Empirical mode reduction in a model of extratropical low-frequency variability

This paper constructs and analyzes a reduced nonlinear stochastic model of extratropical low-frequency variability. To do so, it applies multilevel quadratic regression to the output of a long simulation of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography; the model’s phase space has a dimension of O(10 4 ). The reduced model has 45 variables and captures well the non-Gaussian features of the QG3 model’s probability density function (PDF). In particular, the reduced model’s PDF shares with the QG3 model its four anomalously persistent flow patterns, which correspond to opposite phases of the Arctic Oscillation and the North Atlantic Oscillation, as well as the Markov chain of transitions between these regimes. In addition, multichannel singular spectrum analysis identifies intraseasonal oscillations with a period of 35–37 days and of 20 days in the data generated by both the QG3 model and its low-dimensional analog. An analytical and numerical study of the reduced model starts with the fixed points and oscillatory eigenmodes of the model’s deterministic part and uses systematically an increasing noise parameter to connect these with the behavior of the full, stochastically forced model version. The results of this study point to the origin of the QG3 model’s multiple regimes and intraseasonal oscillations and identify the connections between the two types of behavior.

[1]  J. Wallace,et al.  Teleconnections in the Geopotential Height Field during the Northern Hemisphere Winter , 1981 .

[2]  Michael Ghil,et al.  ADVANCED SPECTRAL METHODS FOR CLIMATIC TIME SERIES , 2002 .

[3]  L. Sirovich,et al.  Coherent structures and chaos: A model problem , 1987 .

[4]  D. Hartmann,et al.  Eddy–Zonal Flow Feedback in the Northern Hemisphere Winter , 2003 .

[5]  R. Preisendorfer,et al.  Principal Component Analysis in Meteorology and Oceanography , 1988 .

[6]  J. Rinne,et al.  A spectral barotropic model in horizontal empirical orthogonal functions , 1975 .

[7]  Padhraic Smyth,et al.  Multiple Regimes in Northern Hemisphere Height Fields via MixtureModel Clustering* , 1999, Journal of the Atmospheric Sciences.

[8]  Prashant D. Sardeshmukh,et al.  The Optimal Growth of Tropical Sea Surface Temperature Anomalies , 1995 .

[9]  Michael Ghil,et al.  Forecasting Northern Hemisphere 700-mb Geopotential Height Anomalies Using Empirical Normal Modes , 1993 .

[10]  A. O'Neill,et al.  Atmospheric multiple equilibria and non‐Gaussian behaviour in model simulations , 2001 .

[11]  Robert Vautard,et al.  On the Source of Midlatitude Low-Frequency Variability. Part II: Nonlinear Equilibration of Weather Regimes , 1988 .

[12]  T. Coleman,et al.  On the Convergence of Reflective Newton Methods for Large-scale Nonlinear Minimization Subject to Bounds , 1992 .

[13]  Brian J. Hoskins,et al.  How well does the ECMWF Ensemble Prediction System predict blocking? , 2003 .

[14]  Michael Ghil,et al.  Statistical significance test for transition matrices of atmospheric Markov chains , 1990 .

[15]  M. Ghil,et al.  Multiple regimes and low‐frequency oscillations in the Southern Hemisphere's zonal‐mean flow , 2002 .

[16]  Franco Molteni,et al.  Toward a dynamical understanding of planetary-scale flow regimes. , 1993 .

[17]  Frank M. Selten,et al.  An Efficient Description of the Dynamics of Barotropic Flow , 1995 .

[18]  Eduardo Damasio Da Costa,et al.  A Qualitatively Realistic Low-Order Model of the Extratropical Low-Frequency Variability Built from Long Records of Potential Vorticity. , 1997 .

[19]  Andrew J. Majda,et al.  A mathematical framework for stochastic climate models , 2001 .

[20]  L. Ferranti,et al.  Northern Hemisphere atmospheric blocking as simulated by 15 atmospheric general circulation models in the period 1979–1988 , 1998 .

[21]  M. Ghil,et al.  Mountain Torques and Northern Hemisphere Low-Frequency Variability. Part I: Hemispheric Aspects , 2004 .

[22]  Michael Ghil,et al.  Intraseasonal Oscillations in a Barotropic Model with Annual Cycle, and Their Predictability , 1995 .

[23]  W. Metz.  Singular Modes and Low-Frequency Atmospheric Variability , 1994 .

[24]  Andrew J. Majda,et al.  A priori tests of a stochastic mode reduction strategy , 2002 .

[25]  J. Wallace,et al.  Annular Modes in the Extratropical Circulation. Part I: Month-to-Month Variability* , 2000 .

[26]  Michael Ghil,et al.  Persistent Anomalies, Blocking and Variations in Atmospheric Predictability , 1985 .

[27]  R. Pierrehumbert,et al.  Dynamics of Weather Regimes: Quasi-Stationary Waves and Blocking. , 1982 .

[28]  Grant Branstator,et al.  The Maintenance of Low-Frequency Atmospheric Anomalies , 1992 .

[29]  Michael Ghil,et al.  ADAPTIVE FILTERING AND PREDICTION OF NOISY MULTIVARIATE SIGNALS: AN APPLICATION TO SUBANNUAL VARIABILITY IN ATMOSPHERIC ANGULAR MOMENTUM , 1993 .

[30]  M. Ghil,et al.  Multiple Flow Regimes in the Northern Hemisphere Winter. Part I: Methodology and Hemispheric Regimes , 1993 .

[31]  M. Watanabe.  Asian Jet Waveguide and a Downstream Extension of the North Atlantic Oscillation , 2004 .

[32]  Robertson,et al.  Mountain Torques and Northern Hemisphere Low-Frequency Variability . Part I : Hemispheric Aspects , 2022 .

[33]  Bayesian Rcvr,et al.  I I I I I I I I I , 1972 .

[34]  J. Holton.  An introduction to dynamic meteorology , 2004 .

[35]  John M. Wallace,et al.  North atlantic oscillatiodannular mode: Two paradigms—one phenomenon , 2000 .

[36]  Cécile Penland,et al.  Random Forcing and Forecasting Using Principal Oscillation Pattern Analysis , 1989 .

[37]  Michael Ghil,et al.  “Waves” vs. “particles” in the atmosphere's phase space: A pathway to long-range forecasting? , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[38]  Stephen Taylor,et al.  Regression Analysis with Applications , 1987 .

[39]  Michael Ghil,et al.  The Extratropical 40-Day Oscillation in the UCLA General Circulation Model. Part II: Spatial Structure , 1996 .

[40]  Michael Ghil,et al.  Multiple Regimes and Low-Frequency Oscillations in the Northern Hemisphere’s Zonal-Mean Flow , 2006 .

[41]  Randall M. Dole,et al.  Persistent Anomalies of the Extratropical Northern Hemisphere Wintertime Circulation: Geographical Distribution and Regional Persistence Characteristics , 1983 .

[42]  John M. Wallace,et al.  Annular Modes in the Extratropical Circulation. Part II: Trends , 2000 .

[43]  Thomas F. Coleman,et al.  On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds , 1994, Math. Program..

[44]  A. Majdaa,et al.  A priori tests of a stochastic mode reduction strategy , 2002 .

[45]  Michael Ghil,et al.  Intraseasonal oscillations in the global atmosphere. I - Northern Hemisphere and tropics , 1991 .

[46]  C. Deser.  On the teleconnectivity of the “Arctic Oscillation” , 2000 .

[47]  Michael Ghil,et al.  A Hierarchy of Data-Based ENSO Models , 2005 .

[48]  Andrew J. Majda,et al.  Low-Order Stochastic Mode Reduction for a Realistic Barotropic Model Climate , 2005 .

[49]  Michael Ghil,et al.  Multilevel Regression Modeling of Nonlinear Processes: Derivation and Applications to Climatic Variability , 2005 .

[50]  W. Robinson.  A Baroclinic Mechanism for the Eddy Feedback on the Zonal Index , 2000 .

[51]  M. Mundt,et al.  Secondary instability, EOF reduction, and the transition to baroclinic chaos , 1994 .

[52]  Michael Ghil,et al.  Solving problems with GCMs: General circulation models and their role in the climate modeling hierarchy , 2000 .

[53]  Michael Ghil,et al.  The Extratropical 40-Day Oscillation in the UCLA General Circulation Model. Part I: Atmospheric Angular Momentum , 1994 .

[54]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[55]  K. Mo,et al.  Cluster analysis of multiple planetary flow regimes , 1988 .

[56]  Masahide Kimoto,et al.  Weather Regimes, Low-Frequency Oscillations, and Principal Patterns of Variability: A Perspective of Extratropical Low-Frequency Variability , 1999 .

[57]  Frank M. Selten,et al.  Baroclinic empirical orthogonal functions as basis functions in an atmospheric model , 1997 .

[58]  Cécile Penland,et al.  A stochastic model of IndoPacific sea surface temperature anomalies , 1996 .

[59]  F. Molteni,et al.  Patterns of low-frequency variability in a three-level quasi-geostrophic model , 1997 .

[60]  S. Childress,et al.  Topics in geophysical fluid dynamics. Atmospheric dynamics, dynamo theory, and climate dynamics. , 1987 .

[61]  Fabio D'Andrea,et al.  Extratropical low-frequency variability as a low-dimensional problem , 2001 .

[62]  Andrew J. Majda,et al.  Systematic Strategies for Stochastic Mode Reduction in Climate , 2003 .

[63]  Christopher R. Winkler,et al.  A Linear Model of Wintertime Low-Frequency Variability. Part I: Formulation and Forecast Skill , 2001 .

[64]  Grant Branstator,et al.  A Striking Example of the Atmosphere's Leading Traveling Pattern , 1987 .

[65]  Michael Ghil,et al.  Intraseasonal Variability in a Barotropic Model with Seasonal Forcing , 1993 .

[66]  Extratropical low‐frequency variability as a low‐dimensional problem. II: Stationarity and stability of large‐scale equilibria , 2002 .

[67]  D. Hartmann,et al.  Eddy–Zonal Flow Feedback in the Southern Hemisphere , 2001 .

[68]  A. Hannachi.  Low-Frequency Variability in a GCM: Three-Dimensional Flow Regimes and Their Dynamics , 1997 .

[69]  Michael Ghil,et al.  Multiple Flow Regimes in the Northern Hemisphere Winter. Part II: Sectorial Regimes and Preferred Transitions , 1993 .

[70]  Michael Ghil,et al.  Bimodal Behavior in the Zonal Mean Flow of a Baroclinic β-Channel Model , 2005 .

[71]  P. Ioannou,et al.  Stochastic forcing of the linearized Navier–Stokes equations , 1993 .

[72]  E. Sarachik,et al.  Empirically Derived Markov Models and Prediction of Tropical Pacific Sea Surface Temperature Anomalies , 2000 .

[73]  Siegfried D. Schubert,et al.  A Statistical-Dynamical Study of Empirically Determined Modes of Atmospheric Variability , 1985 .

[74]  M. Ghil,et al.  Low-Frequency Variability in a Baroclinic β Channel with Land–Sea Contrast , 2003 .

[75]  X. Cheng,et al.  Cluster Analysis of the Northern Hemisphere Wintertime 500-hPa Height Field: Spatial Patterns , 1993 .

[76]  W. Robinson.  Does Eddy Feedback Sustain Variability in the Zonal Index , 1996 .

[77]  Michael Ghil,et al.  Nonlinear Dynamics and Predictability in the Atmospheric Sciences , 1991 .

[78]  Brian F. Farrell,et al.  Stochastic dynamics of the midlatitude atmospheric jet , 1995 .

[79]  Michael Ghil,et al.  Weather Regimes and Preferred Transition Paths in a Three-Level Quasigeostrophic Model. , 2003 .

[80]  F. Molteni.  WEATHER REGIMES AND MULTIPLE EQUILIBRIA , 2003 .

[81]  J. Hurrell.  Decadal Trends in the North Atlantic Oscillation: Regional Temperatures and Precipitation , 1995, Science.

[82]  Vanden Eijnden E,et al.  Models for stochastic climate prediction. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[83]  H. Mukougawa.  A DYNAMICAL MODEL OF “QUASI-STATIONARY” STATES IN LARGE-SCALE ATMOSPHERIC MOTIONS , 1988 .

[84]  Michael Ghil,et al.  Intraseasonal Oscillations in the Extratropics: Hopf Bifurcation and Topographic Instabilities , 1990 .

[85]  G. Branstator.  Organization of Storm Track Anomalies by Recurring Low-Frequency Circulation Anomalies , 1995 .

[86]  G. Plaut,et al.  Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere. , 1994 .

[87]  William H. Press,et al.  Numerical recipes , 1990 .

[88]  A. E. Gill.  Atmosphere-Ocean Dynamics , 1982 .

[89]  Cécile Penland,et al.  Prediction of Tropical Atlantic Sea Surface Temperatures Using Linear Inverse Modeling , 1998 .

[90]  M. Ghil,et al.  mountain torques and atmospheric oscillations , 2001 .