# Daily Streamflow Forecasts Based on Cascade Long Short-Term Memory (LSTM) Model over the Yangtze River Basin

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

^{6}km

^{2}, which accounts for about 18.8% of China’s total land area. Figure 1 shows the locations of the 49 hydrological stations used in this study. The monthly streamflow observed at these 49 stations was collected from the Yangtze River Basin Hydrological Yearbook published by the Yangtze River Conservancy Commission.

#### 2.2. The Conjunctive Surface-Subsurface Process Version 2 (CSSPv2) Model

#### 2.3. The Cascade LSTM Model

#### 2.4. Experimental Design

_{f}). Then, we use historical streamflow, soil moisture, evapotranspiration, and historical precipitation and LSTM_P to predict streamflow (LSTM_S), i.e., ([STRF, SM, ET, and P

_{f}] → STRF), to explore the capability of cascade LSTM model (Figure 2) in streamflow forecast. Note that the above experiments are conducted in the forecasting periods of 1–15 days. This experiment is called “cascade LSTM”.

#### 2.5. Evaluation of Model Performance

## 3. Results

#### 3.1. Evaluation of CSSPv2 Land Model Simulation and Default LSTM Forecast

#### 3.2. Evaluation of Cascade LSTM

#### 3.2.1. Precipitation Forecast Based on LSTM_P

#### 3.2.2. Streamflow Forecast Based on LSTM_S

#### 3.3. Evaluation of Cascade LSTM with Prefect Precipitation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Locations and drainage areas (km

^{2}) of 49 streamflow observational stations over the Yangtze River basin in southern China.

**Figure 3.**(

**a**) Spatial distribution of KGE between observed and CSSPv2 model-simulated monthly streamflow over the Yangtze River basin. (

**b**) The boxplot of KGE for all 49 stations. The boxes represent the 25th and 75th percentiles of KGE, the line and the dot within the box are median and mean values of KGE, respectively, and the whiskers represent 10th and 90th percentiles of KGE.

**Figure 4.**Spatial distributions of KGEs for streamflow forecasts based on default LSTM model at lead times of 1–15 days.

**Figure 5.**The relationship between the watershed area (ln km

^{2}) and the default LSTM streamflow forecast skill (KGE) at the lead times of 1–15 days.

**Figure 6.**The relationship between the watershed area (ln km

^{2}) and the LSTM_P precipitation forecast skill (KGE) at the lead times of 1–15 days.

**Figure 7.**Spatial distributions of the KGE difference (∆ KGE) between the daily streamflow forecasts by the cascade LSTM model and those by the default LSTM model.

**Figure 8.**Performance of streamflow forecasts at different lead times. The left column shows the mean values of KGE, R, β, and γ for 49 stations, and the right column shows their median values.

**Figure 9.**The relationship between the difference of streamflow forecast performance (∆ KGE of the cascade LSTM model and the default LSTM model) and the watershed area (ln km

^{2}) at the lead times of 1–15 days.

**Figure 10.**Spatial distributions of the KGE difference (∆ KGE) between the daily streamflow forecasts by the cascade LSTM with prefect precipitation and those by default LSTM.

**Figure 11.**The relationship between the difference of streamflow forecast performance (∆ KGE of the cascade LSTM model with prefect precipitation and the default LSTM model ) and the watershed area (ln km

^{2}) at the lead times of 1–15 days.

Hyper-Parameter | Set Up |
---|---|

Batch | 16, 32, 64, 128, 256, 512, 1024 |

Hidden cell | 8, 16, 32, 64, 128, 256 |

Dropout rate | 0.01, 0.05, 0.1, 0.15, 0.2, 0.3 |

Learning rate | 0.001, 0.005, 0.01, 0.05, 0.1, 0.2 |

**Table 2.**Percentage (%) of stations that improved compared to the default LSTM model, the cascaded LSTM model (CLSTM), and the cascaded LSTM with the perfect precipitation (CLSTM_P) model KGE and its three components (R, β and γ).

Lead Times | KGE | R | β | γ | ||||
---|---|---|---|---|---|---|---|---|

CLSTM | CLSTM_P | CLSTM | CLSTM_P | CLSTM | CLSTM_P | CLSTM | CLSTM_P | |

1 | 0.61 | 0.70 | 0.53 | 0.86 | 0.57 | 0.65 | 0.59 | 0.65 |

2 | 0.76 | 0.86 | 0.20 | 0.82 | 0.82 | 0.86 | 0.80 | 0.78 |

3 | 0.76 | 0.88 | 0.45 | 0.88 | 0.84 | 0.92 | 0.76 | 0.84 |

4 | 0.86 | 0.88 | 0.53 | 0.90 | 0.80 | 0.88 | 0.69 | 0.80 |

5 | 0.84 | 0.88 | 0.63 | 0.92 | 0.73 | 0.78 | 0.71 | 0.86 |

6 | 0.86 | 0.90 | 0.69 | 0.90 | 0.67 | 0.88 | 0.65 | 0.88 |

7 | 0.88 | 0.94 | 0.82 | 0.94 | 0.63 | 0.84 | 0.65 | 0.88 |

8 | 0.86 | 0.92 | 0.82 | 0.96 | 0.61 | 0.86 | 0.59 | 0.90 |

9 | 0.82 | 0.92 | 0.82 | 0.94 | 0.61 | 0.86 | 0.65 | 0.86 |

10 | 0.80 | 0.92 | 0.86 | 0.94 | 0.51 | 0.86 | 0.63 | 0.86 |

11 | 0.78 | 0.94 | 0.73 | 0.96 | 0.71 | 0.94 | 0.67 | 0.88 |

12 | 0.76 | 0.90 | 0.78 | 0.94 | 0.51 | 0.86 | 0.55 | 0.90 |

13 | 0.76 | 0.90 | 0.80 | 0.96 | 0.61 | 0.84 | 0.51 | 0.92 |

14 | 0.84 | 0.92 | 0.80 | 0.96 | 0.59 | 0.86 | 0.59 | 0.94 |

15 | 0.88 | 0.94 | 0.84 | 0.94 | 0.63 | 0.88 | 0.43 | 0.88 |

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**MDPI and ACS Style**

Li, J.; Yuan, X.
Daily Streamflow Forecasts Based on Cascade Long Short-Term Memory (LSTM) Model over the Yangtze River Basin. *Water* **2023**, *15*, 1019.
https://doi.org/10.3390/w15061019

**AMA Style**

Li J, Yuan X.
Daily Streamflow Forecasts Based on Cascade Long Short-Term Memory (LSTM) Model over the Yangtze River Basin. *Water*. 2023; 15(6):1019.
https://doi.org/10.3390/w15061019

**Chicago/Turabian Style**

Li, Jiayuan, and Xing Yuan.
2023. "Daily Streamflow Forecasts Based on Cascade Long Short-Term Memory (LSTM) Model over the Yangtze River Basin" *Water* 15, no. 6: 1019.
https://doi.org/10.3390/w15061019