Reference evapotranspiration estimation in hyper-arid regions via D-vine copula based-quantile regression and comparison with empirical approaches and machine learning models

Two hyper-arid regions (Atbara and Kassala stations) in Sudan. The study aims to evaluate the potential of the D-vine Copula-based quantile regression (DVQR) model for estimating daily ETo during 2000–2015 based on various input structures. Further, the DVQR model was compared with Multivariate Linear quantile regression (MLQR), Bayesians Model Averaging quantile regression (BMAQR), Empirical Models (EMMs), and Classical Machine Learning (CML). Besides, the CML models including Random Forest (RF), Support Vector Machine (SVM), Extreme Learning Machine (ELM), Extreme Gradient Boosting (XGBoost), and M5 Model Tree (M5Tree) were employed. The original EMMs showed poor performance, which improved after calibration techniques. The DVQR, MLQR, and BMAQR models showed better performance than the calibrated EMMs. However, the DVQR model exhibited the highest accuracy than the MLQR and BMAQR models over two study sites. The M5Tree, SVM, and XGBoost models perfumed better than ELM and RF models at both study sites. The DVQR and XGBoost models showed equivalent performance (R2, NSE, and WIA > 0.99, MAE, and RMSE < 0.2) to the M5Tree and SVM models, but they had significantly more accuracy than the calibrated EMMs, MLQR, BMAQR, ELM, and RF models in two hyper-arid regions. Overall, the high dimensional DVQR model is recommended as a promising alternative technique for estimating daily ETo in hyper-arid climate conditions around the world.