# Comparing Performance of ANN and SVM Methods for Regional Flood Frequency Analysis in South-East Australia

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## Abstract

**:**

## 1. Introduction

^{2}) and root mean square error (RMSE). The ANN, SVR and NLR methods were compared by Vafakhah and Khosrobeigi Bozchaloei [28] using a dataset from 33 stations in Iran. They reported that the SVR was the best-performing method for a regional analysis of flood duration curves. Using a dataset from 202 catchments in Australia, Haddad and Rahman [45] compared the performances of 15 combinations of RFFA methods, including Bayesian generalised least squares (BGLSR), multidimensional scaling (MDS) and SVR. They reported that the MDS-based SVR method using a radial basis function (RBF) kernel was the best-performing model in terms of consistency, accuracy of the results and generalisation.

^{2}and NASH to evaluate the performances of these methods. They reported that the WNN method had a better performance in terms of generalisation capability and accuracy. A dataset from 151 catchments in Canada was used by Desai and Ouarda [47] to compare the performance of different combinations of the canonical correlation analysis (CCA) with ANN, random forest regression (RFR), MLR and ANN ensembles. They reported that a combination of CCA and RFR to be the best-performing method. In another study, Bozchaloei and Vafakhah [48] used 20 years of data recorded from 33 hydrometric stations to estimate design floods, in which they compared the performances of the ANN, ANFIS and NLR methods and reported ANFIS to be the best-performing method. In another study, Kumar et al. [49] used the fuzzy inference system (FIS), ANN and L-moment methods using a dataset of 15–29 years from 17 catchments in India. They reported FIS to be the best-performing method, followed by ANN in terms of accuracy and reliability.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data

^{2}(mean: 349 km

^{2}). The selected catchments were divided into a training dataset (consisting of 126 catchments) and testing dataset (consisting of 55 catchments).

_{62}), mean annual rainfall (MAR), shape factor (SF), mean annual evapotranspiration (MAE), stream density (SDEN), mainstream slope S1085 and fraction forested area (FOREST). It should be noted that all these eight predictor variables were included in the developed ANN and SVM-based RFFA models presented in this study.

_{2}, Q

_{5}, Q

_{10}, Q

_{20}, Q

_{50}and Q

_{100}, respectively). These are estimated by fitting a log-Pearson Type 3 (LP3) distribution to each of the selected station’s AM flood series. The parameters of the GEV distribution were estimated by the Bayesian method. It should be noted that other distributions such as GEV could have been used, but for South-East Australia, LP3 was found to be the best-fit probability distribution in previous FFA studies [50,54]. It should also be noted that the impacts of non-stationarity on the FFA results are worth considering [57], which, however, is beyond the scope of this study.

#### 2.3. ANN-Based RFFA Method

_{i}is the weight coefficient and x

_{i}is the input or independent variable.

#### 2.4. SVM-Based RFFA Method

#### Kernel Functions

## 3. Statistical Metrices Used for Model Evaluation

^{3}/s) estimated by fitting LP3 distribution for each of the selected return periods at the site i (i = 1, N), and Qpred,i (in m

^{3}/s) is the predicted-flood quantiles using either SVM or ANN at site i. Here, N = 55, as there are 55 test catchments.

## 4. Results

_{62}, MAR and SDEN (for Q

_{2}); (ii) AREA, I

_{62}and SDEN (for Q

_{5}and Q

_{10}); (iii) AREA, I

_{62}, SDEN and MAR (for Q

_{20}and Q

_{50}); and (iv) AREA, I

_{62}, MAE and MAR (for Q

_{100}). Table 2 shows the statistical metrices of the best ANN model for different flood quantiles. As shown in Appendix A (Table A1), the best methods were selected based on the most common evaluation statistics, such as MSE, RMSE, RRMSE, REr and Rbias. Table A1 shows some of the best-performing ANN methods with different algorithms; from these, the best one is presented in Table 2 and used for further investigation. Table A2 shows the different parameters used in developing the SVM methods, and Table A3 represents the best-performing SVM methods with different algorithms used in developing the SVM methods. The best-performing SVM methods are selected based on statistical indices and are represented in Table 3 and are used for further investigation. From Table 2, it can be seen that, for the ANN-based models, Q

_{10}has the smallest Rbias and RMSNE values, whereas Q

_{5}has the smallest REr value. From Table 3, it is found that Q

_{2}has the smallest Rbias value, and Q

_{5}has the smallest RMSNE value.

_{ratio}values for ANN and SVM models. As can be seen in this figure, the ANN model shows some overestimation for Q

_{20}, Q

_{50}and Q

_{100}, whereas, for the SVM model, there is an overestimation for Q

_{20}and Q

_{100}. In terms of Q

_{ratio}, the ANN presents better results for Q

_{5}(with a smaller box width) as compared to SVM. As can be seen in Figure 6, the results of Q

_{2}for SVM are better than the ANN. In terms of Q

_{10}, Q

_{20}and Q

_{100}, both the models perform very similarly; however, the median values for SVM seem to be further away from the 1:1 line. The Q

_{ratio}results for Q

_{50}show that the SVM method has a better performance than the ANN, with a smaller box width and median value located near the 1:1 line Overall, the Q

_{5}model for ANN is the best model (with the smallest box width), followed by Q

_{10}(ANN), Q

_{2}(SVM), Q

_{5}(SVM), Q

_{10}(SVM) and Q

_{50}(SVM). For Q

_{100}, both the ANN and SVM and, for Q

_{50}, the ANN shows remarkable overestimations.

_{2}, SVM has a better performance, since it produces a smaller box width with a median value closer to the 0:0 line. The ANN produces better results for Q

_{5}with a smaller box width. In terms of Q

_{10}, Q

_{20}and Q

_{100}, both the models perform similarly; however, SVM produces better results for Q

_{50}. Overall, SVM shows better performance with smaller box widths. In terms of bias, Q

_{5}(ANN), Q

_{10}(ANN) and Q

_{50}(SVM) present the best performances, as the median values are located closer to the 0:0 line. The Q

_{100}model for both the ANN and SVM and Q

_{50}(ANN) and Q

_{20}(SVM) models produce notable overestimations. The best model is found for Q

_{5}(ANN), followed by Q

_{5}(SVM).

_{ratio}values [63]. As seen in Figure 8, catchments with REr values falling in the range of 0–30% are rated as “Good”, catchments with REr values in the range of 31–60% are rated as “Fair” and “Poor” is assigned to the remaining catchments with REr values beyond 61%. Figure 7 shows the qualitative comparison of the performance of the ANN and SVM models for different test catchments based on Q

_{ratio}. In this figure “Good” is assigned to the test catchments with the Q

_{ratio}values falling between 0.8 and 1.3, “Fair” is assigned to the test catchments with Q

_{ratio}values falling in the range of 0.6–0.79 and 1.31–2 and “Poor” is assigned to the remaining test catchments. The ANN method outperforms the SVM method in terms of REr values, because it has a Good-rated performance for more test catchments than SVM—in particular, for smaller return periods. Overall, both the SVM and ANN show a poor performance for Q

_{100}.

_{2}, showing that the ANN method performs better for a greater number of test catchments with lower ranges of Abs RE values.

_{20}as an example. The ANN model performs better than the SVM, having 19 catchments with Abs RE values less than 25%, while there are only 14 catchments for the SVM method. There is no spatial pattern of the Abs RE values of the 55 test catchments.

_{2}and 50.17 for the SVM-Q

_{2}models in the present study. Similarly, Ghaderi et al. [44] reported a RMSE value of 239.94 for their best-performing method (SVM) when comparing it with the ANFIS and GEP methods. Vafakhah and Bozchaloei [28] compared the results of the ANN, SVM and NLR methods and reported a RRMSE of 1.45 for their best-performing method (SVM); these values were 0.79 and 0.80 for our ANN-Q

_{5}and SVM-Q

_{5}models, respectively. Ouarda and Shu [32] compared the results of the ANN method with MLR model and reported a RRMSE value of 36.17 and RMSE value of 27.33 for the ANN method as the best-performing method. Shu and Ouarda [31] used the ANFIS, ANN, NLR and NLR methods and reported RMSE and RRMSE values of 316 and 57, respectively, for their best-performing method. Jingyi and Hall [23] used cluster analysis and ANN methods and reported the best RMSE value of 47 for their best-performing method. The above discussion shows that the ANN and SVM models developed in the present study provided results similar to the relevant international studies.

## 5. Conclusions

_{5}and Q

_{10}with the ANN, giving the smallest median relative error (33–36%). This is notably smaller than the ARR-RFFE model (57%). It should be noted that the ARR-RFFE model adopted only four predictors, whereas the ANN and SVM-based models presented here adopted eight predictor variables, which played a role in reducing the prediction error.

_{100}, both the SVM and ARR-RFFE models provide similar relative errors (64%). In terms of bias, both the ANN and SVM models provide significant overestimations for Q

_{100}. This highlights that the estimation of floods with higher return periods is challenging. even with the artificial intelligence-based models.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Q_{2} | Q_{5} | Q_{10} | Q_{20} | Q_{50} | Q_{100} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Sorted by performance | Network Name | Training Algorithm | Network Name | Training Algorithm | Network Name | Training Algorithm | Network Name | Training Algorithm | Network Name | Training Algorithm | Network Name | Training Algorithm |

RBF 4-22-1 | RBFT | MLP 3-3-1 | BR | MLP 3-3-1 | BR | MLP 4-3-1 | LM | RBF 4-20-1 | RBFT | MLP 4-2-1 | LM | |

MLP 4-8-1 | BFGS 63 | RBF 3-19-1 | RBFT | MLP 3-2-1 | LM | MLP 4-4-1 | LM | RBF 4-18-1 | RBFT | MLP 4-8-1 | LM | |

MLP 4-3-1 | BR | MLP 3-7-1 | BFGS 34 | MLP 3-4-1 | BR | MLP 4-10-1 | LM | MLP 4-6-1 | LM | MLP 4-6-1 | LM | |

MLP 4-2-1 | BFGS 43 | MLP 3-4-1 | BR | MLP 3-5-1 | LM | RBF 4-22-1 | RBFT | MLP 4-7-1 | LM | MLP 4-3-1 | BFGS 7 | |

MLP 4-10-1 | LM | MLP 3-2-1 | BR | RBF 3-23-1 | RBFT | MLP 4-2-1 | LM | MLP 4-4-1 | LM | MLP 4-10-1 | LM | |

MLP 4-6-1 | BFGS 109 | MLP 3-3-1 | LM | MLP 3-8-1 | LM | MLP 4-8-1 | LM | MLP 4-3-1 | LM | MLP 4-5-1 | BFGS 10 | |

MLP 4-2-1 | BR | MLP 3-10-1 | BFGS 71 | MLP 3-3-1 | LM | MLP 4-9-1 | LM | MLP 4-9-1 | LM | MLP 4-9-1 | LM | |

MLP 4-9-1 | LM | MLP 3-5-1 | BFGS 42 | MLP 3-4-1 | LM | MLP 4-7-1 | LM | MLP 4-2-1 | BR | RBF 4-18-1 | RBFT | |

MLP 4-3-1 | SCG | MLP 3-6-1 | BFGS 61 | MLP 3-6-1 | BFGS 53 | MLP 4-6-1 | LM | MLP 4-5-1 | LM | RBF 4-19-1 | RBFT | |

MLP 4-10-1 | BFGS 27 | MLP 3-5-1 | BR | MLP 3-9-1 | LM | MLP 4-5-1 | LM | MLP 4-10-1 | LM | MLP 4-3-1 | LM |

Quantile | SVM Type | Kernel Type | Epsilon/Nu | Capacity | Gamma | Cross-Validation Error | Number of Support Vectors |
---|---|---|---|---|---|---|---|

Q_{2} | 1 | RBF | 0.200 | 10.000 | 0.250 | 0.038 | 22 (13 bounded) |

Q_{5} | 1 | RBF | 0.100 | 6.000 | 0.333 | 0.050 | 45 (39 bounded) |

Q_{10} | 1 | RBF | 0.100 | 10.000 | 0.333 | 0.053 | 59 (48 bounded) |

Q_{20} | 2 | RBF | nu = 0.300 | 3.000 | 0.250 | 0.048 | 43 (33 bounded) |

Q_{50} | 2 | Sigmoid | nu = 0.500 | 10.000 | 0.250 | 0.060 | 66 (61 bounded) |

Q_{100} | 1 | RBF | 0.100 | 8.000 | 0.250 | 0.052 | 54 (42 bounded) |

Q_{2} | Q_{5} | Q_{10} | Q_{20} | Q_{50} | Q_{100} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Sorted by performance | Type(1) | RBF | Type(1) | RBF | Type(1) | RBF | Type(2) | RBF | Type(2) | Sigmoid | Type(1) | RBF |

Type(2) | Polynomial | Type(2) | RBF | Type(2) | RBF | Type(2) | Sigmoid | Type(1) | Linear | Type(2) | Sigmoid | |

Type(2) | RBF | Type(1) | Polynomial | Type(1) | Polynomial | Type(1) | Sigmoid | Type(1) | Polynomial | Type(2) | RBF | |

Type(2) | Linear | Type(2) | Linear | Type(2) | Polynomial | Type(1) | RBF | Type(2) | Linear | Type(2) | Polynomial | |

Type(1) | Polynomial | Type(2) | Polynomial | Type(1) | Sigmoid | Type(1) | Polynomial | Type(1) | Sigmoid | Type(1) | Polynomial | |

Type(1) | Linear | Type(2) | Sigmoid | Type(2) | Sigmoid | Type(2) | Linear | Type(2) | Polynomial | Type(1) | Sigmoid | |

Type(2) | Sigmoid | Type(1) | Linear | Type(2) | Linear | Type(2) | Polynomial | Type(1) | RBF | Type(1) | Linear | |

Type(1) | Sigmoid | Type(1) | Sigmoid | Type(1) | Linear | Type(1) | Linear | Type(2) | RBF | Type(2) | Linear |

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**Figure 6.**Boxplot of Q

_{ratio}values for the ANN and SVM methods. Y-axis presents Q

_{ratio}values.

**Figure 11.**Spatial distribution of Abs RE values for ANN-Q

_{20}and SVM-Q

_{20}for 55 selected test catchments.

Predictor Variable | Name of Variable | Unit | Statistical Parameter | |||
---|---|---|---|---|---|---|

Minimum | Maximum | Mean | Median | |||

AREA | Catchment area | km^{2} | 3.00 | 1010.00 | 349.06 | 304.00 |

I_{62} | Design rainfall intensity with 6-h duration and 2-year return period | mm/h | 24.60 | 87.30 | 39.03 | 37.30 |

MAR | Mean annual rainfall | mm | 484.39 | 1953.23 | 970.50 | 910.37 |

SF | Shape factor | - | 0.25 | 1.62 | 0.78 | 0.78 |

MAE | Mean annual evapotranspiration | mm | 925.90 | 1543.30 | 1112.74 | 1071.90 |

SDEN | Stream density | km^{−1} | 0.51 | 5.47 | 2.06 | 1.61 |

S1085 | Slope of central 75% of the mainstream | m/km | 0.80 | 69.90 | 13.02 | 9.40 |

FOREST | Fraction forest | - | 0.00 | 1.00 | 0.55 | 0.59 |

Quantile | Network Name | Training Algorithm | Median Ratio | MSE | RMSE | RRMSE | REr | Rbias | RMSNE |
---|---|---|---|---|---|---|---|---|---|

Q_{2} | RBF 4-22-1 | RBFT | 1.01 | 2514.63 | 50.15 | 0.82 | 41.97 | 117.37 | 4.57 |

Q_{5} | MLP 3-3-1 | BR | 1.09 | 14,523.69 | 120.51 | 0.79 | 33.27 | 57.65 | 2.67 |

Q_{10} | MLP 3-3-1 | BR | 1.02 | 38,852.75 | 197.11 | 0.80 | 36.10 | 24.20 | 2.28 |

Q_{20} | MLP 4-3-1 | LM | 1.19 | 104,981.21 | 324.01 | 0.89 | 40.45 | 150.56 | 5.61 |

Q_{50} | RBF 4-20-1 | RBFT | 1.31 | 267,171.25 | 516.89 | 0.90 | 44.90 | 141.24 | 3.54 |

Q_{100} | MLP 4-2-1 | LM | 1.47 | 639,427.42 | 799.64 | 1.02 | 54.38 | 145.03 | 4.18 |

Quantile | SVM Type | Kernel Type | Median Ratio | MSE | RMSE | RRMSE | REr | Rbias | RMSNE |
---|---|---|---|---|---|---|---|---|---|

Q_{2} | 1 | RBF | 0.89 | 2516.95 | 50.17 | 0.82 | 42.79 | −32.79 | 2.84 |

Q_{5} | 1 | RBF | 1.13 | 14,886.86 | 122.01 | 0.80 | 37.13 | 75.43 | 2.51 |

Q_{10} | 1 | RBF | 1.14 | 39,363.88 | 198.40 | 0.81 | 41.01 | 103.89 | 3.54 |

Q_{20} | 2 | RBF | 1.41 | 92,444.54 | 304.05 | 0.84 | 46.70 | 94.47 | 2.73 |

Q_{50} | 2 | Sigmoid | 0.94 | 536,655.49 | 732.57 | 1.28 | 45.45 | −43.70 | 5.08 |

Q_{100} | 1 | RBF | 1.57 | 611,790.05 | 782.17 | 1.00 | 64.29 | 166.96 | 4.31 |

Quantiles | ARR RFFA Model REr | SVM-REr | ANN-REr |
---|---|---|---|

Q_{2} | 63.07 | 42.79 | 41.97 |

Q_{5} | 57.25 | 37.13 | 33.27 |

Q_{10} | 57.48 | 41.01 | 36.10 |

Q_{20} | 58.85 | 46.70 | 40.45 |

Q_{50} | 60.39 | 45.45 | 44.90 |

Q_{100} | 64.06 | 64.29 | 54.38 |

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## Share and Cite

**MDPI and ACS Style**

Zalnezhad, A.; Rahman, A.; Nasiri, N.; Vafakhah, M.; Samali, B.; Ahamed, F.
Comparing Performance of ANN and SVM Methods for Regional Flood Frequency Analysis in South-East Australia. *Water* **2022**, *14*, 3323.
https://doi.org/10.3390/w14203323

**AMA Style**

Zalnezhad A, Rahman A, Nasiri N, Vafakhah M, Samali B, Ahamed F.
Comparing Performance of ANN and SVM Methods for Regional Flood Frequency Analysis in South-East Australia. *Water*. 2022; 14(20):3323.
https://doi.org/10.3390/w14203323

**Chicago/Turabian Style**

Zalnezhad, Amir, Ataur Rahman, Nastaran Nasiri, Mehdi Vafakhah, Bijan Samali, and Farhad Ahamed.
2022. "Comparing Performance of ANN and SVM Methods for Regional Flood Frequency Analysis in South-East Australia" *Water* 14, no. 20: 3323.
https://doi.org/10.3390/w14203323