The Relationship between Hurricane Potential Intensity and CAPE

Abstract

he theoretical minimum eyewall pressure of tropical cyclones can be computed from convective available potential energy (CAPE) if the buoyancy in the CAPE is allowed to feed back on the surface pressure via hydrostatic balance. The relationship between this so-called hurricane CAPE and the surface pressure is exploited by a widely used algorithm for hurricane potential intensity (PI). For the observed atmosphere, the algorithm is shown to yield significantly weaker pressure intensity (20%?25%) and velocity intensity (5%?10%) than the most familiar analytical formulas. This discrepancy is found to come mostly from thermodynamic approximations in the formulas.The CAPE?PI algorithm makes a significant adjustment to the hurricane CAPE by subtracting the environmental CAPE. Most of the environmental profile becomes irrelevant as a result. Other steady-state theories retain the influence of the full environmental column. The impact of this choice on the pressure and velocity PI is analyzed. Another important choice?whether to allow the eyewall kinetic energy to contribute to the surface pressure perturbation?is also analyzed and quantified. The analytical formula for the velocity is updated with full moist thermodynamics and compared to the algorithm. The latter emerges as an excellent overall diagnostic of the underlying model. An exact algorithm for the velocity is also derived, based on its relationship to the radial derivative of hurricane CAPE. The thermodynamic efficiency often invoked to interpret velocity PI is identified as a marginal efficiency measured at the point of maximum energy dissipation rate and is contrasted with the global efficiency, which has a direct connection with the pressure intensity.