# Applicability of ε-Support Vector Machine and Artificial Neural Network for Flood Forecasting in Humid, Semi-Humid and Semi-Arid Basins in China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Back-Propagation Learning Algorithm

## 3. Support Vector Machine

**w**and b are weight vector and bias term, respectively, and can be estimated by minimizing the following structural risk function

## 4. Evolutionary Strategy

## 5. Study Area and Data

^{2}, with a mainstream length of 1624 km, and an overall drop of 965 m. It is a subtropical monsoon climate with abundant rainfall and significant rainfall variation, with an annual rainfall of 1638.2 mm. During the spring season from March to early April, the southeasterly wind prevails upon the ground surface, and the amount of precipitation gradually increases. During the period from May to July, the frontal surface often stagnates or swings over the watershed, resulting in continuous rainfall with high rainfall intensity and long rainy seasons. During the summer months of July and September, the weather is hot, with prevailing southerly thunderstorm and typhoon rainfalls. From October to November, the weather is mainly sunny; from December to February, temperatures are low, with rain and snow weather.

^{2}.

^{2}, the river length is 81.3 km, and the distance from the estuary is 31 km. The regional climate features a moderate temperate semi-humid semi-arid zone, which is cold and dry in winter, and dry and windy in spring, with droughts and floods in summer, and which is cool and humid in autumn. The average annual temperature, precipitation, sediment transport, and discharge are 7.8 °C, 509.8 mm, 102 million tons, and 2610 m

^{3}/s, respectively. Floods are caused by heavy rains, with rapid fluctuations, sharp peaks, and short duration. The relationship between water level and discharge is generally poor.

^{2}) describes the proportion of the total statistical variance in the observed dataset that can be explained by the model.

## 6. Results

## 7. Discussion

^{2}and NSE, both models accurately predicted the maximum flow for humid and semi-humid regions. However, the value of AME shows that ANN underestimated the minimum streamflow of the humid area. SVM successfully simulated streamflow of the semi-arid area, while ANN poorly simulated the both minimum and maximum flows of the streamflow, as indicated by R

^{2}, NSE, MSRE, and MRE. The results tie in well with those of [22,62]. Due to the high degree of spatial and temporal variability in semi-arid areas, ANN underperformed, because ANN often fails to find global optima in complex and high-dimensional parameter spaces [63].

^{2}and NSE values. This indicated that the models predicted the streamflow very well, though ANN overestimated the low flow events according to MSRE and MAE, signifying a high deviation of predicted values from the observed values. This result is in agreement with those of [22,64], in which the authors compared the performances of ANN and SVM for streamflow forecasting. From Table 3, in the semi-humid area, the ANN model obtained the highest R

^{2}and NSE values for all of the forecasted period, and also obtained a lower RMSE for all periods than the SVM model. However, SVM performed well when using other evaluation metrics.

^{2}, NSE, RMSE), but perform poorly when estimating low flows because of relative metrics, which are more critical for errors occurring in the lower magnitudes (MRE, MAPE, MSRE) [65]. Ref. [65] used integrated GA to overcome the ANN problem of failing to estimate minimum flows, and also to improve the overall performance of ANN in streamflow simulation. As for semi-arid catchments, both models failed to forecast streamflow, with only the SVM model closely predicting streamflow in the results for the 1-hour-ahead prediction, as indicated by R

^{2}, RMSE, MAE, MAPE and MRE. All metrics critically penalize ANN for 1 h lead time. SVM is penalized more by R

^{2}than ANN as forecasting time increases, whereas MSRE and NSE severely penalize both models with increasing lead times. Regular ANN was compared with wavelet-ANN (WA-ANN) for 1–3-day lead time forecasting, and as indicated by R

^{2}, ANN and WA-ANN obtained 0.62 and 0.78 for a 1 day lead time, and 0.4 and 0.42 for a 3 day lead time, respectively. These results are in agreement with the findings of this paper regarding the decreasing value of R

^{2}obtained with increasing lead times [66]. NSE is used to assess the predictive power of hydrological models. The threshold values indicating a model’s degree of sufficiency are suggested to be between 0.5 < NSE < 0.65. Therefore, the models performed poorly on semi-arid catchments, and only predicted the one-hour lead time, which is still not satisfactory.

^{2}, and RMSE heavily penalized SVM, but not MSRE, MRE and MAPE; while metrics like MAE, MSRE, MRE, and MAPE punished ANN more heavily than overall measures of performance. Therefore, consideration of other analysis tools such as graphical representation is prudent before accepting or rejecting a model based on the values of the metrics without acknowledging the flaws.

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Autocorrelation plots of rainfall and streamflow for (

**a**) Humid, (

**b**) Semi-Humid, (

**c**) Semi-arid catchments.

**Figure 3.**Scatter plots of the target (measure streamflow) versus simulated and forecasted streamflow from 1 h lead time to 5 h lead time for Changhua basin, Chenhe basin and Zhidan basin (

**a**), (

**b**) and (

**c**) respectively for both SVM and ANN models.

**Figure 4.**Observed streamflow versus simulated and forecasted streamflow from 1 h lead time to 5 h lead time for Changhua basin, Chenhe basin and Zhidan basin—(

**a**), (

**b**) and (

**c**), respectively—for both SVM and ANN models.

Humid | ||||||||||

Changhua | Longmengsi | Taohuacun | Shuangshi | Daoshiwu | Lingxia | Yulingguan | Target | |||

SC | 4.07 | 1.99 | 3.98 | 4.59 | 4.1 | 4.39 | 4.45 | 9.25 | ||

Lag | 2 | 2 | 4 | 3 | 2 | 2 | 4 | 3 | ||

Semi-Humid | ||||||||||

Chenhe | Diaoyutai | Houzhengzi | Maichang | Shaliangzi | Banfangzi | Laoshuimo | Xiaowangjian | Jinjing | Target | |

SC | 2.67 | 1.31 | 1.29 | 1 | 1.23 | 1.25 | 1.09 | 0.99 | 4.06 | 9.11 |

Lag | 5 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 8 | 6 |

Semi-Arid | ||||||||||

Yejicha | Wafangzhuang | Huangcaowan | Bachatai | Shunning | Zhifang | Zhidan | Target | |||

SC | 2.36 | 2.06 | 1.64 | 2.46 | 2.02 | 2.16 | 4.81 | 8.32 | ||

Lag | 2 | 1 | 7 | 7 | 7 | 7 | 1 | 2 |

SVM Model | ANN Model | ||||
---|---|---|---|---|---|

Humid | Semi-Humid | Semi-Arid | Humid | Semi-Humid | Semi-Arid |

Longmengsi | Houzhengzi | Yejicha | Taohuacun | Diaoyutai | Yejicha |

Taohuacun | Maichang | Wafangzhuang | Yulingguan | Houzhengzi | Wafangzhuang |

Shuangshi | Shaliangzi | Bachatai | Shuangshi | Maichang | Bachatai |

Daoshiwu | Bafangzi | Shunning | Daoshiwu | Shaliangzi | Shunning |

Xiaowangjian | Zhifang | Laoshuima | Zhifang | ||

Xiaowangjian |

**Table 3.**Performance of SVM and ANN models for streamflow simulation and forecasting of all catchments.

SVM | ANN | |||||||||||

Changhua (Humid) | ||||||||||||

Simulation | Forecast (1 h) | Forecast (2 h) | Forecast (3 h) | Forecast (4 h) | Forecast (5 h) | Simulation | Forecast (1 h) | Forecast (2 h) | Forecast (3 h) | Forecast (4 h) | Forecast (5 h) | |

R^{2} | 0.99 | 0.97 | 0.90 | 0.81 | 0.72 | 0.63 | 0.99 | 0.98 | 0.94 | 0.82 | 0.82 | 0.74 |

NSE | 0.99 | 0.97 | 0.90 | 0.80 | 0.70 | 0.59 | 0.99 | 0.98 | 0.93 | 0.75 | 0.73 | 0.72 |

RMSE (m^{3}/s) | 0.46 | 48.34 | 91.16 | 128.35 | 159.99 | 186.79 | 19.60 | 23.25 | 46.15 | 86.25 | 77.54 | 86.97 |

MAE | 0.34 | 15.12 | 29.22 | 42.07 | 53.94 | 64.70 | 9.39 | 10.73 | 29.97 | 80.90 | 144.55 | 73.32 |

MAPE | 0.00 | 0.10 | 0.20 | 0.30 | 0.41 | 0.55 | 0.09 | 0.11 | 0.46 | 1.61 | 2.84 | 1.25 |

MSRE | 0.00 | 0.31 | 0.70 | 1.16 | 1.97 | 4.40 | 0.31 | 0.28 | 4.56 | 35.26 | 88.39 | 28.52 |

MRE | 0.00 | 0.04 | 0.08 | 0.13 | 0.20 | 0.30 | −0.01 | 0.00 | 0.37 | 1.58 | 2.83 | 1.13 |

Chenhe (Semi-Humid) | ||||||||||||

R^{2} | 0.99 | 0.94 | 0.78 | 0.62 | 0.56 | 0.58 | 0.98 | 0.98 | 0.96 | 0.87 | 0.89 | 0.83 |

NSE | 0.99 | 0.93 | 0.76 | 0.58 | 0.50 | 0.52 | 0.98 | 0.97 | 0.95 | 0.82 | 0.87 | 0.83 |

RMSE (m^{3}/s) | 1.74 | 47.56 | 90.89 | 119.21 | 128.67 | 126.31 | 24.31 | 26.36 | 35.14 | 61.12 | 53.00 | 75.26 |

MAE | 0.30 | 9.98 | 19.75 | 28.99 | 37.73 | 45.97 | 13.50 | 22.37 | 25.04 | 66.06 | 41.78 | 50.52 |

MAPE | 0.00 | 0.07 | 0.15 | 0.25 | 0.36 | 0.49 | 0.45 | 0.44 | 1.03 | 1.47 | 1.62 | 1.46 |

MSRE | 0.00 | 0.07 | 0.59 | 1.42 | 2.72 | 4.65 | 2.52 | 1.32 | 16.87 | 17.02 | 33.42 | 30.89 |

MRE | 0.00 | 0.02 | 0.06 | 0.11 | 0.18 | 0.27 | 0.41 | −0.06 | 0.98 | −0.13 | 1.52 | 1.09 |

Zhidan (Semi-Arid) | ||||||||||||

R^{2} | 0.99 | 0.70 | 0.39 | 0.19 | 0.09 | 0.06 | 0.60 | 0.64 | 0.46 | 0.56 | 0.53 | 0.37 |

NSE | 0.99 | 0.68 | 0.26 | −0.11 | −0.36 | −0.49 | 0.34 | 0.54 | 0.23 | 0.34 | 0.22 | −1.11 |

RMSE (m^{3}/s) | 1.49 | 16.00 | 22.93 | 26.48 | 28.00 | 28.55 | 9.20 | 10.06 | 9.51 | 5.63 | 4.04 | 4.29 |

MAE | 0.20 | 4.70 | 8.00 | 10.37 | 12.14 | 13.52 | 13.24 | 9.08 | 13.43 | 10.63 | 16.41 | 40.11 |

MAPE | 0.26 | 2.18 | 5.54 | 9.80 | 13.46 | 15.94 | 8.97 | 5.45 | 9.07 | 9.05 | 20.15 | 59.35 |

MSRE | 0.28 | 636.73 | 2758.4 | 5963.1 | 8800.2 | 9720.0 | 291.7 | 447.94 | 401.44 | 501.11 | 1599.4 | 12735 |

MRE | 0.25 | 2.03 | 5.29 | 9.46 | 13.04 | 15.46 | −7.47 | −0.61 | −6.69 | 8.85 | 20.01 | 59.30 |

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**MDPI and ACS Style**

Bafitlhile, T.M.; Li, Z.
Applicability of ε-Support Vector Machine and Artificial Neural Network for Flood Forecasting in Humid, Semi-Humid and Semi-Arid Basins in China. *Water* **2019**, *11*, 85.
https://doi.org/10.3390/w11010085

**AMA Style**

Bafitlhile TM, Li Z.
Applicability of ε-Support Vector Machine and Artificial Neural Network for Flood Forecasting in Humid, Semi-Humid and Semi-Arid Basins in China. *Water*. 2019; 11(1):85.
https://doi.org/10.3390/w11010085

**Chicago/Turabian Style**

Bafitlhile, Thabo Michael, and Zhijia Li.
2019. "Applicability of ε-Support Vector Machine and Artificial Neural Network for Flood Forecasting in Humid, Semi-Humid and Semi-Arid Basins in China" *Water* 11, no. 1: 85.
https://doi.org/10.3390/w11010085