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This note is a companion of Marquet and Geleyn (2013, {arXiv:1401.2379[ao-ph]}), where adiabatic lapse rates $\Gamma_{ns}$ and $\Gamma_{sw}$ arederived for non-saturated ($\Gamma_{ns}$) or saturated ($\Gamma_{sw}$) parcelof moist-air. They are computed in terms of the vertical derivative of themoist-air entropy potential temperature $\theta_s$ defined in Marquet (2011,{arXiv:1401.1097 [ao-ph]}). The saturated value $\Gamma_{sw}$ is rewritten inthis note so that a more compact formulation is obtained. The new formulationfor $\Gamma_{sw}$ is expressed in term of a weighting factor $C$. This factormay represent the proportion of an air parcel being in saturated conditions.

Moist-entropic vertical adiabatic lapse rates: the standard cases and some lead towards inhomogeneous conditions