Fluctuations, Response, and Resonances in a Simple Atmospheric Model

  title={Fluctuations, Response, and Resonances in a Simple Atmospheric Model},
  author={Andrey Gritsun and Valerio Lucarini},
  journal={Physica D: Nonlinear Phenomena},
  • A. Gritsun, V. Lucarini
  • Published 15 April 2016
  • Physics, Environmental Science
  • Physica D: Nonlinear Phenomena
Response and Sensitivity Using Markov Chains
Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of
The physics of climate variability and climate change
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 scales of motion, in
Response Formulae for $n$-point Correlations in Statistical Mechanical Systems and Application to a Problem of Coarse Graining
Predicting the response of a system to perturbations is a key challenge in mathematical and natural sciences. Under suitable conditions on the nature of the system, of the perturbation, and of the
Dynamical analysis of blocking events: spatial and temporal fluctuations of covariant Lyapunov vectors
One of the most relevant weather regimes in the midlatitude atmosphere is the persistent deviation from the approximately zonally symmetric jet stream leading to the emergence of so‐called blocking
Resonances in a Chaotic Attractor Crisis of the Lorenz Flow
Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant
Understanding and Predicting Nonlinear Turbulent Dynamical Systems with Information Theory
A new efficient method is developed to improve the computation of the linear response via the Fluctuation Dissipation Theorem (FDT), which makes use of a Gaussian Mixture to describe the unperturbed probability density function in high dimensions and avoids utilizing Gaussian approximations in computing the statistical response.
Edge States in the Climate System: Exploring Global Instabilities and Critical Transitions
Multistability is a ubiquitous feature in systems of geophysical relevance and provides key challenges for our ability to predict a system's response to perturbations. Near critical transitions small
Decomposing the dynamics of the Lorenz 1963 model using unstable periodic orbits: Averages, transitions, and quasi-invariant sets.
Unstable periodic orbits (UPOs) are a valuable tool for studying chaotic dynamical systems, as they allow one to distill their dynamical structure. We consider here the Lorenz 1963 model with the
Decomposing the Dynamics of the Lorenz 1963 model using Unstable Periodic Orbits : Averages , Transitions , and Quasi-Periodic Sets
Unstable periodic orbits (UPOs) are a valuable tool for studying chaotic dynamical systems. They allow one to extract information from a system and to distill its dynamical structure. We consider
Neutral modes of surface temperature and the optimal ocean thermal forcing for global cooling
Inquiry into the climate response to external forcing perturbations has been the central interest of climate dynamics. But the understanding of two important aspects of climate change


A statistical mechanical approach for the computation of the climatic response to general forcings
This paper shows for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings.
Covariant Lyapunov vectors of a quasi‐geostrophic baroclinic model: analysis of instabilities and feedbacks
The classical approach for studying atmospheric variability is based on defining a background state and studying the linear stability of the small fluctuations around such a state. Weakly nonlinear
Stochastic Perturbations to Dynamical Systems: A Response Theory Approach
Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation
Persistent Anomalies, Blocking and Variations in Atmospheric Predictability
Abstract We consider regimes of low-frequency variability in large-scale atmospheric dynamics. The model used for the study of these regimes is the fully-nonlinear, equivalent-barotropic vorticity
Mathematical and physical ideas for climate science
The climate is a forced and dissipative nonlinear system featuring nontrivial dynamics on a vast range of spatial and temporal scales. The understanding of the climate's structural and multiscale
Statistical characteristics, circulation regimes and unstable periodic orbits of a barotropic atmospheric model
  • A. Gritsun
  • Physics, Environmental Science
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2013
This study will try to apply the idea of UPO expansion to the simple atmospheric system based on the barotropic vorticity equation of the sphere to check how well orbits approximate the system attractor, its statistical characteristics and PDF.
Climate Response Using a Three-Dimensional Operator Based on the Fluctuation–Dissipation Theorem
Abstract The fluctuation–dissipation theorem (FDT) states that for systems with certain properties it is possible to generate a linear operator that gives the response of the system to weak external
A mathematical theory of climate sensitivity or, How to deal with both anthropogenic forcing and natural variability?
Recent estimates of climate evolution over the coming century still differ by several degrees. This uncertainty motivates the work presented here. There are two basic approaches to apprehend the
Beyond the linear fluctuation-dissipation theorem: the role of causality
In this paper we tackle the traditional problem of relating the fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also
Unstable periodic trajectories of a barotropic model of the atmosphere
Abstract Unstable periodic trajectories of a chaotic dissipative system belong to the attractor of the system and are its important characteristics. Many chaotic systems have an infinite number of