Forced shallow-water model for the maximum potential intensification rate of tropical cyclones

An axisymmetric model is developed to understand and predict the maximum potential intensification rate (MPIR) of tropical cyclones. The model consists of a potential vorticity (PV) production equation and an invertibility principle, derived from the forced, balanced axisymmetric shallow water equations. The assumptions of the model that make it valid for understanding MPIR are vortex and heating axisymmetry, neglection of the radial PV advection term, lack of negative environmental factors, heating in the deep convective mode only, and heating which always directly forces vortex spin-up. The model also includes a maximum potential intensity limiter on the MPIR. The usefulness of the model is first demonstrated for ideal vortices and heating structures. Then, the model is evaluated against a set of real hurricanes that experienced rapid intensification events. Because accurate radial profiles of the tangential velocity and diabatic heating rate are essential to the model, these data are determined from the FLIGHT+ Dataset. For the real cases, the model is shown to always produce a reasonable upper bound on the observed intensification rate, thus making it a first useful MPIR prediction tool. The development of this model is inspired by Wayne Schubert’s contributions to understanding tropical cyclones through the balanced dynamics.