arXiv subjects

Jonathan Demaeyer

Publications and source records attributed to Jonathan Demaeyer.

At least 19 recordsLinked to original sources

arXiv2026

Emergence of Chaos in the Tropical Atmosphere: Study of the Weak Temperature Gradient System

The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.

physics.ao-ph↗

arXiv2026

Revisiting the Dynamical Properties of Pedlosky's Two-Layer Model for Finite Amplitude Baroclinic Waves

Baroclinic instability is a fundamental mechanism driving atmospheric dynamics. In this work, we revisit Pedlosky's two-layer model for finite amplitude baroclinic waves - a seminal framework for studying the unstable growth of finite perturbations - leveraging modern nonlinear techniques and computational resources. We show that the geophysical state of the baroclinic wave exhibits a rich diversity of dynamical regimes governed by the level of dissipation induced by Ekman boundary layers. In the inviscid limit, we demonstrate that the model is integrable. Upon increasing dissipation, the system undergoes a complex sequence of bifurcations. On one hand, deterministic chaos, identified by means of the Lyapunov exponents, provides a genuine mechanism for destabilization of the wave. On the other hand, in regimes where the wave equilibrates, dependence on the initial condition is crucial, eventually leading to the coexistence of multiple attractors. We study the governing equations of the model and their truncation to a finite-dimensional system of ordinary differential equations, together with the minimal low-order truncated system which is structurally equivalent to the Lorenz model. Its bifurcation diagram allows for elucidating the transition of the wave amplitude from stable equilibration to periodic oscillations - terminating in homoclinic orbits - and, ultimately, deterministic chaos through a period-doubling route. We finally comment on the robustness of these features for higher-dimensional models.

physics.ao-ph↗

arXiv2025

Structural Origins and Real-Time Drivers of Intermittency

In general terms, intermittency is the property for which time evolving systems alternate among two or more different regimes. Predicting the instance when the regime switch will occur is extremely challenging, often practically impossible. Intermittent processes include turbulence, convection, precipitation patterns, as well as several in plasma physics, medicine, neuroscience, and economics. Traditionally, focus has been on global statistical indicators, e.g. the average frequency of regime changes under fixed conditions, or how these vary as a function of the system's parameters. We add a local perspective: we study the causes and drivers of the regime changes in real time, with the ultimate goal of predicting them. Using five different systems, of various complexities, we identify indicators and precursors of regime transitions that are common across the different intermittency mechanisms and dynamical models. For all the systems and intermittency types under study, we find a correlation between the alignment of some Lyapunov vectors and the concomitant, or aftermath, regime change. We discovered peculiar behaviors in the Lorenz 96 and in the Kuramoto-Shivanshinki models. In Lorenz 96 we identified crisis-induced intermittency with laminar intermissions, while in the Kuramoto-Shivanshinki we detected a spatially global intermittency which follows the scaling of type-I intermittency. The identification of general mechanisms driving intermittent behaviors, and in particular the unearthing of indicators spotting the regime change, pave the way to designing prediction tools in more realistic scenarios. These include turbulent geophysical fluids, rainfall patterns, or atmospheric deep convection.

nlin.CD↗

arXiv2025

Using Unstable Periodic Orbits to Understand Blocking Behaviour in a Low Order Land-Atmosphere Model

Unstable Periodic Orbits (UPOs) were used to identify regimes, and transitions between regimes, in a reduced-order coupled atmosphere-land spectral model. In this paper we describe how the chaotic attractor of this model was clustered using the numerically derived set of UPOs. Using continuation software, the origin of these clusters were also investigated. The flow of model trajectories can be approximated using UPOs, a concept known as shadowing. Here we extend that idea to look at the number of times a UPO shadows a model trajectory over a fixed time period, which we call cumulative shadowing. This concept was used to identify sets of UPOs that describe different life cycles of each cluster. The different regions of the attractor that were identified in the current work, and the transitions between these regions, are linked to specific atmospheric features known as atmospheric blocks.

physics.ao-ph↗

arXiv2024

Self-attentive Transformer for Fast and Accurate Postprocessing of Temperature and Wind Speed Forecasts

Current postprocessing techniques often require separate models for each lead time and disregard possible inter-ensemble relationships by either correcting each member separately or by employing distributional approaches. In this work, we tackle these shortcomings with an innovative, fast and accurate Transformer which postprocesses each ensemble member individually while allowing information exchange across variables, spatial dimensions and lead times by means of multi-headed self-attention. Weather forecasts are postprocessed over 20 lead times simultaneously while including up to fifteen meteorological predictors. We use the EUPPBench dataset for training which contains ensemble predictions from the European Center for Medium-range Weather Forecasts' integrated forecasting system alongside corresponding observations. The work presented here is the first to postprocess the ten and one hundred-meter wind speed forecasts within this benchmark dataset, while also correcting two-meter temperature. Our approach significantly improves the original forecasts, as measured by the CRPS, with 16.5\% for two-meter temperature, 10\% for ten-meter wind speed and 9\% for one hundred-meter wind speed, outperforming a classical member-by-member approach employed as a competitive benchmark. Furthermore, being up to six times faster, it fulfills the demand for rapid operational weather forecasts in various downstream applications, including renewable energy forecasting.

cs.LG↗

arXiv2023

Variability and Predictability of a reduced-order land atmosphere coupled model

This study delves into the predictability of atmospheric blocking, zonal, and transition patterns utilizing a simplified coupled model. Initially, we comprehensively scrutinize the model's responses to environmental parameters like solar radiation, surface friction, and atmosphere-ground heat exchange. Subsequently, employing Gaussian mixture clustering, we successfully delineate distinct blocking, zonal, and transition flow regimes, unveiling their dependencies on surface friction. To gauge predictability and persistence, we compute the averaged local Lyapunov exponents for each regime. Our investigation uncovers the presence of zonal, blocking, and transition regimes, particularly under conditions of reduced surface friction. As surface friction increases further, the system transitions to a state characterized by two blocking regimes and a transition regime. Intriguingly, periodic behavior emerges under specific surface friction values, returning to patterns observed under low friction coefficients. Model resolution increase impacts the system in a way that only two regimes are then obtained with the clustering: the transition phase disappears and the predictability drops to roughly 2 days for both of the remaining regimes. In accordance with previous research findings, our study underscores that when all three regimes coexist, zonal patterns exhibit a more extended predictability horizon compared to blocking patterns. Remarkably, transition patterns exhibit reduced predictability when coexisting with the other regimes. In addition, within a specified range of surface friction values where two blocking regimes are found, it is observed that blocked atmospheric situations in the west of the applied topography are marked by instabilities and reduced predictability in contrast to the blockings appearing on the eastern side of the topography.

physics.ao-ph↗

arXiv2023

Extremes of summer Arctic sea ice reduction investigated with a rare event algorithm

Various studies identified possible drivers of extremes of Arctic sea ice reduction, such as observed in the summers of 2007 and 2012, including preconditioning, local feedback mechanisms, oceanic heat transport and the synoptic- and large-scale atmospheric circulations. However, a robust quantitative statistical analysis of extremes of sea ice reduction is hindered by the small number of events that can be sampled in observations and numerical simulations with computationally expensive climate models. Recent studies tackled the problem of sampling climate extremes by using rare event algorithms, i.e., computational techniques developed in statistical physics to reduce the computational cost required to sample rare events in numerical simulations. Here we apply a rare event algorithm to ensemble simulations with the intermediate complexity coupled climate model PlaSim-LSG to investigate extreme negative summer pan-Arctic sea ice area anomalies under pre-industrial greenhouse gas conditions. Owing to the algorithm, we estimate return times of extremes orders of magnitude larger than feasible with direct sampling, and we compute statistically significant composite maps of dynamical quantities conditional on the occurrence of these extremes. We find that extremely low sea ice summers in PlaSim-LSG are associated with preconditioning through the winter sea ice-ocean state, with enhanced downward longwave radiation due to an anomalously moist and warm spring Arctic atmosphere and with enhanced downward sensible heat fluxes during the spring-summer transition. As a consequence of these three processes, the sea ice-albedo feedback becomes active in spring and leads to an amplification of pre-existing sea ice area anomalies during summer.

physics.ao-ph↗

arXiv2023

Multistability in a Coupled Ocean-Atmosphere Reduced Order Model: Non-linear Temperature Equations

Multistabilities were found in the ocean-atmosphere flow, in a reduced order ocean-atmosphere coupled model, when the non-linear temperature equations were solved numerically. In this paper we explain how the full non-linear Stefan-Bolzmann law was numerically implemented, and the resulting change to the system dynamics compared to the original model where these terms were linearised. Multiple stable solutions were found that display distinct ocean-atmosphere flows, as well as different Lyapunov stability properties. In addition, distinct Low Frequency Variability (LFV) behaviour was observed in stable attractors. We investigated the impact on these solutions of changing the magnitude of the ocean-atmospheric coupling, as well as the atmospheric emissivity to simulate an increasing green-house effect. Where multistabilities exist for fixed parameters, the possibility for tipping between solutions was investigated, but tipping did not occur in this version of the model where there is a constant solar forcing. This study was undertaken using a reduced-order quasi-geostrophic ocean-atmosphere model, consisting of two atmosphere layers, and one ocean layer, implemented in the Python programming language.

physics.ao-ph↗

arXiv2021

Identifying efficient ensemble perturbations for initializing subseasonal-to-seasonal prediction

The prediction of the weather at subseasonal-to-seasonal (S2S) timescales is dependent on both initial and boundary conditions. An open question is how to best initialize a relatively small-sized ensemble of numerical model integrations to produce reliable forecasts at these timescales. Reliability in this case means that the statistical properties of the ensemble forecast are consistent with the actual uncertainties about the future state of the geophysical system under investigation. In the present work, a method is introduced to construct initial conditions that produce reliable ensemble forecasts by projecting onto the eigenfunctions of the Koopman or the Perron-Frobenius operators, which describe the time-evolution of observables and probability distributions of the system dynamics, respectively. These eigenfunctions can be approximated from data by using the Dynamic Mode Decomposition (DMD) algorithm. The effectiveness of this approach is illustrated in the framework of a low-order ocean-atmosphere model exhibiting multiple characteristic timescales, and is compared to other ensemble initialization methods based on the Empirical Orthogonal Functions (EOFs) of the model trajectory and on the backward and covariant Lyapunov vectors of the model dynamics. Projecting initial conditions onto a subset of the Koopman or Perron-Frobenius eigenfunctions that are characterized by time scales with fast-decaying oscillations is found to produce highly reliable forecasts at all lead times investigated, ranging from one week to two months. Reliable forecasts are also obtained with the adjoint covariant Lyapunov vectors, which are the eigenfunctions of the Koopman operator in the tangent space. The advantages of these different methods are discussed.

physics.ao-ph↗

arXiv2021

Extratropical low-frequency variability with ENSO forcing: A reduced-order coupled model study

The impact of the El Ni\~no-Southern Oscillation (ENSO) on the extratropics is investigated in an idealized, reduced-order model that has a tropical and an extratropical module. Unidirectional ENSO forcing is used to mimick the atmospheric bridge between the tropics and the extratropics. The variability of the coupled ocean-atmosphere extratropical module is then investigated through the analysis of its pullback attractors (PBAs). This analysis focuses on two types of ENSO forcing generated by the tropical module, one periodic and the other aperiodic. For a substantial range of the ENSO forcing, two chaotic PBAs are found to coexist for the same set of parameter values. Different types of extratropical low-frequency variability are associated with either PBA over the parameter ranges explored. For periodic ENSO forcing, the coexisting PBAs exhibit only weak nonlinear instability. For chaotic forcing, though, they are quite unstable and certain extratropical perturbations induce transitions between the two PBAs. These distinct stability properties may have profound consequences for extratropical climate predictions: in particular, ensemble averaging may no longer help isolate the low-frequency variability signal.

physics.ao-ph↗

arXiv2020

Data assimilation for chaotic dynamics

Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in initial conditions is reduced by the astute combination of model predictions and real-time data. This chapter reviews recent findings from investigations on the impact of chaos on data assimilation methods: for the Kalman filter and smoother in linear systems, analytic results are derived; for their ensemble-based versions and nonlinear dynamics, numerical results provide insights. The focus is on characterising the asymptotic statistics of the Bayesian posterior in terms of the dynamical instabilities, differentiating between deterministic and stochastic dynamics. We also present two novel results. Firstly, we study the functioning of the ensemble Kalman filter in the context of a chaotic, coupled, atmosphere-ocean model with a quasi-degenerate spectrum of Lyapunov exponents, showing the importance of having sufficient ensemble members to track all of the near-null modes. Secondly, for the fully non-Gaussian method of the particle filter, numerical experiments are conducted to test whether the curse of dimensionality can be mitigated by discarding observations in the directions of little dynamical growth of uncertainty. The results refute this option, most likely because the particles already embody this information on the chaotic system. The results also suggest that it is the rank of the unstable-neutral subspace of the dynamics, and not that of the observation operator, that determines the required number of particles. We finally discuss how knowledge of the random attractor can play a role in the development of future data assimilation schemes for chaotic multiscale systems with large scale separation.

physics.data-an↗

arXiv2020

Correcting for Model Changes in Statistical Postprocessing -- An approach based on Response Theory

For most statistical postprocessing schemes used to correct weather forecasts, changes to the forecast model induce a considerable reforecasting effort. We present a new approach based on response theory to cope with slight model changes. In this framework, the model change is seen as a perturbation of the original forecast model. The response theory allows us then to evaluate the variation induced on the parameters involved in the statistical postprocessing, provided that the magnitude of this perturbation is not too large. This approach is studied in the context of simple Ornstein-Uhlenbeck models, and then on a more realistic, yet simple, quasi-geostrophic model. The analytical results for the former case help to pose the problem, while the application to the latter provide a proof-of-concept and assesses the potential performances of response theory in a chaotic system. In both cases, the parameters of the statistical postprocessing used - an Error-in-Variables Model Output Statistics (EVMOS) - are appropriately corrected when facing a model change. The potential application in an operational environment is also discussed.

physics.ao-ph↗

arXiv2020

Statistical Postprocessing for Weather Forecasts -- Review, Challenges and Avenues in a Big Data World

Statistical postprocessing techniques are nowadays key components of the forecasting suites in many National Meteorological Services (NMS), with for most of them, the objective of correcting the impact of different types of errors on the forecasts. The final aim is to provide optimal, automated, seamless forecasts for end users. Many techniques are now flourishing in the statistical, meteorological, climatological, hydrological, and engineering communities. The methods range in complexity from simple bias corrections to very sophisticated distribution-adjusting techniques that incorporate correlations among the prognostic variables. The paper is an attempt to summarize the main activities going on this area from theoretical developments to operational applications, with a focus on the current challenges and potential avenues in the field. Among these challenges is the shift in NMS towards running ensemble Numerical Weather Prediction (NWP) systems at the kilometer scale that produce very large datasets and require high-density high-quality observations; the necessity to preserve space time correlation of high-dimensional corrected fields; the need to reduce the impact of model changes affecting the parameters of the corrections; the necessity for techniques to merge different types of forecasts and ensembles with different behaviors; and finally the ability to transfer research on statistical postprocessing to operations. Potential new avenues will also be discussed.

physics.ao-ph↗

arXiv2018

Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean-atmosphere model on a beta-plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing. The increase of the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The convergence rate of the rate functional for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric time-scale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated to the ocean dynamics, is not fully resolved because of its associated long time scales, even at intermediate orders. This paper highlights the need to investigate the natural variability of the atmosphere-ocean coupled dynamics by associating rate of growth and decay of perturbations to the physical modes described using the formalism of the covariant Lyapunov vectors and to consider long integrations in order to disentangle the dynamical processes occurring at all time scales.

physics.ao-ph↗

arXiv2018

Comparison of stochastic parameterizations in the framework of a coupled ocean-atmosphere model

A new framework is proposed for the evaluation of stochastic subgrid-scale parameterizations in the context of MAOOAM, a coupled ocean-atmosphere model of intermediate complexity. Two physically-based parameterizations are investigated, the first one based on the singular perturbation of Markov operator, also known as homogenization. The second one is a recently proposed parameterization based on the Ruelle's response theory. The two parameterization are implemented in a rigorous way, assuming however that the unresolved scale relevant statistics are Gaussian. They are extensively tested for a low-order version known to exhibit low-frequency variability, and some preliminary results are obtained for an intermediate-order version. Several different configurations of the resolved-unresolved scale separations are then considered. Both parameterizations show remarkable performances in correcting the impact of model errors, being even able to change the modality of the probability distributions. Their respective limitations are also discussed.

physics.ao-ph↗

arXiv2017

The Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0

This paper describes a reduced-order quasi-geostrophic coupled ocean-atmosphere model that allows for an arbitrary number of atmospheric and oceanic modes to be retained in the spectral decomposition. The modularity of this new model allows one to easily modify the model physics. Using this new model, coined the "Modular Arbitrary-Order Ocean-Atmosphere Model" (MAOOAM), we analyse the dependence of the model dynamics on the truncation level of the spectral expansion, and unveil spurious behaviour that may exist at low resolution by a comparison with the higher-resolution configurations. In particular, we assess the robustness of the coupled low-frequency variability when the number of modes is increased. An "optimal" configuration is proposed for which the ocean resolution is sufficiently high, while the total number of modes is small enough to allow for a tractable and extensive analysis of the dynamics.

physics.ao-ph↗

arXiv2017

Stochastic parameterization of subgrid-scale processes: A review of recent physically-based approaches

We review some recent methods of subgrid-scale parameterization used in the context of climate modeling. These methods are developed to take into account (subgrid) processes playing an important role in the correct representation of the atmospheric and climate variability. We illustrate these methods on a simple stochastic triad system relevant for the atmospheric and climate dynamics, and we show in particular that the stability properties of the underlying dynamics of the subgrid processes has a considerable impact on their performances.

cond-mat.stat-mech↗

arXiv2017

Stochastic parameterization of subgrid-scale processes in coupled ocean-atmosphere systems: Benefits and limitations of response theory

A stochastic subgrid-scale parameterization based on the Ruelle's response theory and proposed in Wouters and Lucarini [2012] is tested in the context of a low-order coupled ocean-atmosphere model for which a part of the atmospheric modes are considered as unresolved. A natural separation of the phase-space into an invariant set and its complement allows for an analytical derivation of the different terms involved in the parameterization, namely the average, the fluctuation and the long memory terms. In this case, the fluctuation term is an additive stochastic noise. Its application to the low-order system reveals that a considerable correction of the low-frequency variability along the invariant subset can be obtained, provided that the coupling is sufficiently weak. This new approach of scale separation opens new avenues of subgrid-scale parameterizations in multiscale systems used for climate forecasts.

physics.ao-ph↗