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Comments on "MSE minus CAPE is the True Conserved Variable for an Adiabatically Lifted Parcel"

In a recent paper, Romps (JAS, vol.72, p.3639-3646, 2015, hereafter R15) argues that the moist-air static energy (MSE) is only approximately conserved for an adiabatically lifted parcel, and that the quantity "MSE - CAPE" could be used as a true conserved variable, where CAPE is the convective available energy. It is shown in this comment that the quantity denoted by CAPE in R15 is the opposite of the convective available energy. It is explained that the vertical adiabatic ascent considered in R15 is not realistic, since it generates condensed water of the order of 10 to 20 g/kg at height above 6 km. Moreover, the thermodynamic equations are written in R15 by making several assumptions, not all of which are explicitly mentioned. This comment aims to clarify the hypotheses made in R15. It will show that these assumptions call into question the validity of the moist-air internal energy, enthalpy and entropy functions in R15. It also demonstrates that it is possible to obtain more precise and general formulations for moist-air energy, enthalpy and entropy functions, in particular by using the third law of thermodynamics. The large differences between the thermodynamics formulas derived in R15 and those depending on the third law are illustrated by studying a realistic pseudo-adiabatic vertical profile. The same notations as in R15 will be used as far as possible in this comment.