# A Multi-Factor Combination Model for Medium to Long-Term Runoff Prediction Based on Improved BP Neural Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Area and Dataset

#### 2.2. Prediction Factor Selection Method

#### 2.2.1. Preliminary Factor Selection Method of Spearman Rank Correlation Coefficient

#### 2.2.2. Stepwise Regression Method to Construct a Significant Factor Set

#### 2.3. Medium and Long-Term Runoff Prediction Model Based on Multi-Factor Combination

#### 2.3.1. Improved BP Neural Network Model

- Classic BP Neural Network Model

- (1)
- Network Topology

- (2)
- Network Learning Rules

- 2.
- Problems and Improvements of BP Network

- (1)
- Adaptive Learning Rate $\eta $

- (2)
- Correction of Weight Adjustment Amount

#### 2.3.2. Factor Sensitivity Analysis Method

#### 2.4. Evaluation System for Prediction Results

#### 2.4.1. Single Evaluation Index

- 1.
- Mean Absolute Relative Error

- 2.
- Nash Efficiency Coefficient

- 3.
- 20% Standard Forecast Qualification Rate

- 4.
- Standard Deviation of Relative Error

#### 2.4.2. Comprehensive Evaluation Index

- 1.
- Calculation of Entropy

- 2.
- Calculation of Entropy Weight

## 3. Results

#### 3.1. Preliminary Selection of Factors

#### 3.2. Construction of Significant Climate Factor Set

#### 3.3. Sensitivity Analysis Results

#### 3.4. Multi-Factor Prediction Simulation Results of the Improved BP Neural Network Model

## 4. Discussion

#### 4.1. Comparison of Simulation Accuracy for Different Factor Quantities

#### 4.2. Simulation Comparison of Three Multiple Factor Combination Schemes

#### 4.3. Research Characteristics and Prospects

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Index Set Name | Classification | Number (Items) |
---|---|---|

Climate System Index Sets | Atmospheric circulation index | 88 |

Sea surface temperature index | 26 | |

Other indices | 16 | |

summation | 130 |

**Table 2.**Significant Climate Factor Set Affecting Medium and Long-term Runoff Prediction in a certain coastal area of Jiangsu.

Lag | Previous One Month | Previous Two Months | Previous Three Months | Previous Four Months | Previous Five Months | Previous Six Months |
---|---|---|---|---|---|---|

Factor Number | 55 | 102 | 101 | 32 | 65 | 55 |

66 | 101 | 104 | 101 | 58 | ||

16 | 55 | 26 | 104 | 104 | ||

102 | 31 | 101 | ||||

50 |

Factor Number | Sensitivity | Ranking | Factor Number | Sensitivity | Ranking |
---|---|---|---|---|---|

102(1) | 0.2936 | 1 | 101(4) | 0.0379 | 11 |

55(6) | 0.2617 | 2 | 102(2) | 0.0330 | 12 |

50(1) | 0.2187 | 3 | 31(3) | 0.0321 | 13 |

16(1) | 0.1635 | 4 | 58(5) | 0.0305 | 14 |

101(2) | 0.1216 | 5 | 66(1) | 0.0213 | 15 |

101(5) | 0.0866 | 6 | 104(5) | 0.0205 | 16 |

26(3) | 0.0842 | 7 | 104(4) | 0.0201 | 17 |

101(3) | 0.0831 | 8 | 32(4) | 0.0173 | 18 |

65(5) | 0.0508 | 9 | 55(2) | 0.0147 | 19 |

104(3) | 0.0407 | 10 | 55(1) | 0.0083 | 20 |

Selection Factor | Factor Number | MARE | NSE |
---|---|---|---|

the first 8 factors | 102(1), 55(6), 50(1), 16(1), 101(2), 101(5), 26(3), 101(3) | 0.3800 | 0.45 |

the first 9 factors | 102(1), 55(6), 50(1), 16(1), 101(2), 101(5), 26(3), 101(3), 65(5) | 0.3783 | 0.47 |

the first 10 factors | 102(1), 55(6), 50(1), 16(1), 101(2), 101(5), 26(3), 101(3), 65(5), 104(3) | 0.3770 | 0.50 |

Screening Method | Stepwise Regression | Spearman Related | Sensitivity Analysis |
---|---|---|---|

Factor Number | 55(6) | 55(6) | 102(1) |

32(4) | 32(4) | 55(6) | |

55(2) | 58(5) | 50(1) | |

101(5) | 65(5) | 16(1) | |

66(1) | 101(4) | 101(2) | |

16(1) | 101(3) | 101(5) | |

50(1) | 16(1) | 26(3) | |

102(1) | 55(1) | 101(3) |

MARE (%) | NSE | ∂_{20%} (%) | σ | |
---|---|---|---|---|

Scheme 1 | 37.67 | 0.60 | 37.82 | 0.41 |

Scheme 2 | 48.47 | 0.66 | 37.50 | 0.70 |

Scheme 3 | 36.61 | 0.51 | 33.01 | 0.34 |

MARE (%) | NSE | ∂_{20%} (%) | σ | |
---|---|---|---|---|

Scheme 1 | 43.87 | 0.21 | 36.67 | 0.39 |

Scheme 2 | 50.26 | 0.19 | 30.00 | 0.50 |

Scheme 3 | 38.01 | 0.45 | 31.67 | 0.27 |

MARE (%) | NSE | ∂_{20%} (%) | σ | |
---|---|---|---|---|

Training period | 0.0686 | 0.0900 | 0.0306 | 0.8107 |

Validation period | 0.0400 | 0.8140 | 0.0368 | 0.1092 |

Scheme 1 | Scheme 2 | Scheme 3 | |
---|---|---|---|

Training period | 0.583 | 0.349 | 0.636 |

Validation period | 0.273 | 0.241 | 0.482 |

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**MDPI and ACS Style**

Yan, K.; Gao, S.; Wen, J.; Yao, S.
A Multi-Factor Combination Model for Medium to Long-Term Runoff Prediction Based on Improved BP Neural Network. *Water* **2023**, *15*, 3559.
https://doi.org/10.3390/w15203559

**AMA Style**

Yan K, Gao S, Wen J, Yao S.
A Multi-Factor Combination Model for Medium to Long-Term Runoff Prediction Based on Improved BP Neural Network. *Water*. 2023; 15(20):3559.
https://doi.org/10.3390/w15203559

**Chicago/Turabian Style**

Yan, Kun, Shang Gao, Jinhua Wen, and Shuiping Yao.
2023. "A Multi-Factor Combination Model for Medium to Long-Term Runoff Prediction Based on Improved BP Neural Network" *Water* 15, no. 20: 3559.
https://doi.org/10.3390/w15203559