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

TL;DR

This paper redefines the surface heat fluxes using moist-air enthalpy based on the Third-law of Thermodynamics, introducing a new form of latent heat flux that could improve understanding of energy transfer in the atmosphere.

Contribution

It presents a novel formulation of moist-air enthalpy fluxes using Third-law thermodynamics, including a new latent heat term, enhancing the theoretical basis of surface energy budgets.

Findings

Moist-air enthalpy fluxes can be expressed as the sum of two terms similar to sensible and latent heat fluxes.

A new latent heat flux term, L_h = h_v - h_d, is introduced based on absolute enthalpy reference values.

Implications for improved accuracy in atmospheric energy transfer modeling.

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.