# Support Vector Regression Integrated with Fruit Fly Optimization Algorithm for River Flow Forecasting in Lake Urmia Basin

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## Abstract

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^{3}/s), MAE (2.40 and 3.71 m

^{3}/s) and R (0.82 and 0.81) values had the best performance in forecasting river flows at Babarud and Vaniar stations, respectively. Also, regarding BIC parameters, Q

_{t−1}and π were selected as parsimonious inputs for predicting river flow one month ahead. Overall findings indicated that, although both the FOASVR and M5 predicted the river flows in suitable accordance with observed river flows, the performance of the FOASVR was moderately better than the M5 and periodicity noticeably increased the performance of the models; consequently, FOASVR can be suggested as the most accurate method for forecasting river flows.

## 1. Introduction

## 2. Study Area

_{sx}= 2.13 and 3.19). Furthermore, the low auto-correlations demonstrate the low persistence for both mentioned stations. It should be noted that Lake Urmia is currently in a drought crisis, with the amount of precipitation and consequently river flow having decreased in recent years; therefore, this may cause some difficulties in forecasting river flows.

## 3. Techniques Applied in Modeling

#### 3.1. M5 Model Tree

_{i}is the ith subset of data. After the first step, data in the secondary nodes have lower SD as compared with the initial nodes, so M5 selects the split which expects to maximize error reduction. The main drawback of this step is the production of a large tree, which may cause an overfitting problem. Pruning techniques should be employed in order to fix this problem and to avoid overfitting. Therefore, the second step for developing M5 involves these techniques and substitution of subtrees with linear functions. By applying these two steps, M5 develops a linear model for each subspace.

#### 3.2. Support Vector Regression (SVR)

#### 3.3. Fruit fly Optimization Algorithm (FOA)

^{th}predicted and observed values and n is the entire number of data. The fruit fly saves the finest smell concentration value and the corresponding coordinate among the swarms, then flies toward the next place. When the new result is not superior to the previous iteration, the iteration number reaches its maximum, or the error of the prediction reaches the predefined value, this process will stop. Therefore, optimal values are acquired, and the model has the best performance with these values.

## 4. Evaluation Parameters

_{p}(i), Q

_{o}(i), and n represent the predicted river flow, the observed river flow, and the number of observations, respectively.

## 5. Results and Discussion

_{t−1}, and π, had better accuracy than the M5 and SVR models. M5 also performed better than the SVR model. Overall, FOASVR performed better than SVR and M5. Also, FOA increased the accuracy of SVR by approximately 27% for RMSE and 38% for MAE in the second scenario, which performed roughly (4% RMSE and 14% MAE) better than M5. Without periodicity, FOASVR-3 indicated a 6% better performance than M5-3, and both models performed better than the SVR-5 model. The relative RMSE and MAE differences between the optimal FOASVR-3 model without periodicity and FOASVR-3 model with periodicity input were 18.2% and 17.2%, respectively. From the BIC point of view, FOASVR-2, M5-2, and SVR-4, with the values of 597.55, 581.85, and 701.18, respectively, had better performance in comparison with other models, which means that these scenarios had parsimonious inputs (accurate results with fewer input parameters). So, for this station input combination, (2) was a reasonable choice. The time variation of observed and predicted river flows by the optimal periodic and non-periodic FOASVR, M5, and SVR models is illustrated in Figure 5, Figure 6, Figure 7 and Figure 8. It can be comprehended from the Figure 5 and Figure 6 that all three periodic and non-periodic models considerably underestimate some peak flows. It seems that the precision of these models decreases with increasing flow rate. However, the superior accuracy of FOASVR and M5 to the SVR model can also be comprehended from these figures. Comparison of Figure 5 and Figure 6 visibly indicate that the periodic models better approximate the observed river flows than the non-periodic models. Figure 9 displays the scattered diagrams of the observed and predicted monthly river flows for each method. It is noticeable from the graphs that the SVR model performs worse than the other two methods, especially in the prediction of peak river flows. Comparison of the two figures reveals that the periodic models produce more accurate estimates than non-periodic models. Also, this figure indicates that all models (periodic and non-periodic) overestimate some low flows, and the periodic models perform worse than periodic ones in estimating peak flows. This may be because the peak flows do not have any high correlation with the time of the year (i.e. the periodicity value).

_{t−1}, Q

_{t−2}, Q

_{t−3}, and π performed better than optimal M5-2 comprising Q

_{t−1}and π inputs, and both performed better than the optimal SVR-6 model whose inputs are the same as FOASVR-6. Generally, FOASVR performed better than SVR and M5 models; moreover, the accuracy of SVR was increased by 29.7% and 30.4% related to RMSE and MAE, respectively, in the optimal scenario (FOASVR-6) by applying FOA; also, FOASVR showed 16.8% and 19.7% better performance than M5 in terms of RMSE and MAE, respectively, for this scenario. Without the periodicity component, the optimal FOASVR-1 model performed better than the optimal M5-1 and SVR-3 models. The relative RMSE and MAE differences between the optimal FOASVR-1 model without periodicity and FOASVR-1 model with periodicity input were 25.1% and 19.1%, respectively. The best values for BIC in this station were related to FOASVR-6 with 703.64, M5-2 with 740.34, and SVR-2 with 825.05. In light of the fact that FOASVR-6 was closely followed by FOASVR-4 with the value of 707.09 and FOASVR-2 with the value of 707.53, it is better to choose a combination with fewer input parameters. Thus, the input parameters of Q

_{t−1}and π were selected as a parsimonious scenario for this station, which is similar to the previous station. Figure 7 and Figure 8 demonstrate the time variation of observed and predicted river flows by the optimal periodic and non-periodic FOASVR, M5, and SVR models. As found for the Vaniar station, here also the three periodic and non-periodic models underestimate some peak flows. Comparison of Figure 7 and Figure 8 confirms that appending the periodicity component as the input increases the estimation capacity of the models. The scatter plots of the observed and predicted monthly river flows by each method are shown in Figure 9. As with the previous station, the FOASVR and M5 perform better than the SVR model, especially in the prediction of peak river flows. This figure indicates that the estimates of periodic models are more accurate. According to Figure 9, as at Babarud station, the models overestimate the low flows at the Vaniar station, thereby forecasting shifts from overestimation to underestimation with increasing flow rate.

## 6. Conclusions

_{t−1}and π) were used as parsimonious inputs for FOASVR with values of 581.85 and 707.53 for Babarud and Vaniar stations, respectively. Generally, the FOASVR models performed better than the other two methods in forecasting monthly river flows. However, all methods had some difficulties in forecasting peak river flows, while the FOASVR models provided a better forecast in this case. The presented advancement in river flow prediction can highly empower operational river management to make better decisions and policies. The hybrid model of FOASVR shows promising results in building accurate models for river flow prediction.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Babarud and Vaniar stations, located at Lake Urmia Basin [37].

**Figure 9.**The scatter plots of the observed and forecasted monthly river flows. (

**a**) Babarud station without periodicity, (

**b**) Babarud station with periodicity, (

**c**) Vaniar station without periodicity, (

**d**) Vaniar station with periodicity.

**Figure 10.**Taylor diagrams (TDs) of the monthly predicted river flow. (

**a**) Babarud station, (

**b**) Vaniar station.

**Table 1.**Statistical parameters of the implemented data (X

_{mean}, X

_{max}, X

_{min}, Sx, Csx, a

_{1}, a

_{2}, a

_{3}denote the overall mean, maximum, minimum, standard deviation, skewness, lag-1, lag-2, lag-3 auto-correlation coefficients, respectively).

Station | Data Set | X_{mean} (m^{3}/s) | X_{max} (m^{3}/s) | X_{min} (m^{3}/s) | Sx (m^{3}/s) | Csx (m^{3}/s) | r_{1} | r_{2} | r_{3} |
---|---|---|---|---|---|---|---|---|---|

Babarud | Training data | 8.75 | 66.50 | 0.00 | 9.63 | 2.05 | 0.70 | 0.25 | −0.07 |

Testing data | 4.71 | 43.27 | 0.00 | 7.37 | 2.54 | 0.59 | 0.14 | −0.12 | |

Entire data | 7.74 | 66.50 | 0.00 | 9.28 | 2.13 | 0.69 | 0.25 | −0.05 | |

Vaniar | Training data | 14.28 | 178.29 | 0.00 | 21.35 | 2.94 | 0.62 | 0.15 | −0.11 |

Testing data | 5.66 | 65.30 | 0.00 | 10.50 | 3.02 | 0.50 | 0.11 | −0.05 | |

Entire data | 12.13 | 178.29 | 0.00 | 19.58 | 3.19 | 0.63 | 0.18 | −0.07 |

Model | Input Parameters | Output Parameters |
---|---|---|

1 | Q_{t−1} | Q_{t} |

2 | Q_{t−1}, π | Q_{t} |

3 | Q_{t−1}, Q_{t−2} | Q_{t} |

4 | Q_{t−1}, Q_{t−2}, π | Q_{t} |

5 | Q_{t−1}, Q_{t−2}, Q_{t−3} | Q_{t} |

6 | Q_{t−1}, Q_{t−2}, Q_{t−3}, π | Q_{t} |

Model Input | Model | Statistical Parameters | |||
---|---|---|---|---|---|

RMSE (m^{3}/s) | MAE (m^{3}/s) | R | BIC | ||

Q_{t}_{−}_{1} | SVR-1 | 6.10 | 4.10 | 0.59 | 706.88 |

M5-1 | 5.94 | 3.62 | 0.61 | 696.57 | |

FOASVR-1 | 5.74 | 3.29 | 0.63 | 683.28 | |

Q_{t}_{−}_{1}, π | SVR-2 | 5.97 | 3.88 | 0.61 | 703.79 |

M5-2 | 4.54 | 2.73 | 0.80 | 597.55 | |

FOASVR-2 | 4.36 | 2.40 | 0.82 | 581.85 | |

Q_{t}_{−}_{1}, Q_{t}_{−}_{2} | SVR-3 | 5.98 | 4.04 | 0.62 | 704.44 |

M5-3 | 5.79 | 3.49 | 0.68 | 691.92 | |

FOASVR-3 | 5.33 | 2.90 | 0.70 | 659.80 | |

Q_{t}_{−}_{1}, Q_{t}_{−}_{2}, π | SVR-4 | 5.85 | 3.83 | 0.64 | 701.18 |

M5-4 | 4.55 | 2.83 | 0.80 | 603.67 | |

FOASVR-4 | 4.50 | 2.67 | 0.80 | 599.39 | |

Q_{t}_{−}_{1}, Q_{t}_{−}_{2}, Q_{t}_{−}_{3} | SVR-5 | 5.91 | 3.90 | 0.62 | 705.14 |

M5-5 | 5.79 | 3.50 | 0.68 | 697.18 | |

FOASVR-5 | 5.69 | 3.20 | 0.67 | 690.42 | |

Q_{t}_{−}_{1}, Q_{t}_{−}_{2}, Q_{t}_{−}_{3}, π | SVR-6 | 5.82 | 3.77 | 0.64 | 704.46 |

M5-6 | 4.54 | 2.84 | 0.80 | 608.09 | |

FOASVR-6 | 4.58 | 2.67 | 0.79 | 611.49 |

Model Input | Model | Statistical Parameters | |||
---|---|---|---|---|---|

RMSE (m^{3}/s) | MAE (m^{3}/s) | R | BIC | ||

Q_{t}_{−}_{1} | SVR-1 | 9.33 | 5.60 | 0.50 | 831.52 |

M5-1 | 9.57 | 5.44 | 0.54 | 840.91 | |

FOASVR-1 | 8.78 | 4.77 | 0.57 | 809.04 | |

Q_{t}_{−}_{1}, π | SVR-2 | 9.04 | 5.31 | 0.52 | 825.05 |

M5-2 | 7.19 | 4.46 | 0.77 | 740.34 | |

FOASVR-2 | 6.58 | 3.86 | 0.79 | 707.53 | |

Q_{t}_{−}_{1}, Q_{t}_{−}_{2} | SVR-3 | 9.21 | 5.57 | 0.53 | 831.95 |

M5-3 | 9.80 | 5.46 | 0.59 | 854.92 | |

FOASVR-3 | 8.88 | 4.97 | 0.55 | 818.45 | |

Q_{t}_{−}_{1}, Q_{t}_{−}_{2}, π | SVR-4 | 8.96 | 5.33 | 0.54 | 826.99 |

M5-4 | 7.58 | 4.64 | 0.76 | 765.10 | |

FOASVR-4 | 6.48 | 3.75 | 0.80 | 707.09 | |

Q_{t}_{−}_{1}, Q_{t}_{−}_{2}, Q_{t}_{−}_{3} | SVR-5 | 9.22 | 5.73 | 0.52 | 837.57 |

M5-5 | 9.79 | 5.55 | 0.60 | 859.76 | |

FOASVR-5 | 8.99 | 5.53 | 0.55 | 828.22 | |

Q_{t}_{−}_{1}, Q_{t}_{−}_{2}, Q_{t}_{−}_{3}, π | SVR-6 | 9.01 | 5.53 | 0.53 | 834.27 |

M5-6 | 7.61 | 4.62 | 0.75 | 771.78 | |

FOASVR-6 | 6.33 | 3.71 | 0.81 | 703.64 |

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## Share and Cite

**MDPI and ACS Style**

Samadianfard, S.; Jarhan, S.; Salwana, E.; Mosavi, A.; Shamshirband, S.; Akib, S. Support Vector Regression Integrated with Fruit Fly Optimization Algorithm for River Flow Forecasting in Lake Urmia Basin. *Water* **2019**, *11*, 1934.
https://doi.org/10.3390/w11091934

**AMA Style**

Samadianfard S, Jarhan S, Salwana E, Mosavi A, Shamshirband S, Akib S. Support Vector Regression Integrated with Fruit Fly Optimization Algorithm for River Flow Forecasting in Lake Urmia Basin. *Water*. 2019; 11(9):1934.
https://doi.org/10.3390/w11091934

**Chicago/Turabian Style**

Samadianfard, Saeed, Salar Jarhan, Ely Salwana, Amir Mosavi, Shahaboddin Shamshirband, and Shatirah Akib. 2019. "Support Vector Regression Integrated with Fruit Fly Optimization Algorithm for River Flow Forecasting in Lake Urmia Basin" *Water* 11, no. 9: 1934.
https://doi.org/10.3390/w11091934