arXiv subjects

Corentin Herbert

Publications and source records attributed to Corentin Herbert.

At least 19 recordsLinked to original sources

arXiv2026

Factors governing the existence of an abrupt transition to superrotation in an idealized GCM

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.

physics.ao-ph↗

arXiv2025

Climate impacts of forced equatorial superrotation in an idealized GCM

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 the 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.

physics.ao-ph↗

arXiv2024

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↗

arXiv2024

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↗

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

Statistics of inhomogeneous turbulence in large scale quasi-geostrophic dynamics

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 quasi-geostropic flow in the limit of small Rossby deformation radius, namely the large scale quasi-geostrophic 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 quasi-linear analytical approach with direct numerical simulations. We show that the quasi-linear 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 to measure space dependent inter-scale 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

physics.flu-dyn↗

arXiv2023

Two-dimensional turbulence with local interactions: statistics of the condensate

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 quasi-geostrophic 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 parity+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.

physics.flu-dyn↗

arXiv2021

Coupling rare event algorithms with data-based learned committor functions using the analogue Markov chain

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.

math.DS↗

arXiv2021

Committor Functions for Climate Phenomena at the Predictability Margin: The example of El Ni\~no Southern Oscillation in the Jin and Timmerman model

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 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 Ni\~no 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-Ni\~no, 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.

physics.ao-ph↗

arXiv2021

Instantons and the path to intermittency in turbulent flows

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.

physics.flu-dyn↗

arXiv2020

Computing return times or return periods with rare event algorithms

The average time between two occurrences of the same event, referred to as its return time (or return period), is a useful statistical concept for practical applications. For instance insurances or public agency may be interested by the return time of a 10m flood of the Seine river in Paris. However, due to their scarcity, reliably estimating return times for rare events is very difficult using either observational data or direct numerical simulations. For rare events, an estimator for return times can be built from the extrema of the observable on trajectory blocks. Here, we show that this estimator can be improved to remain accurate for return times of the order of the block size. More importantly, we show that this approach can be generalised to estimate return times from numerical algorithms specifically designed to sample rare events. So far those algorithms often compute probabilities, rather than return times. The approach we propose provides a computationally extremely efficient way to estimate numerically the return times of rare events for a dynamical system, gaining several orders of magnitude of computational costs. We illustrate the method on two kinds of observables, instantaneous and time-averaged, using two different rare event algorithms, for a simple stochastic process, the Ornstein-Uhlenbeck process. As an example of realistic applications to complex systems, we finally discuss extreme values of the drag on an object in a turbulent flow.

cond-mat.stat-mech↗

arXiv2019

Machine learning of committor functions for predicting high impact climate events

There is a growing interest in the climate community to improve the prediction of high impact climate events, for instance ENSO (El-Ni{ñ}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{ñ}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.

physics.ao-ph↗

arXiv2019

Atmospheric bistability and abrupt transitions to superrotation: wave-jet resonance and Hadley cell feedbacks

Strong eastward jets at the equator have been observed in many planetary atmospheres and simulated in numerical models of varying complexity. However, the nature of the transition from a conventional state of the general circulation, with easterlies or weak westerlies in the tropics, to such a superrotating state remains unclear. Is it abrupt or continuous? This question may have far-reaching consequences, as it may provide a mechanism for abrupt climate change in a planetary atmosphere, both through the loss of stability of the conventional circulation and through potential noise-induced transitions in the bistability range. We study two feedbacks which may lead to bistability between a conventional and a superrotating state: the Hadley cell feedback and a wave-jet resonance feedback. We delineate the regime of applicability of these two mechanisms in a simple model of zonal acceleration budget at the equator. Then, we show using numerical simulations of the axisymmetric primitive equations that the wave-jet resonance feedback indeed leads to robust bistability, while the bistability governed by the Hadley cell feedback, although observed in our numerical simulations, is much more fragile in a multilevel model.

physics.ao-ph↗

arXiv2017

Turbulence statistics in a 2D vortex condensate

Disentangling the evolution of a coherent mean-flow and turbulent fluctuations, interacting through the non-linearity of the Navier-Stokes equations, is a central issue in fluid mechanics. It affects a wide range of flows, such as planetary atmospheres, plasmas or wall-bounded flows, and hampers turbulence models. We consider the special case of a two-dimensional flow in a periodic box, for which the mean-flow, a pair of box-size vortices called \emph{condensate}, emerges from turbulence through an inverse cascade process. As was recently shown, a perturbative closure describes correctly the condensate when turbulence is excited at small scales. In this context, we obtain explicit results for the statistics of turbulence, encoded in the Reynolds stress tensor. We demonstrate that the two components of the Reynolds stress, the momentum flux and the turbulent energy, are determined by different mechanisms. It was suggested previously that the momentum flux is fixed by a balance between forcing and mean-flow advection: using unprecedently long numerical simulations, we provide the first direct evidence supporting this prediction. By contrast, combining analytical computations with numerical simulations, we show that the turbulent energy is determined only by mean-flow advection, and obtain for the first time a formula describing its profile in the vortex.

physics.flu-dyn↗

arXiv2017

Predictability of escape for a stochastic saddle-node bifurcation: when rare events are typical

Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable bifurcations of the underlying vector field. Here, we report a new situation, corresponding to a fluctuating system approaching a bifurcation, where both effects collaborate. We show that the problem can be reduced to a single control parameter governing the competition between deterministic and stochastic effects. Two asymptotic regimes are identified: when the control parameter is small (e.g. small noise), deviations from the deterministic case are well described by the Freidlin-Wentzell theory. In particular, escapes over the potential barrier are very rare events. When the parameter is large (e.g. large noise), such events become typical. Unlike pure noise-induced transitions, the distribution of the escape time is peaked around a value which is asymptotically predicted by an adiabatic approximation. We show that the two regimes are characterized by qualitatively different reacting trajectories, with algebraic and exponential divergence, respectively.

cond-mat.stat-mech↗

arXiv2017

An Introduction to Large Deviations and Equilibrium Statistical Mechanics for Turbulent Flows

Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large scales. In this short course, we show how the principles of equilibrium statistical mechanics apply to this problem and predict the condensation of energy at large scales and allow for computing the resulting coherent structures. We focus on the structure of the theory using the language of large deviation theory.

cond-mat.stat-mech↗

arXiv2015

Interplay of waves and eddies in rotating stratified turbulence and the link with kinetic-potential energy partition

The interplay between waves and eddies in stably stratified rotating flows is investigated by means of world-class direct numerical simulations using up to $3072^3$ grid points. Strikingly, we find that the shift from vortex to wave dominated dynamics occurs at a wavenumber $k_R$ which does not depend on Reynolds number, suggesting that partition of energy between wave and vortical modes is not sensitive to the development of turbulence at the smaller scales. We also show that $k_R$ is comparable to the wavenumber at which exchanges between kinetic and potential modes stabilize at close to equipartition, emphasizing the role of potential energy, as conjectured in the atmosphere and the oceans. Moreover, $k_R$ varies as the inverse of the Froude number as explained by the scaling prediction proposed, consistent with recent observations and modeling of the Mesosphere-Lower Thermosphere and of the ocean.

physics.flu-dyn↗

arXiv2015

Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behavior of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number Re=1000, with the ratio between the Brunt-Väisälä frequency N and the inertial frequency f varying from 1/4 to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range 0.02 < Fr < 0.32. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio N/f increases, also in the stratified case, although less and less so. However, when N/f increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing N/f can be interpreted in terms of the waves and vortices, and identify three major effects that can explain this transition based on inviscid invariants arguments.

physics.flu-dyn↗