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.
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.
the Creative Commons Attribution 4.0 License.
Empirical evidence of a fluctuation theorem for the wind mechanical power input into the ocean
Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI, 38000 Grenoble, France
Bertrand Chapron
LOPS, Ifremer, Plouzané, France
Related authors
Achim Wirth
EGUsphere, https://doi.org/10.5194/egusphere-2024-3307, https://doi.org/10.5194/egusphere-2024-3307, 2024
Short summary
Short summary
The hydrostatic approximation is the basis of most simulations of ocean and climate dynamics. It is here evaluated by using a projection method in the 4D Fourier space. The evaluation is analytic.
Felipe L. L. Amorim, Julien Le Meur, Achim Wirth, and Vanessa Cardin
Ocean Sci., 20, 463–474, https://doi.org/10.5194/os-20-463-2024, https://doi.org/10.5194/os-20-463-2024, 2024
Short summary
Short summary
Analysis of a high-frequency time series of thermohaline data measured at the EMSO-E2M3A regional facility in the southern Adriatic Pit (SAP) reveals a significant change in the double-diffusive regime in 2017 associated with the intrusion of extremely salty waters into the area, suggesting salt fingering as the dominant regime. The strong heat loss at the surface during this winter allowed deep convection to transport this high-salinity water from the intermediate to deep layers of the pit.
Sofia Flora, Laura Ursella, and Achim Wirth
Nonlin. Processes Geophys., 30, 515–525, https://doi.org/10.5194/npg-30-515-2023, https://doi.org/10.5194/npg-30-515-2023, 2023
Short summary
Short summary
An increasing amount of data allows us to move from low-order moments of fluctuating observations to their PDFs. We found the analytical fat-tailed PDF form (a combination of Gaussian and two-exponential convolutions) for 2 years of sea surface current increments in the Gulf of Trieste, using superstatistics and the maximum-entropy principle twice: on short and longer timescales. The data from different wind regimes follow the same analytical PDF, pointing towards a universal behaviour.
Achim Wirth and Florian Lemarié
Earth Syst. Dynam., 12, 689–708, https://doi.org/10.5194/esd-12-689-2021, https://doi.org/10.5194/esd-12-689-2021, 2021
Short summary
Short summary
We show that modern concepts of non-equilibrium statistical mechanics can be applied to large-scale environmental fluid dynamics, where fluctuations are not thermal but come from turbulence. The work theorems developed by Jarzynski and Crooks are applied to air–sea interaction. Rather than looking at the average values of thermodynamic variables, their probability density functions are considered, which allows us to replace the inequalities of equilibrium statistical mechanics with equalities.
Achim Wirth
Ocean Sci. Discuss., https://doi.org/10.5194/os-2019-128, https://doi.org/10.5194/os-2019-128, 2020
Revised manuscript not accepted
Short summary
Short summary
The input of mechanical power to the ocean due to the surface wind-stress is considered using data from satellites observations. Its dependence on the coarse-graining scale of the atmospheric and oceanic velocity in space and time is determined. The power input is found to increase monotonically with shorter coarse-graining in time. Results show that including the dynamics at scales below a few degrees reduces considerably the power input by air-sea interaction.
Achim Wirth
Nonlin. Processes Geophys., 26, 457–477, https://doi.org/10.5194/npg-26-457-2019, https://doi.org/10.5194/npg-26-457-2019, 2019
Short summary
Short summary
The conspicuous feature of the atmosphere–ocean system is the large difference in the masses of the two media. In this respect there is a strong analogy to Brownian motion, with light and fast molecules colliding with heavy and slow Brownian particles. I apply the tools of non-equilibrium statistical mechanics for studying Brownian motion to air–sea interaction.
Achim Wirth
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2018-300, https://doi.org/10.5194/gmd-2018-300, 2019
Revised manuscript not accepted
Short summary
Short summary
The dynamics of three local linear models of air-sea-interaction commonly employed in climate or ocean simulations is compared. The models differ by whether or not the ocean velocity is included in the shear calculation applied to the ocean and the atmosphere. Analytic calculations for the models with deterministic and random forcing (white and colored) are presented.The fluctuation-dissipation-relation, the fluctuation-dissipation-theorem and the fluctuation-theorem is discussed.
C. Q. C. Akuetevi and A. Wirth
Ocean Sci., 11, 471–481, https://doi.org/10.5194/os-11-471-2015, https://doi.org/10.5194/os-11-471-2015, 2015
C. Q. C. Akuetevi and A. Wirth
Ocean Sci. Discuss., https://doi.org/10.5194/osd-11-753-2014, https://doi.org/10.5194/osd-11-753-2014, 2014
Revised manuscript not accepted
A. Wirth
Nonlin. Processes Geophys., 20, 25–34, https://doi.org/10.5194/npg-20-25-2013, https://doi.org/10.5194/npg-20-25-2013, 2013
Achim Wirth
EGUsphere, https://doi.org/10.5194/egusphere-2024-3307, https://doi.org/10.5194/egusphere-2024-3307, 2024
Short summary
Short summary
The hydrostatic approximation is the basis of most simulations of ocean and climate dynamics. It is here evaluated by using a projection method in the 4D Fourier space. The evaluation is analytic.
Paul Platzer, Pierre Ailliot, Bertrand Chapron, and Pierre Tandeo
Clim. Past, 20, 2267–2286, https://doi.org/10.5194/cp-20-2267-2024, https://doi.org/10.5194/cp-20-2267-2024, 2024
Short summary
Short summary
Old observations are necessary to understand the atmosphere. When direct observations are not available, one can use indirect observations, such as tide gauges, which measure the sea level in port cities. The sea level rises when local air pressure decreases and when wind pushes water towards the coast. Several centuries-long tide gauge records are available. We show that these can be complementary to direct pressure observations for studying storms and anticyclones in the 19th century.
Felipe L. L. Amorim, Julien Le Meur, Achim Wirth, and Vanessa Cardin
Ocean Sci., 20, 463–474, https://doi.org/10.5194/os-20-463-2024, https://doi.org/10.5194/os-20-463-2024, 2024
Short summary
Short summary
Analysis of a high-frequency time series of thermohaline data measured at the EMSO-E2M3A regional facility in the southern Adriatic Pit (SAP) reveals a significant change in the double-diffusive regime in 2017 associated with the intrusion of extremely salty waters into the area, suggesting salt fingering as the dominant regime. The strong heat loss at the surface during this winter allowed deep convection to transport this high-salinity water from the intermediate to deep layers of the pit.
Sofia Flora, Laura Ursella, and Achim Wirth
Nonlin. Processes Geophys., 30, 515–525, https://doi.org/10.5194/npg-30-515-2023, https://doi.org/10.5194/npg-30-515-2023, 2023
Short summary
Short summary
An increasing amount of data allows us to move from low-order moments of fluctuating observations to their PDFs. We found the analytical fat-tailed PDF form (a combination of Gaussian and two-exponential convolutions) for 2 years of sea surface current increments in the Gulf of Trieste, using superstatistics and the maximum-entropy principle twice: on short and longer timescales. The data from different wind regimes follow the same analytical PDF, pointing towards a universal behaviour.
R. Fablet, M. M. Amar, Q. Febvre, M. Beauchamp, and B. Chapron
ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., V-3-2021, 295–302, https://doi.org/10.5194/isprs-annals-V-3-2021-295-2021, https://doi.org/10.5194/isprs-annals-V-3-2021-295-2021, 2021
Achim Wirth and Florian Lemarié
Earth Syst. Dynam., 12, 689–708, https://doi.org/10.5194/esd-12-689-2021, https://doi.org/10.5194/esd-12-689-2021, 2021
Short summary
Short summary
We show that modern concepts of non-equilibrium statistical mechanics can be applied to large-scale environmental fluid dynamics, where fluctuations are not thermal but come from turbulence. The work theorems developed by Jarzynski and Crooks are applied to air–sea interaction. Rather than looking at the average values of thermodynamic variables, their probability density functions are considered, which allows us to replace the inequalities of equilibrium statistical mechanics with equalities.
Anastasiia Tarasenko, Alexandre Supply, Nikita Kusse-Tiuz, Vladimir Ivanov, Mikhail Makhotin, Jean Tournadre, Bertrand Chapron, Jacqueline Boutin, Nicolas Kolodziejczyk, and Gilles Reverdin
Ocean Sci., 17, 221–247, https://doi.org/10.5194/os-17-221-2021, https://doi.org/10.5194/os-17-221-2021, 2021
Short summary
Short summary
Data from the ARKTIKA-2018 expedition and new satellite data help us to follow rapid changes in the upper layer of the Laptev and East Siberian seas (LS, ESS) in summer 2018. With satellite-derived surface temperature, an improved SMOS salinity, and wind, we study how the fresh river water is mixed with cold sea water and ice-melted water at small time and spatial scales. The wind pushes fresh water northward and northeastward, close to and under the ice, forcing it into the deep Arctic Ocean.
Louis Marié, Fabrice Collard, Frédéric Nouguier, Lucia Pineau-Guillou, Danièle Hauser, François Boy, Stéphane Méric, Peter Sutherland, Charles Peureux, Goulven Monnier, Bertrand Chapron, Adrien Martin, Pierre Dubois, Craig Donlon, Tania Casal, and Fabrice Ardhuin
Ocean Sci., 16, 1399–1429, https://doi.org/10.5194/os-16-1399-2020, https://doi.org/10.5194/os-16-1399-2020, 2020
Short summary
Short summary
With present-day techniques, ocean surface currents are poorly known near the Equator and globally for spatial scales under 200 km and timescales under 30 d. Wide-swath radar Doppler measurements are an alternative technique. Such direct surface current measurements are, however, affected by platform motions and waves. These contributions are analyzed in data collected during the DRIFT4SKIM airborne and in situ experiment, demonstrating the possibility of measuring currents from space globally.
Achim Wirth
Ocean Sci. Discuss., https://doi.org/10.5194/os-2019-128, https://doi.org/10.5194/os-2019-128, 2020
Revised manuscript not accepted
Short summary
Short summary
The input of mechanical power to the ocean due to the surface wind-stress is considered using data from satellites observations. Its dependence on the coarse-graining scale of the atmospheric and oceanic velocity in space and time is determined. The power input is found to increase monotonically with shorter coarse-graining in time. Results show that including the dynamics at scales below a few degrees reduces considerably the power input by air-sea interaction.
Achim Wirth
Nonlin. Processes Geophys., 26, 457–477, https://doi.org/10.5194/npg-26-457-2019, https://doi.org/10.5194/npg-26-457-2019, 2019
Short summary
Short summary
The conspicuous feature of the atmosphere–ocean system is the large difference in the masses of the two media. In this respect there is a strong analogy to Brownian motion, with light and fast molecules colliding with heavy and slow Brownian particles. I apply the tools of non-equilibrium statistical mechanics for studying Brownian motion to air–sea interaction.
Thomas Holding, Ian G. Ashton, Jamie D. Shutler, Peter E. Land, Philip D. Nightingale, Andrew P. Rees, Ian Brown, Jean-Francois Piolle, Annette Kock, Hermann W. Bange, David K. Woolf, Lonneke Goddijn-Murphy, Ryan Pereira, Frederic Paul, Fanny Girard-Ardhuin, Bertrand Chapron, Gregor Rehder, Fabrice Ardhuin, and Craig J. Donlon
Ocean Sci., 15, 1707–1728, https://doi.org/10.5194/os-15-1707-2019, https://doi.org/10.5194/os-15-1707-2019, 2019
Short summary
Short summary
FluxEngine is an open-source software toolbox designed to allow for the easy and accurate calculation of air–sea gas fluxes. This article describes new functionality and capabilities, which include the ability to calculate fluxes for nitrous oxide and methane, optimisation for running FluxEngine on a stand-alone desktop computer, and extensive new features to support the in situ measurement community. Four research case studies are used to demonstrate these new features.
Achim Wirth
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2018-300, https://doi.org/10.5194/gmd-2018-300, 2019
Revised manuscript not accepted
Short summary
Short summary
The dynamics of three local linear models of air-sea-interaction commonly employed in climate or ocean simulations is compared. The models differ by whether or not the ocean velocity is included in the shear calculation applied to the ocean and the atmosphere. Analytic calculations for the models with deterministic and random forcing (white and colored) are presented.The fluctuation-dissipation-relation, the fluctuation-dissipation-theorem and the fluctuation-theorem is discussed.
Fabrice Ardhuin, Yevgueny Aksenov, Alvise Benetazzo, Laurent Bertino, Peter Brandt, Eric Caubet, Bertrand Chapron, Fabrice Collard, Sophie Cravatte, Jean-Marc Delouis, Frederic Dias, Gérald Dibarboure, Lucile Gaultier, Johnny Johannessen, Anton Korosov, Georgy Manucharyan, Dimitris Menemenlis, Melisa Menendez, Goulven Monnier, Alexis Mouche, Frédéric Nouguier, George Nurser, Pierre Rampal, Ad Reniers, Ernesto Rodriguez, Justin Stopa, Céline Tison, Clément Ubelmann, Erik van Sebille, and Jiping Xie
Ocean Sci., 14, 337–354, https://doi.org/10.5194/os-14-337-2018, https://doi.org/10.5194/os-14-337-2018, 2018
Short summary
Short summary
The Sea surface KInematics Multiscale (SKIM) monitoring mission is a proposal for a future satellite that is designed to measure ocean currents and waves. Using a Doppler radar, the accurate measurement of currents requires the removal of the mean velocity due to ocean wave motions. This paper describes the main processing steps needed to produce currents and wave data from the radar measurements. With this technique, SKIM can provide unprecedented coverage and resolution, over the global ocean.
C. Q. C. Akuetevi and A. Wirth
Ocean Sci., 11, 471–481, https://doi.org/10.5194/os-11-471-2015, https://doi.org/10.5194/os-11-471-2015, 2015
C. Q. C. Akuetevi and A. Wirth
Ocean Sci. Discuss., https://doi.org/10.5194/osd-11-753-2014, https://doi.org/10.5194/osd-11-753-2014, 2014
Revised manuscript not accepted
A. Wirth
Nonlin. Processes Geophys., 20, 25–34, https://doi.org/10.5194/npg-20-25-2013, https://doi.org/10.5194/npg-20-25-2013, 2013
Related subject area
Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
Superstatistical analysis of sea surface currents in the Gulf of Trieste, measured by high-frequency radar, and its relation to wind regimes using the maximum-entropy principle
Physically constrained covariance inflation from location uncertainty
Rain process models and convergence to point processes
A waveform skewness index for measuring time series nonlinearity and its applications to the ENSO–Indian monsoon relationship
Recurrence analysis of extreme event-like data
Beyond univariate calibration: verifying spatial structure in ensembles of forecast fields
Vertical profiles of wind gust statistics from a regional reanalysis using multivariate extreme value theory
On fluctuating momentum exchange in idealised models of air–sea interaction
Sofia Flora, Laura Ursella, and Achim Wirth
Nonlin. Processes Geophys., 30, 515–525, https://doi.org/10.5194/npg-30-515-2023, https://doi.org/10.5194/npg-30-515-2023, 2023
Short summary
Short summary
An increasing amount of data allows us to move from low-order moments of fluctuating observations to their PDFs. We found the analytical fat-tailed PDF form (a combination of Gaussian and two-exponential convolutions) for 2 years of sea surface current increments in the Gulf of Trieste, using superstatistics and the maximum-entropy principle twice: on short and longer timescales. The data from different wind regimes follow the same analytical PDF, pointing towards a universal behaviour.
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron
Nonlin. Processes Geophys., 30, 237–251, https://doi.org/10.5194/npg-30-237-2023, https://doi.org/10.5194/npg-30-237-2023, 2023
Short summary
Short summary
This paper provides perspective that the displacement vector field of physical state fields should be determined by the tensor fields associated with the physical fields. The advantage of this perspective is that certain physical quantities can be conserved while applying a displacement vector field to transfer the original physical field. A direct application of this perspective is the physically constrained covariance inflation scheme proposed in this paper.
Scott Hottovy and Samuel N. Stechmann
Nonlin. Processes Geophys., 30, 85–100, https://doi.org/10.5194/npg-30-85-2023, https://doi.org/10.5194/npg-30-85-2023, 2023
Short summary
Short summary
Rainfall is erratic and difficult to predict. Thus, random models are often used to describe rainfall events. Since many of these random models are based more on statistics than physical laws, it is desirable to develop connections between the random statistical models and the underlying physics of rain. Here, a physics-based model is shown to converge to a statistics-based model, which helps to provide a physical basis for the statistics-based model.
Justin Schulte, Frederick Policelli, and Benjamin Zaitchik
Nonlin. Processes Geophys., 29, 1–15, https://doi.org/10.5194/npg-29-1-2022, https://doi.org/10.5194/npg-29-1-2022, 2022
Short summary
Short summary
The skewness of a time series is commonly used to quantify the extent to which positive (negative) deviations from the mean are larger than negative (positive) ones. However, in some cases, traditional skewness may not provide reliable information about time series skewness, motivating the development of a waveform skewness index in this paper. The waveform skewness index is used to show that changes in the relationship strength between climate time series could arise from changes in skewness.
Abhirup Banerjee, Bedartha Goswami, Yoshito Hirata, Deniz Eroglu, Bruno Merz, Jürgen Kurths, and Norbert Marwan
Nonlin. Processes Geophys., 28, 213–229, https://doi.org/10.5194/npg-28-213-2021, https://doi.org/10.5194/npg-28-213-2021, 2021
Josh Jacobson, William Kleiber, Michael Scheuerer, and Joseph Bellier
Nonlin. Processes Geophys., 27, 411–427, https://doi.org/10.5194/npg-27-411-2020, https://doi.org/10.5194/npg-27-411-2020, 2020
Short summary
Short summary
Most verification metrics for ensemble forecasts assess the representation of uncertainty at a particular location and time. We study a new diagnostic tool based on fractions of threshold exceedance (FTE) which evaluates an additional important attribute: the ability of ensemble forecast fields to reproduce the spatial structure of observed fields. The utility of this diagnostic tool is demonstrated through simulations and an application to ensemble precipitation forecasts.
Julian Steinheuer and Petra Friederichs
Nonlin. Processes Geophys., 27, 239–252, https://doi.org/10.5194/npg-27-239-2020, https://doi.org/10.5194/npg-27-239-2020, 2020
Short summary
Short summary
Many applications require wind gust estimates at very different atmospheric altitudes, such as in the wind energy sector. However, numerical weather prediction models usually only derive estimates for gusts at 10 m above the land surface. We present a statistical model that gives the hourly peak wind speed. The model is trained based on a weather reanalysis and observations from the Hamburg Weather Mast. Reliable predictions are derived at up to 250 m, even at unobserved intermediate levels.
Achim Wirth
Nonlin. Processes Geophys., 26, 457–477, https://doi.org/10.5194/npg-26-457-2019, https://doi.org/10.5194/npg-26-457-2019, 2019
Short summary
Short summary
The conspicuous feature of the atmosphere–ocean system is the large difference in the masses of the two media. In this respect there is a strong analogy to Brownian motion, with light and fast molecules colliding with heavy and slow Brownian particles. I apply the tools of non-equilibrium statistical mechanics for studying Brownian motion to air–sea interaction.
Cited articles
Bentamy, A., Grodsky, S. A., Elyouncha, A., Chapron, B., and Desbiolles, F.: Homogenization of scatterometer wind retrievals, Int. J. Climatol., 37, 870–889, 2017. a
Bentamy, A., Piollé, J. F., and Prevos, C.: Global Ocean Wind L4 Reprocessed 6 hourly Observations, CMEMS [data set], available at:
https://resources.marine.copernicus.eu/?option=com_csw&view=details&product_id=WIND_GLO_WIND_L4_REP_OBSERVATIONS_012_006, last access: 1 May 2019. a
Bernie, D., Guilyardi, E., Madec, G., Slingo, J., and Woolnough, S.: Impact of resolving the diurnal cycle in an ocean–atmosphere GCM. Part 1: A diurnally forced OGCM, Clim. Dynam., 29, 575–590, 2007. a
Boffetta, G. and Ecke, R. E.: Two-dimensional turbulence, Annu. Rev. Fluid Mech., 44, 427–451, 2012. a
Bonjean, F. and Lagerloef, G. S.: Diagnostic model and analysis of the surface currents in the tropical Pacific Ocean, J. Phys. Oceanogr., 32, 2938–2954, 2002. a
Bye, J. A.: Large-scale momentum exchange in the coupled atmosphere-ocean, in: Elsevier oceanography series, Elsevier, Amsterdam, Netherlands, 40, 51–61, 1985. a
Csanady, G. T.: Air-sea interaction: laws and mechanisms, Cambridge University Press, Cambridge, United Kingdom, https://doi.org/10.1017/CBO9781139164672, 2001. a
Derrida, B.: Non-equilibrium steady states: fluctuations and large deviations of the density and of the current, J. Stat. Mech.-Theory E., 2007, P07023, https://doi.org/10.1088/1742-5468/2007/07/P07023, 2007. a
Desbiolles, F., Bentamy, A., Blanke, B., Roy, C., Mestas-Nuñez, A. M., Grodsky, S. A., Herbette, S., Cambon, G., and Maes, C.: Two decades [1992–2012] of surface wind analyses based on satellite scatterometer observations, J. Marine Syst., 168, 38–56, 2017. a
Duhaut, T. H. and Straub, D. N.: Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation, J. Phys. Oceanogr., 36, 202–211, 2006. a
Einstein, A.: Zur theorie der Brownschen Bewegung, Ann. Phys., 324, 371–381, 1906. a
Einstein, A.: Investigations on the Theory of the Brownian Movement, Courier Corporation, Dover, ISBN 0486603040, 9780486603049, 1956. a
Etienne, H.: Global Total Surface and 15m Current (COPERNICUS-GLOBCURRENT) from Altimetric Geostrophic Current and Modeled Ekman Current Reprocessing, CMEMS [data set], available at:
https://resources.marine.copernicus.eu/?option=com_csw&view=details&product_id=MULTIOBS_GLO_PHY_REP_015_004, last access: 1 May 2019. a
Evans, D. J., Cohen, E. G., and Morriss, G. P.: Probability of second law violations in shearing steady states, Phys. Rev. Lett., 71, 2401, https://doi.org/10.1103/PhysRevLett.71.2401, 1993. a
Farago, J.: Injected power fluctuations in Langevin equation, J. Stat. Phys., 107, 781–803, 2002. a
Ferrari, R. and Wunsch, C.: Ocean circulation kinetic energy: Reservoirs, sources, and sinks, Annual Review of Fluid Mechanics, 41, 253–282, https://doi.org/10.1146/annurev.fluid.40.111406.102139, 2009. a
Gallavotti, G. and Cohen, E. G.: Dynamical ensembles in nonequilibrium statistical mechanics, Phys. Rev. Lett., 74, 2694, https://doi.org/10.1103/PhysRevLett.74.2694, 1995a. a, b, c, d
Perrin, J.: Atomes (Les), CNRS Editions, Paris, ISBN: 978-2-271-08260-2, 2014. a
Rákos, A. and Harris, R.: On the range of validity of the fluctuation theorem for stochastic Markovian dynamics, J. Stat. Mech.-Theory E., 2008, P05005, https://doi.org/10.1088/1742-5468/2008/05/P05005, 2008. a
Renault, L., McWilliams, J. C., and Masson, S.: Satellite Observations of Imprint of Oceanic Current on Wind Stress by Air-Sea Coupling, Scientific Reports, 7, 17747, https://doi.org/10.1038/s41598-017-17939-1, 2017. a, b
Rimac, A., von Storch, J.-S., and Eden, C.: The total energy flux leaving the ocean's mixed layer, J. Phys. Oceanogr., 46, 1885–1900, 2016. a
Seifert, U.: Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys., 75, 126001, https://doi.org/10.1088/0034-4885/75/12/126001, 2012. a, b, c, d
Seneviratne, S. I., Nicholls, N., Easterling, D., Goodess, C. M., Kanae, S., Kossin, J., Luo, Y., Marengo, J., Mc Innes, K., Rahimi, M., Reichstein, M., Sorteberg, A., Vera, C., Zhang, X., Alexander, L. V., Allen, S., Benito, G., Cavazos, T., Clague, J., Conway, D., Della-Marta, P. M., Gerber, M., Gong, S., Goswami, B. N., Hemer, M., Huggel, C., van den Hurk, B., Kharin, V. V., Kitoh, A., Klein Tank, A. M. G., Li, G., Mason, S. J., McGuire, W., van Oldenborgh, G. J., Orlowsky, B., Smith, S., Thiaw, W., Velegrakis, A., Yiou, P., Zhang, T., Zhou, T., and Zwiers, F. W.: Changes in climate extremes and their impacts on the natural physical environment, in: Managing the risks of extreme events and disasters to advance climate change adaptation: Special report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom, 109–230, 2012. a
Shang, X.-D., Tong, P., and Xia, K.-Q.: Test of steady-state fluctuation theorem in turbulent Rayleigh–Bénard convection, Phys. Rev. E, 72, 015301, https://doi.org/10.1103/PhysRevE.72.015301, 2005. a, b, c
Stocker, T. F., Qin, D., Plattner, G., Tignor, M., Allen, S., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P.: Climate change 2013: the physical science basis. Intergovernmental panel on climate change, working group I contribution to the IPCC fifth assessment report (AR5), Cambridge, United Kingdom, https://doi.org/10.1017/CBO9781107415324, 2013. a
Sudre, J., Maes, C., and Garçon, V.: On the global estimates of geostrophic and Ekman surface currents, Limnology and Oceanography: Fluids and Environments, 3, 1–20, 2013. a
Terray, P., Kamala, K., Masson, S., Madec, G., Sahai, A., Luo, J.-J., and Yamagata, T.: The role of the intra-daily SST variability in the Indian monsoon variability and monsoon-ENSO–IOD relationships in a global coupled
model, Clim. Dynam., 39, 729–754, 2012. a
Van Zon, R. and Cohen, E.: Extended heat-fluctuation theorems for a system with deterministic and stochastic forces, Phys. Rev. E, 69, 056121, https://doi.org/10.1103/PhysRevE.69.056121, 2004. a
Wirth, A.: A Fluctuation–Dissipation Relation for the Ocean Subject to Turbulent Atmospheric Forcing, J. Physical. Oceanogr., 48, 831–843, 2018. a
Wirth, A.: On fluctuating momentum exchange in idealised models of air–sea interaction, Nonlin. Processes Geophys., 26, 457–477, https://doi.org/10.5194/npg-26-457-2019, 2019. a, b, c, d
Zhou, S., Zhai, X., and Renfrew, I. A.: The impact of high-frequency weather systems on SST and surface mixed layer in the central Arabian Sea, J. Geophys. Res.-Oceans, 123, 1091–1104, 2018. a
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.
In non-equilibrium statistical mechanics, which describes forced-dissipative systems such as...