Spatio-temporal insights for wind energy harvesting in South Africa

Abstract: Understanding complex spatial dependency structures is a crucial consideration when attempting to build a modeling framework for wind speeds. Ideally, wind speed modeling should be very efficient since the wind speed can vary significantly from day to day or even hour to hour. But complex models usually require high computational resources. This paper illustrates how to construct and implement a hierarchical Bayesian model for wind speeds using the Weibull density function based on a continuously-indexed spatial field. For efficient (near real-time) inference the proposed model is implemented in the r package R-INLA, based on the integrated nested Laplace approximation (INLA). Specific attention is given to the theoretical and practical considerations of including a spatial component within a Bayesian hierarchical model. The proposed model is then applied and evaluated using a large volume of real data sourced from the coastal regions of South Africa between 2011 and 2021. By projecting the mean and standard deviation of the Matern field, the results show that the spatial modeling component is effectively capturing variation in wind speeds which cannot be explained by the other model components. The mean of the spatial field varies between $\pm 0.3$ across the domain. These insights are valuable for planning and implementation of green energy resources such as wind farms in South Africa. Furthermore, shortcomings in the spatial sampling domain is evident in the analysis and this is important for future sampling strategies. The proposed model, and the conglomerated dataset, can serve as a foundational framework for future investigations into wind energy in South Africa.