the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A Thermodynamic Potential of Seawater in terms of Conservative Temperature
Trevor John McDougall
Paul Barker
Rainer Feistel
Fabien Roquet
Abstract. A thermodynamic potential is found for seawater as a function of Conservative Temperature, Absolute Salinity and pressure. From this thermodynamic potential, all the equilibrium thermodynamic properties of seawater can be derived, just as all these thermodynamic properties can be found from the TEOS-10 Gibbs function (which is a function of in situ temperature, Absolute Salinity and pressure). Present oceanographic practice in the Gibbs SeaWater Oceanographic Toolbox uses a polynomial expression for specific volume (and enthalpy) in terms of Conservative Temperature (as well as of Absolute Salinity and pressure), whereas the relationship between in situ temperature and Conservative Temperature is based on the Gibbs function. This mixed practice introduces (numerically small) inconsistencies and superfluous conversions between variables. The proposed thermodynamic potential of seawater, being expressed as an explicit function of Conservative Temperature, overcomes these small numerical inconsistencies, and in addition, the new approach allows for greater computational efficiency in the evaluation of sea surface temperature from Conservative Temperature.
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Trevor John McDougall et al.
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RC1: 'Comment on egusphere-2023-1568', Anonymous Referee #1, 31 Jul 2023
The authors describe the derivation of a new thermodynamic potential tailored to oceanography, in that its native variables are absolute salinity, conservative temperature and pressure. They also detail its analysis, demonstrating its equivalency to the sea water Gibbs function, currently the backbone of the TEOS-10 thermodynamic framework in broad oceanographic use. It is argued this potential represents a cleaner foundation for oceanic thermodynamics and offers a (modest) savings in computations, and propose to use the potential in the next generation of TEOS-10 software.
This is quite a paper. At places, it is heavy going, as is often the case with thermodynamics. Having said that, I find the paper pleasantly readable and the main points relatively clear (subject to a few caveats outlined below). While the authors are quick to emphasize that the practical value of the work is somewhat modest, resulting small increases in computational accuracy and savings in computer time, I am impressed by the intellectual achievement, i.e. the discovery of a new thermodynamic potential. And the roadmap by which one gets there, in its description, illustrates a considerable amount of creativity and insight, as well as practical knowledge of the nuts and bolts of operational oceanographic thermodynamics.
It would be nice if the potential were given a name other than ‘the Thermodynamic Potential \hat{Phi}’.
Ultimately, I recommend this paper for publication and support the transition to the new potential for use in TEOS-10, although the latter might want to be phased in over some trial period while the field gets some experience with its use. I do have three issues of varying degrees of significance which I now raise which the authors may wish to consider in any revisions. I do not see any of them as insurmountable.
First, around line 255 I believe there are a series of typographical errors mostly involving displaced commas and the dropping of the subscript A on absolute salinity. Although minor, these are the sorts of details that can throw the careful reader for a loss. After that, the authors ask the question in section 3.2 about the equivalency of the new potential to the Gibbs, ultimately answering in the affirmative. The presentation is in its own way convincing, but proceeds by connecting the two potentials in a logical way. More traditionally, the informational equivalence of the various classical potentials is demonstrated by showing they are related to one another via Legendre transforms. Is such a demonstration possible in this case? Or, perhaps, by Legendre transforming this new potential, other potentials might be uncovered. Last, around line 260, the statement is made that two of the more useful features of potential enthalpy are that its derivative with respect to conservative temperature is heat capacity and its derivative with respect to absolute Salinity vanishes. This proceeds quite simply from the definitions of potential enthalpy and Conservative temperature, provided that one accepts the reduction of entropy from its dependence on three thermodynamic variables to two, due to its ‘Potential’ property. But, I took it on as an exercise to work my way through the intervening steps, starting with potential enthalpy as a function of salinity and entropy, and introducing a ‘potential entropy’ variable and formally changing coordinates. I was eventually able to arrive at the conclusion of the authors, but it was a bit of work (assuming I have done everything correctly). Would it be at all useful to include such a demonstration in an appendix? Calculations related to this appear around line 410.
Conceptually, I am also interested by the capacity of this new potential to somewhat cleanly separate buoyancy like seawater characteristics from their chemical potential characteristics. I suppose this reflects the very nearly conservative property of Conservative Temperature, but I still suspect there are some profound implications here. I am on the steep part of the learning curve with regards to this paper.
Citation: https://doi.org/10.5194/egusphere-2023-1568-RC1 -
RC2: 'Comment on egusphere-2023-1568', Stephen M. Griffies, 06 Aug 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1568/egusphere-2023-1568-RC2-supplement.pdf
- CC2: 'Comment on egusphere-2023-1568', Remi Tailleux, 07 Sep 2023
Trevor John McDougall et al.
Trevor John McDougall et al.
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