the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Working at the limit: A review of thermodynamics and optimality of the Earth system
Axel Kleidon
Abstract. Optimality concepts related to energy and entropy have long been proposed in Earth system science, yet they remain obscure, seem contradictory regarding their goal to either maximize or minimize, and have so far only played marginal roles. This review aims to clarify the role of thermodynamics and optimality in Earth system science by showing that it plays a pivotal role in how, and how much, work can be derived from the solar forcing, and that this imposes a major constraint to the dynamics of dissipative structures of the Earth system. This is, however, not as simple as it may sound. It requires a consistent formulation of Earth system processes in thermodynamic terms, including their linkages and interactions. Thermodynamics then constrains the ability of the Earth system to derive work and generate free energy from the solar radiative forcing, which limits the ability to maintain motion, mass transport, geochemical cycling, and biotic activity. It thus limits directly the generation of atmospheric motion and other processes indirectly through their need for transport, such as hydrologic cycling or biotic activity. I demonstrate the application of this thermodynamic Earth system view by deriving first-order estimates associated with atmospheric motion, hydrologic cycling, and terrestrial productivity that agree very well with observations. This supports the notion that the emergent simplicity and predictability inherent in observed climatological variations can be attributed to these processes working as hard as they can, reflecting thermodynamic limits directly or indirectly. I discuss how this thermodynamic interpretation is consistent with established theoretical concepts in the respective disciplines, interpret other optimality concepts in light of this thermodynamic Earth system view, and describe its utility for Earth system science.
Axel Kleidon
Status: final response (author comments only)
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RC1: 'Comment on esd-2022-38', Anonymous Referee #1, 20 Sep 2022
The manuscript "Working at the limit: A review of thermodynamics and optimality of the Earth system" by Axel Kleidon features a review of several mechanisms involving optimality principles and thermodynamics constraints in energy conversions throughout the climate system. In particular, three examples are provided, about the atmospheric mean meridional circulation, the hydrological cycle and the productivity of the terrestrial biosphere. The specimens, though self-consistent, are related in order to discuss the different degrees of efficiency in energy conversion and work production, and comparisons between proposed conceptual models and observations are provided.
Overall, I think that the review is well written, focused on the aim of stimulating further research on the investigation of the climate system (in the wide sense, including the biogeochemical "layer") from the point of view of thermodynamic constraints. I do acknowledge, though, that there has been a lot of criticism on the motivation behind and the application of these approaches, and I believe that they should be more extensively addressed in this manuscript. I also think that this review might be a valid reference on the topic, that is why I recommend that the manuscript is accepted for publication, provided that a more robust set of references is included, and that the mentioned criticisms are taken into account, along with the specific comments and technical corrections proposed below.
Specific comments
- ll. 35-37: here and elsewhere in the text, I believe that a more complete framework of the research literature on methods of computation of the entropy budget in the climate system. I can think, among others, of Goody 2000, Raymond 2013, Bannon 2015, Bannon and Lee 2017, Lucarini and Pascale 2014, Lembo et al. 2019...
- l. 50: as the manuscript here proposed is a review, when the MEP principle is introduced, I think it is also worth informing the reader that the concept has not been unanimously accepted by the community in their theoretical derivation. I can think of Dewar 2007 or Grinstein and Linsker 2007, as examples of this ongoing debate...
- l. 130 and ll. 142-143: not sure I get the point here. Of course, it is impossible to evaluate the entropy production of the system in a microscopic sense, as jumps of quanta of energy. Is it relevant at all in this context?
- l. 148: when I think of heat transport in the atmospheric medium, I do not see molecular diffusion as a mean of transport that is relevant in the macroscopic scale.
- l. 152: it would be interesting to know a bit more about what the author means when talking about "forms" of entropy, as it is not entirely clear at this point of the manuscript;
- l. 172: maybe "entropy change"?
- l. 173: related to my previous comment, if we are talking of "free energy" as a form of energy that is converted with no change of entropy, that would surely not be dissipation. That is why I am a bit confused by the whole definition of "free energy" that is proposed in this context. Could the author clarify on this point?
- Figure 3: not sure I understood what is included in the term "Generation", although it is somewhat described in the text;
- l. 206: as far as I understand it, there are several more general ways to describe a thermodynamic cycle.
- ll. 241-242: this is in general not true, I believe. Despite the fact that you can of course have frictional dissipation anywhere, the contribution to the energy reservoirs is almost negligible, and I cannot think how it can affect the transport, at least in the atmosphere.
- ll. 306-307: I think that a similar formulation for the Carnot cycle within the climate system was provided in Pauluis and Held, 2002.
- l. 369: I think it is a bit misleading to suggest that the use of conceptual models is meant to facilitate proving a point in front of a reader. There is an illuminating communication by Isaac Held on the importance of establishing a hierarchy of models in order to understand how the climate system works, that might be of interest in this context (Held, 2005).
- ll. 436-438: as stated at the beginning, I am not again speculative arguments, but I find it hard to agree with this sentence, just because observations are in rough agreement with the proposed conceptual model.
- l. 449: if this was the aim, it would have been useful to give numbers in order to compare the different contributions. Maybe some table would have been helpful.
- l. 464: it seems to me that you are rather arguing here that the conceptual model that has been designed in order to be consistent with observations is maximizing the energy conversions based on some thermodynamic constraints. Still, there is a missing step before one can claim that the atmosphere is actually operating at its maximum.
- ll. 469-470: but this is something you can also achieve by computing the material entropy production in the Lorenz Energy Cycle, as shown elsewhere (cfr. Lucarini et al. 2014, Lembo et al. 2019).
- ll. 551-553: shouldn’t the phase changes also taken into account here? (cfr. Pauluis and Held 2002).
- ll. 607-609: I have nothing again these approximate calculations, but there are so many assumptions here that I really have the feeling no conclusions can be easily drawn here.
Typos and technical corrections
- l. 17: incredible -> incredibly;
- l. 95: add "were" between "thermodynamics" and "developed";
- l. 527: missing reference;
References
- Bannon, P. R.: Entropy Production and Climate Efficiency, J. Atmos. Sci., 72, 3268–3280, 2015
- Bannon, P. R. and Lee, S.: Toward Quantifying the Climate Heat Engine: Solar Absorption and Terrestrial Emission Temperatures and Material Entropy Production, J. Atmos. Sci., 74, 1721–1734, 2017
- Dewar, R. C.: Maximum entropy production and the fluctuation theorem. J. Phys., 38A, L371, 2005
- Goody, R.: Sources and sinks of climate entropy, Q. J. Roy. Meteorol. Soc., 126, 1953–1970, 2000
- Grinstein, G., and R. Linsker: Comments on a derivation and application of the “maximum entropy production” principle. J. Phys., 40A, 9717, 2007
- Held, I. M. The Gap between Simulation and Understanding in Climate Modeling, Bulletin of the American Meteorological Society, 86(11), 1609-1614, 2005
- Lucarini, V.: Thermodynamic efficiency and entropy production in the climate system, Physical Review E – Statistical, Nonlinear, and Soft Matter Physics, 80, 1–5, 2009
- Lucarini, V. and Pascale, S.: Entropy production and coarse graining of the climate fields in a general circulation model, Clim. Dynam., 43, 981–1000, 2014
- Lucarini, V., Blender, R., Herbert, C., Ragone, F., Pascale, S., and Wouters, J.: Mathematical and physical ideas for climate science, Rev. Geophys., 52, 809–859, 2014
- Pauluis, O. and Held, I. M.: Entropy Budget of an Atmosphere in Radiative–Convective Equilibrium. Part I: Maximum Work and Frictional Dissipation, J. Atmos. Sci., 59, 125–139
- Raymond, D. J.: Sources and sinks of entropy in the atmosphere, J. Adv. Model. Earth Syst., 5, 755–763, 2013
Citation: https://doi.org/10.5194/esd-2022-38-RC1 - AC1: 'Reply on RC1', Axel Kleidon, 06 Feb 2023
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RC2: 'Comment on esd-2022-38', Remi Tailleux, 04 Oct 2022
This review provides an interesting perspective on the various optimality principles --- such as maximising or minimising entropy production, power, or dissipation --- that have been proposed as possible macro thermodynamic laws capable of accounting for some of the observed emergent properties of the Earth climate system. Overall, I find the review clearly written and making some valid and important points, such as the need to distinguish whether irreversible entropy production results from the destruction of free energy or just from passive diffusion of heat within the background stratification. Still, I think that some crucial concepts used by the author are imprecise and would benefit from clarification, as indicated in the comments below.
Major comments
Free energy versus exergy versus APE. I find the discussion of the concepts of free energy versus exergy versus APE somewhat confusing and unclear. In Tailleux (2013) cited by the author, I interpreted exergy as the available energy defined relative to a state of thermodynamic equilibrium with uniform temperature, and APE as available energy defined relative to a state of minimum potential energy obtained from the actual state by means of an adiabatic re-arrangement of mass as per Lorenz (1955) theory. In my mind, there is a significant difference between the two, as transforming exergy into useful work cannot be done without simultaneously destroying exergy and creating entropy irreversibly. In contrast, APE can be converted into useful work (kinetic energy) without the need to destroy any of it nor creating entropy irreversibly. In this regard, APE appears to be a `freer’ form of free energy than exergy. Can the author try to highlight the differences and inter-relations between the different concepts? Does the author define free energy relative to thermodynamic equilibrium, or does he also consider that APE is a form of free energy? An advantage of the exergy concept is that it provides a clear explanation of where the free energy comes from, i.e., from the convexity of the internal energy. If internal energy was not a convex function of entropy, it would not be possible to transform `heat’ into `work’.
Dissipation/generation. It is not clear to me what the author means by ‘dissipation’ or `generation’. As regards dissipation, does the author mean ‘viscous dissipation’ or does his definition also include APE dissipation by diffusive processes, which Tailleux (2009) argued should be regarded as an additional form of Joule heating similar to viscous dissipation? The concept of APE dissipation seems important, because for simple fluids, it is proportional to the rate of irreversible entropy production by diffusive fluxes of heat, which means that there is a link between the production of entropy production due to the destruction of APE (viewed as a form of free energy) and the entropy production due to passive or dynamically inert heat diffusion through the background reference stratification. As regards ‘generation’, it seems to me that it is an ambiguous term. Indeed, I’d like to point out that in the oceans, for instance, oceanographers still do not agree on how to define the power input due to surface buoyancy fluxes as discussed in Tailleux (2010).
On the role of moisture. I believe that the author makes an important point in pointing out that the climate system differs from the kind of heat engines considered in textbooks in that the net heating and cooling are not fixed but to be obtained as part of the solution. Regarding the role of moisture, the author may be aware that Laliberte et al. (2015) have argued that moisture reduces the efficiency of the atmospheric heat engine relative to a dry one. It would be of interest if the author could comment on this and whether he agrees or disagrees from his perspective.
Carnot efficiency versus maximum power efficiency. The author cites a number of studies related to maximum power. Wouldn’t it be relevant to cite endoreversible heat engines and the ideas of Curzon-Ahlborn here?
Minor comments
Abstract. I find the first sentence to be particularly obscure. Could the author be somewhat more specific? Second line: what does ‘it plays’ refer to? If this refers to ‘thermodynamics and optimality’, plural should be used.
Lines 23-26. Could the author be more specific about the `simplicity’ of the examples discussed? This seems to be a bit subjective and left to the appreciation of readers.
Line 87. Might be important that entropy increases irreversibly only in closed systems.
Lines 180. Free energy budgets are important. It seems to me that these are widely used but not called that way. What about APE budgets or the kind of available energy budgets considered by Bannon and co-authors for instance? Could the author be more specific about what he has in mind exactly? What is his definition of free energy?
Line 184: `These all can be formulated in terms of free energy budgets, a concept that is rarely used in Earth system sciences’ I am not sure that this is true, as for me, APE budgets or budgets of available energy represent ‘free energy budgets’ so the author needs to explain what a ‘free energy budget’ would look like and provide examples.
Line 233 – This derivation of the Carnot limit is general and quite different to common textbook derivations. I am a bit puzzled by this statement, as this is the derivation of the Carnot efficiency I am used to, and the one I was taught as an undergrad.
Line 240 – is given by G = D. This may be the case but because I think that there is no consensus about how to define G and D unambiguously in all cases (see my remarks about APE dissipation above), as is the case in the oceans for instance, it is unclear how to link MEP and ideas of maximum power or dissipation in the most general case.
Lines 275-277. What about endoreversible engines and the Curzon-Ahlborn efficiency?
Lines 376 – Against friction. As well as against APE dissipation may be.
Lines 385-390. This assumes that we understand how to define and quantify both power and dissipation in all possible cases, but I don’t think this is true, e.g., discussion in Tailleux (2010) for the oceanic case.
Line 443 – Here the author uses the term ‘frictional dissipation’ where he only used ‘dissipation’ before. See the need for clarifying the term ‘dissipation’ in major comments above.
Line 450 – I agree that this is a particularly important point that I think will need to be more fully recognised and expanded upon in the future.
Line 463 – ‘so that these conversions neither generate nor dissipate free energy’ This is true only for APE but would not apply to exergy for instance, whose transformation into useful work requires destruction.
Line 527 – GPCP – missing reference
References
Bannon, P. Atmospheric available energy https://doi.org/10.1175/JAS-D-12-059.1
Laliberte et al. 2015. Constrained work output of the moist atmospheric heat engine in a warming clime. DOI: 10.1126/science.1257103
Tailleux R. 2009. On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models, and the ocean heat engine controversy. https://doi.org/10.1017/S002211200999111X
Tailleux, R. 2010. Entropy versus APE production: on the buoyancy power input in the oceans energy cycle. https://doi.org/10.1029/2010GL044962
Citation: https://doi.org/10.5194/esd-2022-38-RC2 - AC2: 'Reply on RC2', Axel Kleidon, 06 Feb 2023
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RC3: 'Comment on esd-2022-38', Jonas Nycander, 09 Oct 2022
The comment was uploaded in the form of a supplement: https://esd.copernicus.org/preprints/esd-2022-38/esd-2022-38-RC3-supplement.pdf
- AC3: 'Reply on RC3', Axel Kleidon, 06 Feb 2023
Axel Kleidon
Axel Kleidon
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