A Comparative Study of Mathematical Models for the Tropical Cyclone Intensity–Size Relation

Abstract

Despite considerable progress in tropical cyclone (TC) research, our current understanding and prediction capabilities regarding the TC intensity–size relation remain limited. This study systematically analyzes the key characteristics and performance of different types of mathematical models for TC intensity–size relations using the 6-hourly Tropical Cyclone Extended Best Track Dataset spanning 1988 to 2020. The models investigated include statistical, idealized (e.g., Rankine vortex), parametric, and theoretical models. In addition to directly comparing the solutions obtained from individual models to the observed TC records, we assess the models that can produce a unique finite-sized radial profile of surface winds for each TC record—a minimal requirement to ensure that the predicted radial profile of the surface winds would align with the observed profile. The results reveal that a sufficient condition to guarantee a unique radial profile of surface winds is that the associated model can be written as a radial invariant quantity, although it does not guarantee a finite-sized profile. Only the effective absolute angular momentum (eAAM) model, among all the models examined in this study, meets the minimum requirement. Furthermore, the solutions obtained from the eAAM model are well correlated with their observational counterparts (85 to 95%) with little systematic bias and small absolute mean errors that are very close to the observational resolution. The eAAM model’s ability to capture the complex intensity–size relation of observed TCs, in combination with these desirable features, suggests its high potential for gaining a better understanding of the underlying physics governing the observed TC intensity–size relation.