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 (ET_ref) 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 ET_ref in diverse global climate conditions.

本研究检验了各种分位数回归 (QR) 和机器学习 (ML) 方法的有效性，这些方法是为分析 1987 年至2022. 分析的模型包括基于 D-vine copula 的分位数回归（DVQR）、多元线性分位数回归（MLQR）、贝叶斯模型平均分位数回归（BMAQR）以及机器学习算法，例如极限学习机（ELM）、随机森林 (RF)、M5 模型树 (M5Tree)、最小二乘支持向量回归算法 (LSSVR) 和极限梯度提升 (XGBoost)。此外，还考虑了诸如 Baier 和 Robertson (BARO)、Jensen 和 Haise (JEHA) 以及 Penman (PENM) 模型等经验方程 (EE)。虽然 EE 表现出可接受的性能，但 QR 和 ML 模型表现出卓越的准确性。其中，与 DVQR 和 BMAQR 模型相比，MLQR 模型显示出最高的精度。此外，LSSVR、XGBoost 和 M5Tree 模型的性能优于 ELM 和 RF 模型。值得注意的是，LSSVR、XGBoost 和 MLQR 模型在所有气候条件下都表现出与 M5Tree 和 BMAQR 模型相当的性能（R2 和 NSE > 0.92、MBE 和 RMSE < 0.5、SI > 0.05）。重要的是，这些模型在所有气候下都显着优于 EE、DVQR、ELM 和 RF 模型。总之，高维 QR 和 ML 模型被推荐作为在不同的全球气候条件下准确估计每日 ET _ref 的有前途的替代方案。