the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 May 2024
TEOS-10 and the Climatic Relevance of Ocean-Atmosphere Interaction
Abstract. Unpredicted observations in the climate system, such as recently an excessive ocean warming, are often lacking immediate causal explanations and are challenging the numerical models. As a highly advanced mathematical tool, the Thermodynamic Equation of Seawater – 2010 (TEOS-10) had been established by international bodies as an interdisciplinary standard and is recommended for use in geophysics, such as especially in climate research. From its very beginning, the development of TEOS-10 was supported by Ocean Science through publishing successive stages and results. Here, history and properties of TEOS-10 are briefly reviewed. With focus on the air-sea interface, selected current problems of climate research are discussed and tutorial examples for the possible use of TEOS-10 in the associated context are presented, such as related to ocean heat content, latent heat and rate of marine evaporation, properties of sea spray aerosol, or climatic effects of low-level clouds. Appended to this article, a list of publications and their metrics is provided for illustrating the uptake of TEOS-10 by the scientific community, along with some continued activities, addressing still pending, connected issues such as uniform standard definitions of uncertainties, of relative humidity, seawater salinity or pH.
This article is dedicated to the Jubilee celebrating 20 years of Ocean Science.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1243', Trevor McDougall, 11 May 2024
- AC1: 'Reply on RC1', Rainer Feistel, 16 May 2024
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RC2: 'Comment on egusphere-2024-1243', Remi Tailleux, 09 Jun 2024
- AC2: 'Reply on RC2', Rainer Feistel, 12 Jun 2024
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CC1: 'Comment on egusphere-2024-1243', Pascal Marquet, 16 Jun 2024
My general comments on the EGUsphere preprint paper by Feistel (2024) concern the interest shown in this paper (as in the previous ones since 1993, and in particular in the IAPSW and TEOS10 software) in providing a very precise (even possibly ultimate) version of thermodynamics for the ocean and atmosphere. In particular, the GSW and SIA version of the TEOS-10 software, on which all the applications in this preprint are based, is supposed to provide numerical values of seawater entropy for both the ocean and the atmosphere.
But Rainer Feistel forgot to specify what he mentioned in 1995 with Eberhard Hagen as a co-author, i.e. that the reference values of the entropies of pure water and ocean salts (as well as dry air) can and must be specified via the recommendations of thermodynamics and its third law, i.e. that the entropies of the most stable versions of all solids have a same universal value, which can be cancel out at absolute zero temperature. Differently, Rainer Feistel (like in almost all studies of the moist-air atmosphere and seawater) continues to arbitrarily specify these reference values at zero Celsius (instead of zero Kelvin).
The words of Feistel and Hagen (1995, p.268) were: "Quantities like density or heat capacity, freezing point or osmotic pressure are gauge invariant (...) others like entropy, enthalpy or chemical potential are covariant, i.e. depend on the choice of the free (entropy) constants. This is to be borne in mind when oceanographic sections with these quantities are discussed, or sigma−S (i.e. Entropy-Salinity) diagrams are interpreted, because these graphs will be significantly altered when being transformed."Â
Indeed, most of the physical quantities available as output of the TEOS10 software do not depend on these reference values. However, the entropy function itself, like the available energy (Helmholtz function), and like the available enthalpy (Gibbs function) do depend on these absolute reference values, and therefore on the "third law" of Planck. In this sense, if these quantities are to be used in all applications, their values, calculated as a function of the absolute values of the reference entropies of all the bodies present, must be provided as a matter of course. Rainer Feistel may call the present available atmospheric and oceanographic versions the "practical entropies", whereas it would be highly desirable to have the "thermodynamic absolute entropies" versions for the atmosphere and the ocean.
I show (in a document prepared for this Comment and to be posted soon in zenodo and arXiv):
-(1)- that it is easy to modify the TEOS10 (GSW and SIA) software to impose the relevant absolute reference entropies for pure water, sea-salts and dry air, in order to compute the moist-air and seawater absolute entropies;
-(2)- that Rainer Feistel has at his disposal the way to determined these reference values in many of papers and thermodynamic books cited in the preprint, like Lewis and Randall (1961) for the elements, anions and cations entropies, like Robinson and Stokes (1955, 1970), Millero and Leung (1976) and Millero (1983) for the pure-water and sea-salts entropies, and like Lemmon et al. (2000) for the dry-air entropy;
-(3)- that, if needed, I have computed in 2022 new, updated and (slightly) more accurate values for these absolute entropies;
-(4)- that the impacts of these changes on the vertical profiles of both seawater and moist-air vertical profiles may indeed be large, as shown for a SCIEX-96 CTD profile, for TEOS10 and UNESCO CTD profiles, for the DYCOMS-II stratocumulus profile, and for the Fig. 4 of Feistel et al. (2010);
-(5)- and since the moist-air and seawater entropies are thermodynamic state functions, the difference of these functions between two vertical points cannot be positive, zero or negative depending on this or that arbitrary choice for the reference values, therefore with the need to only rely on the absolute reference values prescribed in the thermodynamic tables to define the (true) absolute version of the entropies;
-(6)- the same is true for the vertical turbulent moist-air and seawater entropy fluxes, which cannot be positive, zero or negative depending on this or that arbitrary choice for the reference values of dry-air and liquid-water entropies, and differently to what is stated in the preprint of Rainer Feistel who do not consider the turbulent or bulk-surface formulation that are usually computed in the NWP models and GCMs (namely expressed for a unit mass of moist air or seawater, and not by considering a certain fix volume with a constant mass of dry air and/or sea salts).It should moreover be mentioned that the "calorimetric" and "theoretical-statistical" versions of the absolute entropies lead to the same results (see the Fig. B1 for N2, O2, Ar, CO2 and H2O in the JAS paper by Marquet and Stevens, 2022), provided that the (small, known) residual entropy for H2O at 0K is taken into account. There is therefore no need to distinguish these two "calorimetric" and "theoretical-statistical" methods of computations (differently to what is suggested in Feistel, 2019, with anyhow a small impact of about 1.8% for this residual entropy for H2O).
It should also be mentioned that, in fact, it was Max Planck who established in 1911 the "third law of thermodynamic" (and used it in all his next books about radiation, 1913, 1914, 1921 and about thermodynamics, 1911, 1913, 1917, 1922, 1930), following and generalizing the work of Walter Nernst in 1906 (and his "heat theorem"). In this sense, the citation of Planck (1906) included in this 2024 preprint (and before in Feistel and Hellmuth, 2020) is anachronistic and unfounded (simply because it was published before the knowledge of the "heat theorem" of Nernst and before the definition of the "third law" by Planck from 1911).
Finally, I would like to add that I have been in contact with Rainer Feistel since 2014, when I had already published several papers in the QJRMS and already demonstrated the impact of reference values for entropy (Marquet, 2011; Marquet and Geleyn, 2013; Marquet, 2014). Rainer Feistel was initially interested and favourable to the possibility of calculating the absolute version of the moist-air entropy, which he then refused to consider despite the answers and explanations (about the absolute reference values for the entropies and the energies) I was able to include in my subsequent papers published in the QJRMS (Marquet, 2015a), in a book-Chapter (Marquet and Geleyn, 2015), in the JAS (Marquet, 2017; Marquet and Dauhut, 2018; Marquet and Stevens, 2022) and in La Météorologie (Marquet, 2019b,c, with the English translations available in arXiv). A list of all my papers are available in https://sites.google.com/view/pascal-marquet
I have extracted from the document prepared for this Comment (and to be posted soon in zenodo and arXiv) several Figures that can illustrate how the reference entropies can influence the vertical profiles and entropy diagrams.
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AC3: 'Reply on CC1', Rainer Feistel, 17 Jun 2024
When an empirical thermodynamic potential for a certain substance is constructed from data sets of lab measurements, two of its adjustable coefficients always remain undetermined. These two coefficients represent the absolute energy and absolute entropy of that substance. In any thermodynamic lab experiments, only differences of energies or entropies can be measured, for example in the form of work applied or heat flux communicated to the sample under investigation.
In turn, consequently, whatever the values of those constants may be, they may not affect any measurable geophysical thermodynamic properties.
For pure water, those constants had arbitrarily been specified by the 5th International Conference on the Properties of Steam in London in 1956, by setting the internal energy and the entropy of liquid water to zero values at the common triple point. In TEOS-10, the SCOR/IAPSO Working Group 127 on Thermodynamics of Seawater followed that IAPWS definition for water and decided on similar reference-state conditions for sea salt and dry air.
Physical values for absolute energies can be derived from theory, such as the relativistic rest energy E = m c² of a given substance. This is a very large number, namely exactly 89 875 517 873 681 764 J/kg for water at the zero point. To properly represent practical changes of energy by some J/kg or much less, numbers with many digits are required. Water properties below 100 K are only poorly known; these uncertainties propagate inevitably into measured values at ambient conditions, such as at the triple point, if the zero point is used as the reference state where the absolute energy is exactly known. Such unnecessary uncertainties can be avoided in practice when instead the triple point is chosen where an exact energy value is specified.
Physical values for absolute entropies can be derived from theory, such as the statistical theory of Boltzmann, Planck and Pauling, S = k log W. If a substance has a single configuration W(0) = 1 at the zero point, its residual entropy S(0) = 0 is zero, in agreemant with the 3rd law of Nernst. If a substance has several zero-point configurations at 0 K, W(0) > 1, such as ice Ih, then this substance has a non-zero residual entropy. In the case of ice, however, the question is not yet ultimately decided whether ice Ih is really an equilibrium phase at 0 K, or whether it may possibly be a meatastable state, while ice XI is the proper equilibrium state with zero residual entropy. Near the zero point, the extremely sluggish relaxation of ice to equilibrium makes experimental decisions of this problem difficult.Â
As with energies, if the zero point is the reference state, also entropies at ambient conditions suffer from large uncertainties due to the poorly known ice properties below 100 K. The triple point chosen as the reference state avoids this unnecessary complication. In the definition of the equation of state of ice Ih by Feistel and Wagner (2006: Tables 8 and 9 therein) and by IAPWS (2006), both the "absolute" and the "IAPWS-95" definitions of the reference state are offered and the resulting uncertainties are compared.
When the reference state conditions of TEOS-10 are modified, such as those of water and of dry air, or of water and sea salt, graphical representations such as entropy-salinity diagrams will change. However, such changes have no physical relevance. Similarly, when surfaces of constant entropy are considered in the atmosphere or in the ocean, those surfaces will be distorted by changes of the reference state conditions. What will remain unaltered, however, is the shape of isentropic trajectories, because the condition of equal entropy of different states does not depend and the value of the common absolute entropy. Similar arguments apply to heat and energy fluxes.
There is no need to distrust the TEOS-10 equations of state with respect to the definition of reference state conditions. Measurable thermodynamic properties in geophysics must be independent of the choice of those conditions, otherwise those quantities are physically improperly specified.
Citation: https://doi.org/10.5194/egusphere-2024-1243-AC3 -
CC2: 'Reply on AC3', Pascal Marquet, 25 Jun 2024
I disagree with almost all Rainer Feistel's answers to my Comments, and the next sections of the PDF are point-by-point Replies to the Reply of Rainer Feistel.
My aim will not to continue a too long exchange with Rainer Feistel, who will likely refuse to offer any other definition of his (equivalent) proxy values for the moist-air and seawater entropies. Nonetheless, my aim is to clearly show to the Editor (and to young and future generations reading the preprint and my Comment and Reply to Rainer Feistel) that the reference values have real impact on many kinds.
Moreover, since Rainer Feistel admits that vertical profiles, vertical sections and entropy diagrams are influenced by these arbitrary choices of reference entropies, he should at least offer as a possibility the calculations of the absolute moist-air and seawater entropies.
I want to recall that it is easy to add simple extra terms for computing draft versions of both the atmospheric and seawater absolute entropies and the liquid-water proxy value from the standard (TEOS10, equivalent) proxy formulations. However, it would be worthwhile redoing the TEOS10 settings/tunings without making arbitrary assumptions while imposing the absolute values of the reference entropies, going beyond the additional terms that I indicate and which are likely of the first order (especially for the ocean).
I recall in the Section 2 that the saturation-pressure relationship (1) derived by Nernst (1918), Planck (1921), Nernst (1921) and Nernst (1926) depends on the absolute value of the entropy for monatomic gases (used to set the translational part of the statistical entropy for all other polyatomic bodies). The same absolute entropies of bodies are also used to determine the equilibrium constants of all chemical reactions, which in turn determine the (measurable) concentrations of O3 in the atmosphere and sea salts in the seawater, and therefore impact the vertical profile of the (measurable) temperature in the stratosphere, in particular.
I explain in the Section 3 that the constants arbitrarily specified by the 5th (1956) International Conference on Properties of Steam are unclear, presently unavailable, not reproduced elsewhere, and looks like a mere old-fashioned and arbitrary gentlemen agreement.
I explains in the Section 4 that the relativistic reference values have no impact on the computations of absolute values for the thermal energies and entropies (merely describing the variation of translational, rotational and vibrational degrees of freedom for atoms and molecules), simply because present atmospheric and oceanic NWP models and GCMs are not designed to describe the thermodynamic impacts and physical processes of nuclear bombs or nuclear reactors in nuclear plants.
I explain in the Section 5 that there is no large uncertainty in the properties of H2O Ice-Ih, with in particular the residual entropy at 0K needed to make the Calorimetric and the Statistical methods coincide. I show in the Fig.1 the values of the specific heat at constant pressure (cp) plotted as a function of the absolute temperature from 0K to T=273.15K, with the numerical values listed in the Table-2. It is with these numerical values that I have plotted the calorimetric curve in the Fig.2, which show that the Statistical method and the Calorimetric method (including the residual entropy for Ice-Ih H2O) lead to the same results for N2, O2, Ar, CO2 and H2O. If the uncertainty in the properties of Ice-Ih below 100K was as important as suggested by Rainer Feistel, it would have been impossible to get the good agreement between the Statistical and Calorimetric methods (including the residual entropy at 0K).
Moreover I show in the Section 6 unpublished zonal sections (Figs.4), unpublished entropy changes at the Mauna Loa laboratory (Figs.5), and unpublished Climate Change of entropies from NWP models, GCMs, Reanalyses and GIEC simulations (Figs.6). All these unpublished results clearly show that the behaviour of the absolute version of the moist-air entropy is special and cannot be confused with other `equivalent' versions of the `entropies', which often produce results with opposite physical behaviour (vertical gradients and changes with time of different magnitudes, or even opposite signs).
I similarly show in the Section 7 that not only the surface of constant entropy (as shown in another example of zonal section in the Fig.9), but also the isentropic trajectories, depend on the choice of the reference values. This was in particular the aim of the study of H2O plumes (pathways) studied by Adriana Bailey (NCAR). I have shown with Adriana (see the Fig.7 and Fig.8) that these H2O plumes preferentially follow the surface of absolute moist-air entropy, with clear difference with the other arbitrary-reference definitions like the equivalent-proxy one computed by the TEOS10 software (these differences are large in the moist and warmer boundary layers and within the Tropics).
I recall in the Section 8 that the reference values of the energy must have an impact on the computations of the value and flux of the moist-air energy, as already explained by Gibbs (1875-1878), as shown and recalled in the Fig.10.
I explain in the Section 8.1 that the entropyflux of -1.0 W/m2/K mentioned in the preprint and suggested first by Ebeling-Feistel (1982) and then retained as such in Feistel-Ebeling (2011), as shown in the Figs.11, is underestimated: it is more likely of about -1.18 to -1.28 W/m2/K. Rainer Feistel should update this value.
I show in the Section 8.2 how the reference values of the moist-air entropy (20) must impact most of the terms in the moist-air (absolute) entropy equation (19), including the turbulent fluxes of the moist-air (absolute) entropy, but with the notable exception of the current version of the moist-air (absolute) entropy production term.
I recall in the Section 8.3 that the turbulence are presently based in all NWP models and GCMs on flux-gradients relationships of the Betts (1973) variables, which must be generalized to the use of the moist-air absolute entropy itself, or even the associated moist-air absolute entropy potential temperature (according to Richardson, 1919, 1922). As a matter of fact, these turbulent terms are not managed by Rainer Feistel, nor the (absolute) entropy flux, nor the temporal change in (absolute) entropy. This may be of a certain importance for several results shown in the preprint, and with a link with a questions asked by Trevor McDougall (RC1) about the Fig. A.16.1 of the TEOS-10 Manual and the `non-conservative production of entropy'. Rainer Feistel should more clearly explain which kind of moist-air (absolute) entropy equation he consider, and which terms are evaluated versus those discarded? In particular, I show in the Figs.12 that it is needed to use the absolute moist-air variable (or the associated potential temperature) to arrive at the properties mentioned in the preprint by Rainer Feistel and the need to have turbulent `fluxes proportional to its driving force' (in that fully justifying the suggestions of Richardson, 1919a,b, 1922, to use the absolute value of the moist-air entropy).
In the Section 9 I include some remaining developments to better explain why Rainer Feistel is wrong when he wrote that: `Measurable thermodynamic properties in geophysics must be independent of the choice of those conditions, otherwise those quantities are physically improperly specified.' In particular I recalled that the need to define absolute reference entropies is related to the definition of the absolute scale of temperature (Fig.13) and to the principle of unattainability of the absolute zero of the temperature (Fig.14).
All Figures are placed in the last Section 10, located before the references.
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CC2: 'Reply on AC3', Pascal Marquet, 25 Jun 2024
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AC3: 'Reply on CC1', Rainer Feistel, 17 Jun 2024
- CC3: 'Comment on egusphere-2024-1243', Olaf Hellmuth, 28 Jun 2024
- AC4: 'Comment on egusphere-2024-1243', Rainer Feistel, 22 Jul 2024
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1243', Trevor McDougall, 11 May 2024
- AC1: 'Reply on RC1', Rainer Feistel, 16 May 2024
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RC2: 'Comment on egusphere-2024-1243', Remi Tailleux, 09 Jun 2024
- AC2: 'Reply on RC2', Rainer Feistel, 12 Jun 2024
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CC1: 'Comment on egusphere-2024-1243', Pascal Marquet, 16 Jun 2024
My general comments on the EGUsphere preprint paper by Feistel (2024) concern the interest shown in this paper (as in the previous ones since 1993, and in particular in the IAPSW and TEOS10 software) in providing a very precise (even possibly ultimate) version of thermodynamics for the ocean and atmosphere. In particular, the GSW and SIA version of the TEOS-10 software, on which all the applications in this preprint are based, is supposed to provide numerical values of seawater entropy for both the ocean and the atmosphere.
But Rainer Feistel forgot to specify what he mentioned in 1995 with Eberhard Hagen as a co-author, i.e. that the reference values of the entropies of pure water and ocean salts (as well as dry air) can and must be specified via the recommendations of thermodynamics and its third law, i.e. that the entropies of the most stable versions of all solids have a same universal value, which can be cancel out at absolute zero temperature. Differently, Rainer Feistel (like in almost all studies of the moist-air atmosphere and seawater) continues to arbitrarily specify these reference values at zero Celsius (instead of zero Kelvin).
The words of Feistel and Hagen (1995, p.268) were: "Quantities like density or heat capacity, freezing point or osmotic pressure are gauge invariant (...) others like entropy, enthalpy or chemical potential are covariant, i.e. depend on the choice of the free (entropy) constants. This is to be borne in mind when oceanographic sections with these quantities are discussed, or sigma−S (i.e. Entropy-Salinity) diagrams are interpreted, because these graphs will be significantly altered when being transformed."Â
Indeed, most of the physical quantities available as output of the TEOS10 software do not depend on these reference values. However, the entropy function itself, like the available energy (Helmholtz function), and like the available enthalpy (Gibbs function) do depend on these absolute reference values, and therefore on the "third law" of Planck. In this sense, if these quantities are to be used in all applications, their values, calculated as a function of the absolute values of the reference entropies of all the bodies present, must be provided as a matter of course. Rainer Feistel may call the present available atmospheric and oceanographic versions the "practical entropies", whereas it would be highly desirable to have the "thermodynamic absolute entropies" versions for the atmosphere and the ocean.
I show (in a document prepared for this Comment and to be posted soon in zenodo and arXiv):
-(1)- that it is easy to modify the TEOS10 (GSW and SIA) software to impose the relevant absolute reference entropies for pure water, sea-salts and dry air, in order to compute the moist-air and seawater absolute entropies;
-(2)- that Rainer Feistel has at his disposal the way to determined these reference values in many of papers and thermodynamic books cited in the preprint, like Lewis and Randall (1961) for the elements, anions and cations entropies, like Robinson and Stokes (1955, 1970), Millero and Leung (1976) and Millero (1983) for the pure-water and sea-salts entropies, and like Lemmon et al. (2000) for the dry-air entropy;
-(3)- that, if needed, I have computed in 2022 new, updated and (slightly) more accurate values for these absolute entropies;
-(4)- that the impacts of these changes on the vertical profiles of both seawater and moist-air vertical profiles may indeed be large, as shown for a SCIEX-96 CTD profile, for TEOS10 and UNESCO CTD profiles, for the DYCOMS-II stratocumulus profile, and for the Fig. 4 of Feistel et al. (2010);
-(5)- and since the moist-air and seawater entropies are thermodynamic state functions, the difference of these functions between two vertical points cannot be positive, zero or negative depending on this or that arbitrary choice for the reference values, therefore with the need to only rely on the absolute reference values prescribed in the thermodynamic tables to define the (true) absolute version of the entropies;
-(6)- the same is true for the vertical turbulent moist-air and seawater entropy fluxes, which cannot be positive, zero or negative depending on this or that arbitrary choice for the reference values of dry-air and liquid-water entropies, and differently to what is stated in the preprint of Rainer Feistel who do not consider the turbulent or bulk-surface formulation that are usually computed in the NWP models and GCMs (namely expressed for a unit mass of moist air or seawater, and not by considering a certain fix volume with a constant mass of dry air and/or sea salts).It should moreover be mentioned that the "calorimetric" and "theoretical-statistical" versions of the absolute entropies lead to the same results (see the Fig. B1 for N2, O2, Ar, CO2 and H2O in the JAS paper by Marquet and Stevens, 2022), provided that the (small, known) residual entropy for H2O at 0K is taken into account. There is therefore no need to distinguish these two "calorimetric" and "theoretical-statistical" methods of computations (differently to what is suggested in Feistel, 2019, with anyhow a small impact of about 1.8% for this residual entropy for H2O).
It should also be mentioned that, in fact, it was Max Planck who established in 1911 the "third law of thermodynamic" (and used it in all his next books about radiation, 1913, 1914, 1921 and about thermodynamics, 1911, 1913, 1917, 1922, 1930), following and generalizing the work of Walter Nernst in 1906 (and his "heat theorem"). In this sense, the citation of Planck (1906) included in this 2024 preprint (and before in Feistel and Hellmuth, 2020) is anachronistic and unfounded (simply because it was published before the knowledge of the "heat theorem" of Nernst and before the definition of the "third law" by Planck from 1911).
Finally, I would like to add that I have been in contact with Rainer Feistel since 2014, when I had already published several papers in the QJRMS and already demonstrated the impact of reference values for entropy (Marquet, 2011; Marquet and Geleyn, 2013; Marquet, 2014). Rainer Feistel was initially interested and favourable to the possibility of calculating the absolute version of the moist-air entropy, which he then refused to consider despite the answers and explanations (about the absolute reference values for the entropies and the energies) I was able to include in my subsequent papers published in the QJRMS (Marquet, 2015a), in a book-Chapter (Marquet and Geleyn, 2015), in the JAS (Marquet, 2017; Marquet and Dauhut, 2018; Marquet and Stevens, 2022) and in La Météorologie (Marquet, 2019b,c, with the English translations available in arXiv). A list of all my papers are available in https://sites.google.com/view/pascal-marquet
I have extracted from the document prepared for this Comment (and to be posted soon in zenodo and arXiv) several Figures that can illustrate how the reference entropies can influence the vertical profiles and entropy diagrams.
-
AC3: 'Reply on CC1', Rainer Feistel, 17 Jun 2024
When an empirical thermodynamic potential for a certain substance is constructed from data sets of lab measurements, two of its adjustable coefficients always remain undetermined. These two coefficients represent the absolute energy and absolute entropy of that substance. In any thermodynamic lab experiments, only differences of energies or entropies can be measured, for example in the form of work applied or heat flux communicated to the sample under investigation.
In turn, consequently, whatever the values of those constants may be, they may not affect any measurable geophysical thermodynamic properties.
For pure water, those constants had arbitrarily been specified by the 5th International Conference on the Properties of Steam in London in 1956, by setting the internal energy and the entropy of liquid water to zero values at the common triple point. In TEOS-10, the SCOR/IAPSO Working Group 127 on Thermodynamics of Seawater followed that IAPWS definition for water and decided on similar reference-state conditions for sea salt and dry air.
Physical values for absolute energies can be derived from theory, such as the relativistic rest energy E = m c² of a given substance. This is a very large number, namely exactly 89 875 517 873 681 764 J/kg for water at the zero point. To properly represent practical changes of energy by some J/kg or much less, numbers with many digits are required. Water properties below 100 K are only poorly known; these uncertainties propagate inevitably into measured values at ambient conditions, such as at the triple point, if the zero point is used as the reference state where the absolute energy is exactly known. Such unnecessary uncertainties can be avoided in practice when instead the triple point is chosen where an exact energy value is specified.
Physical values for absolute entropies can be derived from theory, such as the statistical theory of Boltzmann, Planck and Pauling, S = k log W. If a substance has a single configuration W(0) = 1 at the zero point, its residual entropy S(0) = 0 is zero, in agreemant with the 3rd law of Nernst. If a substance has several zero-point configurations at 0 K, W(0) > 1, such as ice Ih, then this substance has a non-zero residual entropy. In the case of ice, however, the question is not yet ultimately decided whether ice Ih is really an equilibrium phase at 0 K, or whether it may possibly be a meatastable state, while ice XI is the proper equilibrium state with zero residual entropy. Near the zero point, the extremely sluggish relaxation of ice to equilibrium makes experimental decisions of this problem difficult.Â
As with energies, if the zero point is the reference state, also entropies at ambient conditions suffer from large uncertainties due to the poorly known ice properties below 100 K. The triple point chosen as the reference state avoids this unnecessary complication. In the definition of the equation of state of ice Ih by Feistel and Wagner (2006: Tables 8 and 9 therein) and by IAPWS (2006), both the "absolute" and the "IAPWS-95" definitions of the reference state are offered and the resulting uncertainties are compared.
When the reference state conditions of TEOS-10 are modified, such as those of water and of dry air, or of water and sea salt, graphical representations such as entropy-salinity diagrams will change. However, such changes have no physical relevance. Similarly, when surfaces of constant entropy are considered in the atmosphere or in the ocean, those surfaces will be distorted by changes of the reference state conditions. What will remain unaltered, however, is the shape of isentropic trajectories, because the condition of equal entropy of different states does not depend and the value of the common absolute entropy. Similar arguments apply to heat and energy fluxes.
There is no need to distrust the TEOS-10 equations of state with respect to the definition of reference state conditions. Measurable thermodynamic properties in geophysics must be independent of the choice of those conditions, otherwise those quantities are physically improperly specified.
Citation: https://doi.org/10.5194/egusphere-2024-1243-AC3 -
CC2: 'Reply on AC3', Pascal Marquet, 25 Jun 2024
I disagree with almost all Rainer Feistel's answers to my Comments, and the next sections of the PDF are point-by-point Replies to the Reply of Rainer Feistel.
My aim will not to continue a too long exchange with Rainer Feistel, who will likely refuse to offer any other definition of his (equivalent) proxy values for the moist-air and seawater entropies. Nonetheless, my aim is to clearly show to the Editor (and to young and future generations reading the preprint and my Comment and Reply to Rainer Feistel) that the reference values have real impact on many kinds.
Moreover, since Rainer Feistel admits that vertical profiles, vertical sections and entropy diagrams are influenced by these arbitrary choices of reference entropies, he should at least offer as a possibility the calculations of the absolute moist-air and seawater entropies.
I want to recall that it is easy to add simple extra terms for computing draft versions of both the atmospheric and seawater absolute entropies and the liquid-water proxy value from the standard (TEOS10, equivalent) proxy formulations. However, it would be worthwhile redoing the TEOS10 settings/tunings without making arbitrary assumptions while imposing the absolute values of the reference entropies, going beyond the additional terms that I indicate and which are likely of the first order (especially for the ocean).
I recall in the Section 2 that the saturation-pressure relationship (1) derived by Nernst (1918), Planck (1921), Nernst (1921) and Nernst (1926) depends on the absolute value of the entropy for monatomic gases (used to set the translational part of the statistical entropy for all other polyatomic bodies). The same absolute entropies of bodies are also used to determine the equilibrium constants of all chemical reactions, which in turn determine the (measurable) concentrations of O3 in the atmosphere and sea salts in the seawater, and therefore impact the vertical profile of the (measurable) temperature in the stratosphere, in particular.
I explain in the Section 3 that the constants arbitrarily specified by the 5th (1956) International Conference on Properties of Steam are unclear, presently unavailable, not reproduced elsewhere, and looks like a mere old-fashioned and arbitrary gentlemen agreement.
I explains in the Section 4 that the relativistic reference values have no impact on the computations of absolute values for the thermal energies and entropies (merely describing the variation of translational, rotational and vibrational degrees of freedom for atoms and molecules), simply because present atmospheric and oceanic NWP models and GCMs are not designed to describe the thermodynamic impacts and physical processes of nuclear bombs or nuclear reactors in nuclear plants.
I explain in the Section 5 that there is no large uncertainty in the properties of H2O Ice-Ih, with in particular the residual entropy at 0K needed to make the Calorimetric and the Statistical methods coincide. I show in the Fig.1 the values of the specific heat at constant pressure (cp) plotted as a function of the absolute temperature from 0K to T=273.15K, with the numerical values listed in the Table-2. It is with these numerical values that I have plotted the calorimetric curve in the Fig.2, which show that the Statistical method and the Calorimetric method (including the residual entropy for Ice-Ih H2O) lead to the same results for N2, O2, Ar, CO2 and H2O. If the uncertainty in the properties of Ice-Ih below 100K was as important as suggested by Rainer Feistel, it would have been impossible to get the good agreement between the Statistical and Calorimetric methods (including the residual entropy at 0K).
Moreover I show in the Section 6 unpublished zonal sections (Figs.4), unpublished entropy changes at the Mauna Loa laboratory (Figs.5), and unpublished Climate Change of entropies from NWP models, GCMs, Reanalyses and GIEC simulations (Figs.6). All these unpublished results clearly show that the behaviour of the absolute version of the moist-air entropy is special and cannot be confused with other `equivalent' versions of the `entropies', which often produce results with opposite physical behaviour (vertical gradients and changes with time of different magnitudes, or even opposite signs).
I similarly show in the Section 7 that not only the surface of constant entropy (as shown in another example of zonal section in the Fig.9), but also the isentropic trajectories, depend on the choice of the reference values. This was in particular the aim of the study of H2O plumes (pathways) studied by Adriana Bailey (NCAR). I have shown with Adriana (see the Fig.7 and Fig.8) that these H2O plumes preferentially follow the surface of absolute moist-air entropy, with clear difference with the other arbitrary-reference definitions like the equivalent-proxy one computed by the TEOS10 software (these differences are large in the moist and warmer boundary layers and within the Tropics).
I recall in the Section 8 that the reference values of the energy must have an impact on the computations of the value and flux of the moist-air energy, as already explained by Gibbs (1875-1878), as shown and recalled in the Fig.10.
I explain in the Section 8.1 that the entropyflux of -1.0 W/m2/K mentioned in the preprint and suggested first by Ebeling-Feistel (1982) and then retained as such in Feistel-Ebeling (2011), as shown in the Figs.11, is underestimated: it is more likely of about -1.18 to -1.28 W/m2/K. Rainer Feistel should update this value.
I show in the Section 8.2 how the reference values of the moist-air entropy (20) must impact most of the terms in the moist-air (absolute) entropy equation (19), including the turbulent fluxes of the moist-air (absolute) entropy, but with the notable exception of the current version of the moist-air (absolute) entropy production term.
I recall in the Section 8.3 that the turbulence are presently based in all NWP models and GCMs on flux-gradients relationships of the Betts (1973) variables, which must be generalized to the use of the moist-air absolute entropy itself, or even the associated moist-air absolute entropy potential temperature (according to Richardson, 1919, 1922). As a matter of fact, these turbulent terms are not managed by Rainer Feistel, nor the (absolute) entropy flux, nor the temporal change in (absolute) entropy. This may be of a certain importance for several results shown in the preprint, and with a link with a questions asked by Trevor McDougall (RC1) about the Fig. A.16.1 of the TEOS-10 Manual and the `non-conservative production of entropy'. Rainer Feistel should more clearly explain which kind of moist-air (absolute) entropy equation he consider, and which terms are evaluated versus those discarded? In particular, I show in the Figs.12 that it is needed to use the absolute moist-air variable (or the associated potential temperature) to arrive at the properties mentioned in the preprint by Rainer Feistel and the need to have turbulent `fluxes proportional to its driving force' (in that fully justifying the suggestions of Richardson, 1919a,b, 1922, to use the absolute value of the moist-air entropy).
In the Section 9 I include some remaining developments to better explain why Rainer Feistel is wrong when he wrote that: `Measurable thermodynamic properties in geophysics must be independent of the choice of those conditions, otherwise those quantities are physically improperly specified.' In particular I recalled that the need to define absolute reference entropies is related to the definition of the absolute scale of temperature (Fig.13) and to the principle of unattainability of the absolute zero of the temperature (Fig.14).
All Figures are placed in the last Section 10, located before the references.
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CC2: 'Reply on AC3', Pascal Marquet, 25 Jun 2024
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AC3: 'Reply on CC1', Rainer Feistel, 17 Jun 2024
- CC3: 'Comment on egusphere-2024-1243', Olaf Hellmuth, 28 Jun 2024
- AC4: 'Comment on egusphere-2024-1243', Rainer Feistel, 22 Jul 2024
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Rainer Feistel
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