arXiv subjects

Freddy Bouchet

Publications and source records attributed to Freddy Bouchet.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical large deviations and long-range correlations for local weak wave turbulence

Wave turbulence describes the statistical dynamics of dispersive waves with weakly nonlinear interactions. While the classical kinetic equation captures the mean evolution of the wave spectrum, the study of its fluctuations due to finite-size effects and intermittency requires a probabilistic framework for space-time trajectories of the spectrum dynamics. Following the previous large deviation theories for wave turbulence, we develop a simplification meant for qualitative and numerical predictions of measurable quantities. We derive a new large deviation principle in the case of local wave interactions. It fully characterizes typical and rare fluctuations of the spectrum. In a joint article, we obtain a theory which is a generalised form of Macroscopic Fluctuation Theory, but with 2 conserved quantities (mass and energy). In this paper, we use it to analyse the structure of the equation for Gaussian fluctuations around out-of-equilibrium spectra. In addition to the usual equilibrium contribution, we obtain long-range correlations, which can be decomposed into 3 contributions: one is driven by the flux in the bulk and another is driven by the forcing and its possible fluctuations. In addition, these contributions are computed for the first time with a method adapted to boundary conditions where only the fluxes are fixed. The results provide a general, replicable method for analyzing wave turbulence in more complex settings. Finally, the generalization of this theory to the inhomogeneous wave turbulence provides a possible explanation to the instability of the Kolmogorov-Zakharov spectra in some 1D inhomogeneous models with 4-wave interactions such as the Majda-McLaughlin-Tabak. This work opens the discussion regarding universal and non universal properties in two-point correlation functions. This opens new range of study on the phenomena of intermittency which is partially developed here.

physics.flu-dyn↗

arXiv2026

Statistics of Temperature Extremes and Implications for Electrical Power Infrastructure in Continental France

In this article, we present extreme value statistics of temperature extremes over continental France with a focus on their implications for electrical power infrastructure. These are obtained by fitting a non-stationary generalised extreme value distribution using a Bayesian setup, which also provides errors or uncertainty values for all estimates. Within this method, a combination of simulated data from a collection of 28 CMIP6 models and measured records from the E-OBS dataset is used. The investigated climate scenarios are SSP2-4.5, SSP3-7.0 and SSP5-8.5, considering both historical and future climates spanning the years from 1850 to 2099. The method provides full spatial resolution on a 0.25 degree grid, allowing to asses extreme temperatures at arbitrary locations. Leveraging this particular aspect, various maps revealing the spatial structure of annual maximum high temperature extremes over continental France for the median and the statistical upper bound are shown together with summary information for the administrative regions in France towards the end of the century. It is statistically possible that the south west region of Occitanie could reach temperatures of up to 57°C under a high emission scenario by 2080, which is the highest compared to all other regions in continental France. We also perform a comparison to the reference climate adaptation trajectory for France (TRACC - Trajectoire de réchauffement de Référence pour l'Adaptation au Changement Climatique), showing that it potentially underestimates the stated maximum temperatures which could be surpassed by up to +8°C. Furthermore, five reference electrical power infrastructure locations are investigated on how they are potentially affected by temperature extremes with the quantified intensities.

physics.ao-ph↗

arXiv2026

AI-boosted rare event sampling to characterize extreme weather

Weather extremes pose major societal risks, especially in a changing climate, but due to their rarity, they are difficult to study using limited observations or complex climate models. We introduce AI+RES, a framework coupling fast AI weather forecasts with a high-fidelity physics model using a rare-event algorithm to efficiently characterize extremes. This approach enables the study of the statistics and physics of very rare events, such as once per millennium heatwaves at two orders-of-magnitude lower computational cost. AI+RES can be applied broadly across climate science and other fields concerned with rare events.

physics.ao-ph↗

arXiv2026

IPSL-AID: Generative Diffusion Models for Climate Downscaling from Global to Regional Scales

Effective adaptation and mitigation strategies for climate change require high-resolution projections to inform strategic decision-making. Conventional global climate models, which typically operate at resolutions of 150 to 200 kilometers, lack the capacity to represent essential regional processes. IPSL-AID is a global to regional downscaling tool based on a denoising diffusion probabilistic model designed to address this limitation. Trained on ERA5 reanalysis data, it generates 0.25 degree resolution fields for temperature, wind, and precipitation using coarse inputs and their spatiotemporal context. It also models probability distributions of fine-scale features to produce plausible scenarios for uncertainty quantification. The model accurately reconstructs statistical distributions, including extreme events, power spectra, and spatial structures. This work highlights the potential of generative diffusion models for efficient climate downscaling with uncertainty

physics.ao-ph↗

arXiv2026

Rare events algorithm study of extreme double jet summers and their connection to heatwaves over the Northern Hemisphere

Several large scale circulation patterns have been identified in relation to extreme Northern Hemisphere summer heatwaves. Three main ones are a double jet over Eurasia, a positive phase of the summer northern annular mode, and a quasi-wave-3 geopotential height anomaly. While there is some evidence suggesting these patterns are related to each other, the explicit nature of their relation, as well as the explicit mechanisms by which they are related to extreme heatwaves is still not known. The double jet structure has gained attention recently due to evidence that its persistence has been increasing, possibly explaining the rise in the number of extreme heatwaves over Europe. In this paper we study the occurrence and persistence of double jet states in ERA5 and in stationary simulations with the CESM1.2 model, using an index which measures the degree of jet separation. Additionally, we perform simulations with CESM1.2 coupled to a rare event algorithm in order to improve the statistics of rare summer-long double jet states. We find that extreme double jet states are characterised by three centers of extreme high surface temperature and 500hPa geopotential height anomalies, alongside a strong low pressure over the Arctic. The geopotential height anomaly pattern is consistent with both a positive Northern Annular Mode (NAM) and quasi-wave-3 patterns found in the literature. Moreover, we find a large percentage of co-occurrence of heatwaves at these centers, and a double jet state, with the percentage increasing with the duration of the double jet state.

physics.ao-ph↗

arXiv2025

Tackling the Accuracy-Interpretability Trade-off in a Hierarchy of Machine Learning Models for the Prediction of Extreme Heatwaves

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.

cs.LG↗

arXiv2025

Gaussian Framework and Optimal Projection of Weather Fields for Prediction of Extreme Events

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.

physics.ao-ph↗

arXiv2025

The role of edge states for early-warning of tipping points

Tipping points (TP) are often described as low-dimensional bifurcations, and are associated with early-warning signals (EWS) due to critical slowing down (CSD). CSD is an increase in amplitude and correlation of noise-induced fluctuations away from a reference attractor as the TP is approached. But for high-dimensional systems it is not obvious which variables or observables would display the critical dynamics and carry CSD. Many variables may display no CSD, or show changes in variability not related to a TP. It is thus helpful to identify beforehand which observables are relevant for a given TP. Here we propose this may be achieved by knowledge of an unstable edge state that separates the reference from an alternative attractor that remains after the TP. This is because stochastic fluctuations away from the reference attractor are preferentially directed towards the edge state along a most likely path (the instanton). As the TP is approached the edge state and reference attractor typically become closer, and the fluctuations can evolve further along the instanton. This can be exploited to find observables with substantial CSD, which we demonstrate using conceptual dynamical systems models and climate model simulations of a collapse of the Atlantic Meridional Overturning Circulation (AMOC).

nlin.CD↗

arXiv2024

Using rare event algorithms to understand the statistics and dynamics of extreme heatwave seasons in South Asia

Computing the return times of extreme events and assessing the impact of climate change on such return times is fundamental to extreme event attribution studies. However, the rarity of such events in the observational record makes this task a challenging one, even more so for "record-shattering" events that have not been previously observed at all. While climate models could be used to simulate such extremely rare events, such an approach entails a huge computational cost: gathering robust statistics for events with return time of centuries would require a few thousand years of simulation. In this study, we use an innovative tool, rare event algorithm, that allows to sample numerous extremely rare events at a much lower cost than direct simulations. We employ the algorithm to sample extreme heatwave seasons, corresponding to large anomalies of the seasonal average temperature, in a heatwave hotspot of South Asia using the global climate model Plasim. We show that the algorithm estimates the return levels of extremely rare events with much greater precision than traditional statistical fits. It also enables the computation of various composite statistics, whose accuracy is demonstrated through comparison with a very long control run. In particular, our results reveal that extreme heatwave seasons are associated with an anticyclonic anomaly embedded within a large-scale hemispheric quasi-stationary wave-pattern. Additionally, the algorithm accurately represents the intensity-duration-frequency statistics of sub-seasonal heatwaves, offering insights into both seasonal and sub-seasonal aspects of extreme heatwave seasons. This innovative approach could be used in extreme event attribution studies to better constrain the changes in event's probability and intensity with global warming, particularly for events with return times spanning centuries or millennia.

physics.ao-ph↗

arXiv2024

Comparing the influence of Atlantic Multidecadal Variability and spring soil moisture on European summer heat waves

In this work, we study and compare the influence of the Atlantic Multidecadal Variability (AMV) and of spring soil moisture in Southern Europe on the duration and intensity of European summer heat waves. We study common heat waves with return times of a few years like in previous studies, but we also propose a new methodological approach, return time maps, that allows us to study rare heat waves with return times from 10 to 50 years. We use the outputs from three climate models, namely IPSL-CM6A-LR, EC-Earth3, and CNRM-CM6-1, in which North Atlantic sea surface temperatures are restored towards the observed AMV anomalies. The three models give consistent results, with the exception of EC-Earth simulating a much greater influence of soil moisture. Typical AMV or spring soil moisture anomalies induce changes in the temperature and duration of heat waves that are of comparable amplitude, but follow different regional patterns. As might be expected, a positive AMV phase or low soil moisture induces hotter and longer typical heat waves over most of Europe. However, counter-intuitively, they also induce less heat wave days and cooler heat waves over part of Northeast Europe. For more extreme events, the influence of the AMV and soil moisture increase, according to rather similar regional patterns as for typical heat waves. However, while the amplitude of the influence is greater, the regions with decreased heat wave temperature and less heat wave days extend in size.

physics.ao-ph↗

arXiv2024

Extreme heatwave sampling and prediction with analog Markov chain and comparisons with deep learning

We present a data-driven emulator, stochastic weather generator (SWG), suitable for estimating probabilities of prolonged heatwaves in France and Scandinavia. This emulator is based on the method of analogs of circulation to which we add temperature and soil moisture as predictor fields. We train the emulator on an intermediate complexity climate model run and show that it is capable of predicting conditional probabilities (forecasting) of heatwaves out of sample. Special attention is payed that this prediction is evaluated using proper score appropriate for rare events. To accelerate the computation of analogs dimensionality reduction techniques are applied and the performance is evaluated. The probabilistic prediction achieved with SWG is compared with the one achieved with Convolutional Neural Network (CNN). With the availability of hundreds of years of training data CNNs perform better at the task of probabilistic prediction. In addition, we show that the SWG emulator trained on 80 years of data is capable of estimating extreme return times of order of thousands of years for heatwaves longer than several days more precisely than the fit based on generalised extreme value distribution. Finally, the quality of its synthetic extreme teleconnection patterns obtained with stochastic weather generator is studied. We showcase two examples of such synthetic teleconnection patterns for heatwaves in France and Scandinavia that compare favorably to the very long climate model control run.

physics.ao-ph↗

arXiv2023

Assessing the Probability of Extremely Low Wind Energy Production in Europe at Sub-seasonal to Seasonal Time Scales

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.

physics.ao-ph↗

arXiv2023

Functional renormalisation group approach to shell models of turbulence

Shell models are simplified models of hydrodynamic turbulence, retaining only some essential features of the original equations, such as the non-linearity, symmetries and quadratic invariants. Yet, they were shown to reproduce the most salient properties of developed turbulence, in particular universal statistics and multi-scaling. We set up the functional renormalisation group (RG) formalism to study generic shell models. In particular, we formulate an inverse RG flow, which consists in integrating out fluctuation modes from the large scales (small wavenumbers) to the small scales (large wavenumbers), which is physically grounded and has long been advocated in the context of turbulence. Focusing on the Sabra shell model, we study the effect of both a large-scale forcing, and a power-law forcing exerted at all scales. We show that these two types of forcing yield different fixed points, and thus correspond to distinct universality classes, characterised by different scaling exponents. We find that the power-law forcing leads to dimensional (K41-like) scaling, while the large-scale forcing entails anomalous scaling.

physics.flu-dyn↗

arXiv2023

Robust intra-model teleconnection patterns for extreme heatwaves

We investigate the statistics and dynamics of extreme heat waves over different areas of Europe. We find heatwaves over France and Scandinavia to be associated with recurrent wavenumber three teleconnection patterns in surface temperature and mid-tropospheric geopotential height. For heatwaves with return times of 4 years these teleconnection patterns and their dynamics are robustly represented in a hierarchy of models of different complexity and in reanalysis data. For longer return times, reanalysis records are too short to give statistically significant results, while models confirm the relevance of these large scale patterns for the most extreme heatwaves. A time series analysis shows that heatwave indices defined at synoptic scale are fairly well described by Gaussian stochastic processes, and that these Gaussian processes reproduce well return time plots even for very rare events. These results suggest that extreme heatwaves over different areas of Europe show recurrent typical behaviours in terms of long-range spatial correlations and subseasonal-scale temporal correlations. These properties are consistently represented among models of different complexity and observations, thus suggesting their relevance for a better understanding of the drivers and causes of the occurrence of extreme midlatitude heatwaves and their predictability.

physics.ao-ph↗

arXiv2023

Data-driven methods to estimate the committor function in conceptual ocean models

In recent years, several climate subsystems have been identified that may undergo a relatively rapid transition compared to the changes in their forcing. Such transitions are rare events in general, and simulating long-enough trajectories in order to gather sufficient data to determine transition statistics would be too expensive. Conversely, rare events algorithms like TAMS (trajectory-adaptive multilevel sampling) encourage the transition while keeping track of the model statistics. However, this algorithm relies on a score function whose choice is crucial to ensure its efficiency. The optimal score function, called the committor function, is in practice very difficult to compute. In this paper, we compare different data-based methods (analog Markov chains, neural networks, reservoir computing, dynamical Galerkin approximation) to estimate the committor from trajectory data. We apply these methods on two models of the Atlantic Ocean circulation featuring very different dynamical behavior. We compare these methods in terms of two measures, evaluating how close the estimate is from the true committor and in terms of the computational time. We find that all methods are able to extract information from the data in order to provide a good estimate of the committor. Analog Markov Chains provide a very reliable estimate of the true committor in simple models but prove not so robust when applied to systems with a more complex phase space. Neural network methods clearly stand out by their relatively low testing time, and their training time scales more favorably with the complexity of the model than the other methods. In particular, feedforward neural networks consistently achieve the best performance when trained with enough data, making this method promising for committor estimation in sophisticated climate models.

physics.ao-ph↗

arXiv2023

Dynamical large deviations for an inhomogeneous wave kinetic theory: linear wave scattering by a random medium

The wave kinetic equation predicts the averaged temporal evolution of a continuous spectral density of waves either randomly interacting or scattered by the fine structure of a medium. In a wide range of systems, the wave kinetic equation is derived from a fundamental equation of wave motion, which is symmetric through time-reversal. By contrast, the corresponding wave kinetic equation is time-irreversible. A similar paradox appears whenever one makes a mesoscopic description of the evolution of a very large number of microscopic degrees of freedom. Recently, it has been understood that the kinetic description itself, at a mesoscopic level, should not break time-reversal symmetry. The proper theoretical or mathematical tool to derive a mesoscopic time-reversal stochastic process is large deviation theory, for which the deterministic wave kinetic equation appears as the most probable evolution. This paper follows Bouchet (2020) and a series of other works that derive the large deviation Hamiltonians of the classical kinetic theories. We propose a derivation of the large deviation principle for the linear scattering of waves by a weak random potential in an inhomogeneous situation. This problem involves microscopic scales corresponding to the typical wavelengths and periods of the waves and mesoscopic ones which are the scales of spatial inhomogeneities in the spectral density and the time needed for the random scatterers to alter the wave spectrum. The main assumption of the kinetic regime is a large separation of these microscopic and mesoscopic scales. We choose a generic model of wave scattering by weak disorder: the Schrödinger equation with a random potential. We derive the path large deviation principle for the local spectral density and discuss its main properties. We show that the mesoscopic process obeys a time-reversal symmetry at the level of large deviations. (abridged)

cond-mat.stat-mech↗

arXiv2023

Sample-path large deviations for stochastic evolutions driven by the square of a Gaussian process

Recently, a number of physical models has emerged described by a random process with increments given by a quadratic form of a fast Gaussian process. We find that the rate function which describes sample-path large deviations for such a process can be computed from the large domain size asymptotic of a certain Fredholm determinant. The latter can be evaluated analytically using a theorem of Widom which generalizes the celebrated Szegő-Kac formula to the multi-dimensional case. This provides a large class of random dynamical systems with time scale separation for which an explicit sample-path large deviation functional can be found. Inspired by problems in hydrodynamics and atmosphere dynamics, we construct a simple example with a single slow degree of freedom driven by the square of a fast multi-variate Gaussian process and analyse its large deviations functional using our general results. Even though the noiseless limit of this example has a single fixed point, the corresponding large deviations effective potential has multiple fixed points. In other words, it is the addition of noise that leads to metastability. We use the explicit answers for the rate function to construct instanton trajectories connecting the metastable states.

cond-mat.stat-mech↗

arXiv2023

Probabilistic forecasts of extreme heatwaves using convolutional neural networks in a regime of lack of data

Understanding extreme events and their probability is key for the study of climate change impacts, risk assessment, adaptation, and the protection of living beings. Forecasting the occurrence probability of extreme heatwaves is a primary challenge for risk assessment and attribution, but also for fundamental studies about processes, dataset and model validation, and climate change studies. In this work we develop a methodology to build forecasting models which are based on convolutional neural networks, trained on extremely long climate model outputs. We demonstrate that neural networks have positive predictive skills, with respect to random climatological forecasts, for the occurrence of long-lasting 14-day heatwaves over France, up to 15 days ahead of time for fast dynamical drivers (500 hPa geopotential height fields), and also at much longer lead times for slow physical drivers (soil moisture). This forecast is made seamlessly in time and space, for fast hemispheric and slow local drivers. We find that the neural network selects extreme heatwaves associated with a North-Hemisphere wavenumber-3 pattern. The main scientific message is that most of the time, training neural networks for predicting extreme heatwaves occurs in a regime of lack of data. We suggest that this is likely to be the case for most other applications to large scale atmosphere and climate phenomena. For instance, using one hundred years-long training sets, a regime of drastic lack of data, leads to severely lower predictive skills and general inability to extract useful information available in the 500 hPa geopotential height field at a hemispheric scale in contrast to the dataset of several thousand years long. We discuss perspectives for dealing with the lack of data regime, for instance rare event simulations and how transfer learning may play a role in this latter task.

physics.ao-ph↗