Bayesian Generalised Additive Extreme Value Modelling of Maximum Wind Speeds in a Semi-Arid Region

Extreme wind speed poses significant risks to infrastructure, agriculture, and the economy in South Africa, particularly in semi-arid regions such as the Northern Cape. Accurate modelling of extreme wind speed is, therefore, essential for disaster preparedness and climate adaptation. Hybrid Generalised Additive Extreme Value (GAEV) models, in which the location, scale, and shape parameters of the Generalised Extreme Value distribution are allowed to vary smoothly with covariates through spline functions, offer a flexible approach to this problem, but such models have rarely been applied to extreme wind speed, and comparisons of frequentist and Bayesian estimation within this framework remain scarce in semi-arid regions. This study addresses that gap using daily maximum wind speed, maximum temperature, and maximum relative humidity data for Kimberley and Upington, two stations in the Northern Cape Province of South Africa with contrasting semi-arid and desert climates, respectively, covering the period 1 January 2000 to 31 August 2026 (9740 daily observations per station). The hybrid GAEV models were estimated using both frequentist (maximum likelihood, via the evgam package) and Bayesian (Markov Chain Monte Carlo, via the brms package) methods, with 80% of the observations used for in-sample model fitting and the remaining 20% reserved for out-of-sample prediction evaluation. Model performance was assessed using goodness-of-fit tests, model selection criteria, and prediction accuracy metrics, including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and the pinball loss at τ=0.95 for the upper-tail quantile. The results show that the frequentist and Bayesian GAEV models performed comparably in-sample, but the Bayesian approach produced lower out-of-sample RMSE and MAE, indicating stronger generalisation to unseen data. The pinball loss was nearly identical under the two approaches, differences below 0.006. However, the Scale model performed best for the Kimberley data, particularly for tail prediction accuracy. These findings suggest that Bayesian GAEV models offer more reliable out-of-sample predictions of typical daily maximum extreme wind speed in semi-arid regions, while upper-tail predictions are equally reliable under either approach, with implications for risk assessment and disaster preparedness planning.