Alternative expressions for the maximum potential intensity of tropical cyclones

Based on several assumptions, including gradient-wind balance in the free troposphere, Emanuel's formulation of maximum potential intensity (E-PI) combines parameters of the tropical atmosphere into a characteristic value of the maximum wind speeds of tropical cyclones. Most cyclones never reach their E-PI, while some exceed it (the so-called superintensity). Here, we show that, while in E-PI the radial temperature gradient at the radius of maximum wind is set by the thermodynamics of the free troposphere, it depends on the boundary layer dynamics and can change sign in the vicinity of the radius of maximum wind. Assuming horizontal isothermy at the radius of maximum wind leads to an alternative formulation of potential intensity exceeding E-PI. This explains some cases of superintensity, as illustrated on the example of Hurricane Isabel 2003. A reevaluation of previous analyses reveals inconsistency in justifying superintensity solely by supergradient winds. In Hurricane Isabel 2003, maximum superintensity is associated with minimal gradient-wind imbalance. We show that in both E-PI and in the formulation assuming horizontal isothermy, the maximum kinetic energy density approximately equals the partial pressure of water vapor at the surface, while all the remaining environmental parameters at their characteristic values are collapsed to a factor close to unity. We demonstrate that this equality between maximum kinetic energy density and water vapor partial pressure corresponds to the equality between the rates of kinetic energy generation within the boundary layer and the release of potential energy from condensation in the atmospheric column at the radius of maximum wind.