  Emanuel's Maximum Potential Intensity (E-PI) derives the maximum velocity of
tropical cyclones from environmental parameters based on distinct sets of
assumptions applied to the upper atmosphere, the boundary layer and the air-sea
interface. At the top of the boundary layer at the radius of maximum wind E-PI
relates the centrifugal acceleration (squared maximum velocity divided by
radius) to the radial gradient of saturated moist entropy. The proportionality
coefficient equals the difference between air temperatures in the outflow
region and at the top of the boundary layer. We show that a different
relationship between the same quantities derives straightforwardly from the
definition of saturated moist entropy and the gradient wind balance. Here the
proportionality coefficient depends on the local mixing ratio of water vapor
and the degree of adiabaticity of the radial gradient of air temperature. The
robust alternative relationship reveals that when, as originally assumed in the
E-PI derivation, the air is horizontally isothermal, E-PI at the top of the
boundary layer underestimates the squared maximum velocity by approximately
twofold. This provides an explanation to the "superintensity" phenomenon
(maximum wind speeds exceeding E-PI). The discrepancy increases (diminishes)
when the air temperature at the point of maximum wind declines (grows) towards
the storm center. The established theoretical relationships are illustrated
with the data for Hurricane Isabel 2003 and their implications for assessing
the maximum intensity of tropical storms are discussed.
