433 citations · 1.4k across the 21 of their papers we have counts for
23 papers
Random templex encodes topological tipping points in noise-driven chaotic dynamics
Gisela D. Charó, Michael Ghil, Denisse Sciamarella
Random attractors are the time-evolving pullback attractors of stochastically perturbed, deterministically chaotic dynamical systems. These attractors have a structure that changes…
Asymptotic behavior of the forecast-assimilation process with unstable dynamics
Dan Crisan, Michael Ghil
Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper…
A multi-model ensemble Kalman filter for data assimilation and forecasting
Eviatar Bach, Michael Ghil
Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulatio…
Extratropical low-frequency variability with ENSO forcing: A reduced-order coupled model study
Stéphane Vannitsem, Jonathan Demaeyer, Michael Ghil
The impact of the El Niño-Southern Oscillation (ENSO) on the extratropics is investigated in an idealized, reduced-order model that has a tropical and an extratropical module. Unid…
Reduced-Order Models for Coupled Dynamical Systems: Data-driven Methods and the Koopman Operator
Manuel Santos Gutiérrez, Valerio Lucarini, Mickaël D. Chekroun +1
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and t…
Noise-driven Topological Changes in Chaotic Dynamics
Gisela D. Charó, Mickaël D. Chekroun, Denisse Sciamarella +1
Noise modifies the behavior of chaotic systems in both quantitative and qualitative ways. To study these modifications, the present work compares the topological structure of the d…
Ranking IPCC Models Using the Wasserstein Distance
Gabriele Vissio, Valerio Lembo, Valerio Lucarini +1
We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance prov…
The Physics of Climate Variability and Climate Change
Michael Ghil, Valerio Lucarini
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many s…
Arnold maps with noise: Differentiability and non-monotonicity of the rotation number
L. Marangio, J. Sedro, S. Galatolo +2
Arnold's standard circle maps are widely used to study the quasi-periodic route to chaos and other phenomena associated with nonlinear dynamics in the presence of two rationally un…
Estimating model evidence using ensemble-based data assimilation with localization - The model selection problem
Sammy Metref, Alexis Hannart, Juan Ruiz +3
IIn recent years, there has been a growing interest in applying data assimilation (DA) methods, originally designed for state estimation, to the model selection problem. In this se…
Estimating model evidence using data assimilation
Alberto Carrassi, Marc Bocquet, Alexis Hannart +1
We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model…
Low-Dimensional Galerkin Approximations of Nonlinear Delay Differential Equations
Mickaël D. Chekroun, Michael Ghil, Honghu Liu +1
This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert s…
DADA: Data Assimilation for the Detection and Attribution of Weather- and Climate-related Events
Alexis Hannart, Alberto Carrassi, Marc Bocquet +5
We describe a new approach allowing for systematic causal attribution of weather and climate-related events, in near-real time. The method is purposely designed to facilitate its i…
Low-frequency variability and heat transport in a low-order nonlinear coupled ocean-atmosphere model
Stéphane Vannitsem, Jonathan Demaeyer, Lesley De Cruz +1
We formulate and study a low-order nonlinear coupled ocean-atmosphere model with an emphasis on the impact of radiative and heat fluxes and of the frictional coupling between the t…
Data-driven non-Markovian closure models
Dmitri Kondrashov, Mickaël D. Chekroun, Michael Ghil
This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensi…
Climate dynamics and fluid mechanics: Natural variability and related uncertainties
Michael Ghil, Mickaël D. Chekroun, Eric Simonnet
The purpose of this review-and-research paper is twofold: (i) to review the role played in climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding a…
Averaging of time-periodic systems without a small parameter
Mickaël D. Chekroun, Michael Ghil, Jean Roux +1
In this article, we present a new approach to averaging in non-Hamiltonian systems with periodic forcing. The results here do not depend on the existence of a small parameter. In f…
A delay differential model of ENSO variability, Part 2: Phase locking, multiple solutions, and dynamics of extrema
Ilya Zaliapin, Michael Ghil
We consider a highly idealized model for El Nino/Southern Oscillation (ENSO) variability, as introduced in an earlier paper. The model is governed by a delay differential equation…
French Roadmap for complex Systems 2008-2009
Paul Bourgine, David Chavalarias, Edith Perrier +78
This second issue of the French Complex Systems Roadmap is the outcome of the Entretiens de Cargese 2008, an interdisciplinary brainstorming session organized over one week in 2008…
Transport on river networks: A dynamical approach
Ilya Zaliapin, Efi Foufoula-Georgiou, Michael Ghil
This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and sugge…
Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system
Alberto Carrassi, Michael Ghil, Anna Trevisan +1
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum phy…
Boolean Delay Equations: A simple way of looking at complex systems
Michael Ghil, Ilya Zaliapin, Barbara Coluzzi
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative…
Data-Adaptive Wavelets and Multi-Scale Singular Spectrum Analysis
P. Yiou, D. Sornette, M. Ghil
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series of length whose intermittency can give rise…