Forced, Balanced, Axisymmetric Shallow Water Model for Understanding Short-Term Tropical Cyclone Intensity and Wind Structure Changes

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 its simplicity, 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.

Projective Integration for Hyperbolic Shallow Water Moment Equations

“…A classical example of such axisymmetric cases are tsunamis [7,21]. In [6], axisymmetric shallow water equations are used to understand the intensity of tropical cyclones. Axisymmetric currents have also been thoroughly studied using the axisymmetric shallow water equations, see, e.g., [16] and [19].…”

“…The SWE formulated in cylindrical coordinates are widely used. The reason for this is that for many classical applications such as tsunamis [7,2] and tropical cyclones [6], a system expressed in cylindrical coordinates is more appropriate. From a mathematical point of view, a coordinate transformation can also be beneficial.…”

Tropical cyclone rapid intensification and the excitation of inertia-gravity waves on the edges of an evolving potential vorticity structure

“…In fact, it is the appearance of this exponential function that is the crux of the rapid intensification process. In order to make practical use of this and related theoretical results, Hendricks et al (2021) have introduced and tested a minimal, axisymmetric, shallow water modeling system (SWAMI) as an aid to forecasting short-term tropical cyclone intensity and wind structure changes. Now consider the transformation of the nonlinear equations (Eq.…”

Applying Latent Data Assimilation to a Fluid Dynamics Problem

“…For instance, Cavaleri and Rizzoli refer to the deployment of wind-wave forecasting models in the Northern Adriatic Sea to predict storms, with errors of effective wave height ranging from 10% to 20% [6]. Moreover, there exists a Shallow Water Axisymmetric Intensity Model, tailored for anticipating cyclonic phenomena characterized by transient intensity [7]. Such prognostications enable scientists to make informed suggestions for disaster preparedness and sustainable development.…”