Accurate wind pattern modelling is crucial for various applications, including renewable energy, agriculture, and climate adaptation. In this paper, we introduce the wrapped Gaussian spatial process (WGSP), as well as the projected Gaussian spatial process (PGSP) custom-tailored for South Africa's intricate wind behaviour. Unlike conventional models struggling with the circular nature of wind direction, the WGSP and PGSP adeptly incorporate circular statistics to address this challenge. Leveraging historical data sourced from meteorological stations throughout South Africa, the WGSP and PGSP significantly increase predictive accuracy while capturing the nuanced spatial dependencies inherent to wind patterns. The superiority of the PGSP model in capturing the structural characteristics of the South African wind data is evident. As opposed to the PGSP, the WGSP model is computationally less demanding, allows for the use of less informative priors, and its parameters are more easily interpretable. The implications of this study are far-reaching, offering potential benefits ranging from the optimisation of renewable energy systems to the informed decision-making in agriculture and climate adaptation strategies. The WGSP and PGSP emerge as robust and invaluable tools, facilitating precise modelling of wind patterns within the dynamic context of South Africa.

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