A Physical Model of Tropical Cyclone Central Pressure Filling at Landfall

Abstract

We derive a simple physically based analytic model which describes the pressure filling of a tropical cyclone (TC) over land. Starting from the axisymmetric mass continuity equation in cylindrical coordinates we derive that the half-life decay of the pressure deficit between the environment and TC centre is proportional to the initial radius of maximum surface wind speed. The initial pressure deficit and column-mean radial inflow speed into the core are the other key variables. The assumptions made in deriving the model are validated against idealised numerical simulations of TC decay over land. Decay half-lives predicted from a range of initial TC states are tested against the idealized simulations and are in good agreement. Dry idealised TC decay simulations show that without latent convective heating, the boundary layer decouples from the vortex above leading to a fast decay of surface winds while a mid-level vortex persists.

The Dependence of Tropical Cyclone Pressure Tendency on Size

“…We derive a simple but useful new model of pressure tendency. Sparks and Toumi (2022) applied mass continuity in cylindrical coordinates to relate average pressure changes within a given radius to column radial wind speeds at that radius (Equation 1). From here our new model diverges.…”

“…Sparks and Toumi (2022) modeled the TC as an axisymmetric vortex, considering only horizontal motion, and showed that the tendency of the average surface pressure within a cylinder of radius r can be written as, $$$\frac{\partial \langle P(r)\rangle }{\partial t}=-\frac{2P(r){\mathcal{V}}_{r}(r)}{r}.$$$ where P is the surface pressure with angled brackets denoting the areal average within radius r and $${\mathcal{V}}_{r}$$ is the density‐weighted column mean radial wind velocity. In the vicinity of the inner core, $${\mathcal{V}}_{r}$$ is positive (directed away from the center) for intensification and negative for TC decay.…”

“…Sparks and Toumi (2022) developed a model for TC central pressure deficit decay at landfall based on mass conservation. This model was used to explain the dependence of landfall decay rate on TC size in a series of idealized numerical experiments.…”

“…Montgomery et al (2001) and Wang and Toumi (2022b) propose turbulent frictional decay as an important driver, but the effect of size is not considered. Sparks and Toumi (2022) developed a model for TC central pressure deficit decay at landfall based on mass conservation. This model was used to explain the dependence of landfall decay rate on TC size in a series of idealized numerical experiments.…”

“…Here we generalize those ideas to develop a new model applicable to both TC intensification and decay and test it against observations of TC size central pressure changes. Sparks and Toumi (2022) modeled the TC as an axisymmetric vortex, considering only horizontal motion, and showed that the tendency of the average surface pressure within a cylinder of radius r can be written as,…”