Empirical evidence of a fluctuation theorem for the wind mechanical power input into the ocean

Wirth, Achim; Chapron, Bertrand

doi:https://doi.org/10.5194/npg-28-371-2021

Articles | Volume 28, issue 3

https://doi.org/10.5194/npg-28-371-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/npg-28-371-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 28, issue 3

Research article

|

04 Aug 2021

Research article |

| 04 Aug 2021

Empirical evidence of a fluctuation theorem for the wind mechanical power input into the ocean

Achim Wirth and Bertrand Chapron

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Final revised paper (published on 04 Aug 2021)
Preprint (discussion started on 02 Oct 2020)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'review', Anonymous Referee #1, 20 Oct 2020
RC2: 'Review', Anonymous Referee #2, 12 Nov 2020
AC1: 'Answer to reviewers', Achim Wirth, 01 Dec 2020
AC2: 'revised manuscript with highlighted modifications', Achim Wirth, 01 Dec 2020
EC1: 'Usage of 'extreme' event and 'characteristic' time in manuscript', Balasubramanya Nadiga, 03 Dec 2020
- AC3: 'answer to editor', Achim Wirth, 07 Dec 2020

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Achim Wirth on behalf of the Authors (01 Dec 2020) Manuscript

ED: Referee Nomination & Report Request started (03 Dec 2020) by Balasubramanya Nadiga

RR by Anonymous Referee #1 (14 Dec 2020)

RR by Anonymous Referee #2 (18 Dec 2020)

Suggestions for revision or reasons for rejection

\begin{center} Review of \\
Empirical evidence of a fluctuation theorem for the wind mechanical power input into the ocean by Wirth and Chapron
\end{center}

{\bf Summary and recommendation}: The revised version of this paper only differs in minor ways from the previous one and has not really improved. The more I read the paper, the more I find it confusing. Although it is easy to follow, I think that this paper does not sufficiently pay attention to details, does not sufficiently justify or explain its methodology, and does not critically discuss its results and their robustness enough. The following provides a list of what needs to be improved to meet the scientific standard required for publication. All the issues listed should be addressable relatively easily. All is required is that the authors try to put themselves in the shoes of a regular oceanographer.

{\bf Major Issues} \\
\begin{itemize}
\item {\bf Definition of the wind stress}: The first main issue that I find problematic is the authors’ claim that the wind power input is dominated by the shear stress component of the wind stress without any form of justification to back up this claim. I also find it problematic that the authors never mention or acknowledge the existence of the form stress due to atmospheric pressures fluctuations on surface waves and swell, Grachev et al. (2003) https://doi.org/10.1175/1520-0485(2003)033%3C2408:WSVOOW%3E2.0.CO;2 for instance. As far as I am aware, the ‘wave’ stress is not in general negligible, as it can cause the wind stress direction to be different from that of the wind and drive an atmospheric jet in the regions of light wind, see Hanley and Belcher (2010). Of course, the authors have the right to retain only the shear stress in their calculations if they want to, but they should explicitly acknowledge that this is an approximation that could potentially invalidate their results. Moreover, I also checked the paper by Fairall et al. (2006) cited by the authors as the basis for the wind stress calculations and found that the authors’ approach seems to be different. Indeed, in Fairall et al., the wind stress is calculated as $τ=ρ_a C_d S(U_10-U_o)$, where S is the average atmospheric wind, not the instantaneous wind relative to ocean surface currents. Moreover, it is not clear from the paper what Uo the authors are using in their calculation of the wind stress. The formula should be used with the total surface velocity including both ageostrophic and geostrophic component, but the way the paper is written suggests that the authors may have used the 15 meters velocity instead. It is essential that the authors clarify this point.
\item {\bf Definition of the wind power input}: The second main issue that I find problematic is the authors’ definition of the wind power input. As far as I know, the wind power input is by definition the product of the total wind stress by the total surface oceanic velocity, which can be decomposed as the sum of a geostrophic plus ageostrophic part. I think that the authors are right that a large fraction of the wind power input goes into mixing the mixed layer and ultimately dissipated into heat, but my understanding is that this is related to the ageostrophic work. Indeed, Roquet et al. (2011) https://doi.org/10.1175/JPO-D-11-024.1 provides physical arguments for why the work against the geostrophic component should be the one driving the large-scale circulation. Based on previous work, I would therefore expect that the right way to compute the wind power input would be by using the surface geostrophic component of the GlobCurrent product. What is the justification of using the 15 meters current? Moreover, the GlobCurrent product description says that both the Ekman and geostrophic components, as well as their sum, is available at 15m. Which one do the authors use? This absolutely needs to be clarified. Moreover, it is essential that the computations are repeated by using the surface geostrophic velocity and the computation of the wind stress actually proposed by Fairall et al. (2006).
\item {\bf Negative power input}: The physical meaning of the negative power input events is unclear. If the computations were done for the full wind stress and the ocean surface velocity, they would correspond to instances where momentum is transferred from the ocean to the atmosphere. These events have received some attention in the literature, e.g., Hanley and Belcher (2010) https://doi.org/10.1175/2010JPO4377.1 but these involve the role of swell in regions of light winds. What do these negative events mean here? The authors claim that strong negative events would cause mixing and turbulence (without providing any reference to back up their claim) However, the authors chose the 15 m precisely to avoid this situation, to focus exclusively on a quantity that drives the large-scale circulation, not the turbulence. Doesn’t that suggest that their whole approach is inconsistent?
\end{itemize}

\par \indent
{\bf Specific comments}
\begin{enumerate}
\item Page 1, Line 1: Abstract ‘The ocean dynamics is predominantly driven by the shear-stress between […]’ I don’t think that this is true. As stated in my previous review, the form stress due to pressure fluctuations on surfaces well and swell often represents a significant component of the wind stress, which can even modify the direction of the wind stress relative to that of the wind. In any case, why is it important for the argument that only the shear stress be retained in the calculation rather than the full wind stress? The authors need to explain why they don’t want to include the wave stress in their calculation.
\item Page 1, Line 15: ‘[…] which is described by the fluxes of mechanical power’ Is that the right expression? What is the expression for such fluxes?
\item Page 1, Line 17: ‘In the present work we do not discuss the various physical processes occurring at the air sea interface which are important’ It concerns me that the authors don’t feel it is needed to discuss the physical processes relevant to their argument. The authors need to acknowledge the different contributions making up the wind stress and explain and justify why they neglect the wave stress
\item Page 1, Line 22: ‘The energy exchange is not conservative and most of the mechanical energy is dissipated’ I still do not understand what the authors want to say, and what is the point they are trying to make. The answer does not help.
\item Page 2, Line 24: ‘Furthermore, the research interest […]’ The examples of whether and climate seems ill chosen, since there is as much interest in the fluctuations as in the average. Climate is by definition an averaged quantity, and estimating the state of the atmosphere at any point in time is crucial for initialising weather forecasts.
\item Section Power input. I still don’t understand what the authors are doing. The expression differs from that of Fairall et al. (1996), for which the term within the square root only involves the atmosphere wind, not the wind relative to ocean surface currents, see major issue above.
\item Section 4 – Data. I checked the GlobCurrent product description, and it seems to me that this section does not represent an accurate description. In particular, the GlobCurrent website states that different velocities are provided at either: 1) significant wave height, 2) z=0, 3) z=15m. Moreover, both the Ekman and geostrophic velocity are separately available at z = 0 and z = 15m, which is not acknowledged. The authors need to do a better job at explaining what GlobCurrent actually provides, and which exact quantity they are using, whether it is the geostrophic current only or not.
\item Section 6 – Discussion. ‘We obtain clear evidence that a FT applies to data within the recirculation’ I disagree that this has been scientifically established, because the authors did not test the sensitivity of their conclusions to the various assumptions made. In particular, the authors need to test whether their results still hold if they use the surface geostrophic velocity and the correct expression for the wind stress.
\item Page 9: ‘Extreme negative events lead to strong transfer of energy to small scale turbulence in the atmospheric and oceanic boundary layers, […]’ What is the evidence backing up such a claim? Is this a fact or a speculation? What do they mean by extreme negative events? Doesn’t a negative event correspond to transfer of momentum from the oceans to the atmosphere?
\end{enumerate}

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ED: Reconsider after major revisions (further review by editor and referees) (31 Dec 2020) by Balasubramanya Nadiga

AR by Achim Wirth on behalf of the Authors (25 Jan 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (15 Feb 2021) by Balasubramanya Nadiga

RR by Anonymous Referee #3 (19 May 2021)

RR by Anonymous Referee #4 (02 Jun 2021)

Suggestions for revision or reasons for rejection

In full disclosure, I didn’t know of the existence of the fluctuation theorem before reading this paper, so please forgive me if some of the comments below may appear naïve or out of place.

I am not opposed to the research presented in this manuscript, but I don’t understand who it is addressing. If it is addressed to the GFD community, as the motivations and discussion suggest, more efforts should be made to explain why the FT is important and why should one care about it for the power input into the ocean. Yes, we expect some negative values of power input into the ocean over a certain averaging in time and space, and their probability is linked with those of positive values, but so what? Why are these rare negative events particularly relevant for the dynamics of the ocean? In this manuscript, the discussion of the relevance of FT for ocean dynamics is often hand-wavy or redirected to other articles. From an outsider’s point of view, it looks like the method is blindly applied to the power input without explaining what oceanic knowledge is gained from it. Turbulence has an imprint on many oceanic quantities, why focusing on power input specifically?

Some more specific points are detailed below:

On page 6, the authors argue that the pdfs become more centered around unity as tau increases. I don’t see this. I would argue that they all converge somewhere between 0 and 1, why is this?

Why is the z-axis not always the same for left and right panels, and why isn’t the z range not the same for the curves in each panel? For example, in Figure 1, p(z,tau) 1250 has values between -1 and 1 (pink curve in the left panel). Yet, S(z,tau)/tau has values only until 0.5, shouldn’t S be defined in the range [0 1]?

Page 9 lines 14-16, the authors argue that improbable events are key for the ocean without explaining why. A very simplified consensus in the literature is that most of the mechanical energy input into the ocean comes from the wind while most of the energy dissipation comes from interaction with topography. Are the authors arguing that a non-negligible part of this dissipation occurs via the interaction with the atmosphere itself?

Top of page 10, “This suggests that an increased energy cascade, in the extension of boundary currents …” I don’t understand this argument. First, why should we expect an energy cascade in the extension of boundary currents? Is it a direct or inverse cascade? A baroclinically unstable jet will create eddies in the vicinity of the deformation scale, and these can be recycled in the jet itself or advected away. The resulting energy flux in such a small box around the jet is non-trivial and interactions are most likely dominated by non-local transfers. Second, what is the link between the energy cascade and the likelihood of a negative power input event?

Page 10, paragraph about “FTs in the more general context of climate dynamics”. This paragraph is important if the manuscript is addressed to the GFD community, yet it is very superficial and speculative. The authors should make an effort of developing these points in a more precise manner and add examples with relevant literature.

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ED: Publish subject to minor revisions (review by editor) (08 Jun 2021) by Balasubramanya Nadiga

AR by Achim Wirth on behalf of the Authors (14 Jun 2021) Author's response Author's tracked changes Manuscript

ED: Publish as is (01 Jul 2021) by Balasubramanya Nadiga

AR by Achim Wirth on behalf of the Authors (05 Jul 2021)

Short summary

In non-equilibrium statistical mechanics, which describes forced-dissipative systems such as air–sea interaction, there is no universal probability density function (pdf). Some such systems have recently been demonstrated to exhibit a symmetry called a fluctuation theorem (FT), which strongly constrains the shape of the pdf. Using satellite data, the mechanical power input to the ocean by air–sea interaction following or not a FT is questioned. A FT is found to apply over specific ocean regions.