A Dynamical Model of the Inner-Core Evolution of Landfalling Tropical Cyclones. Part I: Model Formulation and Fundamental Behaviors

This two-part study proposes a simple dynamical model, TRACE (Total Relative Angular-momentum and energy Constrained Evolution), to describe the intensity decay and structural changes of a tropical cyclone (TC) inner core during landfall. The model’s behavior is investigated both analytically and through comparison with observations. In Part I, we formulate the TRACE model and address two key questions: (1) What controls the decay rate of maximum wind speed V max ? and (2) What dynamical mechanisms govern structural changes, including the evolution of the radius of maximum wind ( R max ) and the radii of 64-kt and 50-kt winds ( R 64 and R 50 )? The TRACE framework is based on the axisymmetric momentum and continuity equations. It connects the evolution of the storm-scale kinetic energy of the swirling wind ( K swirl ) and the total relative angular momentum ( M rel ) to changes in TC intensity and inner-core structure. An analytical solution for a simplified case confirms that TCs decay faster when they are initially more intense, possess a more compact inner core, or move over a rougher land surface. Furthermore, the inner-core evolution is classified into three regimes: (i) core expansion and spin-down, (ii) core contraction and spin-down, and (iii) core contraction and spin-up, depending on the ratio of the fractional decay rates of K swirl and M rel . In most overland cases, storms satisfy the condition for the first regime, leading to R max expansion. Conversely, core contraction can occur when frictional drag acts selectively outside the inner core, such as during pre-landfall stages.