# Combined Forecasting of Streamflow Based on Cross Entropy

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analysis of Streamflow Characteristics

^{2}and it is located mainly in the territory of Jilin. According to data obtained at the Wudaogou hydrology station in Huadian City (catchment area of 12,391 km

^{2}), the change in the amplitude of its water level is 7.69 m, the average annual streamflow is 26.4 billion m

^{3}, the average flow is 83.70 m

^{3}/s, the maximum peak discharge is 3010 m

^{3}/s (1975), the minimum flow rate is 0.44 m

^{3}/s (1979), the mean annual sediment volume is 0.48 kg/s, and the annual transportation of sediment is 121 million metric tons.

^{3}in 1995 and 1080 m

^{3}in 2010), the trend and the actual numerical value of the monthly streamflow are relatively strong in each year. Therefore, the selection of reasonably similar years can improve the accuracy of streamflow predictions.

## 3. Data Processing Method

#### 3.1. Data Preprocessing

_{max}is the maximum value in the sample.

#### 3.2. Selecting Similar Years

_{0}and Xm

_{0}:

## 4. Streamflow Forecasting Model Based on CE

#### 4.1. Combined Forecasting Model

_{t}, ${\omega}_{it}$ is the weight of the ith model at time t, and ${\widehat{y}}_{it}$ is the predicted value of the ith model at time t, then the problem of combined forecasting is described as follows:

#### 4.2. The CE Model

_{it}= w

_{0}, set iteration number z = 1;

## 5. Results and Analysis

#### 5.1. Comparison of the Results Obtained with a Single Method

#### 5.2. Comparison with Other Combined Forecasting Models

#### 5.3. Influence of the Historical Data Length on the Prediction Results

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Annual streamflow, annual rainfall, and the ratio of the two curves at Wudaogou station during 1965–2010.

**Figure 4.**Forecast annual streamflow curve. (

**a**) Annual forecast results in 2009; (

**b**) Annual forecast results in 2010.

Year | ARIMA | GM | RBF | CE | ||||
---|---|---|---|---|---|---|---|---|

MRPE | RMSE | MRPE | RMSE | MRPE | RMSE | MRPE | RMSE | |

2006 | 10.95% | 6.96% | 10.55% | 4.79% | 10.58% | 3.98% | 10.53% | 3.67% |

2007 | 10.66% | 5.77% | 9.23% | 5.61% | 9.07% | 4.89% | 8.95% | 5.01% |

2008 | 9.71% | 6.01% | 10.12% | 5.85% | 9.25% | 5.28% | 9.77% | 5.32% |

2009 | 9.89% | 5.25% | 10.35% | 6.08% | 7.32% | 5.01% | 7.24% | 4.99% |

2010 | 11.27% | 7.38% | 11.59% | 8.91% | 8.56% | 7.97% | 8.30% | 6.67% |

Average | 10.50% | 6.27% | 10.37% | 6.25% | 8.96% | 5.43% | 8.96% | 5.13% |

Year | EW | RM | CE | |||
---|---|---|---|---|---|---|

MPE | RMSE | MPE | RMSE | MPE | RMSE | |

2006 | 10.76% | 3.75% | 10.53% | 3.71% | 10.53% | 3.67% |

2007 | 9.23% | 5.56% | 9.14% | 5.34% | 8.95% | 5.01% |

2008 | 9.74% | 5.30% | 9.78% | 5.29% | 9.77% | 5.32% |

2009 | 7.55% | 5.09% | 7.43% | 5.25% | 7.24% | 4.99% |

2010 | 10.07% | 7.24% | 9.52% | 7.08% | 8.30% | 6.67% |

Average | 9.47% | 5.39% | 9.28% | 5.33% | 8.96% | 5.13% |

Case | RBF | RM | CE | |||
---|---|---|---|---|---|---|

MPE | RMSE | MPE | RMSE | MPE | RMSE | |

Case 1 | 9.01% | 5.62% | 9.31% | 5.37% | 8.98% | 5.14% |

Case 2 | 9.37% | 5.71% | 9.42% | 5.43% | 9.11% | 5.25% |

Case 3 | 12.94% | 7.87% | 11.28% | 7.01% | 10.50% | 6.62% |

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**MDPI and ACS Style**

Men, B.; Long, R.; Zhang, J. Combined Forecasting of Streamflow Based on Cross Entropy. *Entropy* **2016**, *18*, 336.
https://doi.org/10.3390/e18090336

**AMA Style**

Men B, Long R, Zhang J. Combined Forecasting of Streamflow Based on Cross Entropy. *Entropy*. 2016; 18(9):336.
https://doi.org/10.3390/e18090336

**Chicago/Turabian Style**

Men, Baohui, Rishang Long, and Jianhua Zhang. 2016. "Combined Forecasting of Streamflow Based on Cross Entropy" *Entropy* 18, no. 9: 336.
https://doi.org/10.3390/e18090336