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Register a new userExergy in meteorology: Definition and properties of moist-air available enthalpy
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Pascal Marquet
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The exergy of the dry atmosphere can be considered as another aspect of the meteorological theories of available energies. The local and global properties of the dry available enthalpy function, also called flow exergy, were investigated in a previous paper (Marquet, Q. J. R. Meteorol. Soc., Vol 117, p.449-475, 1991). The concept of exergy is well defined in thermodynamics, and several generalizations to chemically reacting systems have already been made. Similarly, the concept of moist available enthalpy is presented in this paper in order to generalize the dry available enthalpy to the case of a moist atmosphere. It is a local exergy-like function which possesses a simple analytical expression where only two unknown constants are to be determined, a reference temperature and a reference pressure. The moist available enthalpy, $a_m$, is defined in terms of a moist potential change in total entropy. The local function $a_m$ can be separated into temperature, pressure and latent components. The latent component is a new component that is not present in the dry case. The moist terms have been estimated using a representative cumulus vertical profile. It appears that the modifications brought by the moist formulation are important in comparison with the dry case. Other local and global properties are also investigated and comparisons are made with some other available energy functions used in thermodynamics and meteorology.
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This study presents a new formulation for the norms and scalar products used in tangent linear or adjoint models to determine forecast errors and sensitivity to observations and to calculate singular vectors. The new norm is derived from the concept of moist-air available enthalpy, which is one of the availability functions referred to as exergy in general thermodynamics. It is shown that the sum of the kinetic energy and the moist-air available enthalpy can be used to define a new moist-air squared norm which is quadratic in: 1) wind components; 2) temperature; 3) surface pressure; and 4) water vapor content. Preliminary numerical applications are performed to show that the new weighting factors for temperature and water vapor are significantly different from those used in observation impact studies, and are in better agreement with observed analysis increments. These numerical applications confirm that the weighting factors for water vapor and temperature exhibit a large increase with height (by several orders of magnitude) and a minimum in the middle troposphere, respectively.
A framework is introduced to compare moist `potential temperatures. The equivalent potential temperature, $theta_e,$ the liquid water potential temperature, $theta_ell,$ and the entropy potential temperature, $theta_s$ are all shown to be potential temperatures in the sense that they measure the temperature moist-air, in some specified state, must have to have the same entropy as the air-parcel that they characterize. They only differ in the choice of reference state composition: $theta_ell$ describes the temperature a condensate-free state, $theta_e$ a vapor-free state, and $theta_s$ a water-free state would require to have the same entropy as the given state. Although in this sense $theta_e,$ $theta_ell,$ and $theta_s$ are all different flavors of the same thing, only $theta_ell$ satisfies the stricter definition of a `potential temperature, as corresponding to a reference temperature accessible by an isentropic and closed transformation of a system in equilibrium; only $theta_e$ approximately measures the ability of moist-air to do work; and only $theta_s$ measures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperature, $theta$ in the limit as the water mass fraction goes to zero. As is well known, $theta$ does mix linearly and inherits all the favorable (entropic, enthalpic, and potential temperature) properties of its various -- but descriptively less rich -- moist counterparts. All, involve quite complex expressions, but admit relatively simple and useful approximations. Of the three moist `potential temperatures, $theta_s$ is the least familiar, but the most well mixed in the broader tropics, a property that merits further study as a basis for constraining mixing processes.
Calculations of entropy fluxes and production rate have been evaluated with some success to study atmospheric processes. However, recurring questions arise as to how best to take into account entropy flux due to radiation, for example. This article raises another kind of question: how to define the entropy of the atmosphere itself, which is composed of variable proportions of dry air (nitrogen, oxygen, argon, etc.) and water (vapour, liquid, ice). The specific values of the entropy for such a variable composition system depend on the reference values of its components. Most of the current definitions are based on entropies set at zero for dry air and liquid water at zero degrees Celsius. Differently, the third law of thermodynamics assumes that the entropy of all species cancels out for the more stable solid state at the zero of absolute temperatures. In this paper, we analyze the possible consequences of this absolute definition of entropy of moist air on the calculation of entropy fluxes. The impacts of moisture are significant and these new calculation methods seem to be able to modify the budgets of atmospheric entropy, with possible impacts on the nature of the equilibrium of the atmosphere resulting from entropic imbalances induced by radiations.
This article describes the third law of thermodynamics. This law is often poorly known and is often decried, or even considered optional and irrelevant to describe weather and climate phenomena. This, however, is inaccurate and contrary to scientific facts. A rather exhaustive historical study is proposed here in order to better understand, in another article to come, why the third principle can be interesting for the atmosphere sciences.
This paper is the second part of a previous paper (Marquet, 2019) dealing with the need to define the entropy with an absolute way, by using the third law of thermodynamics. In this second part it is shown that there is a need and interest to define a potential temperature which is a synonym of the moist-air absolute entropy, with several possible novel applications to study meteorology and climate processes.
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