skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Fixed points, stable manifolds, weather regimes, and their predictability

Abstract

In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemble forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.

Authors:
 [1];  [2];  [3]
  1. Laboratoire de Meteorologie Dynamique (CNRS and IPSL), Paris (France)
  2. Laboratoire de Meteorologie Dynamique (CNRS and IPSL), Paris (France)
  3. Univ. of California, Los Angeles, CA (United Staes). Atmospheric and Oceanic Sciences and Inst. of Geophysics and Planetary Physics
Publication Date:
Research Org.:
Laboratoire de Meteorologie Dynamique (CNRS and IPSL), Ecole Normale Superieure, Paris (France)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER)
OSTI Identifier:
1076437
Grant/Contract Number:  
FG02-07ER64439
Resource Type:
Accepted Manuscript
Journal Name:
Chaos: An Interdisciplinary Journal of Nonlinear Science
Additional Journal Information:
Journal Volume: 19; Journal Issue: 4; Journal ID: ISSN 1054-1500
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; atmospheric flow, local predictability, multiple regimes, separatrix

Citation Formats

Deremble, Bruno, D'Andrea, Fabio, and Ghil, Michael. Fixed points, stable manifolds, weather regimes, and their predictability. United States: N. p., 2009. Web. doi:10.1063/1.3230497.
Deremble, Bruno, D'Andrea, Fabio, & Ghil, Michael. Fixed points, stable manifolds, weather regimes, and their predictability. United States. doi:10.1063/1.3230497.
Deremble, Bruno, D'Andrea, Fabio, and Ghil, Michael. Tue . "Fixed points, stable manifolds, weather regimes, and their predictability". United States. doi:10.1063/1.3230497. https://www.osti.gov/servlets/purl/1076437.
@article{osti_1076437,
title = {Fixed points, stable manifolds, weather regimes, and their predictability},
author = {Deremble, Bruno and D'Andrea, Fabio and Ghil, Michael},
abstractNote = {In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemble forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.},
doi = {10.1063/1.3230497},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
number = 4,
volume = 19,
place = {United States},
year = {2009},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Predictability in the large: an extension of the concept of Lyapunov exponent
journal, January 1997

  • Aurell, E.; Boffetta, G.; Crisanti, A.
  • Journal of Physics A: Mathematical and General, Vol. 30, Issue 1
  • DOI: 10.1088/0305-4470/30/1/003

Poincaré recurrence: old and new
conference, January 2012


The statistical properties of general atmospheric circulation: Observational evidence and a minimal theory of bimodality
journal, July 1986

  • Benzi, R.; Malguzzi, P.; Speranza, A.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 112, Issue 473
  • DOI: 10.1002/qj.49711247306

Observations of fine-scale transport structure in the upper troposphere from the High-performance Instrumented Airborne Platform for Environmental Research
journal, January 2007

  • Bowman, Kenneth P.; Pan, Laura L.; Campos, Teresa
  • Journal of Geophysical Research, Vol. 112, Issue D18
  • DOI: 10.1029/2007JD008685

The Singular-Vector Structure of the Atmospheric Global Circulation
journal, May 1995


Bred Vectors of the Zebiak–Cane Model and Their Potential Application to ENSO Predictions
journal, January 2003


Multiple Flow Equilibria in the Atmosphere and Blocking
journal, July 1979


A Numerical Method for Predicting the Perturbations of the Middle Latitude Westerlies
journal, May 1949


Sensitivity analysis of atmospheric low-frequency variability
journal, October 1997

  • Corti, S.; Palmer, T. N.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 123, Issue 544
  • DOI: 10.1002/qj.49712354413

Homoclinic Dynamics: A Scenario for Atmospheric Ultralow-Frequency Variability
journal, May 2002


A Mechanism for Atmospheric Regime Behavior
journal, June 2004


Extratropical low-frequency variability as a low-dimensional problem. II: Stationarity and stability of large-scale equilibria
journal, April 2002


Extratropical low-frequency variability as a low-dimensional problem I: A simplified model
journal, April 2001

  • D'Andrea, Fabio; Vautard, Robert
  • Quarterly Journal of the Royal Meteorological Society, Vol. 127, Issue 574
  • DOI: 10.1002/qj.49712757413

Weather Regime Prediction Using Statistical Learning
journal, May 2007

  • Deloncle, A.; Berk, R.; D’Andrea, F.
  • Journal of the Atmospheric Sciences, Vol. 64, Issue 5
  • DOI: 10.1175/JAS3918.1

Analysis of a six-component atmospheric spectral model: chaos, predictability and vacillation
journal, August 1989


Low-frequency variability of the large-scale ocean circulation: A dynamical systems approach
journal, January 2005


RISE: Undergraduates Find That Regime Changes in Lorenz's Model are Predictable
journal, April 2004

  • Evans, Erin; Bhatti, Nadia; Pann, Lisa
  • Bulletin of the American Meteorological Society, Vol. 85, Issue 4
  • DOI: 10.1175/BAMS-85-4-520

Hilbert problems for the geosciences in the 21st century
journal, January 2001


"Waves" vs. "particles" in the atmosphere's phase space: A pathway to long-range forecasting?
journal, February 2002

  • Ghil, M.; Robertson, A. W.
  • Proceedings of the National Academy of Sciences, Vol. 99, Issue Supplement 1
  • DOI: 10.1073/pnas.012580899

Stability and Lyapunov stability of dynamical systems: A differential approach and a numerical method
journal, August 1987

  • Goldhirsch, Isaac; Sulem, Pierre-Louis; Orszag, Steven A.
  • Physica D: Nonlinear Phenomena, Vol. 27, Issue 3
  • DOI: 10.1016/0167-2789(87)90034-0

Characterization of Strange Attractors
journal, January 1983


Local predictability in a simple model of atmospheric balance
journal, January 2003

  • Gyarmati, G.; Szunyogh, I.; Patil, D. J.
  • Nonlinear Processes in Geophysics, Vol. 10, Issue 3
  • DOI: 10.5194/npg-10-183-2003

Finding finite-time invariant manifolds in two-dimensional velocity fields
journal, March 2000

  • Haller, G.
  • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 10, Issue 1
  • DOI: 10.1063/1.166479

Simulated annealing and weather regimes classification
journal, October 1995


Sloping convection in a rotating fluid
journal, January 1975


Intransitive Multiple Equilibria in Eddy-Active Barotropic Flows
journal, August 1987


A System Simulation Approach to Ensemble Prediction
journal, June 1996


Multiple Equilibria, Periodic, and Aperiodic Solutions in a Wind-Driven, Double-Gyre, Shallow-Water Model
journal, May 1995


Intraseasonal Oscillations in the Extratropics: Hopf Bifurcation and Topographic Instabilities
journal, December 1990


Relation between Kinematic Boundaries, Stirring, and Barriers for the Antarctic Polar Vortex
journal, April 2002


Multiple Flow Regimes in the Northern Hemisphere Winter. Part I: Methodology and Hemispheric Regimes
journal, August 1993


Predicting weather regime transitions in Northern Hemisphere datasets
journal, July 2007


Empirical Mode Reduction in a Model of Extratropical Low-Frequency Variability
journal, July 2006

  • Kondrashov, D.; Kravtsov, S.; Ghil, M.
  • Journal of the Atmospheric Sciences, Vol. 63, Issue 7
  • DOI: 10.1175/JAS3719.1

Persistent Anomalies, Blocking and Variations in Atmospheric Predictability
journal, March 1985


Deterministic Nonperiodic Flow
journal, March 1963


The Mechanics of Vacillation
journal, September 1963


Atmospheric Predictability as Revealed by Naturally Occurring Analogues
journal, July 1969


On the Existence of a Slow Manifold
journal, August 1986


Regimes in Simple Systems
journal, August 2006

  • Lorenz, Edward N.
  • Journal of the Atmospheric Sciences, Vol. 63, Issue 8
  • DOI: 10.1175/JAS3727.1

Mountain Torques and Northern Hemisphere Low-Frequency Variability. Part I: Hemispheric Aspects
journal, June 2004


Mountain Torques and Northern Hemisphere Low-Frequency Variability.Part II: Regional Aspects
journal, June 2004


Detection of a 40–50 Day Oscillation in the Zonal Wind in the Tropical Pacific
journal, July 1971


Description of Global-Scale Circulation Cells in the Tropics with a 40–50 Day Period
journal, September 1972


Distinct metastable atmospheric regimes despite nearly Gaussian statistics: A paradigm model
journal, May 2006

  • Majda, A. J.; Franzke, C. L.; Fischer, A.
  • Proceedings of the National Academy of Sciences, Vol. 103, Issue 22
  • DOI: 10.1073/pnas.0602641103

The Extratropical 40-Day Oscillation in the UCLA General Circulation Model. Part I: Atmospheric Angular Momentum
journal, June 1994


The Extratropical 40-Day Oscillation in the UCLA General Circulation Model. Part II: Spatial Structure
journal, July 1996


Weather Regimes: Recurrence and Quasi Stationarity
journal, April 1995


Cluster analysis of multiple planetary flow regimes
journal, January 1988


The ECMWF Ensemble Prediction System: Methodology and validation
journal, January 1996

  • Molteni, F.; Buizza, R.; Palmer, T. N.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 122, Issue 529
  • DOI: 10.1002/qj.49712252905

The Index Cycle and its role in the General Circulation
journal, April 1950


Separating fast and slow modes in coupled chaotic systems
journal, January 2004


Two Kinds of Vacillation in Rotating Laboratory Experiments
journal, February 1967


Multiple equilibria in thermosolutal convection due to salt-flux boundary conditions
journal, December 1992


Multiple equilibria and stable oscillations in thermosolutal convection at small aspect ratio
journal, May 1995


Changes of Probability Associated with El Niño
journal, December 2000


Climate modeling
journal, January 1974


Low-Frequency Variability in Shallow-Water Models of the Wind-Driven Ocean Circulation. Part I: Steady-State Solution*
journal, April 2003


Low-Frequency Variability in Shallow-Water Models of the Wind-Driven Ocean Circulation. Part II: Time-Dependent Solutions*
journal, April 2003


Multiple Regimes in Northern Hemisphere Height Fields via MixtureModel Clustering*
journal, November 1999


On the existence of multiple climate regimes
journal, January 2004

  • Stephenson, D. B.; Hannachi, A.; O'Neill, A.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 130, Issue 597
  • DOI: 10.1256/qj.02.146

Multiplicative Noise and Non-Gaussianity: A Paradigm for Atmospheric Regimes?
journal, May 2005

  • Sura, Philip; Newman, Matthew; Penland, Cécile
  • Journal of the Atmospheric Sciences, Vol. 62, Issue 5
  • DOI: 10.1175/JAS3408.1

Experimental and numerical studies of an eastward jet over topography
journal, July 2001


Ensemble Forecasting at NMC: The Generation of Perturbations
journal, December 1993


Ensemble Forecasting at NCEP and the Breeding Method
journal, December 1997


Invariant Manifolds, Quasi-Geostrophy and Initialization
journal, March 1986


Transitions Between Blocked and Zonal Flows in a Rotating Annulus with Topography
journal, November 1997


Predictability of a Coupled Model of ENSO Using Singular Vector Analysis. Part II: Optimal Growth and Forecast Skill
journal, September 1997


A Model El Niñ–Southern Oscillation
journal, October 1987


    Works referencing / citing this record:

    Multiple equilibria and oscillatory modes in a mid-latitude ocean-forced atmospheric model
    journal, January 2012

    • Deremble, B.; Simonnet, E.; Ghil, M.
    • Nonlinear Processes in Geophysics, Vol. 19, Issue 5
    • DOI: 10.5194/npg-19-479-2012

    Multiple equilibria and oscillatory modes in a mid-latitude ocean-forced atmospheric model
    journal, January 2012

    • Deremble, B.; Simonnet, E.; Ghil, M.
    • Nonlinear Processes in Geophysics, Vol. 19, Issue 5
    • DOI: 10.5194/npg-19-479-2012

    Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns
    journal, April 2016

    • Lucarini, Valerio; Ragone, Francesco; Lunkeit, Frank
    • Journal of Statistical Physics, Vol. 166, Issue 3-4
    • DOI: 10.1007/s10955-016-1506-z