While it is expected that the large-scale tropical circulation should undergo some changes in a warmer climate, it remains an open question whether its characteristic features, such as the Hadley cell, the intertropical convergence zone, or the weak surface easterlies, could take a completely different shape. As an example, it has been hypothesized that Earth's atmosphere may have experienced equatorial superrotation i.e., westerly winds at the equator during its history. The possibility of equatorial superrotation has been studied in a range of planetary atmospheres, including Earth-like ones, with the objective of understanding the underlying dynamical processes. However, the broader impact that this dramatic circulation change would have on the climate system is practically unexplored. This is the question we address here. We perform idealized GCM simulations with an imposed equatorial torque to investigate how a forced superrotating atmosphere affects surface temperature and the water cycle. We show that these effects are quite large and directly related to the global circulation changes, which extend beyond the tropical atmosphere. Using tools including a forcing/feedback analysis and a moist energy balance model, we argue that the dominant mechanism is changes in atmospheric energy transport, driven in particular by the collapse of the meridional overturning circulation, and to a smaller extent by the appearance of an equatorial jet, and the concomitant redistribution of moisture in the tropics, leading to a much weaker relative humidity gradient which has strong radiative effects.

Some numerical simulations of very warm climates suggest that the Earth's atmosphere may undergo a transition to a state of equatorial superrotation, where the zonal-mean zonal wind in the tropics is westerly. However, major uncertainties remain about the circumstances under which such a transition could happen. A natural first step towards reducing these uncertainties is to better understand the dynamical processes involved in the transition in idealized setups. However, simple numerical experiments have reported very different responses to tropical diabatic heating in different models, with both a continuous and an abrupt transition to superotation. In this paper, we investigate the mechanisms controlling the nature of the transition. We show that in an idealized Held-Suarez framework, it is governed by both the meridional temperature gradient and the bottom friction coefficient. These two parameters control a competition between two feedback mechanisms: a positive tropical wave-jet mechanism, and a negative feedback mechanism related to absorption of extratropical waves near their critical latitudes in the tropics.

Ice shelves fringing the Antarctic continent experience low or high basal melt rates depending on local shelf conditions, ocean circulation and intensity of ice-sea-air exchanges. Recent studies have uncovered potential cold-to-warm transitions in specific ice-shelf cavities, which could lead to a dramatic increase in sea-level rise. Here we demonstrate that brine rejection in coastal polynyas promotes bistable dynamics in ice-shelf cavities, which would be otherwise monostable, for a broad diversity of Circumpolar Deep Water temperatures. We develop a generic low-dimensional box model featuring warm and cold circulation modes and apply it to nine ice-shelf cavities. We find that most ice-shelf cavities are in a bistable regime and are therefore susceptible to irreversible abrupt transitions for a realistic range of sea-ice formation rates. Bistability is robust to changes in cavity parameterization. However, the vertical mixing scheme at the ice-shelf front can be tuned to make the transitions reversible.

When performing predictions that use Machine Learning (ML), we are mainly interested in performance and interpretability. This generates a natural trade-off, where complex models generally have higher skills but are harder to explain and thus trust. Interpretability is particularly important in the climate community, where we aim at gaining a physical understanding of the underlying phenomena. Even more so when the prediction concerns extreme weather events with high impact on society. In this paper, we perform probabilistic forecasts of extreme heatwaves over France, using a hierarchy of increasingly complex ML models, which allows us to find the best compromise between accuracy and interpretability. More precisely, we use models that range from a global Gaussian Approximation (GA) to deep Convolutional Neural Networks (CNNs), with the intermediate steps of a simple Intrinsically Interpretable Neural Network (IINN) and a model using the Scattering Transform (ScatNet). Our findings reveal that CNNs provide higher accuracy, but their black-box nature severely limits interpretability, even when using state-of-the-art Explainable Artificial Intelligence (XAI) tools. In contrast, ScatNet achieves similar performance to CNNs while providing greater transparency, identifying key scales and patterns in the data that drive predictions. This study underscores the potential of interpretability in ML models for climate science, demonstrating that simpler models can rival the performance of their more complex counterparts, all the while being much easier to understand. This gained interpretability is crucial for building trust in model predictions and uncovering new scientific insights, ultimately advancing our understanding and management of extreme weather events.

Heat waves are a growing issue in the current climate, causing damage to human societies and other living beings. As climate warms, heat waves are one of the extreme events that will be exacerbated by the rising average temperatures. Understanding the mechanisms that drive heat waves is hence of vital importance to analyze them and to make predictions to mitigate their impacts. However, the rarity of any extreme event makes it particularly hard to study, especially if one wishes to understand the relation between predictors and probability, for instance using machine learning techniques, which are notoriously data-hungry. A possible solution is to use climate model simulations, but they introduce biases and can be prohibitively expensive to run for appropriate dataset lengths. In this work, we introduce a simple and powerful statistical model, that is able to skillfully predict rare heat waves in a regime of lack of data, as it is the case for the ERA5 reanalysis dataset. We focus on two-week heat waves over France, and we notice that composite maps of very extreme events are similar to the ones of much less extreme ones. This holds true for an increasing hierarchy of model complexity, including ERA5. We can thus analyze very extreme events by looking at less rare ones, having the advantage of increasing the available statistics. This effect can be explained assuming that the set of predictors and the heat wave amplitude are jointly gaussian. The prediction task can be thus rephrased into estimating the conditional probability of an extreme heat wave happening conditioned on the state of the set of predictors. This quantity, called committor function, is generally hard to estimate given the high dimensionality of the variables involved. Our assumption performs a dimensionality reduction, where an estimate is obtained through an optimal linear projection. The projection map will suggest the most relevant predictors. We first demonstrate that this Gaussian approximation performs well on a 8000 years run of a model of intermediate complexity, PlaSim, for both analysis and prediction tasks when 500 hPa geopotential height, temperature and soil moisture are used as input fields. When we compare with a machine learning estimation of the committor, which is possible here thanks to the huge amount of available data, our Gaussian model is less skillful, but not by much. We then apply the Gaussian assumption to the 500hPa geopotential height field of the ERA5 dataset, outperforming the neural networks and extending the predictability horizon by several days. The prediction method we propose is simple and effective. It opens possibilities to achieve skilfull predictions that outperform all known approaches, for instance machine learning, notably when data is scarce. Our method also serves as a better baseline than the climatology to benchmark more complex approaches. Since our statistical model is also interpretable, this framework has potential to go beyond prediction skill only and, thanks to the optimal projection map, foster the study of fast and slow drivers, and the effect climate change has on them.

Extreme events are the major weather-related hazard for humanity. It is then of crucial importance to have a good understanding of their statistics and to be able to forecast them. However, lack of sufficient data makes their study particularly challenging. In this work, we provide a simple framework for studying extreme events that tackles the lack of data issue by using the entire available dataset, rather than focusing on the extremes of the dataset. To do so, we make the assumption that the set of predictors and the observable used to define the extreme event follow a jointly Gaussian distribution. This naturally gives the notion of an optimal projection of the predictors for forecasting the event. We take as a case study extreme heatwaves over France, and we test our method on an 8000-year-long intermediate complexity climate model time series and on the ERA5 reanalysis dataset. For a-posteriori statistics, we observe and motivate the fact that composite maps of very extreme events look similar to less extreme ones. For prediction, we show that our method is competitive with off-the-shelf neural networks on the long dataset and outperforms them on reanalysis. The optimal projection pattern, which makes our forecast intrinsically interpretable, highlights the importance of soil moisture deficit and quasi-stationary Rossby waves as precursors to extreme heatwaves.

The European energy system will undergo major transformations in the coming decades to implement mitigation measures and comply with the Paris Agreement. In particular, the share of weather-dependent wind generation will increase significantly in the European energy mix. The most extreme fluctuations of the production at all time scales need to be taken into account in the design of the power system. In particular, extreme long-lasting low wind energy production events constitute a specific challenge, as most flexibility solutions do not apply at time scales beyond a few days. However, the probability and amplitude of such events has to a large extent eluded quantitative study so far due to lack of sufficiently long data. In this letter, using a 1000-year climate simulation, we study rare events of wind energy production that last from a few weeks to a few months over the January-February period, at the scale of a continent (Europe) and a country (France). The results show that the fluctuations of the capacity factor over Europe exhibit nearly Gaussian statistics at all time scales. A similar result holds over France for events longer than about two weeks and return times up to a few decades. In that case, the return time curves follow a universal curve. Furthermore, a simple Gaussian process with the same covariance structure as the data gives good estimates of the amplitude of the most extreme events. This method allows to estimate return times for rare events from shorter but more accurate data sources. We demonstrate this possibility with reanalysis data.

Two-dimensional turbulence self-organizes through a process of energy accumulation at large scales, forming a coherent flow termed a condensate. We study the condensate in a model with local dynamics, the large-scale quasigeostrophic equation, observed here for the first time. We obtain analytical results for the mean flow and the two-point, second-order correlation functions, and validate them numerically. The condensate state requires partiy+time-reversal symmetry breaking. We demonstrate distinct universal mechanisms for the even and odd correlators under this symmetry. We find that the model locality is imprinted in the small scale dynamics, which the condensate spatially confines.

Understanding and predicting extreme events is one of the major challenges for the study of climate change impacts, risk assessment, adaptation, and the protection of living beings. Extreme heatwaves are, and likely will be in the future, among the deadliest weather events. They also increase strain on water resources, food security and energy supply. Developing the ability to forecast their probability of occurrence a few days, weeks, or even months in advance would have major consequences to reduce our vulnerability to these events. Beyond the practical benefits of forecasting heat waves, building statistical models for extreme events which are interpretable is also highly beneficial from a fundamental point of view. Indeed, they enable proper studies of the processes underlying extreme events such as heat waves, improve dataset or model validation, and contribute to attribution studies. Machine learning provides tools to reach both these goals. We will first demonstrate that deep neural networks can predict the probability of occurrence of long-lasting 14-day heatwaves over France, up to 15 days ahead of time for fast dynamical drivers (500 hPa geopotential height field), and at much longer lead times for slow physical drivers (soil moisture). Those results are amazing in terms of forecasting skill. However, these machine learning models tend to be very complex and are often treated as black boxes. This limits our ability to use them for investigating the dynamics of extreme heat waves. To gain physical understanding, we have then designed a network architecture which is intrinsically interpretable. The main idea of this architecture is that the network first computes an optimal index, which is an optimal projection of the physical fields in a low-dimensional space. In a second step, it uses a fully non-linear representation of the probability of occurrence of the event as a function of the optimal index. This optimal index can be visualized and compared with classical heuristic understanding of the physical process, for instance in terms of geopotential height and soil moisture. This fully interpretable network is slightly less efficient than the off-the-shelf deep neural network. We fully quantify the performance loss incurred when requiring interpretability and make the connection with the mathematical notion of committor functions. This new machine learning tool opens the way for understanding optimal predictors of weather and climate extremes. This has potential for the study of slow drivers, and the effect of climate change on the drivers of extreme events.

A remarkable feature of two-dimensional turbulence is the transfer of energy from small to large scales. This process can result in the self-organization of the flow into large, coherent structures due to energy condensation at the largest scales. We investigate the formation of this condensate in a quasigeostropic flow in the limit of small Rossby deformation radius, namely the large-scale quasigeostrophic model. In this model potential energy is transferred up-scale while kinetic energy is transferred down-scale in a direct cascade. We focus on a jet mean flow and carry out a thorough investigation of the second-order statistics for this flow, combining a quasilinear analytical approach with direct numerical simulations. We show that the quasilinear approach applies in regions where jets are strong and is able to capture all second-order correlators in that region, including those related to the kinetic energy. This is a consequence of the blocking of the direct cascade by the mean flow in jet regions, suppressing fluctuation-fluctuation interactions. The suppression of the direct cascade is demonstrated using a local coarse-graining approach allowing us to measure space dependent interscale kinetic energy fluxes, which we show are concentrated in between jets in our simulations. We comment on the possibility of a similar direct cascade arrest in other two-dimensional flows, arguing that it is a special feature of flows in which the fluid element interactions are local in space.

In the coming decades, the European energy system will undergo major transformations, like widespread electrification and fast development of variable renewable energy, in order to reach carbon neutrality and comply with the Paris Agreement. As a consequence, energy production will increasingly depend on weather variability, and the future European energy system needs to be designed to cushion this variability, at all time scales. In particular, rare events leading to extreme fluctuations in energy production or demand can be expected to play a major part in this design. For instance, one of the main challenging events is a combination of low renewable energy production with high demand for a long time period. To know how much flexibility will be needed (seasonal storage such as green gas reserves, number of auxiliary thermal power plants, needs in terms of demand-side management, etc.) and assess its cost, one needs to estimate the probability of occurrence of such events. However, observations of renewable energy production or climate variables are too short to quantitatively study these critical events. Therefore we need to rely on climate and energy models, and to develop dedicated tools to study extreme events of energy production and demand. Here, we study the extreme imbalance between renewable generation and demand in Europe, at the sub-seasonal to seasonal scale. Based on a state-of-the-art climate model (CESM1.2.2) with extremely long simulations, we couple models of wind, solar PV, and demand with climate variables to obtain very long time series of energy production and demand. We consider 9 scenarios of renewable installed capacities to assess the probability of occurrence of extreme residual loads (demand minus renewable production). We study the statistics of extremely rare events that last for several weeks to several months. The results show that extremely high residual loads are dominated by extremely low wind energy production events in winter, that are not visible in historical data. Leveraging our very long time series, we compute return time curves for extreme wind energy fluctuations. These curves tell us how frequent energy shortfalls of a given amplitude are. We find a renormalization such that return time curves depend weakly on the scenario. The estimation of such return times relies crucially on the available amount of data. We show that good approximations can be obtained from simple stochastic processes.

Rare events, such as heat waves, floods, or hurricanes, play a crucial role in climate dynamics mainly due to the large impact they have. Predicting the occurrence of such events is thus a major challenge. In this talk, we introduce the relevant mathematical object for predicting a future event: the committor function is the probability that an event will occur, conditioned on the current state of the system. Computing this quantity from observations is an extremely difficult task since rare events have a very low probability of occurring and may not even have been observed in measurements made to date. Similarly, direct simulation of such events with comprehensive climate models comes at a prohibitive computational cost. Hence, rare event algorithms have been devised to simulate rare events efficiently, avoiding the computation of long periods of typical fluctuations. The effectiveness of these algorithms strongly relies on the knowledge of a measure of how close the event of interest is to occur, called the “score function”. The main difficulty is that the optimal score function is the committor function which is exactly the quantity to be computed. Therefore, it is very natural to consider an iterative procedure where the data produced by the algorithm is used to improve the score function, which in turn improves the algorithm, and so on. In this presentation, we propose a data-driven approach for computing the committor function, based on a Markov chain approximation of the dynamics of the system (the analogue method). We first illustrate this approach for a paradigmatic toy model of multistability for atmospheric dynamics with six variables (the Charney-Devore model). Secondly, we apply this methodology to data generated from a climate model, in order to study and predict the occurrence of extreme heat waves. In both cases, we show that it is possible to obtain fairly precise estimates of the committor function, even when few observations are available. In the second part of the talk, we show the advantage of coupling the analogue Markov chain with a rare event algorithm. Indeed, the committor learned with the analogue Markov chain can be used as a score function performing better than user-defined score functions, as we show for the Charney-Devore model. This new approach is promising for studying rare events in complex dynamics: the rare events can be simulated with a minimal prior knowledge and the results are much more precise than those obtained with a user-designed score function.

The potential impact of tipping points for climate dynamics is now widely recognized. Furthermore, paleoclimate records suggest that abrupt climate changes have indeed occurred in Earth’s past, potentially on timescales which do not exceed a decade. Several tipping elements, involving various components of the climate system, such as the ocean circulation, sea-ice, continental ice sheets, vegetation, and their couplings, have been suggested. Yet, it remains virtually unknown whether the large-scale atmospheric circulation, the component of the climate system with shortest response time, may undergo bifurcations that could trigger abrupt climate change. In this talk I will discuss the possibility of abrupt transitions of the large-scale circulation in the tropics. Specifically, I will consider potential reversals of the mean zonal winds, from the weak easterlies observed in current climate to a "superrotation" state with prevailing westerly winds. The superrotating state exhibits a strongly reduced Hadley circulation. I will discuss positive feedback mechanisms and their relevance for the Earth across a hierarchy of models of increasing complexity. A low-dimensional model based on Rossby wave resonance exhibits bistability, and provides a simple criterion for the region of parameter space where this regime exists. We then study the nature of the transition to superrotation in a dry dynamical core, forced in an idealized manner. The main result is that there exists a parameter regime where the dry primitive equations support two coexisting states, with and without an equatorial jet. We will discuss the role of parameters such as the meridional temperature gradient and the boundary layer friction on the existence of this bifurcation.

Processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. We consider cascade trajectories through scales as realizations of a stochastic Langevin process for which multiplicative noise is an intrinsic feature of the turbulent state. The trajectories are conditioned on their entropy exchange. Such selected trajectories concentrate around an optimal path, called instanton, which is the minimum of an effective action. The action is derived from the Langevin equation, estimated from measured data. In particular instantons with negative entropy pinpoint the trajectories responsible for the emergence of non-Gaussian statistics at small-scales.

Many phenomena in the climate system lie in the gray zone between weather and climate: they are not amenable to deterministic forecast, but they still depend on the initial condition. A natural example is mediumrange forecasting, which is inherently probabilistic because it lies beyond the deterministic predictability time of the atmosphere, but for which statistically significant prediction can be made which depend on the current state of the system. Similarly, one may ask the probability of occurrence of an El Niño event several months ahead of time. In this paper, we introduce a quantity which corresponds precisely to this type of prediction problem: the committor function is the probability that an event takes place within a given time window, as a function of the initial condition. We explain the main mathematical properties of this probabilistic concept, and compute it in the case of a low-dimensional stochastic model for El-Niño, the Jin and Timmerman model. In this context, we show that the ability to predict the probability of occurrence of the event of interest may differ strongly depending on the initial state. The main result is the new distinction between intrinsic probabilistic predictability (when the committor function is smooth and probability can be computed which does not depend sensitively on the initial condition) and intrinsic probabilistic unpredictability (when the committor function depends sensitively on the initial condition). We also demonstrate that the Jin and Timmerman model might be the first example of a stochastic differential equation with weak noise for which transition between attractors do not follow the Arrhenius law, which is expected based on large deviation theory and generic hypothesis.

Rare events play a crucial role in many physics, chemistry, and biology phenomena, when they change the structure of the system, for instance in the case of multistability, or when they have a huge impact. Rare event algorithms have been devised to simulate them efficiently, avoiding the computation of long periods of typical fluctuations. We consider here the family of splitting or cloning algorithms, which are versatile and specifically suited for far-from-equilibrium dynamics. To be efficient, these algorithms need to use a smart score function during the selection stage. Committor functions are the optimal score functions. In this work we propose a new approach, based on the analogue Markov chain, for a data-based learning of approximate committor functions. We demonstrate that such learned committor functions are extremely efficient score functions when used with the Adaptive Multilevel Splitting algorithm. We illustrate our approach for a gradient dynamics in a three-well potential, and for the Charney-DeVore model, which is a paradigmatic toy model of multistability for atmospheric dynamics. For these two dynamics, we show that having observed a few transitions is enough to have a very efficient data-based score function for the rare event algorithm. This new approach is promising for use for complex dynamics: the rare events can be simulated with a minimal prior knowledge and the results are much more precise than those obtained with a user-designed score function.

Many phenomena in the climate system lie in the gray zone between weather and climate: they are not amenable to deterministic forecast, but they still depend on the initial condition. A natural example is medium-range forecasting, which is inherently probabilistic because it lies beyond the predictability time of the atmosphere. Similarly, one may ask the probability of occurrence of an El Niño event several months ahead of time or the probability of occurrence of a heat wave a few weeks in advance based on the observed atmospheric circulation. In this talk, we introduce a quantity which corresponds precisely to this type of prediction problem: the committor function is the probability for an event to occur in the future, as a function of the current state of the system.In the first part of this presentation, we explain the main mathematical properties of this probabilistic concept, and compute it in the case of a low-dimensional stochastic model for El-Niño, the Jin and Timmerman model. This example allows us to show that the ability to predict the probability of occurrence of the event of interest may differ strongly depending on the initial state: in some regions of phase space, the committor function is smooth (intrinsic probabilistic predictability) and in some other regions, it depends sensitively on the initial condition (intrinsic probabilistic unpredictability). We stress that this predictability concept is markedly different from the deterministic unpredictability arising because of chaotic dynamics and exponential sensivity to initial conditions.The second part of the talk is about how to efficiently compute the committor function from data through several data-driven approaches, such as direct estimates, kernel-based methods and neural networks. We discuss two examples: a) the computation of committor function for the Jin and Timmerman model, b) the computation of committor function for extreme heat waves. Both systems are highly nonlinear but, considering the dimensionality of the two, their level of complexity is profoundly different. This therefore allows us to explore and discuss the performance and limits of the different methods proposed.Finally, we propose a method for learning effective dynamics by introducing a Markov chain on the data. Using the Markov chain we are able to quickly and easily compute many interesting quantities of the original system, including the committor function. The goal is to overcome some of the limitations of the methods introduced previously and to develop a robust algorithm that can be useful even in the lack of data.

One of the big challenges today is to appropriately describe heat waves, which are relevant due to their impact on human society. Common characteristics in mid-latitudes involve meanders of the westerly flow and concomitant large anticyclonic anomalies of the geopotential field. These anomalies form the so-called teleconnection patterns, and thus it is natural to ask how robust such structures are in various models and how much data we require to make statistically significant inferences. In addition, it is natural to ask what are the precursor phenomena that would improve forecasting capabilities of the heat waves. In particular, what kind of long term effect does the soil moisture have and how it compares to the respective quantitative contribution to the predictability of the teleconnection patterns.In order to answer these questions we perform various types of regression on a climate model. We construct the composite maps of the geopotential height at 500 hPa and estimate return times of heatwaves of different severity. Of particular interest to us is a committor function, which is essentially a probability a heat wave occurs given the current state of the system. Committor functions can be efficiently computed using the analogue method, which involves learning a Markov chain that produces synthetic trajectories from the real trajectories. Alternatively they can be estimated using machine learning approach. Finally we compare the composite maps in real dynamics to the ones generated by the Markov chain and observe how well the rare events are sampled, for instance to allow extending the return time plots.

There is a growing interest in the climate community to improve the prediction of high impact climate events, for instance ENSO (El-Ni{\~n}o-Southern Oscillation) or extreme events, using a combination of model and observation data. In this note we explain that, in a dynamical context, the relevant quantity for predicting a future event is a committor function. We explain the main mathematical properties of this probabilistic concept. We compute and discuss the committor function of the Jin and Timmerman model of El-Ni{\~n}o. Our first conclusion is that one should generically distinguish between states with either intrinsic predictability or intrinsic unpredictability. This predictability concept is markedly different from the deterministic unpredictability arising because of chaotic dynamics and exponential sensibility to initial conditions. The second aim of this work is to compare the inference of a committor function from data, either through a direct approach or through a machine learning approach using neural networks. We discuss the consequences of this study for future applications to more complex data sets.