• Baldwin, M. P., D. B. Stephenson, D. W. J. Thompson, T. J. Dunkerton, A. J. Charlton, and A. O’Neill, 2003: Stratospheric memory and skill of extended-range weather forecasts. Science, 301, 636640, https://doi.org/10.1126/science.1087143.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bartlett, M. S., 1978: An Introduction to Stochastic Processes with Special Reference to Methods and Applications. By M. S. Bartlett. J. Inst. Actuaries, 81, 198199, https://doi.org/10.1017/S0020268100035964.

    • Search Google Scholar
    • Export Citation
  • Boljka, L., T. G. Shepherd, and M. Blackburn, 2018: On the coupling between barotropic and baroclinic modes of extratropical atmospheric variability. J. Atmos. Sci., 75, 18531871, https://doi.org/10.1175/JAS-D-17-0370.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bracegirdle, T. J., C. R. Holmes, J. S. Hosking, G. J. Marshall, M. Osman, M. Patterson, and T. Rackow, 2020: Improvements in circumpolar Southern Hemisphere extratropical atmospheric circulation in CMIP6 compared to CMIP5. Earth Space Sci., 7, e2019EA001065, https://doi.org/10.1029/2019EA001065.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Branstator, G., 1995: Organization of storm track anomalies by recurring low-frequency circulation anomalies. J. Atmos. Sci., 52, 207226, https://doi.org/10.1175/1520-0469(1995)052<0207:OOSTAB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Burrows, D. A., G. Chen, and L. Sun, 2016: Barotropic and baroclinic eddy feedbacks in the midlatitude jet variability and responses to climate change–like thermal forcings. J. Atmos. Sci., 74, 111132, https://doi.org/10.1175/JAS-D-16-0047.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Byrne, N. J., T. G. Shepherd, T. Woollings, and R. A. Plumb, 2016: Annular modes and apparent eddy feedbacks in the Southern Hemisphere. Geophys. Res. Lett., 43, 38973902, https://doi.org/10.1002/2016GL068851.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, G., and R. A. Plumb, 2009: Quantifying the eddy feedback and the persistence of the zonal index in an idealized atmospheric model. J. Atmos. Sci., 66, 37073720, https://doi.org/10.1175/2009JAS3165.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Feldstein, S. B., 1998: An observational study of the intraseasonal poleward propagation of zonal mean flow anomalies. J. Atmos. Sci., 55, 25162529, https://doi.org/10.1175/1520-0469(1998)055<2516:AOSOTI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Feldstein, S. B., and S. Lee, 1998: Is the atmospheric zonal index driven by an eddy feedback? J. Atmos. Sci., 55, 30773086, https://doi.org/10.1175/1520-0469(1998)055<3077:ITAZID>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gerber, E. P., and G. K. Vallis, 2007: Eddy–zonal flow interactions and the persistence of the zonal index. J. Atmos. Sci., 64, 32963311, https://doi.org/10.1175/JAS4006.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gerber, E. P., L. M. Polvani, and D. Ancukiewicz, 2008a: Annular mode time scales in the Intergovernmental Panel on Climate Change Fourth Assessment Report models. Geophys. Res. Lett., 35, L22707, https://doi.org/10.1029/2008GL035712.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gerber, E. P., S. Voronin, and L. M. Polvani, 2008b: Testing the annular mode autocorrelation time scale in simple atmospheric general circulation models. Mon. Wea. Rev., 136, 15231536, https://doi.org/10.1175/2007MWR2211.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hassanzadeh, P., and Z. Kuang, 2016a: The linear response function of an idealized atmosphere. Part I: Construction using Green’s functions and applications. J. Atmos. Sci., 73, 34233439, https://doi.org/10.1175/JAS-D-15-0338.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hassanzadeh, P., and Z. Kuang, 2016b: The linear response function of an idealized atmosphere. Part II: Implications for the practical use of the fluctuation–dissipation theorem and the role of operator’s nonnormality. J. Atmos. Sci., 73, 34413452, https://doi.org/10.1175/JAS-D-16-0099.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hassanzadeh, P., and Z. Kuang, 2019: Quantifying the annular mode dynamics in an idealized atmosphere. J. Atmos. Sci., 76, 11071124, https://doi.org/10.1175/JAS-D-18-0268.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., 1988: Pips and pops: The reduction of complex dynamical systems using principal interaction and oscillation patterns. J. Geophys. Res., 93, 11 01511 021, https://doi.org/10.1029/JD093iD09p11015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Held, I. M., 2005: The gap between simulation and understanding in climate modeling. Bull. Amer. Meteor. Soc., 86, 16091614, https://doi.org/10.1175/BAMS-86-11-1609.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Held, I. M., and M. J. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75, 18251830, https://doi.org/10.1175/1520-0477(1994)075<1825:APFTIO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • James, I. N., and J. P. Dodd, 1996: A mechanism for the low-frequency variability of the mid-latitude troposphere. Quart. J. Roy. Meteor. Soc., 122, 11971210, https://doi.org/10.1002/qj.49712253309.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jeevanjee, N., P. Hassanzadeh, S. Hill, and A. Sheshadri, 2017: A perspective on climate model hierarchies. J. Adv. Model. Earth Syst., 9, 17601771, https://doi.org/10.1002/2017MS001038.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kidson, J. W., 1988: Interannual variations in the Southern Hemisphere circulation. J. Climate, 1, 11771198, https://doi.org/10.1175/1520-0442(1988)001<1177:IVITSH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, S., S.-W. Son, K. Grise, and S. B. Feldstein, 2007: A mechanism for the poleward propagation of zonal mean flow anomalies. J. Atmos. Sci., 64, 849868, https://doi.org/10.1175/JAS3861.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Limpasuvan, V., and D. L. Hartmann, 1999: Eddies and the annular modes of climate variability. Geophys. Res. Lett., 26, 31333136, https://doi.org/10.1029/1999GL010478.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lindgren, E. A., A. Sheshadri, and R. A. Plumb, 2020: Frequency-dependent behavior of zonal jet variability. Geophys. Res. Lett., 47, e2019GL086585, https://doi.org/10.1029/2019GL086585.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lorenz, D. J., 2014: Understanding midlatitude jet variability and change using Rossby wave chromatography: Wave–mean flow interaction. J. Atmos. Sci., 71, 36843705, https://doi.org/10.1175/JAS-D-13-0201.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lorenz, D. J., and D. L. Hartmann, 2001: Eddy–zonal flow feedback in the Southern Hemisphere. J. Atmos. Sci., 58, 33123327, https://doi.org/10.1175/1520-0469(2001)058<3312:EZFFIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lorenz, D. J., and D. L. Hartmann, 2003: Eddy–zonal flow feedback in the Northern Hemisphere winter. J. Climate, 16, 12121227, https://doi.org/10.1175/1520-0442(2003)16<1212:EFFITN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lubis, S. W., C. S. Y. Huang, N. Nakamura, N.-E. Omrani, and M. Jucker, 2018a: Role of finite-amplitude Rossby waves and nonconservative processes in downward migration of extratropical flow anomalies. J. Atmos. Sci., 75, 13851401, https://doi.org/10.1175/JAS-D-17-0376.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lubis, S. W., C. S. Y. Huang, and N. Nakamura, 2018b: Role of finite-amplitude eddies and mixing in the life cycle of stratospheric sudden warmings. J. Atmos. Sci., 75, 39874003, https://doi.org/10.1175/JAS-D-18-0138.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ma, D., P. Hassanzadeh, and Z. Kuang, 2017: Quantifying the eddy–jet feedback strength of the annular mode in an idealized GCM and reanalysis data. J. Atmos. Sci., 74, 393407, https://doi.org/10.1175/JAS-D-16-0157.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nakamura, N., and D. Zhu, 2010: Finite-amplitude wave activity and diffusive flux of potential vorticity in eddy–mean flow interaction. J. Atmos. Sci., 67, 27012716, https://doi.org/10.1175/2010JAS3432.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nie, Y., Y. Zhang, G. Chen, X.-Q. Yang, and D. A. Burrows, 2014: Quantifying barotropic and baroclinic eddy feedbacks in the persistence of the southern annular mode. Geophys. Res. Lett., 41, 86368644, https://doi.org/10.1002/2014GL062210.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Penland, C., 1989: Random forcing and forecasting using principal oscillation pattern analysis. Mon. Wea. Rev., 117, 21652185, https://doi.org/10.1175/1520-0493(1989)117<2165:RFAFUP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Robert, L., G. Rivière, and F. Codron, 2017: Positive and negative eddy feedbacks acting on midlatitude jet variability in a three-level quasigeostrophic model. J. Atmos. Sci., 74, 16351649, https://doi.org/10.1175/JAS-D-16-0217.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Robinson, W. A., 1991: The dynamics of the zonal index in a simple model of the atmosphere. Tellus, 43A, 295305, https://doi.org/10.3402/tellusa.v43i5.11953.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Robinson, W. A., 2000: A baroclinic mechanism for the eddy feedback on the zonal index. J. Atmos. Sci., 57, 415422, https://doi.org/10.1175/1520-0469(2000)057<0415:ABMFTE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ronalds, B., E. Barnes, and P. Hassanzadeh, 2018: A barotropic mechanism for the response of jet stream variability to Arctic amplification and sea ice loss. J. Climate, 31, 70697085, https://doi.org/10.1175/JCLI-D-17-0778.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Saggioro, E., and T. G. Shepherd, 2019: Quantifying the timescale and strength of Southern Hemisphere intraseasonal stratosphere-troposphere coupling. Geophys. Res. Lett., 46, 13 47913 487, https://doi.org/10.1029/2019GL084763.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sheshadri, A., and R. A. Plumb, 2017: Propagating annular modes: Empirical orthogonal functions, principal oscillation patterns, and time scales. J. Atmos. Sci., 74, 13451361, https://doi.org/10.1175/JAS-D-16-0291.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simpson, I. R., P. Hitchcock, T. G. Shepherd, and J. F. Scinocca, 2011: Stratospheric variability and tropospheric annular-mode timescales. Geophys. Res. Lett., 38, L20806, https://doi.org/10.1029/2011GL049304.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simpson, I. R., T. G. Shepherd, P. Hitchcock, and J. F. Scinocca, 2013: Southern annular mode dynamics in observations and models. Part II: Eddy feedbacks. J. Climate, 26, 52205241, https://doi.org/10.1175/JCLI-D-12-00495.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Son, S.-W., and S. Lee, 2006: Preferred modes of variability and their relationship with climate change. J. Climate, 19, 20632075, https://doi.org/10.1175/JCLI3705.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Son, S.-W., S. Lee, S. B. Feldstein, and J. E. Ten Hoeve, 2008: Time scale and feedback of zonal-mean-flow variability. J. Atmos. Sci., 65, 935952, https://doi.org/10.1175/2007JAS2380.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sparrow, S., M. Blackburn, and J. D. Haigh, 2009: Annular variability and eddy–zonal flow interactions in a simplified atmospheric GCM. Part I: Characterization of high- and low-frequency behavior. J. Atmos. Sci., 66, 30753094, https://doi.org/10.1175/2009JAS2953.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, D. W. J., and J. M. Wallace, 1998: The Arctic oscillation signature in the wintertime geopotential height and temperature fields. Geophys. Res. Lett., 25, 12971300, https://doi.org/10.1029/98GL00950.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, D. W. J., and J. M. Wallace, 2000: Annular modes in the extratropical circulation. Part I: month-to-month variability. J. Climate, 13, 10001016, https://doi.org/10.1175/1520-0442(2000)013<1000:AMITEC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, D. W. J., and E. A. Barnes, 2014: Periodic variability in the large-scale Southern Hemisphere atmospheric circulation. Science, 343, 641645, https://doi.org/10.1126/science.1247660.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, D. W. J., and J. D. Woodworth, 2014: Barotropic and baroclinic annular variability in the Southern Hemisphere. J. Atmos. Sci., 71, 14801493, https://doi.org/10.1175/JAS-D-13-0185.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, D. W. J., and Y. Li, 2015: Baroclinic and barotropic annular variability in the Northern Hemisphere. J. Atmos. Sci., 72, 11171136, https://doi.org/10.1175/JAS-D-14-0104.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zurita-Gotor, P., 2014: On the sensitivity of zonal-index persistence to friction. J. Atmos. Sci., 71, 37883800, https://doi.org/10.1175/JAS-D-14-0067.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
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An Eddy–Zonal Flow Feedback Model for Propagating Annular Modes

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  • 1 Rice University, Houston, Texas
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Abstract

The variability of the zonal-mean large-scale extratropical circulation is often studied using individual modes obtained from empirical orthogonal function (EOF) analyses. The prevailing reduced-order model of the leading EOF (EOF1) of zonal-mean zonal wind, called the annular mode, consists of an eddy–mean flow interaction mechanism that results in a positive feedback of EOF1 onto itself. However, a few studies have pointed out that under some circumstances in observations and GCMs, strong couplings exist between EOF1 and EOF2 at some lag times, resulting in decaying-oscillatory, or propagating, annular modes. Here, we introduce a reduced-order model for coupled EOF1 and EOF2 that accounts for potential cross-EOF eddy–zonal flow feedbacks. Using the analytical solution of this model, we derive conditions for the existence of the propagating regime based on the feedback strengths. Using this model, and idealized GCMs and stochastic prototypes, we show that cross-EOF feedbacks play an important role in controlling the persistence of the annular modes by setting the frequency of the oscillation. We find that stronger cross-EOF feedbacks lead to less persistent annular modes. Applying the coupled-EOF model to the Southern Hemisphere reanalysis data shows the existence of strong cross-EOF feedbacks. The results highlight the importance of considering the coupling of EOFs and cross-EOF feedbacks to fully understand the natural and forced variability of the zonal-mean large-scale circulation.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Sandro Wellyanto Lubis, slubis@rice.edu

Abstract

The variability of the zonal-mean large-scale extratropical circulation is often studied using individual modes obtained from empirical orthogonal function (EOF) analyses. The prevailing reduced-order model of the leading EOF (EOF1) of zonal-mean zonal wind, called the annular mode, consists of an eddy–mean flow interaction mechanism that results in a positive feedback of EOF1 onto itself. However, a few studies have pointed out that under some circumstances in observations and GCMs, strong couplings exist between EOF1 and EOF2 at some lag times, resulting in decaying-oscillatory, or propagating, annular modes. Here, we introduce a reduced-order model for coupled EOF1 and EOF2 that accounts for potential cross-EOF eddy–zonal flow feedbacks. Using the analytical solution of this model, we derive conditions for the existence of the propagating regime based on the feedback strengths. Using this model, and idealized GCMs and stochastic prototypes, we show that cross-EOF feedbacks play an important role in controlling the persistence of the annular modes by setting the frequency of the oscillation. We find that stronger cross-EOF feedbacks lead to less persistent annular modes. Applying the coupled-EOF model to the Southern Hemisphere reanalysis data shows the existence of strong cross-EOF feedbacks. The results highlight the importance of considering the coupling of EOFs and cross-EOF feedbacks to fully understand the natural and forced variability of the zonal-mean large-scale circulation.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Sandro Wellyanto Lubis, slubis@rice.edu
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