Related papers: On the definition of a moist-air potential vortici…
It is important to be able to calculate the moist-air entropy of the atmosphere with precision. A potential temperature has already been defined from the third law of thermodynamics for this purpose. However, a doubt remains as to whether…
The aim of this note is to describe several meteorological properties shown in a conference talk (Marquet, January 2022) for the moist-air specific entropy, the associated potential temperature ($\theta_s$) defined in Marquet (2011) and the…
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…
A moist entropy potential temperature -- denoted by ${\theta}_{s}$ -- is defined analytically in terms of the specific entropy for moist air. The expression for ${\theta}_{s}$ is valid for a general mixing of dry air, water vapour and…
Internal energy, enthalpy and entropy are the key quantities to study thermodynamic properties of the moist atmosphere, because they correspond to the First (internal energy and enthalpy) and Second (entropy) Laws of thermodynamics. The aim…
Potential vorticity (PV) is one of the most important quantities in atmospheric science. The PV of each fluid parcel is known to be conserved in the case of a dry atmosphere. However, a parcel's PV is not conserved if clouds or phase…
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…
Moist-air norms and inner-products are currently used in atmospheric science for computing dry or moist singular vectors and for determining forecast errors or sensitivity to observations based on tangent linear and adjoint models. A new…
The moist-air entropy can be used to analyze and better understand the general circulation of the atmosphere or convective motions. Isentropic analyses are commonly based on studies of different equivalent potential temperatures, all of…
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…
Many definitions of moist potential vorticity (PV) have been proposed to extend the dry theory of Ertel PV. None of the moist PV definitions seem to have all of the desirable properties of the dry Ertel PV. For instance, dry PV is not only…
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…
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…
In the context of two-dimensional (2D) turbulence, we apply the maximum entropy production principle (MEPP) by enforcing a local conservation of energy. This leads to an equation for the vorticity distribution that conserves all the…
The moist-air entropy is defined in Marquet (QJRMS 2011, arXiv:1401.1097) by $\boxed{s = s_{ref} + c_{pd} \: \ln(\theta_{s})}$ in terms of two constant values ($s_{ref}$, $c_{pd}$) and a potential entropy temperature denoted by $\theta_s$.…
We consider a rotating non-hydrostatic flow with arbitrary stratification and argue that 1) the appropriate form of potential vorticity (PV) for this system is in terms of isopycnal deviation and 2) the decomposition into energetically…
Like any fluid heated from below, the atmosphere is subject to vertical instability which triggers convection. Convection occurs on small time and space scales, which makes it a challenging feature to include in climate models. Usually…
The aim of this note is to derive the mixed-phase version of the moist-air entropy potential temperature $\theta_s$ derived in Marquet (2011). This mixed-phase version is suitable to describe parcels where liquid water and ice are allowed…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
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…