A consistent treatment of mixed‐phase saturation for atmospheric thermodynamics

Abstract

Ice processes are integral to the formation and maintenance of high‐level clouds and can contribute substantially to the buoyancy of deep moist convection. These processes are represented in modern microphysics parameterisations but are commonly ignored in theoretical treatments of moist thermodynamics. While many thermodynamic variables can be defined uniquely for saturation with respect to liquid water and ice, it is desirable to account for the presence of mixed‐phase condensate, which is common in real clouds. Here, a simple yet novel representation of mixed‐phase saturation is introduced. Using this approach, analytical equations are derived for a variety of thermodynamic variables under mixed‐phase conditions. These include mixed‐phase versions of the saturation vapour pressure, saturated lapse rates, isobaric wet‐bulb temperature, and equivalent potential temperature. A new formulation of the ice–liquid water potential temperature is also presented, together with a method for calculating the mixed‐phase pseudo wet‐bulb temperature and wet‐bulb potential temperature. In addition, two new thermodynamic quantities are introduced: the isobaric saturation‐point temperature, a mixed‐phase analogue of the dew‐point and frost‐point temperatures, and the lifting saturation level, a mixed‐phase analogue of the lifting condensation and lifting deposition levels. Differences between each mixed‐phase variable and its liquid‐ and ice‐only counterparts are quantified across a wide range of atmospheric conditions. A Python library for evaluating these variables, developed during the course of this work, is also briefly introduced.