A Hybrid Linear–Gaussian Process Framework with Adaptive Covariance Selection for Spatio-Temporal Wind Speed Forecasting

Accurate wind speed forecasting is essential for the efficient integration of wind energy into power systems, as it directly influences generation scheduling, grid stability, and energy market operations. Forecast errors can lead to significant economic losses, including increased balancing costs, inefficient dispatch of backup generation, and penalties in electricity markets. However, wind behaviour is highly complex due to the influence of synoptic weather systems, terrain variability, and turbulence, which makes accurate prediction particularly challenging. This paper proposes a hybrid modelling framework that combines a linear regression mean model with Gaussian process (GP) residual modelling to improve forecast accuracy. Monitoring stations were grouped based on geographic coordinates and elevation, with cluster validation using the Hopkins statistic and silhouette analysis. The results show that for high-elevation inland stations (cluster 2), GP residual modelling improves forecast accuracy by up to 16.3%. In contrast, for low-elevation coastal stations (cluster 1), the GP approach does not yield improvements, indicating that its effectiveness depends strongly on the underlying wind regime.