# Heuristic Methods for Reservoir Monthly Inflow Forecasting: A Case Study of Xinfengjiang Reservoir in Pearl River, China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data Sets

#### 2.1. Study Area

^{2}and reaches a total length of 2400 km. The rainy season extends from April to September, followed by a dry season from October to March.

^{2}, which accounts for about one quarter of the East River Basin area. The average annual rainfall is about 1974.7 mm. The annual inflow at the dam site is about 192 m

^{3}/s. Since being put into production in October 1960, the reservoir began to play comprehensive benefit in power generation, flood control, navigation, water supply, etc. The reservoir is equipped with four units and its installed capacity arrives 302 million watts. The average annual energy generation is 0.99 billion kW·h. As the largest artificial reservoir with multi-year regulating storage in south China, the reservoir has the total capacity of 13.90 billion m

^{3}, where the dead storage capacity is 4.31 billion m

^{3}. Its normal water level is 116 m at non-flood season while the corresponding storage is 10.8 billion m

^{3}. Its flood control level is 114 m during the first half of flood season from 1 April to 30 June, whilst that is 115 m during the second half of flood season from 1 July to 30 September.

#### 2.2. Division of Data

_{mean}, S

_{d}, X

_{min}, X

_{max}, and R

_{ange}respectively stand for the mean, standard deviation, minimum, maximum, and range of various data sets. We can find that the monthly inflow data for Xinfengjiang reservoir varies over a relative wide range from 9.3 to 1506 m

^{3}/s. The scope of the training data set includes that of testing and validation sets fully. The statistical parameters of the training set are close to the testing and validation sets. Hence, the data used for various data sets are representative of the same population, so there is no need to extrapolate beyond the range of the data for training.

Datasets | Statistic | ||||
---|---|---|---|---|---|

X_{mean} | S_{d} | X_{min} | X_{max} | R_{ange} | |

Training set | 204.1 | 14.3 | 9.3 | 1506.0 | 1496.7 |

Testing set | 192.1 | 13.9 | 24.5 | 1300.2 | 1275.7 |

Validation set | 176.3 | 13.3 | 22.3 | 1496.4 | 1474.1 |

Original data | 195.3 | 14.0 | 9.3 | 1506.0 | 1496.7 |

#### 2.3. Data Preprocessing

## 3. Forecasting Methodology

#### 3.1. Artificial Neural Network (ANN)

**Y**is the output vector. f is the transfer function.

**W**is the weight vector.

**X**is the weight vector.

**B**is the bias vector.

#### 3.2. Support Vector Machine (SVM)

#### 3.3. Genetic Algorithm (GA)

_{i}is the i-th observed data;

**X**

_{i}is the i-th input data vector; $SVM\left({\mathit{X}}_{i},\text{\theta}\right)$ represents the corresponding simulated value of SVM.

#### 3.4. Hybrid Forecasting Method

**A**

_{1}and SVM

**S**

_{1}forecasting model are driven to forecast the targeted reservoir inflow data, respectively, gaining two different forecasting results. Secondly, a new ANN model

**A**

_{2}is built for the operational prediction, where the two different forecasting results of ANN and SVM are selected as the input variables and the real reservoir inflow data is used as the desired value. The two-stage forecasting process can be helpful to eliminate random errors of different models and improve the prediction ability to a certain degree. The framework of the proposed hybrid method is shown in Figure 5, and the process is described as below.

**A**

_{1}and SVM model

**S**

_{1}, and use the abovementioned data to train both models, respectively, where GA is employed for the parameter selection of the SVM model

**S**

_{1}.

**A**

_{2}structure and use the processed data of the ANN model

**A**

_{1}and SVM model

**S**

_{1}as the input variables to train the model

**A**

_{2}.

## 4. Statistical Measures

## 5. Results and Discussion

#### 5.1. Input Variables Determination

_{t}

_{+1}at the time t+1. Hence, the relationship between the output and input variables can be expressed as the following Equation:

#### 5.2. Development of Various Models

#### 5.2.1. ANN Model **A**_{1} Development

**A**

_{1}architecture is (12, 15, 1).

#### 5.2.2. SVM Model **S**_{1} Development

Trial No. | Optimal Parameters (C, ε, σ) | Training | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAPE | MAE | NS | R | RMSE | MAPE | MAE | NS | R | ||

1 | (10.653, 1.032, 0.078) | 151.00 | 59.19 | 87.85 | 0.49 | 0.70 | 153.90 | 70.23 | 93.03 | 0.42 | 0.64 |

2 | (9.827, 0.435, 0.064) | 144.82 | 54.29 | 85.60 | 0.53 | 0.73 | 133.07 | 61.87 | 82.54 | 0.56 | 0.75 |

3 | (2.783, 0.678, 0.125) | 152.46 | 61.54 | 88.08 | 0.48 | 0.69 | 152.51 | 66.38 | 89.44 | 0.43 | 0.65 |

4 | (9.425, 0.823, 0.081) | 118.66 | 70.48 | 82.44 | 0.68 | 0.83 | 96.60 | 75.73 | 74.36 | 0.77 | 0.89 |

5 | (11.803, 1.254, 0.708) | 147.80 | 64.17 | 88.98 | 0.51 | 0.71 | 154.22 | 74.28 | 94.58 | 0.41 | 0.65 |

#### 5.2.3. ANN Model **A**_{2} Development

**A**

_{2}uses the results of both ANN model

**A**

_{1}and SVM model

**S**

_{1}as its input variables. There are two inputs and one output in the model. A typical three-layer network is used. The sigmoid transfer function is used in all neurons of the hidden layer and the output layer. To ensure the generalization, all variables are normalized, and a trial-and-error process is repeated to determine the optimal hidden layer nodes. The number of neuron in the hidden layer vary from two to nine, and all the statistical indexes of different network structures are recorded and compared during the calculation procedure. Finally, the optimal neural network adopted was (2, 5, 1), as shown in Figure 8, which was selected as the final forecasting model.

#### 5.3. Comparison and Discussion

**A**

_{1}and

**A**

_{2}for Xinfengjiang reservoir are (12, 15, 1) and (2, 5, 1), respectively. Moreover, using GA for parameter selection, the SVM model with parameters (C, ε, σ) = (9.425, 0.823, 0.081) is the forecasting model for Xinfengjiang reservoir.

Models | Training | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAPE | MAE | NS | R | RMSE | MAPE | MAE | NS | R | |

SVM | 118.66 | 70.48 | 82.44 | 0.68 | 0.83 | 96.60 | 75.73 | 74.36 | 0.77 | 0.89 |

ANN | 118.60 | 55.20 | 79.73 | 0.68 | 0.83 | 102.09 | 63.68 | 73.49 | 0.74 | 0.87 |

Hybrid Method | 95.86 | 48.28 | 62.44 | 0.79 | 0.89 | 85.72 | 49.78 | 58.33 | 0.82 | 0.91 |

**Figure 9.**Comparison of forecasted versus observed data by various methods during the validation period.

**Figure 11.**Scatter plots of forecasted versus observed data by various methods during the validation period. (

**a**) SVM; (

**b**) ANN and (

**c**) Hybrid method.

^{3}/s in June 2015, while the forecast value of the SVM, ANN, and hybrid method are 1355.5, 1381.3, and 1405.7 m

^{3}/s, about 9.4%, 7.7% and 6.1% underestimation, respectively. For the second maximum peak inflow in June 2008, the SVM, ANN, and the hybrid method can obtain 776.5, 792.3, and 840.5 m

^{3}/s instead of the observed 1066 m

^{3}/s, about 27.2%, 25.7% and 21.2% underestimation, respectively. Moreover, for the 16 peak flows, the absolute average relative error of the SVM, ANN, and the hybrid method are 15.2%, 15.5% and 10.6%, respectively. Thus, it can be concluded that for peak inflow prediction, the hybrid method can obtain better forecast precision than SVM and ANN, while there is no significant difference between ANN and SVM.

**Table 4.**Peak flow estimates of three models for Xinfengjiang reservoir during the validation period.

Peak No. | Date | Observed | Forecast Peak | Relative Error (%) | ||||
---|---|---|---|---|---|---|---|---|

Peak | SVM | ANN | Hybrid Method | SVM | ANN | Hybrid Method | ||

1 | 1999/9 | 362.0 | 327.9 | 346.9 | 369.5 | −9.4 | −4.2 | 2.1 |

2 | 2000/4 | 497.9 | 516.0 | 507.5 | 434.9 | 3.6 | 1.9 | −12.7 |

3 | 2001/6 | 618.1 | 530.3 | 488.4 | 492.9 | −14.2 | −21.0 | −20.3 |

4 | 2002/8 | 352.6 | 349.1 | 376.7 | 386.2 | −1.0 | 6.8 | 9.5 |

5 | 2003/6 | 336.2 | 272.0 | 285.6 | 334.4 | −19.1 | −15.1 | −0.5 |

6 | 2004/5 | 202.8 | 237.3 | 236.8 | 225.8 | 17.0 | 16.8 | 11.3 |

7 | 2005/6 | 1496.4 | 1355.5 | 1381.3 | 1405.7 | −9.4 | −7.7 | −6.1 |

8 | 2006/6 | 783.8 | 583.2 | 598.1 | 679.5 | −25.6 | −23.7 | −13.3 |

9 | 2007/6 | 687.5 | 555.7 | 581.4 | 592.1 | −19.2 | −15.4 | −13.9 |

10 | 2008/6 | 1066.0 | 776.5 | 792.3 | 840.5 | −27.2 | −25.7 | −21.2 |

11 | 2009/6 | 228.2 | 211.5 | 252.4 | 236.1 | −7.3 | 10.6 | 3.5 |

12 | 2010/6 | 867.5 | 701.4 | 626.7 | 677.5 | −19.2 | −27.8 | −21.9 |

13 | 2011/5 | 369.6 | 293.5 | 244.1 | 319.3 | −20.6 | −34.0 | −13.6 |

14 | 2012/6 | 442.3 | 315.6 | 348.7 | 419.6 | −28.6 | −21.2 | −5.1 |

15 | 2013/5 | 860.9 | 766.5 | 794.2 | 778.3 | −11.0 | −7.7 | −9.6 |

16 | 2014/5 | 616.2 | 544.8 | 567.0 | 584.9 | −11.6 | −8.0 | −5.1 |

Average (absolute) | 15.2 | 15.5 | 10.6 |

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Cheng, C.-T.; Feng, Z.-K.; Niu, W.-J.; Liao, S.-L.
Heuristic Methods for Reservoir Monthly Inflow Forecasting: A Case Study of Xinfengjiang Reservoir in Pearl River, China. *Water* **2015**, *7*, 4477-4495.
https://doi.org/10.3390/w7084477

**AMA Style**

Cheng C-T, Feng Z-K, Niu W-J, Liao S-L.
Heuristic Methods for Reservoir Monthly Inflow Forecasting: A Case Study of Xinfengjiang Reservoir in Pearl River, China. *Water*. 2015; 7(8):4477-4495.
https://doi.org/10.3390/w7084477

**Chicago/Turabian Style**

Cheng, Chun-Tian, Zhong-Kai Feng, Wen-Jing Niu, and Sheng-Li Liao.
2015. "Heuristic Methods for Reservoir Monthly Inflow Forecasting: A Case Study of Xinfengjiang Reservoir in Pearl River, China" *Water* 7, no. 8: 4477-4495.
https://doi.org/10.3390/w7084477