# Performance of Machine Learning Techniques for Meteorological Drought Forecasting in the Wadi Mina Basin, Algeria

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of the Study Area

^{2}and is located between 00°22′59″ and 01°09′02″ east, as well as between 34°41′57″ and 35°35′27″ north (Figure 1). It has four significant tributaries: Wadi Haddad, Wadi Abd, Wadi Mina, and Wadi Taht. The elevation varies between 164 and 1327 m. The topography of the basin is complex and uneven. The study region features a continental climate with dramatic seasonal temperature variations, such as bitterly cold winters and sweltering summers. The yearly precipitation averages between 200 and 500 mm, with most of it falling between November and March. The average yearly temperature is between 16 and 19.5 °C. Over half of the basin is covered in a variety of plant types, including 32% scrubs, 35.8% woods, and cereal crops [21]. Monthly rainfall and runoff records are available for five rainfall and hydrometric stations over 40 years (1974–2009) (Figure 1 and Table 1).

#### 2.2. Standardized Precipitation Index (SPI)

#### 2.3. Machine Learning Models

#### 2.3.1. Support Vector Machine (SVM)

_{i}and Y

_{i}are the independent and dependent variables, respectively; ${\beta}_{0}$ is constant; ${\beta}_{n}$ is the slope coefficient of each X

_{i}; and $\u03f5$ is the model error term or residuals.

#### 2.3.2. Additive Regression (AR)

^{2}). Furthermore, a sum of m regression trees is used, i.e., f(x) = ∑ g(x; T

_{j}, M

_{j}), ranging between j = 1 and j = m, which allows for the estimation of f(x). BART is expressed in Equation (11):

#### 2.3.3. Bagging

_{m}, m = 1, …, M, which were then merged into one class. As a result, the weight of this class was derived from the combined weight of the individual predictor classes, as per Equation (12):

_{m}was determined as m = 1, …, M, then more accurate classifications would have a greater effect than less accurate classifications. As the weak Hm classification was slightly more accurate than the random classification [29], the latter was referred to as the weak H

_{m}classification. The input datasets were also modeled using regression trees. The uniqueness of each tree was based on its ability to forecast changes in the training dataset. As a final step, the weighted average of each regression tree’s projections was calculated.

#### 2.3.4. Random Subspace (RSS)

#### 2.3.5. Random Forest (RF)

## 3. Model Evaluation

## 4. Results and Discussion

#### 4.1. Input Variables Selection

#### 4.2. Comparison Models of SPI Drought Index

## 5. Conclusions and Recommendations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**Plots showing predicted and observed SPI values for 3, 6, 9, and 12 timeframes during training and testing periods at sub-basin 1.

**Figure 9.**Plots showing the predicted and observed SPI values for 3-, 6-, 9-, and 12-month timeframes during the cross-validation periods at sub-basin 1.

**Figure 10.**Plots showing the predicted and observed SPI values for 3, 6, 9, and 12 month timeframes during validating the performance at sub-basin 2.

ID | Name | Longitude | Latitude | Elevation (m) | |
---|---|---|---|---|---|

S1 | 013306 | Oued Abtal | 0°40′33.97″ E | 35°28′03.59″ N | 354 |

S2 | 013401 | Sidi Abdelkader Djillali | 0°34′08.35″ E | 35°29′20.71″ N | 225 |

SPI Values | Drought Category | Probability (%) |
---|---|---|

Greater than or equal to 2.0 | Extremely wet | 2.3 |

Greater than or equal to 1.5 and less than 2.0 | Very wet | 4.4 |

Greater than or equal to 1.0 and less than 1.5 | Moderate wet | 9.2 |

Greater than or equal to −1.0 and less than 1.0 | Near normal | 68.2 |

Greater than or equal to −1.0 and less than −1.5 | Moderately dry | 9.2 |

Greater than or equal to −1.5 and less than −2.0 | Severely dry | 4.4 |

Less than or equal to −2.0 | Extremely dry | 2.3 |

Performance Indices | Formula | Range | Ideal Level | Description |
---|---|---|---|---|

Correlation coefficient | $\mathrm{CC}=\frac{{\sum}_{i=1}^{N}\left[\left({\mathrm{SPI}}_{Obs}-\overline{{\mathrm{SPI}}_{Obs}}\right)\left({\mathrm{SPI}}_{Pre}-\overline{{\mathrm{SPI}}_{Pre}}\right)\right]}{\sqrt{{\sum}_{i=1}^{N}{\left({\mathrm{SPI}}_{Obs}-\overline{{\mathrm{SPI}}_{Obs}}\right)}^{2}}\sqrt{{\sum}_{i=1}^{N}{\left({\mathrm{SPI}}_{Pre}-\overline{{\mathrm{SPI}}_{Pre}}\right)}^{2}}}$ | (−1 to +1) | +1 | Calculates how similar the observed value is to the expected value. |

Mean absolute error | $\mathrm{MAE}=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}\left|{\mathrm{SPI}}_{Pre},-{\mathrm{SPI}}_{Obs}\right|$ | (0 to ∞) | 0 | Analyzes the error size on an average. |

Root mean square error | $\mathrm{RMSE}=\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{\left[{\mathrm{SPI}}_{Pre}-{\mathrm{SPI}}_{Obs}\right]}^{2}}$ | (0 to ∞) | 0 | Indicates how observed values differ from estimated values. |

Relative absolute error | $\mathrm{RAE}={\displaystyle \sum _{i=1}^{N}}\left|{\mathrm{SPI}}_{Pre}-{\mathrm{SPI}}_{Obs}\right|/{\displaystyle \sum _{i=1}^{N}}\left|\overline{{\mathrm{SPI}}_{Obs}}-{\mathrm{SPI}}_{Obs}\right|$ | (0 to ∞) | 0 | Conducts a performance evaluation of the machine learning algorithm. |

Root relative squared error | $\mathrm{RRSE}={\displaystyle \sum _{i=1}^{N}}{\left({\mathrm{SPI}}_{Pre}-{\mathrm{SPI}}_{Obs}\right)}^{2}/{\displaystyle \sum _{i=1}^{N}}{\left(\overline{{\mathrm{SPI}}_{Obs}}-{\mathrm{SPI}}_{Obs}\right)}^{2}$ | (0 to ∞) | 0 | In contrast to RMSE, the relative squared error (RSE) allows the comparison of models with errors expressed in various units. |

Sub Basin Name | Inputs Variables | Target Variable |
---|---|---|

Sub-basin 1 | SPI-3 (t-1); SPI-3 (t-2) | SPI-3 |

SPI-6 (t-1); SPI-6 (t-2); SPI-6 (t-5); SPI-6 (t-7) | SPI-6 | |

SPI-9 (t-1) | SPI-9 | |

SPI-12 (t-1) | SPI-12 |

**Table 5.**Evaluation metrics of the model outputs for various timelines during the training and testing phases.

Model | Training Phase | Testing Phase | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

CC | MAE | RMSE | RAE | RRSE | CC | MAE | RMSE | RAE | RRSE | |

SPI-3 | ||||||||||

Support vector machine | 0.684 | 0.557 | 0.725 | 70.225 | 73.247 | 0.701 | 0.453 | 0.579 | 68.038 | 71.463 |

Additive regression | 0.711 | 0.544 | 0.696 | 68.638 | 70.366 | 0.677 | 0.475 | 0.596 | 71.313 | 73.552 |

Bagging | 0.796 | 0.466 | 0.606 | 58.722 | 61.195 | 0.645 | 0.478 | 0.622 | 71.721 | 76.792 |

Random subspace | 0.667 | 0.608 | 0.765 | 76.724 | 77.278 | 0.542 | 0.553 | 0.684 | 83.019 | 84.405 |

Random forest | 0.960 | 0.230 | 0.304 | 29.056 | 30.683 | 0.592 | 0.526 | 0.682 | 78.926 | 84.088 |

SPI-6 | ||||||||||

Support vector machine | 0.824 | 0.447 | 0.596 | 56.157 | 56.729 | 0.811 | 0.355 | 0.452 | 58.505 | 57.447 |

Additive regression | 0.833 | 0.442 | 0.581 | 55.454 | 55.309 | 0.770 | 0.402 | 0.492 | 66.219 | 62.530 |

Bagging | 0.864 | 0.399 | 0.529 | 50.116 | 50.396 | 0.800 | 0.360 | 0.461 | 59.361 | 58.638 |

Random subspace | 0.864 | 0.403 | 0.530 | 50.560 | 50.434 | 0.811 | 0.359 | 0.450 | 59.243 | 57.137 |

Random forest | 0.925 | 0.303 | 0.401 | 38.083 | 38.161 | 0.735 | 0.420 | 0.545 | 69.188 | 69.239 |

SPI-9 | ||||||||||

Support vector machine | 0.882 | 0.359 | 0.472 | 46.288 | 47.242 | 0.866 | 0.306 | 0.381 | 45.599 | 46.795 |

Additive regression | 0.878 | 0.371 | 0.479 | 47.823 | 47.953 | 0.822 | 0.362 | 0.440 | 53.940 | 53.993 |

Bagging | 0.909 | 0.321 | 0.415 | 41.398 | 41.605 | 0.845 | 0.339 | 0.414 | 50.576 | 50.830 |

Random subspace | 0.897 | 0.336 | 0.441 | 43.272 | 44.152 | 0.863 | 0.315 | 0.388 | 46.932 | 47.606 |

Random forest | 0.947 | 0.233 | 0.320 | 30.030 | 32.041 | 0.806 | 0.357 | 0.463 | 53.275 | 56.859 |

SPI-12 | ||||||||||

Support vector machine | 0.908 | 0.305 | 0.431 | 37.412 | 41.963 | 0.880 | 0.283 | 0.371 | 38.061 | 41.520 |

Additive regression | 0.898 | 0.341 | 0.454 | 41.772 | 44.268 | 0.823 | 0.343 | 0.453 | 46.134 | 50.702 |

Bagging | 0.927 | 0.278 | 0.386 | 34.138 | 37.596 | 0.866 | 0.305 | 0.394 | 41.092 | 44.043 |

Random subspace | 0.924 | 0.283 | 0.394 | 34.728 | 38.386 | 0.874 | 0.297 | 0.380 | 39.914 | 42.553 |

Random forest | 0.956 | 0.212 | 0.303 | 25.977 | 29.514 | 0.808 | 0.381 | 0.483 | 51.226 | 54.028 |

Model | CC | MAE | RMSE | RAE | RRSE |
---|---|---|---|---|---|

SPI-3 | |||||

Support vector machine | 0.674 | 0.569 | 0.734 | 71.44 | 73.94 |

Additive regression | 0.645 | 0.600 | 0.758 | 75.3839 | 76.384 |

Bagging | 0.638 | 0.600 | 0.764 | 75.325 | 76.964 |

Random subspace | 0.586 | 0.642 | 0.811 | 80.603 | 81.653 |

Random forest | 0.615 | 0.611 | 0.797 | 76.788 | 80.255 |

SPI-6 | |||||

Support vector machine | 0.818 | 0.455 | 0.606 | 56.654 | 57.369 |

Additive regression | 0.765 | 0.518 | 0.683 | 64.604 | 64.637 |

Bagging | 0.799 | 0.481 | 0.634 | 59.940 | 60.016 |

Random subspace | 0.799 | 0.481 | 0.632 | 59.915 | 59.885 |

Random forest | 0.749 | 0.565 | 0.724 | 70.457 | 68.512 |

SPI-9 | |||||

Support vector machine | 0.877 | 0.368 | 0.480 | 46.883 | 47.479 |

Additive regression | 0.840 | 0.420 | 0.543 | 53.613 | 53.726 |

Bagging | 0.856 | 0.396 | 0.517 | 50.529 | 51.186 |

Random subspace | 0.856 | 0.395 | 0.517 | 50.355 | 51.152 |

Random forest | 0.839 | 0.434 | 0.555 | 55.339 | 54.907 |

SPI-12 | |||||

Support vector machine | 0.908 | 0.305 | 0.431 | 37.412 | 41.963 |

Additive regression | 0.898 | 0.341 | 0.454 | 41.772 | 44.268 |

Bagging | 0.927 | 0.278 | 0.386 | 34.138 | 37.596 |

Random subspace | 0.924 | 0.283 | 0.394 | 34.728 | 38.386 |

Random forest | 0.956 | 0.212 | 0.303 | 25.977 | 29.514 |

CC | MAE | RMSE | RAE | RRSE | |
---|---|---|---|---|---|

SPI-3 | 0.642 | 0.575 | 0.751 | 72.927 | 77.370 |

SPI-6 | 0.811 | 0.445 | 0.580 | 58.958 | 58.548 |

SPI-9 | 0.865 | 0.379 | 0.493 | 51.304 | 50.172 |

SPI-12 | 0.885 | 0.331 | 0.466 | 42.81 | 46.639 |

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## Share and Cite

**MDPI and ACS Style**

Achite, M.; Elshaboury, N.; Jehanzaib, M.; Vishwakarma, D.K.; Pham, Q.B.; Anh, D.T.; Abdelkader, E.M.; Elbeltagi, A. Performance of Machine Learning Techniques for Meteorological Drought Forecasting in the Wadi Mina Basin, Algeria. *Water* **2023**, *15*, 765.
https://doi.org/10.3390/w15040765

**AMA Style**

Achite M, Elshaboury N, Jehanzaib M, Vishwakarma DK, Pham QB, Anh DT, Abdelkader EM, Elbeltagi A. Performance of Machine Learning Techniques for Meteorological Drought Forecasting in the Wadi Mina Basin, Algeria. *Water*. 2023; 15(4):765.
https://doi.org/10.3390/w15040765

**Chicago/Turabian Style**

Achite, Mohammed, Nehal Elshaboury, Muhammad Jehanzaib, Dinesh Kumar Vishwakarma, Quoc Bao Pham, Duong Tran Anh, Eslam Mohammed Abdelkader, and Ahmed Elbeltagi. 2023. "Performance of Machine Learning Techniques for Meteorological Drought Forecasting in the Wadi Mina Basin, Algeria" *Water* 15, no. 4: 765.
https://doi.org/10.3390/w15040765