Directional statistical modelling of tropical storm tracks and intensities: A novel framework for forecasting and preparedness

Abstract

Accurate modelling of tropical storm tracks and intensities requires statistical methods that respect the intrinsic directional geometry of storm motion. Conventional approaches frequently rely on Euclidean approximations, which may distort inference, bias parameter estimation, and mischaracterize predictive uncertainty on spherical manifolds. This paper develops a geometry-aware statistical framework for analysing tropical storm dynamics by explicitly incorporating circular and spherical structures. The proposed methodology integrates circular descriptive analysis, regime-specific movement modelling, circular regression for wind intensity, spherical state-space filtering for trajectory evolution, and direction-dependent extreme value modelling for severe events. Storm headings (ϕ) and turning behaviour (θ) are modelled using von Mises and wrapped Cauchy distributions, while extreme wind intensities are characterized within a generalized Pareto framework with direction-dependent parameters (ξ, σ). The practical utility of the approach is demonstrated through comprehensive empirical benchmarking against Euclidean baselines, homogeneous directional models, and machine-learning alternatives, alongside Monte Carlo simulation studies assessing estimator bias, variance stability, and regime recovery. Results indicate systematic improvements in trajectory prediction, wind intensity forecasting, model parsimony, and uncertainty calibration (coverage). These statistical gains translate into more reliable preparedness decisions within a cost–loss framework. Overall, the findings demonstrate that explicitly respecting circular and spherical geometry yields tangible inferential, predictive, and decision-theoretic advantages for tropical cyclone risk assessment.

Journal of Statistical Research 2026, Vol. 60, No. 1, pp. 113-131.