Regional Flood Frequency Analysis Using the FCM-ANFIS Algorithm: A Case Study in South-Eastern Australia
Abstract
:1. Introduction
2. Material and Methods
2.1. Study Area
2.1.1. Catchment Area (AREA)
2.1.2. Design Rainfall Intensity (I62)
2.1.3. Mean Annual Rainfall (MAR)
2.1.4. Shape Factor (SF)
2.1.5. Mean Annual Evapotranspiration (MAE)
2.1.6. Stream Density (SDEN)
2.1.7. S1085
2.1.8. Forest
2.2. Methodology
2.2.1. Adaptive Neuro-Fuzzy Inference System (ANFIS)
2.2.2. Grid Partitioning (GP)
2.2.3. Subtractive Clustering (SC)
2.2.4. Fuzzy C-Means (FCM)
- Assuming initial locations for each cluster centre.
- Each data-point joins the cluster with the nearest cluster centre.
- New cluster centres are computed and considered the centroids of clusters.
- Terminate the process if the cluster partition is stable. If not, go to the second step.
2.2.5. Quantile Regression Technique (QRT)
2.2.6. Statistical Measures Used in Evaluation
3. Results and Discussion
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Predictor Variable | Name of Variable | Unit | Statistical Parameter | ||
---|---|---|---|---|---|
Minimum | Maximum | Mean | |||
AREA | Catchment area | km2 | 3.00 | 1010.00 | 349.06 |
I62 | Design rainfall intensity with 6 h duration and 2 years return period | mm/h | 24.60 | 87.30 | 39.03 |
MAR | Mean annual rainfall | mm | 484.39 | 1953.23 | 970.50 |
SF | Shape factor | - | 0.25 | 1.62 | 0.78 |
MAE | Mean annual evapo-transpiration | mm | 925.90 | 1543.30 | 1112.74 |
SDEN | Stream density | km−1 | 0.51 | 5.47 | 2.06 |
S1085 | Slope of central 75% of the mainstream | m/km | 0.80 | 69.90 | 13.02 |
FOREST | Fraction forest | - | 0.00 | 1.00 | 0.55 |
nCluster_FCM | Rad_SC | MF-Type and mf_n_GP | |
---|---|---|---|
Q2 | 8 | 0.76 | Trimf-2 |
Q5 | 2 | 0.39 | Trimf-2 |
Q10 | 5 | 0.37 | Trimf-2 |
Q20 | 3 | 0.77 | Gauss2mf-5 |
Q50 | 2 | 0.78 | Gauss2mf-5 |
Q100 | 3 | 0.79 | Trimf-2 |
Q2 | Q5 | Q10 | Q20 | Q50 | Q100 |
---|---|---|---|---|---|
Trimf-2 | Trimf-2 | Trimf-2 | Gauss2mf-5 | Gauss2mf-5 | Trimf-2 |
Gauss2mf-5 | Trapmf-2 | Pimf-2 | Dsigmf-5 | Dsigmf-5 | Gauss2mf-5 |
dsigmf-5 | Pimf-2 | Trapmf-2 | Trapmf-5 | Trapmf-5 | Trapmf-5 |
Trapmf-5 | Gaussmf-2 | Dsigmf-2 | Trimf-2 | Gauss2mf-2 | Dsigmf-5 |
Gbellmf-5 | Gbellmf-2 | Gauss2mf-2 | Gaussmf-2 | Trimf-2 | Pimf-5 |
Gaussmf-2 | Gauss2mf-2 | Gbellmf-2 | Trapmf-2 | Gbellmf-5 | Gauss2mf-4 |
Gauss2mf-2 | Dsigmf-2 | Gaussmf-2 | Gbellmf-2 | Gaussmf-5 | Trapmf-4 |
Quantile | Q2 | Q5 | Q10 | Q20 | Q50 | Q100 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Statistics | QRT | FCM | QRT | FCM | QRT | FCM | QRT | FCM | QRT | FCM | QRT | FCM |
REr | 43.10 | 51.43 | 39.10 | 38.18 | 35.58 | 39.96 | 38.88 | 46.90 | 40.01 | 53.23 | 48.12 | 59.80 |
QT_pred/QT_obs (Median) | 0.93 | 0.95 | 0.97 | 1.07 | 0.97 | 1.11 | 1.05 | 1.23 | 1.00 | 1.11 | 1.07 | 1.45 |
RMSE | 49.91 | 50.88 | 115.46 | 119.05 | 190.22 | 206.06 | 289.55 | 315.90 | 507.50 | 531.49 | 749.58 | 845.69 |
RBias | 31.76 | 44.60 | 32.32 | 67.60 | 38.23 | 87.67 | 41.72 | 53.66 | 46.43 | 44.29 | 57.25 | 61.43 |
RMSNE | 1.13 | 2.06 | 1.32 | 2.64 | 1.50 | 3.02 | 1.61 | 2.34 | 1.78 | 1.85 | 2.09 | 2.90 |
RRMSE | 0.82 | 0.84 | 0.75 | 0.78 | 0.77 | 0.84 | 0.79 | 0.87 | 0.88 | 0.93 | 1.01 | 1.08 |
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Zalnezhad, A.; Rahman, A.; Vafakhah, M.; Samali, B.; Ahamed, F. Regional Flood Frequency Analysis Using the FCM-ANFIS Algorithm: A Case Study in South-Eastern Australia. Water 2022, 14, 1608. https://doi.org/10.3390/w14101608
Zalnezhad A, Rahman A, Vafakhah M, Samali B, Ahamed F. Regional Flood Frequency Analysis Using the FCM-ANFIS Algorithm: A Case Study in South-Eastern Australia. Water. 2022; 14(10):1608. https://doi.org/10.3390/w14101608
Chicago/Turabian StyleZalnezhad, Amir, Ataur Rahman, Mehdi Vafakhah, Bijan Samali, and Farhad Ahamed. 2022. "Regional Flood Frequency Analysis Using the FCM-ANFIS Algorithm: A Case Study in South-Eastern Australia" Water 14, no. 10: 1608. https://doi.org/10.3390/w14101608
APA StyleZalnezhad, A., Rahman, A., Vafakhah, M., Samali, B., & Ahamed, F. (2022). Regional Flood Frequency Analysis Using the FCM-ANFIS Algorithm: A Case Study in South-Eastern Australia. Water, 14(10), 1608. https://doi.org/10.3390/w14101608