**The goal of the game is to explore the effects of mitigation and adaptation choices to extreme climate events at the local, regional and global levels**. Can you achieve a greener trajectory than the IPCC RCP 4.5 emission scenario by playing ClimarisQ? Explore the feedback mechanisms (notably physical, but also economic and social) that produce extreme effects on the climate system.

In the game, you make decisions on a continental scale and see the impact of these decisions on the economy, politics and the environment. You will have to deal with extreme events (heat waves, cold waves, heavy rainfall and drought) generated by a real climate model. Then, you will have to try to balance the “popularity”, “ecology” and “finance” gauges as long as possible. Fulfill all the missions to explore different climates. **The game-over displays both the PPM (parts per million) of CO2 deviation from the intermediate scenario of greenhouse gas emissions established by the IPCC (RCP4.5), as well as the number of survival game turns**. These elements stimulate thinking about climate change and motivate the player to do better next time. Thanks to the hazards introduced by the extreme events and cards, every game is different!

**To play the last Web version of ClimarisQ click** here!

**To download and play the last Android/Google version of ClimarisQ click** here!

Geophysical systems are usually described by a set of dynamical equations that are often non-linear and chaotic (Ghil and Lucarini, 2020). Errors about the initial state can grow, shrink, or stay constant with time, depending on error projections onto unstable, stable or neutral subspaces of the dynamical system. The properties of these subspaces can be measured by the Lyapunov exponents (Eckmann and Ruelle, 1985). Knowing the spectrum of Lyapunov exponents is thus immensely important as it can guide prediction strategies or inform decision making (Kalnay, 2003).

In particular, knowledge of the unstable modes can instruct the number of model realizations in an ensemble forecast system, or the deployment of efficient observation network. A notable example is the design of data assimilation (DA) that can be guided by the instability properties of the dynamical system assimilating data. Unfortunately, computing the Lyapunov exponents is extremely costly and computational burden grows quickly with the system’s dimension.

In Chen et al. (2021), we took the opposite viewpoint and showed that it is possible to use the output of DA to infer some fundamental properties of the spectrum of the Lyapunov exponents. Building upon previous studies (Bocquet et al., 2017; Bocquet and Carrassi, 2017), we derived a relation involving the error of DA, the size of the unstable-neutral subspace and the largest Lya- punov exponent.

Our numerical analysis is based on the new Vissio and Lucarini (2020) model, an extension of the Lorenz (1996) system that is able to mimic the co-existence of wave-like and turbulent features in the atmosphere and the interplay between dynamical and thermodynamical variables, in such a way that the Lorenz (1955) energy cycle can be established. Our results demonstrate the robustness of the relation between the skill of DA and the instability property for varying model parameters, especially, as expected, under strong observational constraint. We also look at the Kolmogorov- Sinai entropy, estimated as the a sum of all positive Lyapunov exponents (Eckmann and Ruelle, 1985), which measures the rate at which information is lost, and relate it to the skill of DA. As shown in Figure 1, the first Lyapunov exponent and the Kolmogorov-Sinai entropy appears clearly linearly related to the RMSE of the analysis, as predicted by the theory. Deviations from the linear trend are seen in the weakly unstable cases (see Chen et al. (2021) for rationale of this behaviour).

From the linear relation, our approach implies an efficient way to infer the largest Lyapunov exponent and the Kolmogorov-Sinai entropy under varying model parameters. Although further investigation is needed for more complex scenarios, this study paves the path to exploring the sen- sitivity of model instability to model parameters even in complex, high-dimensional geophysical systems.

**References**

Bocquet, M. and Carrassi, A.: Four-dimensional ensemble variational data assimilation and the unstable subspace, Tellus A: Dynamic Meteorology and Oceanography, 69, 1304504, https://doi.org/10.1080/16000870.2017.1304504, 2017.

Bocquet, M., Gurumoorthy, K. S., Apte, A., Carrassi, A., Grudzien, C., and Jones, C. K. R. T.: Degenerate Kalman Filter Error Covariances and Their Convergence onto the Unsta- ble Subspace, SIAM/ASA Journal on Uncertainty Quantification, 5, 304–333, https://doi.org/ 10.1137/16M1068712, 2017.

Chen, Y., Carrassi, A., and Lucarini, V.: Inferring the instability of a dynamical system from the skill of data assimilation exercises, Nonlinear Processes in Geophysics, 28, 633–649, https://doi.org/10.5194/npg-28-633-2021, 2021.

Eckmann, J. P. and Ruelle, D.: Ergodic theory of chaos and strange attractors, Reviews of Modern Physics, 57, 617–656, 1985.

Ghil, M. and Lucarini, V.: The physics of climate variability and climate change, Rev. Mod. Phys., 92, 035 002, https://doi.org/10.1103/RevModPhys.92.035002, 2020.

Kalnay, E.: Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, Cambridge, 2003.

Lorenz, E.: Available potential energy and the maintenance of the general circulation, Tellus, 7, 157–167, 1955.

Lorenz, E. N.: Predictability – a problem partly solved, in: Predictability of Weather and Climate, edited by Palmer, T. and Hagedorn, R., pp. 40–58, Cambridge University Press, 1996.

Vissio, G. and Lucarini, V.: Mechanics and thermodynamics of a new minimal model of the atmo- sphere, EPJ Plus, 135, 807, https://doi.org/10.1140/epjp/s13360-020-00814-w, 2020.

]]>Attributing extreme events to climate change requires estimating the probability and frequency of the event in a world with and without climate change. These factual and counterfactual worlds can be constructed by using a series of observations which span several decades. Let’s suppose that the series start just after world war 2 and they have a continuous record till today, then the attribution assumes that the first part of the period, e.g. 1948-1978, is not influenced by anthropogenic climate change while the recent past is, e.g. 1991-2021. The event must then be defined: if we set a high threshold on temperature or precipitation amounts, we can then compute the probability of exceeding the threshold in the two worlds and this provides us with the estimate of return time and probability of the event in the two worlds. Another possibility for attribution is to use climate models, with or without anthropogenic forcing and repeat the procedure.

While the procedure seems straightforward, there are many hidden difficulties: the choice of the factual and counterfactual worlds, which leaves to the scientists a certain freedom, but also the choice of the region of interest and of the observable: using the daily maximum temperature rather than the average daily temperature on the same region may lead to different results. Finally, some extremes can be produced by very different dynamical configurations, so that the role of the atmospheric circulation should be taken into account in attribution studies.

To overcome these problems, attribution scientists team together, share data and ideas and critically discuss their findings in an international effort called World Weather Attribution. One of the founders, Geert Jan van Oldenborgh (1961-2021) who sadly passed away recently, greatly contributed to this cause by setting up the Climate Explorer platform, totally open, where everyone can download relevant data for attribution and counter check the validity and the transparency of these studies.

The European Union also supports the effort in attribution as it builds awareness of global climate change and its more impactful events on human society and natural ecosystems. There, at least three large projects on attribution and extreme events running right now thanks to the European Union: XAIDA, CLINT and DAMOCLES. To discover their activities we warmly invite the reader to follow their handles on twitter.

]]>A group of scientists within the Nonlinear Processes in Geosciences (NP) Division of the European Geosciences Union (EGU) is launching in the campfire framework a series of webinars on “Scaling and multifractals: from historical perspectives to recent developments.”

The aim of the **campfire** is to hear first-hand from internationally recognized experts of the field their personal perspectives on scaling and multifractals. They will share their thoughts on the historical background of the field as well as its recent developments and future goals. This unique opportunity, targeted to both early career scientists and established researchers, aims at fostering discussions within the research community to push it toward pursuing past achievements.

To register, send an email to sympa@liste.enpc.fr with subject **subscribe egu_np_campfire_multifractals**.

Registration is free but mandatory. Link to connect will be sent shortly before the webinar.

Website: https://hmco.enpc.fr/scaling-and-multifractals-campfire/.

Schedule (CET used) :

**11/01/2022 10:00-11:30**

Bérengère Dubrulle : “Global and local multifractal analysis”

Daniel Schertzer : “A century of cascades and the emergence of multifractal operators”

**18/01/2022 16:00-17:30**

Shaun Lovejoy : “Multifractals, Intermittency, Spectra and Climate Variability Across Scales”

Witek Krajewski : “Scaling of peak flows in a river network”

**25/01/2022 10:00-11:30**

Andreas Langousis : “Robust estimation of rainfall extremes and their evolution in a changing climate: A CONUS-wide assessment based on multifractal theory”

Adrian Tuck : “Scaling Up: Molecular to Meteorological via Symmetry Breaking”

**01/02/2022 16:00-17:30**

François Schmitt : “Discrete and continuous multifractal cascade models: historical roots and application to turbulence”

Charles Meneveau : “A new multifractal version of Navier-Stokes based model of velocity gradients in turbulence”

Organizing committee:

Auguste Gires (HM&Co – ENPC)

Tommaso Alberti (INAF-IAPS, Italy)

Yongxiang Huang (Xiamen University, China)

Spectral characterization of atmospheric variability has led to the discovery of temporal scaling regimes extending from minutes to millions of years. Instrumental data has allowed us to characterize well the scaling regimes up to decadal timescales, showing a steep non-stationary turbulent regime up to weekly timescales in many atmospheric fields, then transitioning at longer timescales to a rather flat regime first termed the local spectral plateau. This description from steep to flat regimes corresponds to the so-called Hasselman model by this year’s eponymous Nobel laureate. More recently the turbulent regime and spectral plateau were termed weather and macroweather regimes by Lovejoy and Schertzer, and found to have spatially varying scaling exponents. The temporal scaling characteristics of a stochastic process is an indication of its autocorrelation, or memory, and informs us about the underlying dynamics.

The structure of climate variability at longer timescales is still subject of debate, and it is still unclear whether another transition into a non-stationary regime happens due to internal dynamics, and at which timescales. The classical view held that climate variability could be described as a sum of oscillatory processes driven by the Milankovitch orbital forcing and a relatively white background noise. However, spectral analysis of paleoclimate archives over long timescales have invariably shown a scaling background continuum of variability. This implies the existence of nonlinear mechanisms able to redistribute the sharply peaked orbital forcing to other timescales.

The nature of paleoclimate archives poses challenges to spectral analysis as the data are often of irregular resolution. To apply spectral methods which assume regular sampling, it is thus generally necessary to use interpolation in order to regularize the data. Interpolation acts as a filter in the Fourier domain and can significantly bias estimates of scaling exponents. There are interpolation-free alternatives such as the Lomb-Scargle periodogram which can be calculated for arbitrary sampling times.

In this paper, we evaluated the precision and accuracy of three methods to estimate the scaling exponent of irregular surrogate data mimicking paleoclimate archives: the multitaper spectrum with linear interpolation, the Lomb-Scargle periodogram, and the first-order Haar structure function. The latter is a wavelet-based method performed in real space which can be easily adapted to take in irregular data due to the simplicity of the Haar Wavelet. While all methods performed similarly for regular data of stationary timeseries, the interpolation-free methods allowed more accurate estimates for irregular timeseries by utilizing the shorter timescales which were otherwise biased by interpolation. The Lomb-Scargle periodogram however was found unsuitable for non-stationary timeseries and is thus unsuitable to detect the presence of a non-stationary low-frequency regime. The Haar structure function was relatively robust to irregularity and over a wide range of scaling exponents, and is thus a safe choice for the analysis of irregular geophysical timeseries.

]]>These studies [1-3], and the discussion they later sparked in the 70s-80s [5] hinted a quantification of risk for an abrupt climate change due to a sudden nuclear winter, caused by a full-scale nuclear war, or even a large asteroid impact or super-volcano eruption. The idea is simple: such catastrophic events would quickly unleash smog and particulate matter into the atmosphere, covering it from sunlight. In such conditions, if solar radiation cannot reach the Earth’s surface persistently for a few years, then the global temperature will quickly drop. The problem is that even when the sky eventually clears out, if the ground is fully frozen, and sea-ice has developed beyond a critical latitudinal extent, the system cannot return to the warm climate, because the snowball earth is a stable climate. Given the current astronomical configuration, the Earth can exhibit at least two stable climate states, the warm and the snowball; see in Fig. 1 the bifurcation diagram from the EBM used in [3,10], where in red is the Warm branch, in blue the Snowball and in green the unstable branch, versus the non-dimensional parameter μ=S/S0, with S0=1365W/m2. In realistic conditions, transitioning from one state to the other is quite hard and rare. Paleoclimatology studies reveal that the Earth has indeed suffered at least two global glaciations in the past, namely 630 and 715 million years ago, and many less severe ice-ages [6-8].

Building upon [1-3] and with tools from Dynamical systems theory, together with modern climate models, it is possible to not only reconstruct and study the snowball climate state, but also to explore a rich “world” of possible climate states. This viewpoint was recently put forward by Valerio Lucarini and collaborators, where at given physical parameters, the possible climate states can be seen as lying on a high-dimensional dynamical landscape. This allows to unfold the multiscale and multistable nature of one of the most complex physical systems, a planetary climate [4]. By multiscale we identify how climatic characteristics and elements (e.g. rainforests, deserts, circulation patterns, etc.) extend in a multitude of spatial scales. By multistable we describe how stable such climatic characteristics and elements are with respect to temporal scales. More interestingly, this allows for their hierarchical categorization based on their spatial extent and stability properties; see Fig. 2 where one moves from level 1 to 3.

In the late 70s, Klaus Hasselmann [9], using arguments of time-scale separation, proposed the idea of describing the impact of fast weather variables (atmosphere) on slower climatic variables (oceanic, cryosphere, land vegetation etc.) via stochastic perturbations modulated by Gaussian noise; therefore, enhancing climate variability, which was vital for earlier climate models. In the context of Fig. 2, by introducing some form of appropriately defined noise into the system, it is possible to explore the different levels of hierarchy of the underlying dynamical landscape. For instance, in a series of works [10-14] Gaussian perturbations are introduced to the present-day mean of solar irradiance S0 to trigger global transitions between the warm and snowball state in several climate models, ranging from a simple EBM to intermediate complexity climate models with ocean and sea-ice dynamics. This approach not only quantifies the most probable transition paths in this landscape but can also provide an evaluation of the transition probability at a given noise amplitude, as it can estimate the values of the generalized energy barriers that separate the competing stable states. In [14] the authors applied a data-driven manifold learning method to classify regions of stability within the dynamical landscape and even locate a metastable third climate state, colder than our present day warm, but with an ice-free latitudinal band.

Finally, there is a further freedom in the type of the chosen noise, as a noise different than Gaussian can be applied. In a recent preprint [15] the authors chose a Lévy type of noise which is different from Gaussian in the sense that the system can exhibit strong “kicks”. They applied it to an EBM like [3,10] and concluded that transition paths and probabilities will be different when choosing a Gaussian versus a Lévy type of noise. This is seen in Fig. 3, where a 2D coarse-grained projection of the phase space can be obtained by measuring the joint probability density function (PDF) of the system’s evolution considering the globally averaged surface temperature T versus the Equator minus Poles temperature difference ΔΤ. The deterministic attractors are given by the colored points, where red-warm, blue-snowball, green-unstable, and the averaged paths in blue and red. Notice that, sudden and dramatic events, such as massive nuclear war, a large asteroid impact or a super-volcano eruption, mentioned before, could be seen as “kick” events, and therefore well described by a Lévy type of noise. Combining the two types of noise in the same process is also possible. A promising expectation for future directions would be to quantify transition probabilities in local and multistable climatic elements and assess the risk of the associated tipping points [16].

**References**

1. Budyko MI. 1969 The effect of solar radiation variations on the climate of the Earth. Tellus 21, 611–619. https://doi.org/10.3402/tellusa.v21i5.10109

2. Sellers WD. 1969 A global climatic model based on the energy balance of the earth-atmosphere system. J. Appl. Meteorol. 8, 392–400. https://journals.ametsoc.org/view/journals/apme/8/3/1520-0450_1969_008_0392_agcmbo_2_0_co_2.xml

3. Ghil M. 1976 Climate stability for a Sellers-type model. J. Atmos. Sci. 33, 3–20. https://journals.ametsoc.org/view/journals/atsc/33/1/1520-0469_1976_033_0003_csfast_2_0_co_2.xml

4. Ghil M, Lucarini V. 2020 The physics of climate variability and climate change. Rev. Mod. Phys. 92, 035002. https://doi.org/10.1103/RevModPhys.92.035002

5. Oldfield, J.D. (2016), Mikhail Budyko’s (1920–2001) contributions to Global Climate Science: from heat balances to climate change and global ecology. WIREs Clim Change, 7: 682-692. https://doi.org/10.1002/wcc.412

6. Pierrehumbert R, Abbot D, Voigt A, Koll D. 2011 Climate of the neoproterozoic. Annu. Rev. Earth Planet Sci. 39, 417–460. https://doi.org/10.1146/annurev-earth-040809-152447

7. Hoffman PF, Kaufman AJ, Halverson GP, Schrag DP. 1998 A neoproterozoic snowball earth. Science 281, 1342–1346. https://doi.org/10.1126/science.281.5381.1342

8. Hoffman, PF., et al. “Snowball Earth climate dynamics and Cryogenian geology-geobiology.” Science Advances 3.11 (2017): e1600983. https://doi.org/10.1126/sciadv.1600983

9. K. Hasselmann (1976) Stochastic climate models Part I. Theory, Tellus, 28:6, 473-485, https://doi.org/10.3402/tellusa.v28i6.11316

10. Bódai T, Lucarini V, Lunkeit F, Boschi R. 2015 Global instability in the Ghil–Sellers model. Clim. Dyn. 44, 3361–3381. https://doi.org/10.1007/s00382-014-2206-5

11. Lucarini V, Bódai T. 2017 Edge states in the climate system: exploring global instabilities and critical transitions. Nonlinearity 30, R32–R66. https://doi.org/10.1088/1361-6544/aa6b11

12. Lucarini V, Bódai T. 2019 Transitions across melancholia states in a climate model: reconciling the deterministic and stochastic points of view. Phys. Rev. Lett. 122, 158701. https://doi.org/10.1103/PhysRevLett.122.158701

13. Lucarini V, Bódai T. 2020 Global stability properties of the climate: melancholia states, invariant measures, and phase transitions. Nonlinearity 33, R59–R92. https://doi.org/10.1088/1361-6544/ab86cc

14. Margazoglou, G., Grafke, T., Laio, A., and Lucarini, V.: Dynamical landscape and multistability of a climate model, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477, 20210 019, https://doi.org/10.1098/rspa.2021.0019, 2021.

15. Lucarini, V., Serdukova, L., and Margazoglou, G.: Lévy-noise versus Gaussian-noise-induced Transitions in the Ghil-Sellers Energy Balance Model, Nonlin. Processes Geophys. Discuss. [preprint], https://doi.org/10.5194/npg-2021-34, in review, 2021.

16. Lenton, TM., et al. “Climate tipping points—too risky to bet against.” (2019): 592-595. https://doi.org/10.1038/d41586-019-03595-0

Berengere is senior scientist at the Centre National de la Recherche Scientifique and presently Director of the Les Houches Physics School. She received her PhD in astrophysics in 1990 under the supervision of J.-P. Zahn. She is a specialist of turbulence, and its application to astro and geophysical flows using theoretical, numerical or experimental approaches. Her major achievements are about theory of the solar system formation, statistical modeling of large scales and their bifurcations, or mathematical aspects of the small scale structure, in connection with singularities and intermittency. She was involved in the VKS dynamo experiment and in the SHREK superfluid (quantum) turbulence experiment.

**1. Just to break the ice and to be obvious: what were your feelings when you received the news that you received the Richardson medal?**

Of course, first of all I was very happy. I was also very honored to receive this award because Richardson prize is special to me since he was one of the pioneers in turbulence and I tried to apply many concepts proposed by him one century ago, especially the concept of energy cascade that is continuously present in my career. But I also felt a bit frustrated that I cannot share this award with all my colleagues and collaborators who contributed a lot in my research. Indeed, I have a philosophy of work-life: if you want to go fast, go alone, if you want to go far, go together.

**2. You received it for “for outstanding contributions to the field of geophysical and astrophysical turbulence, and for a unique approach to the study of experimental turbulent flows using statistical mechanics”, but why your approach is unique in turbulence?**

I am not sure my work is unique in turbulence but it may be original in the sense that it mixes theories, numerics, and experiments. I indeed developed a lot of theoretical tools I applied in experiments and numerical simulations as well as to real-world data. What is great for turbulence is that you can approach it from many aspects, you can look at large vs. small scales, you can apply a lot of tools from mathematics and physics, different concepts from dynamical systems and fractals/multifractals, and so on. I can say that I just used turbulence to do a lot of different things in physics. Indeed I mostly used the same device, the von Karman flow, to do many things in different fields of physics, ranging from climate to astrophysics.

**3. What was you first contact with turbulence and why turbulence entered in your life?**

That’s an interesting question. My first contact with turbulence was on a rock in a little place named LaFontasse near the Pyrenees where my grandparents had their summerhouse. After sun set we climb on the rock with my cousins and we had the possibility to see the night sky, with its comets, asteroids, the Milky Way. Starting from that I really wanted to study how all that works and I started studying astrophysical turbulence. I discovered that turbulence is a fashinating field since it is the unique case in which we have the equations governing phenomena since 1823 (the Navier-Stokes equations), but we cannot solve them, neither analytically nor numerically! So, we cannot exactly simulate the climate or the motion of galaxies.

Since the start of my carreer my goal is therefore to develop new concepts in turbulence such that Navier-Stokes equations can be simulated in an easiest way on laptop, focusing on properties of turbulent vortices and using mathematics, physics, mechanics, astro-/geo-physics.

**4. What were the key people that contributed to increase your motivation on this field?**

Oh well, the list is very long so I will make a selection. The first is my PhD advisor Jean-Paul Zahn, an outstanding physicist who tought me that I have to always check the physical meaning of any mathematical results. He was the founder of the speciality I used later in my career, i.e., to use laboratory experiments to deduce important results in natural systems. The second person who was very important for me is Uriel Frisch, the one who told me everything on turbulence starting at beginning of the 1990s. During these years I had the chance meet and work with several important people working in the field of turbulence like Michel Hénon, Yves Gagne and Bernard Castaing. They also taught me how to interact with students. They were very famous but they were also very modest and available for young people. I hope I learned well their lessons! Then, , I also have to thank my young collaborators, all my PhD s and post-docs like Jean-Philippe Laval, Davide Faranda, and many others. They were all important because working with young people increase your enthusiasm and your desire to do. They are the best part of my work! I also have to thank my senior colleagues Francois, Caroline, Sergey, Didier, and so on. I did not mention many others but all together we did go far!

**5. Finally, the usual question: what do you wish for the future and how young/established researchers can contribute to the growth of your field and of nonlinear sciences?**

What I really wish is less competition, more collaboration. At this time it is like a dream but I hope it can be realized soon in the future. Another thing is to follow your motivation in your field, not for publishing on high factor journals or for being awarded a medal, but for increasing your curiosity and searching for the beauty of Nature.

]]>Achim obtained his PhD at the University of Nice (Franc), doing research on turbulence theory. He then moved to oceanography working at UCLA (USA) and Geomar (Germany). Since 2005 he holds a permanent position at CNRS working in the LEGI laboratory at the Université Grenoble Alpes (France). From 2014 to 2019 he was director of LEGI. His recent research is on applying methods of non-equilibrium thermodynamics to air-sea interaction.

Today, fluctuations are the focus of research in statistical mechanics, which was traditionally concerned with averages. Fluctuations in a thermodynamic system usually appear at spatial scales which are small enough so that thermal, molecular, motion leaves an imprint on the dynamics as first considered by Albert Einstein. The importance of fluctuations is, however, not restricted to small systems. Fluctuations can leave their imprint on the dynamics at all scales when (not necessarily thermal) fluctuations are strong enough.

In non-equilibrium statistical mechanics, which describes forced-dissipative systems, as air-sea interaction and many other components of the climate system, 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.

FTs have been established analytically for Langevin type problems with thermal fluctuations. Most experimental data comes also from micro systems subject to thermal fluctuations. The thermodynamic frame of the quantities considered, as entropy, heat and work is not necessary to establish FTs. Examples of non-thermal fluctuations are the experimental data of the drag-force exerted by a turbulent flow and the local entropy production in turbulent Rayleigh-Bénard convection. For these non-Gaussian quantities the existence of a FT was suggested empirically. Our work, based on observations of atmospheric winds and oceanic currents, is strongly inspired by these investigations of the FT in data from laboratory experiments of turbulent flows.

The ocean dynamics is predominantly driven by the shear-stress between the atmospheric winds and ocean currents. The mechanical power input to the ocean is fluctuating in space and time and the atmospheric wind sometimes decelerates the ocean currents. Building on 24-years of global satellite observations, the input of mechanical power to the ocean is analysed. A Fluctuation Theorem (FT) holds when the logarithm of the ratio between the occurrence of positive (when the ocean gains energy by air-sea interaction) and negative events (when the ocean looses energy by air-sea interaction), of a certain magnitude of the power input, is a linear function of this magnitude and the averaging period. The flux of mechanical power to the ocean shows evidence of a FT, for regions within the recirculation area of the subtropical gyre, but not over extensions of western boundary currents. A FT puts a strong constraint on the temporal distribution of fluctuations of power input, connects variables obtained with different length of temporal averaging, guides the temporal down- and up-scaling and constrains the episodes of improbable events.

]]>By conducting statistical analyses of weather data for decades, climate scientists agree that the frequency of extreme events has already clearly increased: regardless of the variable studied, the scale or the model chosen, we see that the probability of these events in the current world is greater than in a world without human impacts. This is one of the main outcomes of the new IPCC report AR6.

To make predictions on the evolution of extreme events, climate scientists constantly keep an eye on the data accumulated in the past. This allows them to test the reliability of the models, but also to have a point of comparison with the data that is recorded today.

Despite the improvement of the monitoring of our planet with the appearance of satellites, the incomplete data of the more distant past leaves a gap that is difficult to fill. From this gap, researchers inherit difficulties in predicting the evolution of certain phenomena: for example, climatologists can determine on physical bases that the intensity of hurricanes will increase, it is difficult to predict the evolution of the frequency of these events, because even if we manage to simulate them with climate models, we don’t have good statistics from the past.

In fact, before we had a global view of our planet, it was simply impossible to know the existence of hurricanes that did not touch land. In this case, could the improved detection of the last decades be the reason for this tendency to perceive more extreme events? This bias exists. But in reality, climatologists validate the models with data series as accuratly as possible which come from historical weather stations. This allows to reduce biases in climate model simulations.

Despite some uncertainties, recent improvements in climate models are providing researchers with precise information about the future: For example, heat waves will become more intense because of the global rise in temperatures but there is an additional effect that is added to this: the slowing down of atmospheric circulation in the summer means that high pressure systems are becoming more persistent over Europe. The addition of these two phenomena increases the frequency and intensity of these episodes. These are just a few examples. So, as time goes by and techniques improve, our future is taking shape in the eyes of researchers who know how to decipher our climate past.

]]>Japanese-born Syukuro Manabe, presently senior meteorologist at Princeton University, provided an undisputed contribution to the development of the first numerical models for weather and climate, together with Joseph Smagorinsky at GFDL and Jim Hansen at GISS. His work on radiative-convective models [3], including radiative transfer modules in early-era GFD models [4], are milestones for our current understanding of the greenhouse effect, its influence on the hydrological cycle, and ultimately our ability to predict long-term climate response [5][6].

Klaus Hasselmann, born and educated in Hamburg (although living in the UK in the years of the Second World War, with his family fleeing from the atrocities of the Nazis), is currently Professor Emeritus at the University of Hamburg, formerly founding director of the Max Planck Institute for Meteorology. His revolutionary insight was to describe climate variability in terms of what was ultimately understood as a generalized Langevin equation (e.g. [7]), with a timescale separation between modes of the climate response and weather, with the latter treated as stochastic noise [8][9], This was a breakthrough achievement, seminal to many fields of modern climate science. In particular, this approach proved essential for numerical modelling, when it comes to the formulation of sub-grid scale processes through so-called stochastic parametrisations (eg. [10][11] for a theoretical framework). Moreover, the Nobel committee recognised the relevance of the optimal fingerprinting approach for the detection of the anthropogenic climate change signal [12].

It is perhaps less intuitive to recognise the outcome of research studies by Giorgio Parisi, professor at Sapienza University of Rome, president of the Accademia dei Lincei, in terms of advances in the field of climate change studies. Many in the NP community might be familiar with the concept of “stochastic resonance” [13] and the effect of macroscopic fluctuations on the transition of a chaotic system from one statistically steady state to another. Together with Catherine Nicolis, who was independently developing a similar idea at the Royal Meteorological Institute of Belgium [14], Parisi, Roberto Benzi, Alfonso Sutera and Angelo Vulpiani, formalised this idea in the early 80s, with many implications for the study of tipping points and abrupt transitions in the climate system [15][16]. Parisi was actually awarded the Nobel Prize on a different basis, especially for his discoveries on the behavior of spin glasses and the Ising model for ferromagnets [17][18]. Even if the behavior of ferromagnets might sound nothing like familiar to a climate scientist, it should not be surprising that researchers, such as Ken Golden at Utah University, are actually trying to understand and model the behavior of melt ponds over sea ice, with their huge implications for the sea-ice albedo feedback and the climate change signal as a result, by adapting an Ising model of phase transitions [19]!

The incredible careers and multi-disciplinary scientific achievements of this year’s Nobel laureates, bridging the gap between climate studies and so many different fields of research, are the evidence that non-linear mechanisms in complex chaotic systems are a genuinely fundamental and highly relevant physical problem.

*[1] Advanced information. NobelPrize.org. Nobel Prize Outreach AB 2021. Tue. 19 Oct 2021.*

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*[17] Parisi G (1979) Toward a Mean Field Theory for Spin Glasses. Phys. Lett. A 73, 203*

*[18] Parisi G (1979) Infinite number of order parameters for spin-glasses Phys. Rev. Lett. 43, 1754*

*[19] Ma Y-P, Sudakov I., Strong, C, and Golden KM (2019). Ising model for melt ponds on Arctic sea ice. New Journal of Physics, 21(6), 063029. httpWe s://doi.org/10.1088/1367-2630/AB26DB*