Abstract
A minimal modeling system for understanding tropical cyclone intensity and wind structure changes is introduced: Shallow Water Axisymmetric Model for Intensity (SWAMI). The forced, balanced, axisymmetric shallow water equations are reduced to a canonical potential vorticity (PV) production and inversion problem, whereby PV is produced through a mass sink (related to the diabatic heating) and inverted through a PV/absolute–angular–momentum invertibility principle. Because the invertibility principle is nonlinear, a Newton–Krylov method is used to iteratively obtain a numerical solution to the discrete problem. Two versions of the model are described: a physical radius version which neglects radial PV advection (SWAMI-r) and a potential radius version that naturally includes the advection in the quasi-Lagrangian coordinate (SWAMI-R). In idealized numerical simulations, SWAMI-R produces a thinner and more intense PV ring than SWAMI-r, demonstrating the role of axisymmetric radial PV advection in eyewall evolution. SWAMI-R always has lower intensification rates than SWAMI-r because the reduction in PV footprint effect dominates the peak magnitude increase effect. SWAMI-r is next demonstrated as a potentially useful short-term wind structure forecasting tool using the newly added FLIGHT+ Dataset azimuthal means for initialization and forcing on three example cases: a slowly intensifying event, a rapid intensification event, and a secondary wind maximum formation event. Then, SWAMI-r is evaluated using 63 intensifying cases. Even though the model is minimal, it is shown to have some skill in short-term intensity prediction, highlighting the known critical roles of the relationship between the radial structures of the vortex inertial stability and diabatic heating rate. Because of the simplicity of the models, SWAMI simulations are completed in seconds. Therefore, they may be of some use for hurricane nowcasting to short-term (less than 24 h) intensity and structure forecasting. Due to its favorable assumptions for tropical cyclone intensification, a potential use of SWAMI is a reasonable short-term upper-bound intensity forecast if the storm intensifies.
Highlights
Tropical cyclones (TCs) intensify through latent heating in deep convective clouds near the center of circulation [1,2]
The results are identical to the θ = 0 K h−1 case (Figure 1). These results demonstrate that both Shallow Water Axisymmetric Model for Intensity (SWAMI)-r and SWAMI-R can be used with the maximum potential intensity (MPI) limiter when a tropical cyclone is close to its MPI to prevent unbridled intensification past the MPI
We have introduced a minimal modeling system, referred to as the Shallow Water Axisymmetric Model for Intensity (SWAMI), for understanding short-term TC intensity and wind structure changes
Summary
Tropical cyclones (TCs) intensify through latent heating in deep convective clouds near the center of circulation [1,2]. In Eliassen’s model, a second-order linear transverse circulation equation was derived to understand the slow vortex response to heat and momentum sources under the assumptions of gradient and hydrostatic balance. A recent example of a TC model that uses PV prediction and inversion is the work in [33], the authors of which obtained analytic solutions to the shallow water equations using the wave-vortex approximation to understand the intensification of TCs. The purpose of the present work is to develop a minimal model for understanding short-term (lead times of less than 24 h) intensity and wind structure changes in real TCs using PV production and inversion. Motivated by the works in [13,33], the evolution of the TC vortex in the minimal model is dependent on the radial structure of tangential velocity (or equivalently, inertial stability) and the diabatic heating rate. The models are designed to describe the TC evolution in the lower troposphere
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