 The inclusion of formula_42 acts to multiply the total heat input rate by the factor formula_43.Mathematically, this has the effect of replacing formula_9 with formula_10 in the denominator of the Carnot efficiency.An alternative definition for the maximum potential intensity, which is mathematically equivalent to the above formulation, is

where CAPE stands for the Convective Available Potential Energy, formula_47 is the CAPE of an air parcel lifted from saturation at sea level in reference to the environmental sounding, formula_48 is the CAPE of the boundary layer air, and both quantities are calculated at the radius of maximum wind.