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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.

The slope of the quasi-linear relation between planetary outgoing longwave radiation (OLR) and surface temperature (T_S) is an important parameter measuring the sensitivity of Earth’s climate system. The primary objective of this study is to seek a general explanation for the quasi-linear OLR–T_Srelation that remains valid regardless of the strength of the atmospheric window’s narrowing effect on planetary thermal emission at higher temperatures. The physical understanding of the quasi-linear OLR–T_Srelation and its slope is gained from observation analysis, climate simulations with radiative–convective equilibrium and general circulation models, and a series of online feedback suppression experiments. The observed quasi-linear OLR–T_Srelation manifests a climate footprint of radiative (such as the greenhouse effect) and nonradiative processes (poleward energy transport). The former acts to increase the meridional gradient of surface temperature and the latter decreases the meridional gradient of atmospheric temperatures, causing the flattening of the meridional profile of the OLR. Radiative processes alone can lead to a quasi-linear OLR–T_Srelation that is more steeply sloped. The atmospheric poleward energy transport alone can also lead to a quasi-linear OLR–T_Srelation by rerouting part of the OLR to be emitted from a warmer place to a colder place. The combined effects of radiative and nonradiative processes make the quasi-linear OLR–T_Srelation less sloped with a higher degree of linearity. In response to anthropogenic radiative forcing, the slope of the quasi-linear OLR–T_Srelation is further reduced via stronger water vapor feedback and enhanced poleward energy transport.

Recent investigations have revealed that dynamics of complex networks and systems are crucially dependent on the temporal structures. Accurate detection of the time instant at which a system changes its internal structures has become a tremendously significant mission, beneficial to fully understanding the underlying mechanisms of evolving systems, and adequately modeling and predicting the dynamics of the systems as well. In real-world applications, due to a lack of prior knowledge on the explicit equations of evolving systems, an open challenge is how to develop a practical and model-free method to achieve the mission based merely on the time-series data recorded from real-world systems. Here, we develop such a model-free approach, named temporal change-point detection (TCD), and integrate both dynamical and statistical methods to address this important challenge in a novel way. The proposed TCD approach, basing on exploitation of spatial information of the observed time series of high dimensions, is able not only to detect the separate change points of the concerned systems without knowing, a priori, any information of the equations of the systems, but also to harvest all the change points emergent in a relatively high-frequency manner, which cannot be directly achieved by using the existing methods and techniques. Practical effectiveness is comprehensively demonstrated using the data from the representative complex dynamics and real-world systems from biology to geology and even to social science.

The central theme of this study is to explore if and how the intensity of a tropical cyclone (TC) is related to its size. This subject has puzzled atmospheric scientists since the work of Deppermann, but the existence of this relationship still remains elusive. The improved understanding of the intensity–size relationship of TCs will help coastal communities to prepare for the maximum potential damage as both the intensity and size have important impacts on wind damages, storm surges, and flooding. This study considers 33 years (1988–2020) of TC records of maximum surface winds and radii of maximum and gale-force winds over the North Atlantic basin derived from the Extended Best Track Dataset. Analysis of these TC records reveals a robust positive correlation between loss of Earth and relative angular momentum. This finding together with the inspiration from the seminal work of Emanuel and his collaborators leads us to combine absolute angular momentum and its frictional loss as a radially invariant quantity, referred to as “effective absolute angular momentum” (eAAM), for radial profiles of TC surface winds. It is demonstrated that the eAAM model can reproduce the observed complex intensity–size relationship of TCs, which can be further reduced to a quasi-linear one after factoring out the angular momentum loss and the radius of maximum surface winds. The findings of this study would not only advance our understanding of the complex TC intensity–size relation, but also allow for operational assessments of TC severity and potential damage just using its outer wind information.