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

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

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