong | 162.3 | 1160.5 | 770.3 | 0.66 | 59.1 |

13 | Gwangdong | 120.7 | 1311.2 | 721.4 | 0.55 | 70.1 |

Segment | Magnitude of Flow | Range of Percentile |
---|---|---|

Q1 | Highest flows | 0 to 0.25 |

Q2 | Higher flows | 0.25 to 0.5 |

Q3 | Lower flows | 0.5 to 0.75 |

Q4 | Lowest flows | 0.75 to 1 |

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**MDPI and ACS Style**

Choi, J.; Won, J.; Jang, S.; Kim, S.
Learning Enhancement Method of Long Short-Term Memory Network and Its Applicability in Hydrological Time Series Prediction. *Water* **2022**, *14*, 2910.
https://doi.org/10.3390/w14182910

**AMA Style**

Choi J, Won J, Jang S, Kim S.
Learning Enhancement Method of Long Short-Term Memory Network and Its Applicability in Hydrological Time Series Prediction. *Water*. 2022; 14(18):2910.
https://doi.org/10.3390/w14182910

**Chicago/Turabian Style**

Choi, Jeonghyeon, Jeongeun Won, Suhyung Jang, and Sangdan Kim.
2022. "Learning Enhancement Method of Long Short-Term Memory Network and Its Applicability in Hydrological Time Series Prediction" *Water* 14, no. 18: 2910.
https://doi.org/10.3390/w14182910