Definition of Total Energy budget equation in terms of moist-air Enthalpy surface flux

Abstract: Uncertainty exists concerning the proper formulation of surface heat fluxes, namely the sum of "sensible" and "latent" heat fluxes, and in fact concerning these two fluxes if they are considered as separate fluxes. In fact, eddy flux of moist-air energy must be defined as the eddy transfer of moist-air specific enthalpy ($\overline{w' h'}$), where the specific enthalpy ($h$) is equal to the internal energy of moist air plus the pressure divided by the density (namely $h = e_{\rm int} + p/\rho$). The fundamental issue is to compute this local (specific) moist-air enthalpy ($h$), and in particular to determine absolute reference value of enthalpies for dry air and water vapour $(h_d){\rm ref}$ and $(h_v){\rm ref}$. New results shown in Marquet (QJRMS 2015, arXiv:1401.3125) are based on the Third-law of Thermodynamics and can allow these computations. In this note, this approach is taken to show that Third-law based values of moist-air enthalpy fluxes is the sum of two terms. These two terms are similar to what are called "sensible" and "latent" heat fluxes in existing surface energy budget equation. However, a new kind of "latent heat" ($L_h = h_v - h_d$) is emerging in the definition of this new moist-air enthalpy flux. Some impacts of this new "latent heat" flux ($L_h : \overline{w' T'}$) are described in this brief version of a paper to be submitted to the QJRMS.