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

TL;DR

This paper refines the derivation of moist-entropy-based adiabatic lapse rates for moist air, providing a more compact formulation for saturated conditions and introducing a weighting factor to represent saturation proportion.

Contribution

It presents a new, simplified formulation of the saturated moist-entropy adiabatic lapse rate using a weighting factor for saturation conditions.

Findings

Derived a more compact formula for saturated lapse rate.

Introduced a weighting factor C for saturation proportion.

Enhanced understanding of moist-entropy lapse rates.

Abstract

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