This study examines the effectiveness of various quantile regression (QR) and machine learning (ML) methodologies developed for analyzing the relationship between meteorological parameters and daily reference evapotranspiration (ETref) across diverse climates in Iran spanning from 1987 to 2022. The analyzed models include D-vine copula-based quantile regression (DVQR), multivariate linear quantile regression (MLQR), Bayesian model averaging quantile regression (BMAQR), as well as machine learning algorithms such as extreme learning machine (ELM), random forest (RF), M5 model Tree (M5Tree), least squares support vector regression algorithm (LSSVR), and extreme gradient boosting (XGBoost). Additionally, empirical equations (EEs) such as Baier and Robertson (BARO), Jensen and Haise (JEHA), and Penman (PENM) models were considered. While the EEs demonstrated acceptable performance, the QR and ML models exhibited superior accuracy. Among these, the MLQR model displayed the highest accuracy compared to DVQR and BMAQR models. Moreover, LSSVR, XGBoost, and M5Tree models outperformed ELM and RF models. Notably, LSSVR, XGBoost, and MLQR models exhibited comparable performance (R2 and NSE > 0.92, MBE and RMSE < 0.5, and SI > 0.05) to M5Tree and BMAQR models across all climates. Importantly, these models significantly outperformed EEs, DVQR, ELM, and RF models in all climates. In conclusion, high-dimensional QR and ML models are recommended as promising alternatives for accurately estimating daily ETref in diverse global climate conditions.
