# Monthly Runoff Interval Prediction Based on Fuzzy Information Granulation and Improved Neural Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Sources

^{2}. A schematic diagram of Wei River Basin is shown in Figure 1.

^{2}, which is an important control station upstream of the Wei River. Weijiabu Hydrological Station is located in Meixian City, Baoji City, with a catchment area of 37,006 km

^{2}, and is an important control station in the middle reaches of the Wei River. Zhangjiashan Hydrological Station is located on the tributary Jing River, which is a key observation station in China.

#### 2.2. Methods

#### 2.2.1. Fuzzy Information Granulation

#### 2.2.2. BP Neural Network Improved by Genetic Algorithm

_{i}′ represents the runoff data after standardized; X

_{i}represents the original runoff data.

#### 2.3. Modeling and Evaluation

#### 2.3.1. FIG-GA-BP Prediction Model Construction

#### 2.3.2. Interval Prediction Evaluation Index

- (1)
- FICP

- (2)
- FIAW

#### 2.4. Data Pre-Processing

## 3. Results

#### 3.1. Feature Selection

#### 3.2. Results Analysis

## 4. Discussion

## 5. Conclusions

- (1)
- The interval prediction method based on fuzzy information granulation can be applied to runoff prediction. In the three hydrological stations, the FICP values are greater than 0.9 for both the FIG-GA-BP model and the FIG-BP model, reflecting good prediction effect. Compared with the traditional probability model, it does not need to use the probability density function, requires fewer parameters, and reduces the prediction workload.
- (2)
- The prediction effect of the FIG-GA-BP model in Weijiabu, Linjiacuan, and Zhangjiashan hydrologic stations is better than that of FIG-BP model, and the FICP is 0.98, which is greater than 0.95. The overall prediction performance is good. The results show that the interval prediction model based on fuzzy information granulation is an effective tool for predicting nonstationary time series data and is a new method for solving the uncertainty in runoff prediction. The prediction interval of runoff enables decision makers to better recognize the uncertainty of runoff and thus make more reasonable decisions for water resource management.
- (3)
- The FIG-GA-BP model proposed in this paper is more suitable for the interval prediction of runoff series and can provide information support for decision makers of water resource management. Furthermore, the center of the prediction interval can be used as the result of point value prediction.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**PACF value of runoff data of Weijiabu. The blue lines indicates the upper and lower bounds of the autocorrelation coefficient, and the part beyond the boundary indicates that there is a correlation.

**Figure 6.**Prediction results in Weijiabu from three models: (

**a**) FIG-GA-BP; (

**b**) FIG-BP; (

**c**) FIG-WNN. The black circle represents prediction failure.

**Figure 7.**Prediction results in Linjiacun from three models: (

**a**) FIG-GA-BP; (

**b**) FIG-BP; (

**c**) FIG-WNN. The black circle represents prediction failure.

**Figure 8.**Prediction results in Zhangjiashan from three models: (

**a**) FIG-GA-BP; (

**b**) FIG-BP; (

**c**) FIG-WNN. The black circle represents prediction failure.

**Figure 9.**Point prediction results in hydrologic station by four models: (

**a**) Weijiabu; (

**b**) Linjiacun; (

**c**) Zhangjiashan.

Hydrological Station | Min | Mean | Max | SD |
---|---|---|---|---|

Weijiabu | 1.61 | 87.71 | 728.42 | 113.752 |

Linjiacun | 0.40 | 60.33 | 434.00 | 63.77 |

Zhangjiashan | 0 | 37.10 | 340.07 | 51.38 |

Hydrological Station | Model | FICP | FINAW | QR (%) | ARE (%) | RMSE |
---|---|---|---|---|---|---|

Weijiabu | FIG-GA-BP | 0.98 | 0.46 | 81 | 12 | 18.51 |

FIG-BP | 0.95 | 0.69 | 72 | 18 | 74.40 | |

FIG-WNN | 0.94 | 0.72 | 76 | 17 | 33.95 | |

BP | \ | \ | 77 | 15 | 38.47 | |

Linjiacun | FIG-GA-BP | 0.98 | 0.63 | 84 | 14 | 18.63 |

FIG-BP | 0.94 | 0.87 | 80 | 13 | 18.42 | |

FIG-WNN | 0.93 | 0.76 | 64 | 25 | 23.12 | |

BP | \ | \ | 78 | 18 | 20.32 | |

Zhangjiashan | FIG-GA-BP | 0.98 | 0.23 | 89 | 11 | 7.64 |

FIG-BP | 0.97 | 0.57 | 82 | 18 | 14.23 | |

FIG-WNN | 0.94 | 0.66 | 67 | 30 | 24.56 | |

BP | \ | \ | 81 | 14 | 7.68 |

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## Share and Cite

**MDPI and ACS Style**

Yang, X.; Zhang, X.; Xie, J.; Zhang, X.; Liu, S. Monthly Runoff Interval Prediction Based on Fuzzy Information Granulation and Improved Neural Network. *Water* **2022**, *14*, 3683.
https://doi.org/10.3390/w14223683

**AMA Style**

Yang X, Zhang X, Xie J, Zhang X, Liu S. Monthly Runoff Interval Prediction Based on Fuzzy Information Granulation and Improved Neural Network. *Water*. 2022; 14(22):3683.
https://doi.org/10.3390/w14223683

**Chicago/Turabian Style**

Yang, Xinyu, Xiao Zhang, Jiancang Xie, Xu Zhang, and Shihui Liu. 2022. "Monthly Runoff Interval Prediction Based on Fuzzy Information Granulation and Improved Neural Network" *Water* 14, no. 22: 3683.
https://doi.org/10.3390/w14223683