NOTES AND CORRESPONDENCE Comments on ‘‘Moist Convective Velocity and Buoyancy Scales’’

Recently, both Rennó and Ingersoll (1996, hereafter RI) and Emanuel and Bister (1996, hereafter EB) derive theoretical formulas for the convective available potential energy (CAPE), the fractional area covered by active updrafts, and the vertical velocity in the active updrafts for atmospheres in radiative–convective equilibrium. The theories of RI and EB differ primarily in the means of closure for the mass flux of cumulus convection. Emanuel and Bister state that ‘‘the predictions of our theory differ considerably from those of Rennó and Ingersoll; for example, the buoyancy and velocity scales are independent of the magnitude of the radiative forcing.’’ The numerical experiments EB present support this notion that CAPE is relatively insensitive to the magnitude of the radiative forcing of the atmosphere. The quote above and the inference of EB’s paper is that the RI theory for CAPE will not satisfy these numerical experiments and therefore is invalid. In this comment, we present an alternative formula for CAPE using the same closure assumptions as RI. Furthermore, we will show that the predictions of CAPE by RI are not inconsistent with the numerical experiments presented in EB. Thus we will conclude it is inappropriate for EB to dismiss the theory of RI based upon the evidence presented by EB to date. Rennó and Ingersoll derive the following expression for the CAPE of an atmosphere in radiative–convective equilibrium: