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Pascal Marquet

Publications and source records attributed to Pascal Marquet.

At least 37 records · Page 2Linked to original sources
arXiv2019

Application of the second law to the atmosphere: impacts of the third-law definition for the moist-air entropy

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.

physics.ao-ph↗
arXiv2019

The first and second order approximations of the third-law moist-air entropy potential temperature

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 this entropy potential temperature can be represented with simple but accurate first- or second-order approximate formulas. These approximations are rigorously defined in this paper using mathematical arguments and numerical adjustments to some datasets. The differentials of these approximations lead to simple but accurate formulations for tendencies, gradients and turbulent fluxes of the moist-air entropy. Several physical consequences based on these approximations are described and can serve to better understand moist-air processes (like turbulence or diabatic forcing) or properties of certain moist-air quantities (like the static energies).

physics.ao-ph↗
arXiv2018

Exergy in meteorology: Definition and properties of moist-air available enthalpy

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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arXiv2017

A Third-Law Isentropic Analysis of a Simulated Hurricane

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 which are assumed to fully represent the entropy of moist air. It is, however, possible to rely either on statistical physics or the third law of thermodynamics when defining and computing the absolute entropy of moist air and to study the corresponding third-law potential temperature, which is different from the previous ones. The third law assumes that the entropy for the most stable crystalline state of all substances is zero when approaching absolute zero temperature. This paper shows that the way all these moist-air potential temperatures are defined has a large impact on: (i) the plotting of the isentropes for a simulation of the Hurricane DUMILE; (ii) the changes in moist-air entropy computed for a steam cycle defined for this Hurricane; (iii) the analyses of isentropic stream functions computed for this Hurricane; and (iv) the computations of the heat input, the work function, and the efficiency defined for this steam cycle. The moist-air entropy is a state function and the isentropic analyses must be completely determined by the local moist-air conditions. The large differences observed between the different formulations of moist-air entropy are interpreted as proof that the isentropic analyses of moist-air atmospheric motions must be achieved by using the third-law potential temperature defined from general thermodynamics.

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arXiv2017

On consequences of measurements of turbulent Lewis number from observations

Almost all parameterizations of turbulence in NWP models and GCM make the assumption of equality of exchange coefficients for heat $K_h$ and water $K_w$. However, large uncertainties exists in old papers published in the 1950s, 1960s and 1970s, where the turbulent Lewis number Le_t $= K_h / K_w$ have been evaluated from observations and then set to Le_t$=1$. The aim of this note is: 1) to trust the recommendations of Richardson (1919), who suggested to use the moist-air entropy as a variable on which the turbulence is acting; 2) to compute a new exchange coefficients $K_s$ for the moist-air entropy; 3) to determine the values of the new entropy-Lewis number Le_ts $= K_s / K_w$ from observations (Météopole-Flux and Cabauw masts) and from LES and SCM outputs for the IHOP case (Couvreux et al., 2005). It is shown that values of Le_ts significantly different from $1$ are frequently observed and may have large consequences on the way the turbulence fluxes are computed in NWP models and GCMs.

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arXiv2016

Comments on "Isentropic Analysis of a Simulated Hurricane"

This paper describes Comments to the paper of Mrowiec et al. published in the J. Atmos. Sci. in May 2016 (Vol 73, Issue 5, pages 1857-1870) and entitled "Isentropic analysis of a simulated hurricane". It is explained that the plotting of isentropic surfaces (namely the isentropes) requires a precise definition of the specific moist-air entropy, and that most of existing "equivalent potential temperatures" lead to inaccurate definitions of isentropes. It is shown that the use of the third law of thermodynamics leads to a definition of the specific moist-air entropy (and of a corresponding potential temperature) which allow the plotting of unambigous moist-air isentropes. Numerical applications are shown by using a numerical simulation of the hurricane DUMILE.

physics.ao-ph↗
arXiv2016

The mixed-phase version of moist-air entropy

The aim of this note is to derive the mixed-phase version of the moist-air entropy potential temperature $θ_s$ derived in Marquet (2011). This mixed-phase version is suitable to describe parcels where liquid water and ice are allowed to coexist, with possible under- or super-saturations, with possible supercooled water and with possible different temperatures for dry air and water vapour, on the one hand, condensed water and ice, on the other hand. The impact of this new mixed-phase version for $θ_s$ are evaluated by using high latitudes, SHEBA/FIRE-ACE vertical profiles depicted in Figure 7 of Morisson et al. (2011).

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arXiv2015

Comments on "MSE minus CAPE is the True Conserved Variable for an Adiabatically Lifted Parcel"

In a recent paper, Romps (JAS, vol.72, p.3639-3646, 2015, hereafter R15) argues that the moist-air static energy (MSE) is only approximately conserved for an adiabatically lifted parcel, and that the quantity "MSE - CAPE" could be used as a true conserved variable, where CAPE is the convective available energy. It is shown in this comment that the quantity denoted by CAPE in R15 is the opposite of the convective available energy. It is explained that the vertical adiabatic ascent considered in R15 is not realistic, since it generates condensed water of the order of 10 to 20 g/kg at height above 6 km. Moreover, the thermodynamic equations are written in R15 by making several assumptions, not all of which are explicitly mentioned. This comment aims to clarify the hypotheses made in R15. It will show that these assumptions call into question the validity of the moist-air internal energy, enthalpy and entropy functions in R15. It also demonstrates that it is possible to obtain more precise and general formulations for moist-air energy, enthalpy and entropy functions, in particular by using the third law of thermodynamics. The large differences between the thermodynamics formulas derived in R15 and those depending on the third law are illustrated by studying a realistic pseudo-adiabatic vertical profile. The same notations as in R15 will be used as far as possible in this comment.

physics.ao-ph↗
arXiv2015

A moist "available enthalpy" norm: definition and comparison with existing "energy" norms

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 moist-air norm is defined starting from old results published in Marquet (QJRMS 1993) and based on the "Available Enthalpy" approach, namely one of the Exergy function defined in general thermodynamics. Some interesting and promising impacts of this new "Available Enthalpy" norm are described in this brief version of a paper to be submitted to the QJRMS.

physics.ao-ph↗
arXiv2015

Formulations of moist thermodynamics for atmospheric modelling

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 of this chapter is to search for analytical formulas for the specific values of enthalpy and entropy and for the moist-air mixture composing the atmosphere. The Third Law of thermodynamics leads to the definition of absolute reference values for thermal enthalpies and entropies of all atmospheric species. It is shown in this Chapter 22 that it is possible to define and compute a general moist-air entropy potential temperature, which is really an equivalent of the moist-air specific entropy in all circumstances (saturated, or not saturated). Similarly, it is shown that it is possible to define and compute the moist-air specific enthalpy, which is different from the thermal part of what is called Moist-Static-Energy in atmospheric studies.

physics.ao-ph↗
arXiv2015

An improved approximation for the moist-air entropy potential temperature $θ_s$

The moist-air entropy is defined in Marquet (QJRMS 2011, arXiv:1401.1097) by $\boxed{s = s_{ref} + c_{pd} \: \ln(θ_{s})}$ in terms of two constant values ($s_{ref}$, $c_{pd}$) and a potential entropy temperature denoted by $θ_s$. It is shown in Marquet (2011) that a quantity denoted by $(θ_{s})_1$ plays the role of a leading order approximation of $θ_{s}$. The aim of this note is to demonstrate in a more rigorous way that $(θ_{s})_1$ is indeed the leading order approximation of $θ_{s}$, and to derive a second order approximation which may be used in computations of values, gradients or turbulent fluxes of moist-air entropy. Some impacts of this second order approximation are described in this brief version of a note to be submitted to the QJRMS.

physics.ao-ph↗
arXiv2015

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

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 $h = e_{\rm int} + p/ρ$). 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.

physics.ao-ph↗
arXiv2014

The available-enthalpy (flow-exergy) cycle. Part-II: applications to idealized baroclinic waves

The local available-enthalpy cycle proposed in Part I of this paper is applied to document energetics of three numerical simulations, representing life cycles of idealized baroclinic waves. An improved temporal numerical scheme defined in Part I is used in this study, together with the Arpege-IFS model using a T42 triangular truncation. A 45°N and 200 hPa dry unstable jet is constructed with the most unstable mode at zonal wave number 8. Energetic impacts of both horizontal and vertical diffusion schemes are determined separately. The role of ageostrophic winds within the Ekman layer is investigated, leading to an explanation for large observed values for the dissipation terms and to a new formulation of the potential-energy conversions. The magnitudes of these new conversion terms are compared with those of the usual barotropic and baroclinic conversions. A new version for the available-enthalpy cycle is proposed. It is suitable for open systems and it includes explicitly the potential-energy component as a transitional reservoir. Finally, some results from Intensive Observing Period 15 of the Fronts and Atlantic Storm-Track EXperiment (FASTEX) are compared with those from the idealized diabatic experiment.

physics.ao-ph↗
arXiv2014

The available-enthalpy (flow-exergy) cycle. Part-I: introduction and basic equations

A diagnostic package is derived from the concept of specific available enthalpy, leading to the definition of a local and complete energy cycle. It is useful to understand the transformations of energy occurring at any particular pressure level or pressure layer of a limited area domain. The global version of this diagnostic tool is very similar to the cycle of Lorenz, but the local counterpart contains several additional terms, with zonal, eddy and static-stability components close to definitions already given by Pearce. The new cycle takes into account the flow of energy components across the vertical and horizontal boundaries, with additional conversion terms involving potential energy, leading to accurate computations of dissipation and generation terms obtained as residuals. A new accurate temporal scheme is proposed in order to allow use of a large time interval in future numerical applications. Finally, comments are made on the arbitrary choice for two constant reference values for pressure and temperature.

physics.ao-ph↗
arXiv2014

Definition of a moist-air entropy potential temperature. Application to FIRE-I data flights

A moist entropy potential temperature -- denoted by $θ_{s}$ -- is defined analytically in terms of the specific entropy for moist air. The expression for $θ_{s}$ is valid for a general mixing of dry air, water vapour and possible condensed water species. It verifies the same conservative properties as the moist entropy, even for varying dry air or total water content. The moist formulation for $θ_{s}$ is equal to the dry formulation $θ$ if dry air is considered and it verifies new properties valid for the moist air cases, both saturated or under-saturated ones. Exact and approximate versions of $θ_{s}$ are evaluated for several Stratocumulus cases, in particular by using the aircraft observations FIRE-I experiment data sets. It appears that there is no (or small) jump in $θ_{s}$ at the top of the PBL. The mixing in moist entropy is almost complete in the PBL, with the same values observed in the clear air and the cloudy regions, including the very top of the entrainment region. The Randall-Deardorff CTEI analysis may be interpreted as a mixing in moist entropy criterion. The iso-$θ_{s}$ lines are plotted on skew $T$-$\ln(p)$ and conserved variable diagrams. All these properties could suggest some hints on the use of moist entropy (or $θ_{s}$) in cloud modelling or in mixing processes, with the marine Stratocumulus considered as a paradigm of moist turbulence.

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