# Runoff Prediction in the Xijiang River Basin Based on Long Short-Term Memory with Variant Models and Its Interpretable Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data Processing

#### 2.1. Study Area

^{2}, 79% of the total area of the Pearl River Basin. The elevation of the basin is high in the Northwest and low in the Southeast. The Yunnan-Guizhou Plateau is in the Northwest, hills and basins are in the middle, and a plain delta is in the East. The terrain of the XJB is complex, and there are significant spatial differences in meteorological and hydrological elements. Based on this, the XJB is divided into four sub-basins: the Upper Xijiang River Basin, the Liu River Basin, the Yu River Basin, and the Middle-Lower Xi River Basin. The hydrological control stations for these sub-basins are Qianjiang (QJ), Liuzhou (LZ), Guigang (GG), and Wuzhou (WZ), respectively.

#### 2.2. Data Processing

## 3. Methodology

#### 3.1. Model Introduction

_{t}determines the amount of previous cell state information to be discarded; the input gate determines the proportion of newly acquired information to be stored in the current cell state C

_{t}; and the output gate O

_{t}determines the final output information at this moment. The specific formulas are as follows:

_{t}is the input vector, h

_{t−}

_{1}is the output information of the previous unit state, σ is the sigmoid activation function, $\otimes $ represents the vector multiplication, W

_{f}, W

_{i}, W

_{c}, and W

_{o}are the weight matrices of the neural network, and b

_{f}, b

_{i}, b

_{c}, and b

_{o}are the bias vectors.

#### 3.2. Wavelet Analysis

_{i}|i = 1, 2, …, n} and Y = {y

_{i}|i = 1, 2, …, n}, their continuous wavelet transforms are ${W}_{n}^{X}(s)$ and ${W}_{n}^{Y}(s)$, respectively. Then, the cross-wavelet spectrum can be defined as follows:

#### 3.3. Evaluation Indicators

_{obs}represents the observed values, Q

_{f}represents the predicted values, $\overline{{Q}_{obs}}$ represents the mean of the observed values, and n is the number of observed values.

#### 3.4. Interpretable Machine Learning Method

_{S}represents the feature subset S of the input value x; f(x

_{S}) represents the predicted value of the feature subset S; i is the feature to calculate the Shapley Value; N is the feature set; f(x

_{S}

_{∪{}

_{i}

_{}}) represents the predicted value of the feature subset S plus feature i; |S| represents the cardinality of the feature subset S; |N| represents the cardinality of the entire feature set N.

## 4. Results

#### 4.1. Feature Selection

#### 4.1.1. Selection of Atmospheric Circulation Factors

#### 4.1.2. Delayed Effect Analysis

#### 4.2. Driving Effect of Atmospheric Circulation Factors on Runoff Change

#### 4.3. Comparative Analysis of Model Prediction Performance

#### 4.3.1. Prediction Performance of Different Models in the Same Forecast Period

^{3}m

^{3}/s), and MAE values ranging from 0.137 to 0.869 (10

^{3}m

^{3}/s). Moreover, the LSTM model exhibited superior predictive performance in the testing dataset as well, with NSE ranging from 0.950 to 0.960, RMSE ranging from 0.221 to 0.833 (10

^{3}m

^{3}/s), and MAE ranging from 0.195 to 0.698 (10

^{3}m

^{3}/s). The NSE value of the CNN-LSTM model was approximately 0.92 across all four stations, and the Conv-LSTM and Bi-LSTM models exhibited an NSE value of approximately 0.91 in GG and WZ. Furthermore, the NSE value remained steady at around 0.93 in QJ and LZ. It could be concluded that although the Conv-LSTM and Bi-LSTM models had good generalization ability, their predictive performance was affected by station data, and their prediction accuracy at different stations had greater uncertainty compared to that of the LSTM and CNN-LSTM models. In addition, due to the differences in the actual runoff at different stations, RMSE and MAE exhibited varying patterns. Among them, the RMSE and MAE values in WZ were significantly larger than those at the other three stations, which was because the WZ station was located downstream of the XJB and to some extent aggregates the runoff from the other three upstream stations.

#### 4.3.2. Prediction Performance of Optimal Model under Different Foresight Periods

#### 4.4. Interpretability Analysis of LSTM Model

## 5. Discussion

#### 5.1. Reasons for Differences in Model Prediction Accuracy

#### 5.2. Uncertainty

#### 5.3. Advantages and Limitations

## 6. Conclusions

- (1)
- The NPI is the most influential atmospheric circulation factor affecting the runoff in the XJB.
- (2)
- When comparing different models with the same forecast period, the LSTM model had higher NSE results in the QJ, LZ, GG, and WZ, with values of 0.950, 0.960, 0.954, and 0.955, respectively. These values were higher than those in the other three models tested at the same stations. Therefore, it can be concluded that the LSTM model is the optimal choice among the four models used in this study.
- (3)
- With the optimal model, the LSTM model, its prediction results decreased as the foresight period increased. Specifically, the NSE decreased by 4.7% when the foresight period increased from one month to two months, and it decreased by 3.9% when the foresight period increased from two months to three months. This suggested that although the decrease in the NSE was slow as the foresight period increased, there was a converging trend of a declining NSE with a longer foresight period.
- (4)
- Based on SHAP values, an interpretability analysis was conducted on the LSTM model. The results showed that in the XJB, historical runoff had the greatest impact on runoff prediction results, followed by precipitation, evaporation, and the NPI. Evaporation was negatively correlated with runoff, while historical runoff, precipitation, and the NPI were positively correlated.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**The schematic diagrams of different models: (

**a**) LSTM, (

**b**) CNN-LSTM, (

**c**) Conv-LSTM, and (

**d**) Bi-LSTM.

**Figure 3.**Time-lag selection is based on the highest correlation coefficients, with HR, P, E, NPI, and PR denoting historical runoff, precipitation, evaporation, North Pacific Index, and predicted runoff, respectively.

**Figure 4.**Cross-wavelet coherence spectrum (the arrow pointing to the right (left) indicates an in-phase (anti-phase) relationship between runoff and other factors. The area enclosed by the thick black solid line represents the region passing a 95% confidence test. The same below).

**Figure 6.**Comparison of observed and predicted runoff in the (

**a**) QJ, (

**b**) LZ, (

**c**) GG, and (

**d**) WZ stations, respectively.

**Figure 7.**Comparison of observed and predicted runoffs based on the (

**a1**,

**a2**) LSTM, (

**b1**,

**b2**) CNN-LSTM, (

**c1**,

**c2**) Conv-LSTM, and (

**d1**,

**d2**) Bi-LSTM models, respectively.

**Figure 8.**Taylor plots of training set in the (

**a**) QJ, (

**b**) LZ, (

**c**) GG, and (

**d**) WZ stations, respectively, with the horizontal and vertical coordinates representing standard deviation, the internal dashed line representing RMSE, the outer arc representing the correlation coefficient, and the same below.

**Figure 9.**Taylor plots of test set in the (

**a**) QJ, (

**b**) LZ, (

**c**) GG, and (

**d**) WZ stations, respectively.

**Figure 10.**Importance rankings of input features in the (

**a**) QJ, (

**b**) LZ, (

**c**) GG, and (

**d**) WZ stations, respectively.

**Figure 11.**Global influence map of input features in the (

**a**) QJ, (

**b**) LZ, (

**c**) GG, and (

**d**) WZ stations, respectively. The positive values represent positive correlation and negative values represent negative correlation.

Evaluation Indicators | Formula | Optimal Value |
---|---|---|

RMSE | $RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum {}_{i=1}^{n}{({Q}_{f}-{Q}_{obs})}^{2}}}$ | 0 |

MAE | $MAE={\displaystyle \sum _{i=1}^{n}\left|{Q}_{f}-{Q}_{obs}\right|}/n$ | 0 |

NSE | $NSE=1-{\displaystyle \sum _{i=1}^{n}{\left({Q}_{f}-{Q}_{obs}\right)}^{2}}/{\displaystyle \sum _{i=1}^{n}{\left({Q}_{obs}-\overline{{Q}_{obs}}\right)}^{2}}$ | 1 |

**Table 2.**The correlation coefficient between monthly runoff and atmospheric circulation factors with a 1-month delay.

Hydrological Station | ENSO | PDO | NAO | AO | AMO | DMI | NPI | PNA | SSI |
---|---|---|---|---|---|---|---|---|---|

QJ | 0.026 | 0.013 | −0.029 | 0.073 | −0.032 | −0.015 | 0.512 ** | −0.052 | 0.018 |

LZ | 0.072 | 0.055 | −0.049 | 0.087 * | 0.026 | 0.024 | 0.452 ** | −0.088 * | 0.034 |

GG | −0.021 | −0.063 | −0.042 | 0.064 | −0.028 | −0.026 | 0.487 ** | −0.056 | 0.008 |

WZ | 0.040 | 0.024 | −0.001 | 0.098 ** | −0.031 | 0.006 | 0.517 ** | −0.087 * | 0.021 |

Station | Model | Training Set | Test Set | ||||
---|---|---|---|---|---|---|---|

NSE | RMSE (10 ^{3} m^{3}/s) | MAE (10 ^{3} m^{3}/s) | NSE | RMSE (10 ^{3} m^{3}/s) | MAE (10 ^{3} m^{3}/s) | ||

QJ | LSTM | 0.944 | 0.456 | 0.274 | 0.950 | 0.249 | 0.203 |

CNN-LSTM | 0.921 | 0.529 | 0.308 | 0.920 | 0.305 | 0.244 | |

Conv-LSTM | 0.920 | 0.535 | 0.312 | 0.939 | 0.275 | 0.218 | |

Bi-LSTM | 0.927 | 0.526 | 0.296 | 0.942 | 0.269 | 0.212 | |

LZ | LSTM | 0.959 | 0.252 | 0.137 | 0.960 | 0.241 | 0.210 |

CNN-LSTM | 0.925 | 0.338 | 0.163 | 0.926 | 0.343 | 0.282 | |

Conv-LSTM | 0.929 | 0.337 | 0.231 | 0.925 | 0.363 | 0.326 | |

Bi-LSTM | 0.916 | 0.362 | 0.251 | 0.926 | 0.340 | 0.269 | |

GG | LSTM | 0.933 | 0.405 | 0.237 | 0.954 | 0.221 | 0.195 |

CNN-LSTM | 0.922 | 0.416 | 0.248 | 0.923 | 0.286 | 0.242 | |

Conv-LSTM | 0.927 | 0.415 | 0.246 | 0.919 | 0.296 | 0.249 | |

Bi-LSTM | 0.928 | 0.412 | 0.242 | 0.922 | 0.288 | 0.245 | |

WZ | LSTM | 0.950 | 1.318 | 0.869 | 0.955 | 0.833 | 0.698 |

CNN-LSTM | 0.934 | 1.439 | 0.901 | 0.923 | 1.060 | 0.818 | |

Conv-LSTM | 0.900 | 1.695 | 0.928 | 0.906 | 1.197 | 0.922 | |

Bi-LSTM | 0.920 | 1.460 | 0.916 | 0.911 | 1.153 | 0.867 |

**Table 4.**Comparison of prediction effect of LSTM model in test set under different foresight periods.

Forecast Period | Error Indicator | QJ | LZ | GG | WZ |
---|---|---|---|---|---|

1 month | NSE | 0.950 | 0.960 | 0.954 | 0.955 |

RMSE (10^{3} m^{3}/s) | 0.249 | 0.241 | 0.221 | 0.833 | |

MAE (10^{3} m^{3}/s) | 0.203 | 0.210 | 0.195 | 0.698 | |

2 month | NSE | 0.897 | 0.901 | 0.889 | 0.893 |

RMSE (10^{3} m^{3}/s) | 0.295 | 0.274 | 0.243 | 1.310 | |

MAE (10^{3} m^{3}/s) | 0.266 | 0.280 | 0.244 | 0.832 | |

3 month | NSE | 0.858 | 0.863 | 0.859 | 0.849 |

RMSE (10^{3} m^{3}/s) | 0.312 | 0.290 | 0.269 | 1.664 | |

MAE (10^{3} m^{3}/s) | 0.297 | 0.321 | 0.276 | 0.920 |

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## Share and Cite

**MDPI and ACS Style**

Tian, Q.; Gao, H.; Tian, Y.; Jiang, Y.; Li, Z.; Guo, L.
Runoff Prediction in the Xijiang River Basin Based on Long Short-Term Memory with Variant Models and Its Interpretable Analysis. *Water* **2023**, *15*, 3184.
https://doi.org/10.3390/w15183184

**AMA Style**

Tian Q, Gao H, Tian Y, Jiang Y, Li Z, Guo L.
Runoff Prediction in the Xijiang River Basin Based on Long Short-Term Memory with Variant Models and Its Interpretable Analysis. *Water*. 2023; 15(18):3184.
https://doi.org/10.3390/w15183184

**Chicago/Turabian Style**

Tian, Qingqing, Hang Gao, Yu Tian, Yunzhong Jiang, Zexuan Li, and Lei Guo.
2023. "Runoff Prediction in the Xijiang River Basin Based on Long Short-Term Memory with Variant Models and Its Interpretable Analysis" *Water* 15, no. 18: 3184.
https://doi.org/10.3390/w15183184