On the computation of moist-air specific thermal enthalpy

The specific thermal enthalpy of a moist-air parcel is defined analytically following a method in which specific moist entropy is derived from the Third Law of thermodynamics. Specific thermal enthalpy is computed by integrating specific heat content with respect to absolute temperature and including the impacts of various latent heats (i.e., solid condensation, sublimation, melting, and evaporation). It is assumed that thermal enthalpies can be set to zero at $0$ K for the solid form of the main chemically inactive components of the atmosphere (solid-$\alpha$ oxygen and nitrogen, hexagonal ice). The moist thermal enthalpy is compared to already existing formulations of moist static energy (MSE). It is shown that the differences between thermal enthalpy and the thermal part of MSE may be quite large. This prevents the use of MSE to evaluate the enthalpy budget of a moist atmosphere accurately, a situation that is particularly true when dry-air and cloud parcels mix because of entrainment/detrainment processes along the edges of cloud. Other differences are observed when MSE or moist-air thermal enthalpy is plotted on a psychrometric diagram or when vertical profiles of surface deficit are plotted.