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Uncertainty exists concerning the proper formulation of surface heat fluxes,namely the sum of "sensible" and "latent" heat fluxes, and in fact concerningthese two fluxes if they are considered as separate fluxes. In fact, eddy fluxof moist-air energy must be defined as the eddy transfer of moist-air specificenthalpy ($\overline{w' h'}$), where the specific enthalpy ($h$) is equal tothe 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 thislocal (specific) moist-air enthalpy ($h$), and in particular to determineabsolute reference value of enthalpies for dry air and water vapour $(h_d)_{\rmref}$ 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 allowthese computations. In this note, this approach is taken to show that Third-lawbased values of moist-air enthalpy fluxes is the sum of two terms. These twoterms are similar to what are called "sensible" and "latent" heat fluxes inexisting 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-airenthalpy flux. Some impacts of this new "latent heat" flux ($L_h \:\overline{w' T'}$) are described in this brief version of a paper to besubmitted to the QJRMS.

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