# Modeling of Monthly Rainfall–Runoff Using Various Machine Learning Techniques in Wadi Ouahrane Basin, Algeria

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## Abstract

**:**

## 1. Introduction

^{2}), normalized RMSE, MSE, and coefficient of efficiency for the training and testing phases. According to the findings, gene expression programming was found to be the most precise and highly effective technique. Xiao et al. [20] developed a backpropagation neural network, a generalized regression neural network (GRNN), an ELM, and a wavelet neural network (WNN) for runoff forecasting in the Xijiang River. The GRNN model performed better in runoff forecasting by considering flood propagation time. The WNN model exhibited the highest accuracy in the 7-day lead time for water level. This study suggested a machine learning-based runoff forecasting model would enhance flood and drought early warning systems. Singh et al. [21] used MARS, SVM, multiple linear regression (MLR), and random forest (RF) for rainfall–runoff prediction in the Gola watershed, Uttarakhand. The performance of models was assessed using numerical indices (i.e., R

^{2}, RMSE, NSE, and percent bias) along with graphical charting (i.e., scatter plots, relative error plots, violin plots, line diagrams, and Taylor diagrams). In all case studies, the RF outperformed the other models in terms of daily runoff forecasting in both the training and testing phases.

## 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 do8: Update the position of an artificial gorilla using Equations (10)–(19) 9: iter: = iter + 1 10: end while11: 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

^{2}region is a section of the Wadi Cheliff basin (Figure 3). The research area was mapped using a digital elevation model (12.5 m horizontal resolution), which displays a maximum altitude of 991 m and a minimum altitude of 165 m. A little, few kilometers long tributary of Wadi Cheliff is called Wadi Ouahrane. The flow of water in this basin is controlled by six pluviometric stations. The Wadi Ouahrane basin is constrained by the Wadi Allala basin to the north, the Wadi Sly basin to the south, the Wadi Fodda basin to the east, and the Wadi Ras basin to the west. With an average interannual rainfall of 333 mm from 1972 to 2018, evapotranspiration (ET) is 1050 mm, and the mean annual flow is equal to 0.472 m

^{3}/s; this basin has a Mediterranean climate. The yearly average temperature is 18 Celsius. The monthly rainfall datasets were obtained at six stations between 1972 and 2018, and these dataset records are used in this study. The meteorological information was given by the National Meteorological Organization and the National Water Resources Agency of Algeria.

_{mean}, respectively. However, the correlation between inputs and targets is not close to 1 or −1. Also, the statistical criteria for input and target variables are presented in Table 1. According to this table, although the coefficient of variation in runoff data is lower than the inputs, its skewness coefficient is significantly higher than the inputs. Therefore, the runoff data studied do not follow the normal distribution and have high dispersion. These observations prove the nonlinear runoff production in this basin. Consequently, powerful nonlinear methods are expected to be needed for rainfall–runoff modeling in this basin.

## 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 do4: Calculate the Pearson correlation coefficient (R) between the feature and target data. 5: If R < threshold of R6: Remove feature from the input data 7: end if8: i: = i + 1 9: end while10: Apply PCA to the remaining input data 11: Return the final inputs list |

## 5. Results and Discussion

_{min}, T

_{mean}, T

_{max}, Rh_mean, and SW) is considered an input. The second scenario resembles the first scenario, with the difference that a 0 to 24-month lag time is imposed on input data and the R threshold is equal to 0.05. The third to fifth scenarios are the same as the second scenario in input data; however, the main difference is the application of IMF and the R threshold value of 0.1. The MaxNumIMF in the third to fifth scenarios equals 3, 4, and 5, respectively. Since the size of the input dataset in the third to fifth scenarios is large, the PCA is employed for dimension reduction.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Scatter plot of the best ML algorithms for modeling rainfall–runoff in the training period.

**Figure 9.**Scatter plot of the best ML algorithms for modeling rainfall–runoff in the testing period.

**Figure 10.**Cumulative distribution function (CDF) for observed and modeled runoff under (

**a**) scenario1, (

**b**) scenario2, (

**c**) scenario3, (

**d**) scenatio4, and (

**e**) scenatio5.

Statistics | Q (m^{3}/s) | S1 | S2 | S3 | S4 | S5 | S6 | T_{min} (°C) | T_{mean} (°C) | T_{max} (°C) | RH_{mean} (%) | 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, T_{min}, T_{mean}, T_{max}, Rh_mean, SW | - | - | - |

2 | R_1, R_2, R_3, R_4, R_5, R_6, T_{min}, T_{mean}, T_{max}, Rh_mean, SW Lag = 0:24 month | 0.05 | - | - |

3 | R_1, R_2, R_3, R_4, R_5, R_6, T_{min}, T_{mean}, T_{max}, 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, T_{min}, T_{mean}, T_{max}, 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, T_{min}, T_{mean}, T_{max}, 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 |

**Table 4.**Results of rainfall–runoff modeling using machine learning algorithms for the training period.

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 |

**Table 5.**Results of rainfall–runoff modeling using machine learning algorithms for the testing period.

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 |

**Table 6.**Bias analysis in rainfall–runoff modeling using machine learning algorithms over training, testing, and all periods.

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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**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Anaraki, 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