Lachgar et al. (2026) A Comprehensive Study of Bayesian and Ensemble Models with Prediction Intervals for Reference Evapotranspiration Estimation in the Region of Fez, Morocco

Identification

• Journal: Lecture notes in networks and systems
• Year: 2026
• Date: 2026-01-01
• Authors: Nisrine Lachgar, Moad Essabbar, Hajar Saikouk, Achraf Berrajaa, Ahmed El Hilali Alaoui
• DOI: 10.1007/978-3-032-07718-9_9

Research Groups

• Euromed University of Fes (UEMF), Fes, Morocco
• Laboratory of Conception and Systems, Faculty of Sciences, Mohammed V University, Rabat, Morocco
• Department of Computer Science, Faculty of Sciences, Mohammed First University, Oujda, Morocco

Short Summary

This study evaluates four machine learning models (BRR, GPR, RFQR, GBR) for reference evapotranspiration (ET0) estimation in Fez, Morocco, incorporating prediction interval analysis to quantify uncertainty. Gaussian Process Regressor (GPR) demonstrated the highest accuracy and smallest prediction intervals, proving most consistent in managing ET0 data complexity.

Objective

• To assess the performance of Bayesian Ridge Regression (BRR), Gaussian Process Regressor (GPR), Random Forest with Quantile Regression (RFQR), and Gradient Boosting Regressor (GBR) in predicting reference evapotranspiration (ET0) and quantifying prediction uncertainty using prediction interval analysis in the Fez region of Morocco.

Study Configuration

• Spatial Scale: Region of Fez, Morocco.
• Temporal Scale: Not explicitly stated for the data used, but the objective is ET0 estimation, which typically involves daily or monthly scales.

Methodology and Data

• Models used: Bayesian Ridge Regression (BRR), Gaussian Process Regressor (GPR), Random Forest with Quantile Regression (RFQR), Gradient Boosting Regressor (GBR).
• Data sources: Reference evapotranspiration (ET0) data, likely derived from meteorological observations for the Fez region.

Main Results

• Gaussian Process Regressor (GPR) was identified as the most consistent model, showing remarkable accuracy and the smallest prediction intervals, indicating its strong capacity to handle complex ET0 data.
• Bayesian Ridge Regression (BRR) was computationally efficient but exhibited wider prediction intervals, suggesting higher uncertainty.
• Gradient Boosting Regressor (GBR) and Random Forest with Quantile Regression (RFQR) demonstrated competitive performance, achieving a good balance between prediction accuracy and uncertainty quantification.
• Model performance was evaluated using Coefficient of determination (R2), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Squared Error (MSE), Mean Prediction Interval Width (MPIW), and Prediction Interval Coverage Probability (PICP).

Contributions

• Provides a comprehensive comparison of Bayesian and ensemble machine learning models for ET0 estimation, specifically incorporating prediction interval analysis for uncertainty quantification.
• Identifies GPR as a highly effective model for ET0 estimation in the Fez region, capable of managing data complexity and providing reliable uncertainty estimates.
• Highlights the complementary importance of both prediction precision and uncertainty quantification in water resource management applications.

Funding

• Not explicitly stated in the provided paper text.

Citation

@article{Lachgar2026Comprehensive,
  author = {Lachgar, Nisrine and Essabbar, Moad and Saikouk, Hajar and Berrajaa, Achraf and Alaoui, Ahmed El Hilali},
  title = {A Comprehensive Study of Bayesian and Ensemble Models with Prediction Intervals for Reference Evapotranspiration Estimation in the Region of Fez, Morocco},
  journal = {Lecture notes in networks and systems},
  year = {2026},
  doi = {10.1007/978-3-032-07718-9_9},
  url = {https://doi.org/10.1007/978-3-032-07718-9_9}
}