An equation for moist entropy in a precipitating and icy atmosphere

This paper addresses an equation for moist entropy in the framework of cloud-resolving models. After rewriting the energy equation with moist entropy in the place of temperature, an equation for moist entropy is obtained. The equation expresses the internal and external sources of moist entropy explicitly, providing a basis for the use of moist entropy as a prognostic variable in long-term cloud-resolving modeling. In addition, a precise formula for the surface flux of moist entropy from the underlying surface into the air above is derived. The equation for moist entropy is used to express the Neelin-Held model for the diagnosis of large-scale vertical velocity. After applying the model to a tropical oceanic atmosphere with mean annual soundings, the paper shows the sensitivity of large-scale vertical circulations to the radiative cooling rate and the surface flux of moist entropy, which demonstrates the necessity for a precise equation for moist entropy in the analysis and modeling of large-scale tropical circulations.