Measurement and forecasting of the diffuse fraction of solar irradiance using a hybrid stacking model in Saudi Arabia

Accurate quantification and robust predictive modeling of diffuse solar irradiance ratios are essential for optimizing photovoltaic (PV) system efficiency, particularly in regions characterized by pronounced climatic heterogeneity. This study investigates the spatial variability of diffuse horizontal irradiance ([Formula: see text]) and short-term forecasts of the diffuse fraction ([Formula: see text]) across six representative Saudi Arabian stations, encompassing coastal, desert, and high-altitude environments. A hybrid stacking ensemble model was developed using a multi-algorithmic framework integrating Random Forest (RF), Light Gradient Boosting Machine (LGBM), and Gradient Boosting Regressor (GBR) algorithms within a meta-learning architecture. Model optimization was achieved through recursive feature selection and gradient-boosted meta-learning, to effectively capture complex nonlinear dependencies among atmospheric predictors under diverse sky conditions. Results revealed pronounced geographic variability in diffuse solar irradiance, with coastal stations exhibiting higher [Formula: see text] values due to maritime aerosol scattering; Jeddah recorded the highest mean [Formula: see text] (283.7 W/m²) and maximum diffuse fraction ([Formula: see text] = 0.95). In contrast, high-elevation sites such as Abha exhibited the lowest mean irradiance (142.7 W/m²). The proposed ensemble model demonstrated superior predictive performance relative to individual learners, achieving up to a 62.48% reduction in [Formula: see text] and maintaining high correlation coefficients (R = 0.94-0.97) across stations. Forecast-horizon evaluation confirmed robust short-term accuracy, with [Formula: see text] increasing moderately from 0.0292 W/m² for a 12-h horizon to 0.0478 W/m² for a 48-h horizon, while seasonal assessments revealed optimal performance during spring and summer, with normalized [Formula: see text] values as low as 11.64%. These findings highlight the ensemble model's robustness and adaptability, providing a scalable, high-fidelity approach for operational solar forecasting and energy management.