Fluctuations, Response, and Resonances in a Simple Atmospheric Model
arXiv:1604.04386 · doi:10.1016/j.physd.2017.02.015
Abstract
We study the response of a simple quasi-geostrophic barotropic model of the atmosphere to various classes of perturbations affecting its forcing and its dissipation using the formalism of the Ruelle response theory. We investigate the geometry of such perturbations by constructing the covariant Lyapunov vectors of the unperturbed system and discover in one specific case - orographic forcing - a substantial projection of the forcing onto the stable directions of the flow. This results into a resonant response shaped as a Rossby-like wave that has no resemblance to the unforced variability in the same range of spatial and temporal scales. Such a climatic surprise corresponds to a violation of the fluctuation-dissipation theorem, in agreement with the basic tenets of nonequilibrium statistical mechanics. The resonance can be attributed to a specific group of rarely visited unstable periodic orbits of the unperturbed system. Our results reinforce the idea of using basic methods of nonequilibrium statistical mechanics and high-dimensional chaotic dynamical systems to approach the problem of understanding climate dynamics.
arXiv comment20 pages, 12 figures; final revision of the paper
References in corpus (21)
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Characterizing dynamics with covariant Lyapunov vectors
- A review of linear response theory for general differentiable dynamical systems
- Climate dynamics and fluid mechanics: Natural variability and related uncertainties
- Stochastic Climate Theory and Modelling
- Theory and computation of covariant Lyapunov vectors
- Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems
- Mathematical and Physical Ideas for Climate Science
- A new framework for climate sensitivity and prediction: a modelling perspective
- A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings
- Nonequilibrium and irreversibility
- Predicting Climate Change using Response Theory: Global Averages and Spatial Patterns
- Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach
- Computing covariant vectors, Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study
- Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig relations
- Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system
- Stochastic perturbations to dynamical systems: a response theory approach
- Beyond the linear Fluctuation-Dissipation Theorem: the Role of Causality
- Dynamical Analysis of Blocking Events: Spatial and Temporal Fluctuations of Covariant Lyapunov Vectors
- Covariant Lyapunov Vectors of a Quasi-geostrophic Baroclinic Model: Analysis of Instabilities and Feedbacks
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- Response Theory and Phase Transitions for the Thermodynamic Limit of Interacting Identical Systems
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- Adjoint shadowing directions in hyperbolic systems for sensitivity analysis
- Universal Upper Estimate for Prediction Errors under Moderate Model Uncertainty
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- Covariant Lyapunov Vectors and Finite-Time Normal Modes for Geophysical Fluid Dynamical Systems
- Reduced Markovian Descriptions of Brownian Dynamics: Toward an Exact Theory
- Fast differentiation of hyperbolic chaos
- Predictors and Predictands of Linear Response in Spatially Extended Systems
- A General Framework for Linking Free and Forced Fluctuations via Koopmanism
- Metastability, atmospheric midlatitude circulation regimes and large-scale teleconnection: a data-driven approach
- Kolmogorov Modes and Linear Response of Jump-Diffusion Models
- Introduction to the Special Issue on the Statistical Mechanics of Climate