Modeling of Monthly Rainfall–Runoff Using Various Machine Learning Techniques in Wadi Ouahrane Basin, Algeria
Abstract
:1. Introduction
2. Materials and Methods
2.1. Multivariate Empirical Mode Decomposition (EMD)
- Over the entire signal length, the number of zero-crossings and the number of local maxima and minima are either equal to or at least differ by one.
- The average upper and lower envelopes calculated by local maxima and minima should be equal to zero.
2.2. Principle Component Analysis (PCA)
2.3. Multivariate Nonlinear Regression (MNLR)
2.4. Artificial Neural Networks (ANNs)
2.5. K-Nearest Neighbor (KNN)
2.6. Multivariate Adaptive Regression Spline (MARS)
2.7. M5 Model Tree (M5)
2.8. Least Square Support Vector Machine (LSSVM)
2.9. Random Forest Regression (RF)
2.10. Gorilla Troop Optimizer (GTO)
2.11. Hybrid of LSSVM and KNN with Gorilla Troop Optimizer
Algorithm 1. KNN–GTO and LSSVM–GTO |
1: Initialize parameters of GTO 2: Load inputs and target variables dataset 3: Generate the initial population of GTO 4: Train and test KNN and LSSVM for each artificial gorilla 5: Calculate the fitness function (MSE) for each artificial gorilla 6: iter: =1 7: while iter < Max_Iter do 8: Update the position of an artificial gorilla using Equations (10)–(19) 9: iter: = iter + 1 10: end while 11: Return the best solution (optimal W and K for KNN, and gamma and σ for LSSVM) |
2.12. Assessment Criteria
3. Case Study and Data Description
4. Presented Framework for Modeling Rainfall–Runoff
Algorithm 2 feature selection |
1: Load input data and target data 2: Apply lag times to input data 3: while i < number of input features do 4: Calculate the Pearson correlation coefficient (R) between the feature and target data. 5: If R < threshold of R 6: Remove feature from the input data 7: end if 8: i: = i + 1 9: end while 10: Apply PCA to the remaining input data 11: Return the final inputs list |
5. Results and Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Statistics | Q (m3/s) | S1 | S2 | S3 | S4 | S5 | S6 | Tmin (°C) | Tmean (°C) | Tmax (°C) | RHmean (%) | WS (m/s) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Rainfall (mm/Month) | ||||||||||||
Mean | 0.47 | 30.29 | 40.57 | 27.81 | 32.48 | 35.44 | 33.96 | 12.34 | 25.8 | 28.01 | 50.38 | 2.58 |
Standard deviation | 1.54 | 32.15 | 48.01 | 30.3 | 34.2 | 38.44 | 34.63 | 6.09 | 7.07 | 9.2 | 26.63 | 0.71 |
Minimum | 0 | 0 | 0 | 0 | 0 | 0 | 0 | −1.5 | 0 | 0 | 0 | 0.6 |
Maximum | 18.1 | 167.6 | 336.4 | 156.3 | 175.05 | 265.2 | 172.3 | 24.7 | 51.83 | 96.27 | 82.5 | 4.9 |
Coefficient of variation | 0.31 | 0.94 | 0.85 | 0.92 | 0.95 | 0.92 | 0.98 | 2.03 | 2.69 | 2.8 | 1.89 | 3.63 |
Skewness coefficient | 6.82 | 1.28 | 1.81 | 1.42 | 1.29 | 1.72 | 1.23 | 0.17 | 0.36 | 0.92 | −1.09 | −0.12 |
Scenarios | Inputs | Threshold of R | Pre-Processing | Post-Processing |
---|---|---|---|---|
1 | R_1, R_2, R_3, R_4, R_5, R_6, Tmin, Tmean, Tmax, Rh_mean, SW | - | - | - |
2 | R_1, R_2, R_3, R_4, R_5, R_6, Tmin, Tmean, Tmax, Rh_mean, SW Lag = 0:24 month | 0.05 | - | - |
3 | R_1, R_2, R_3, R_4, R_5, R_6, Tmin, Tmean, Tmax, Rh_mean, SW Lag = 0:24 month | 0.1 | IMF (MaxNumIMF = 3) | PCA |
4 | R_1, R_2, R_3, R_4, R_5, R_6, Tmin, Tmean, Tmax, Rh_mean, SW Lag = 0:24 month | 0.1 | IMF (MaxNumIMF = 4) | PCA |
5 | R_1, R_2, R_3, R_4, R_5, R_6, Tmin, Tmean, Tmax, Rh_mean, SW Lag = 0:24 month | 0.1 | IMF (MaxNumIMF = 5) | PCA |
Scenarios | Algorithm | N1/N2 | γ/σ | minLSize/sThreshold | mF/C | NumTree | K |
---|---|---|---|---|---|---|---|
1 | ANN | 1/5 | - | - | - | - | - |
LSSVM | - | 4.90/6.00 | - | - | - | - | |
M5 | - | - | 64/0.01 | - | - | - | |
MARS | - | - | - | 5/4 | - | - | |
RF | - | - | 4/0.05 | - | 100 | - | |
LSSVM–GTO | - | 5.23/6.19 | - | - | - | - | |
KNN | - | - | - | - | - | 13 | |
KNN–GTO | - | - | - | - | - | 4 | |
2 | ANN | 15/4 | - | - | - | - | - |
LSSVM | - | 10/5 | - | - | - | - | |
M5 | - | - | 64/0.01 | - | - | - | |
MARS | - | - | - | 5/4 | - | - | |
RF | - | - | 8/0.01 | - | 100 | - | |
LSSVM–GTO | - | 100/8.16 | - | - | - | - | |
KNN | - | - | - | - | - | 2 | |
KNN–GTO | - | - | - | - | - | 2 | |
3 | ANN | 10/7 | - | - | - | - | - |
LSSVM | - | 10/5 | - | - | - | - | |
M5 | - | - | 64/0.01 | - | - | - | |
MARS | - | - | - | 5/4 | - | - | |
RF | - | - | 32/0.1 | - | 100 | - | |
LSSVM–GTO | - | 100/7.43 | - | - | - | - | |
KNN | - | - | - | - | - | 3 | |
KNN–GTO | - | - | - | - | - | 1 | |
4 | ANN | 12/4 | - | - | - | - | - |
LSSVM | - | 10/5 | - | - | - | - | |
M5 | - | - | 64/0.1 | - | - | - | |
MARS | - | - | - | 30/6 | - | - | |
RF | - | - | 32/0.01 | - | 100 | - | |
LSSVM–GTO | - | 1.38/2.33 | - | - | - | - | |
KNN | - | - | - | - | - | 4 | |
KNN–GTO | - | - | - | - | - | 1 | |
5 | ANN | 7/7 | - | - | - | - | - |
LSSVM | - | 10/5 | - | - | - | - | |
M5 | - | - | 64/0.1 | - | - | - | |
MARS | - | - | - | 30/4 | - | - | |
RF | - | - | 8/0.01 | - | 100 | - | |
LSSVM–GTO | - | 100/8.35 | - | - | - | - | |
KNN | - | - | - | - | - | 5 | |
KNN–GTO | - | - | - | - | - | 4 |
Scenarios | Algorithm | MAE | RMSE | RRMSE | R | NSE | KGE |
---|---|---|---|---|---|---|---|
1 | ANN | 0.4540 | 1.3057 | 0.9052 | 0.4608 | 0.1786 | −0.1042 |
LSSVM | 0.3175 | 0.7779 | 0.7240 | 0.7135 | 0.4745 | 0.3187 | |
M5 | 0.5356 | 1.4645 | 0.8855 | 0.4625 | 0.2139 | 0.0477 | |
MARS | 0.5679 | 1.4487 | 0.8759 | 0.4804 | 0.2308 | 0.0717 | |
RF | 0.3314 | 1.0234 | 0.6188 | 0.8354 | 0.6161 | 0.4567 | |
MNLR | 0.4304 | 0.8965 | 0.8343 | 0.5497 | 0.3022 | 0.1695 | |
LSSVM–GTO | 0.3174 | 0.7776 | 0.7237 | 0.7138 | 0.4749 | 0.3192 | |
KNN | 0.5667 | 1.6160 | 0.9238 | 0.4109 | 0.1444 | −0.1271 | |
KNN–GTO | 0.5364 | 1.6365 | 0.9355 | 0.4277 | 0.1226 | −0.1896 | |
2 | ANN | 0.0209 | 0.0446 | 0.0345 | 0.9996 | 0.9988 | 0.9749 |
LSSVM | 0.1582 | 0.4317 | 0.3266 | 0.9827 | 0.8931 | 0.7108 | |
M5 | 0.4137 | 0.9160 | 0.7525 | 0.6574 | 0.4322 | 0.3368 | |
MARS | 0.3545 | 0.8260 | 0.6380 | 0.7693 | 0.5918 | 0.5312 | |
RF | 0.1968 | 0.7060 | 0.4956 | 0.9085 | 0.7537 | 0.6003 | |
MNLR | 0.4526 | 0.6950 | 0.5709 | 0.8205 | 0.6731 | 0.6271 | |
LSSVM–GTO | 0.0703 | 0.1859 | 0.1406 | 0.9972 | 0.9802 | 0.8773 | |
KNN | 0.2498 | 0.8191 | 0.5750 | 0.8207 | 0.6685 | 0.5678 | |
KNN–GTO | 0.0013 | 0.0127 | 0.0089 | 1.0000 | 0.9999 | 0.9969 | |
3 | ANN | 0.0000 | 0.0000 | 0.0000 | 1.0000 | 1.0000 | 1.0000 |
LSSVM | 0.1268 | 0.3296 | 0.2015 | 0.9941 | 0.9593 | 0.8232 | |
M5 | 0.1856 | 0.7773 | 0.4796 | 0.8771 | 0.7694 | 0.7387 | |
MARS | 0.4922 | 1.0055 | 0.8394 | 0.5418 | 0.2935 | 0.1580 | |
RF | 0.2838 | 0.8688 | 0.5312 | 0.9236 | 0.7171 | 0.5305 | |
MNLR | 0.4343 | 0.6578 | 0.5491 | 0.8353 | 0.6977 | 0.6557 | |
LSSVM–GTO | 0.0529 | 0.1304 | 0.0797 | 0.9989 | 0.9936 | 0.9344 | |
KNN | 0.3353 | 0.9785 | 0.5865 | 0.8206 | 0.6551 | 0.5454 | |
KNN–GTO | 0.2839 | 0.8923 | 0.5348 | 0.8631 | 0.7132 | 0.5837 | |
4 | ANN | 0.0277 | 0.0440 | 0.0300 | 0.9996 | 0.9991 | 0.9892 |
LSSVM | 0.1688 | 0.4213 | 0.2811 | 0.9874 | 0.9208 | 0.7525 | |
M5 | 0.3262 | 0.9896 | 0.6500 | 0.7592 | 0.5764 | 0.5127 | |
MARS | 0.4541 | 0.7097 | 0.4662 | 0.8844 | 0.7821 | 0.7533 | |
RF | 0.2547 | 0.8613 | 0.5068 | 0.9040 | 0.7424 | 0.5878 | |
MNLR | 0.5617 | 0.9386 | 0.6262 | 0.7790 | 0.6068 | 0.5489 | |
LSSVM–GTO | 0.0628 | 0.1525 | 0.1001 | 0.9981 | 0.9899 | 0.9184 | |
KNN | 0.3389 | 0.9946 | 0.6533 | 0.7579 | 0.5721 | 0.4838 | |
KNN–GTO | 0.0001 | 0.0016 | 0.0011 | 1.0000 | 1.0000 | 0.9998 | |
5 | ANN | 0.0405 | 0.0693 | 0.0403 | 0.9994 | 0.9984 | 0.9498 |
LSSVM | 0.1523 | 0.3627 | 0.2499 | 0.9908 | 0.9374 | 0.7790 | |
M5 | 0.0795 | 0.4670 | 0.3217 | 0.9467 | 0.8962 | 0.8833 | |
MARS | 0.5338 | 1.1197 | 0.6983 | 0.7149 | 0.5111 | 0.4340 | |
RF | 0.2694 | 0.8038 | 0.4673 | 0.9604 | 0.7810 | 0.5769 | |
MNLR | 0.4770 | 0.7890 | 0.5436 | 0.8389 | 0.7037 | 0.6627 | |
LSSVM–GTO | 0.0588 | 0.1302 | 0.0897 | 0.9986 | 0.9919 | 0.9252 | |
KNN | 0.2279 | 0.8323 | 0.4819 | 0.8875 | 0.7671 | 0.6455 | |
KNN–GTO | 0.0001 | 0.0021 | 0.0012 | 1.0000 | 1.0000 | 0.9998 |
Scenarios | Algorithm | MAE | RMSE | RRMSE | R | NSE | KGE | Friedman Ranking |
---|---|---|---|---|---|---|---|---|
1 | ANN | 0.4827 | 1.5902 | 0.9017 | 0.4684 | 0.1820 | −0.1069 | 35.3333 |
LSSVM | 0.7111 | 2.1998 | 0.9625 | 0.2941 | 0.0679 | −0.2475 | 45.3333 | |
M5 | 0.5516 | 1.1938 | 0.9569 | 0.4099 | 0.0787 | 0.0760 | 35.6667 | |
MARS | 0.5333 | 1.1759 | 0.9426 | 0.4172 | 0.1061 | 0.1119 | 33.3333 | |
RF | 0.5239 | 1.2307 | 0.9865 | 0.3974 | 0.0208 | 0.1007 | 36.6667 | |
MNLR | 0.8219 | 2.2490 | 0.9840 | 0.2186 | 0.0257 | −0.2600 | 48.8333 | |
LSSVM–GTO | 0.7111 | 2.1998 | 0.9625 | 0.2940 | 0.0679 | −0.2474 | 45.3333 | |
KNN | 0.3545 | 0.7886 | 0.9072 | 0.4470 | 0.1720 | 0.0744 | 27.6667 | |
KNN–GTO | 0.3156 | 0.7537 | 0.8671 | 0.5006 | 0.2435 | 0.0502 | 24.8333 | |
2 | ANN | 0.6039 | 1.8606 | 0.9227 | 0.4193 | 0.1432 | 0.0838 | 39.3333 |
LSSVM | 0.5587 | 1.6312 | 0.8277 | 0.6487 | 0.3105 | 0.0923 | 29.6667 | |
M5 | 0.4699 | 1.6769 | 0.7885 | 0.6787 | 0.3743 | 0.1388 | 23.3333 | |
MARS | 0.4682 | 1.5109 | 0.7493 | 0.6625 | 0.4350 | 0.3069 | 17.8333 | |
RF | 0.4893 | 1.5880 | 0.8834 | 0.4788 | 0.2147 | −0.0066 | 34.0000 | |
MNLR | 0.7810 | 1.7083 | 0.8033 | 0.5944 | 0.3507 | 0.1959 | 31.0000 | |
LSSVM–GTO | 0.5491 | 1.5716 | 0.7975 | 0.6690 | 0.3599 | 0.1570 | 24.3333 | |
KNN | 0.4925 | 1.6548 | 0.9205 | 0.4460 | 0.1472 | −0.2137 | 37.5000 | |
KNN–GTO | 0.3823 | 1.5340 | 0.8534 | 0.5365 | 0.2671 | 0.0273 | 29.6667 | |
3 | ANN | 0.5885 | 1.1976 | 0.6946 | 0.7428 | 0.5144 | 0.5419 | 13.1667 |
LSSVM | 0.4661 | 0.9855 | 0.7543 | 0.6998 | 0.4274 | 0.2388 | 14.8333 | |
M5 | 0.4572 | 1.2876 | 0.9547 | 0.3579 | 0.0827 | −0.1658 | 35.1667 | |
MARS | 0.5875 | 1.6682 | 0.7769 | 0.6411 | 0.3925 | 0.3570 | 22.6667 | |
RF | 0.5245 | 1.1745 | 0.8989 | 0.4489 | 0.1869 | −0.0441 | 33.0000 | |
MNLR | 0.7334 | 1.6685 | 0.7771 | 0.6350 | 0.3922 | 0.2339 | 26.3333 | |
LSSVM–GTO | 0.4675 | 0.9404 | 0.7197 | 0.7167 | 0.4787 | 0.2911 | 13.0000 | |
KNN | 0.2897 | 0.7242 | 0.6031 | 0.8053 | 0.6340 | 0.5264 | 5.0000 | |
KNN–GTO | 0.2354 | 0.6521 | 0.5431 | 0.8746 | 0.7032 | 0.5316 | 3.1667 | |
4 | ANN | 0.4257 | 1.2139 | 0.7069 | 0.7414 | 0.4971 | 0.5129 | 10.5000 |
LSSVM | 0.4576 | 1.3281 | 0.8070 | 0.6323 | 0.3446 | 0.1247 | 23.0000 | |
M5 | 0.5240 | 1.5408 | 0.9678 | 0.3241 | 0.0574 | −0.0401 | 40.1667 | |
MARS | 0.5581 | 1.0767 | 0.6763 | 0.7356 | 0.5397 | 0.4471 | 12.5000 | |
RF | 0.4124 | 0.8672 | 0.7951 | 0.6471 | 0.3638 | 0.1145 | 17.8333 | |
MNLR | 0.6971 | 1.1739 | 0.7133 | 0.7004 | 0.4880 | 0.4188 | 16.0000 | |
LSSVM–GTO | 0.5097 | 1.2447 | 0.7818 | 0.6646 | 0.3849 | 0.0786 | 22.5000 | |
KNN | 0.3052 | 0.9475 | 0.5951 | 0.8469 | 0.6436 | 0.4863 | 6.1667 | |
KNN–GTO | 0.1640 | 0.4741 | 0.2978 | 0.9607 | 0.9108 | 0.7141 | 1.3333 | |
5 | ANN | 0.2895 | 0.7241 | 0.7124 | 0.7193 | 0.4892 | 0.3207 | 7.8333 |
LSSVM | 0.4999 | 1.4501 | 0.8313 | 0.5962 | 0.3046 | 0.0991 | 28.1667 | |
M5 | 0.4582 | 1.4096 | 0.8080 | 0.5973 | 0.3429 | 0.1317 | 23.8333 | |
MARS | 0.7892 | 1.4660 | 1.0491 | 0.2993 | −0.1077 | 0.0406 | 43.8333 | |
RF | 0.4198 | 0.8954 | 0.8810 | 0.4904 | 0.2190 | −0.0040 | 27.3333 | |
MNLR | 0.7695 | 1.4628 | 0.8385 | 0.5659 | 0.2924 | 0.2631 | 30.3333 | |
LSSVM–GTO | 0.4979 | 1.4151 | 0.8112 | 0.6039 | 0.3378 | 0.1526 | 25.1667 | |
KNN | 0.3212 | 0.7952 | 0.8114 | 0.5972 | 0.3374 | 0.3034 | 18.3333 | |
KNN–GTO | 0.1728 | 0.4016 | 0.4098 | 0.9162 | 0.8310 | 0.7187 | 1.6667 |
ANN | LSSVM | M5 | MARS | RF | MNLR | LSSVM–GTO | KNN | KNN–GTO | |
---|---|---|---|---|---|---|---|---|---|
Training | −0.49 | 2.26 | 0.00 | 0.00 | 0.03 | 0.00 | 1.25 | −4.68 | 0.02 |
Testing | 18.23 | 22.21 | 25.41 | 9.00 | 36.54 | −11.28 | 48.66 | −6.36 | −23.90 |
All | 4.97 | 7.20 | 5.94 | 2.10 | 8.12 | −2.79 | 12.33 | −5.07 | −5.57 |
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Anaraki, M.V.; Achite, M.; Farzin, S.; Elshaboury, N.; Al-Ansari, N.; Elkhrachy, I. Modeling of Monthly Rainfall–Runoff Using Various Machine Learning Techniques in Wadi Ouahrane Basin, Algeria. Water 2023, 15, 3576. https://doi.org/10.3390/w15203576
Anaraki MV, Achite M, Farzin S, Elshaboury N, Al-Ansari N, Elkhrachy I. Modeling of Monthly Rainfall–Runoff Using Various Machine Learning Techniques in Wadi Ouahrane Basin, Algeria. Water. 2023; 15(20):3576. https://doi.org/10.3390/w15203576
Chicago/Turabian StyleAnaraki, Mahdi Valikhan, Mohammed Achite, Saeed Farzin, Nehal Elshaboury, Nadhir Al-Ansari, and Ismail Elkhrachy. 2023. "Modeling of Monthly Rainfall–Runoff Using Various Machine Learning Techniques in Wadi Ouahrane Basin, Algeria" Water 15, no. 20: 3576. https://doi.org/10.3390/w15203576