• Barnston, A. G., , and R. E. Livezey, 1987: Classification, seasonality and persistence of low-frequency atmospheric circulation patterns. Mon. Wea. Rev., 115 , 10831126.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 1985: Analysis of general circulation model sea-surface temperature anomaly simulations using a linear model. Part I: Forced solutions. J. Atmos. Sci., 42 , 22252241.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 1990: Low-frequency patterns induced by stationary waves. J. Atmos. Sci., 47 , 629648.

  • Branstator, G., 1992: The maintenance of low-frequency atmospheric anomalies. J. Atmos. Sci., 49 , 19241945.

  • DeWeaver, E., , and S. Nigam, 2000: Zonal-eddy dynamics of the North Atlantic Oscillation. J. Climate, 13 , 38933914.

  • Graham, R. J., , M. Gordon, , P. J. McLean, , S. Ineson, , M. R. Huddleston, , M. K. Davey, , A. Brookshaw, , and R. T. H. Barnes, 2005: A performance comparison of coupled and uncoupled versions of the Met Office seasonal prediction general circulation model. Tellus, 57A , 320339.

    • Search Google Scholar
    • Export Citation
  • Greenbaum, A., 1997: Frontiers in applied mathematics. Iterative Methods for Solving Linear Systems. Vol. 17, SIAM, 220 pp.

  • Hall, N. M. J., , and P. D. Sardeshmukh, 1998: Is the time-mean Northern Hemisphere flow baroclinically unstable? J. Atmos. Sci., 55 , 4156.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., , M. Ting, , and H. Wang, 2002: Northern winter stationary waves: Theory and modeling. J. Climate, 15 , 21252144.

  • Horel, J. D., , and J. M. Wallace, 1981: Planetary-scale atmospheric phenomena associated with the Southern Oscillation. Mon. Wea. Rev., 109 , 813829.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , and D. J. Karoly, 1981: The steady linear responses of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci., 38 , 11791196.

    • Search Google Scholar
    • Export Citation
  • Hurrell, J. W., , Y. Kushnir, , G. Ottersen, , and M. Visbeck, 2003: An overview of the North Atlantic Oscillation. The North Atlantic Oscillation, Geophys. Monogr., Vol. 134, Amer. Geophys. Union, 1–35.

  • Jin, F-F., , and B. J. Hoskins, 1995: The direct response to tropical heating in a baroclinic atmosphere. J. Atmos. Sci., 52 , 307319.

  • Jin, F-F., , L-L. Pan, , and M. Watanabe, 2006: Dynamics of synoptic eddy and low-frequency flow interaction. Part I: A linear closure. J. Atmos. Sci., 63 , 16771694.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 341 pp.

  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Kimoto, M., , F-F. Jin, , M. Watanabe, , N. Watanabe, , and N. Yasutomi, 2001: Zonal-eddy coupling and a neutral mode theory for the Arctic Oscillation. Geophys. Res. Lett., 28 , 737740.

    • Search Google Scholar
    • Export Citation
  • Kushnir, Y., , and J. M. Wallace, 1989: Low-frequency variability in the Northern Hemisphere winter: Geographical distribution, structure and time-scale dependence. J. Atmos. Sci., 46 , 31223142.

    • Search Google Scholar
    • Export Citation
  • Meurant, G., 1999: Computer Solution of Large Linear Systems. Elsevier, 776 pp.

  • Navarra, A., 1990: Steady linear response to thermal forcing of an anomaly model with an asymmetric climatology. J. Atmos. Sci., 47 , 148169.

    • Search Google Scholar
    • Export Citation
  • Pan, L-L., , F-F. Jin, , and M. Watanabe, 2006: Dynamics of synoptic eddy and low-frequency flow interaction. Part III: Baroclinic model results. J. Atmos. Sci., 63 , 17091725.

    • Search Google Scholar
    • Export Citation
  • Peng, S., , and J. S. Whitaker, 1999: Mechanisms determining the atmospheric response to midlatitude SST anomalies. J. Climate, 12 , 13931408.

    • Search Google Scholar
    • Export Citation
  • Peng, S., , and W. A. Robinson, 2001: Relationships between atmospheric internal variability and the responses to an extratropical SST anomaly. J. Climate, 14 , 29432959.

    • Search Google Scholar
    • Export Citation
  • Rodwell, M. J., , D. P. Rowell, , and C. K. Folland, 1999: Oceanic forcing of the wintertime North Atlantic Oscillation and European climate. Nature, 398 , 320323.

    • Search Google Scholar
    • Export Citation
  • Ting, M., , and I. M. Held, 1990: The stationary wave response to a tropical SST anomaly in an idealized GCM. J. Atmos. Sci., 47 , 25462566.

    • Search Google Scholar
    • Export Citation
  • Ting, M., , and N-C. Lau, 1993: A diagnostic and modeling study of the monthly mean wintertime anomalies appearing in a 100-year GCM experiment. J. Atmos. Sci., 50 , 28452867.

    • Search Google Scholar
    • Export Citation
  • Ting, M., , and P. D. Sardeshmukh, 1993: Factors determining the extratropical response to equatorial diabatic heating anomalies. J. Atmos. Sci., 50 , 907918.

    • Search Google Scholar
    • Export Citation
  • Ting, M., , and L. Yu, 1998: Steady response to tropical heating in wavy linear and nonlinear baroclinic models. J. Atmos. Sci., 55 , 35653582.

    • Search Google Scholar
    • Export Citation
  • Uppala, S. M., and Coauthors, 2005: The ERA-40 re-analysis. Quart. J. Roy. Meteor. Soc., 131 , 29613012.

  • Wallace, J. M., 2000: North Atlantic Oscillation/annular mode: Two paradigms—One phenomenon. Quart. J. Roy. Meteor. Soc., 126 , 791805.

    • Search Google Scholar
    • Export Citation
  • Wallace, J. M., , and D. S. Gutzler, 1981: Teleconnections in the geopotential height field during the Northern Hemisphere winter. Mon. Wea. Rev., 109 , 784812.

    • Search Google Scholar
    • Export Citation
  • Watanabe, M., , and M. Kimoto, 2000: Atmosphere-ocean thermal coupling in the North Atlantic: A positive feedback. Quart. J. Roy. Meteor. Soc., 126 , 33433369. Corrigendum. 127 , 733734.

    • Search Google Scholar
    • Export Citation
  • Watanabe, M., , and F-F. Jin, 2003: A moist linear baroclinic model: Coupled dynamical–convective response to El Niño. J. Climate, 16 , 11211139.

    • Search Google Scholar
    • Export Citation
  • Watanabe, M., , and F-F. Jin, 2004: Dynamical prototype of the Arctic Oscillation as revealed by a neutral singular vector. J. Climate, 17 , 21192138.

    • Search Google Scholar
    • Export Citation
  • Yanai, M., , C. Li, , and Z. Song, 1992: Seasonal heating of the Tibetan Plateau and its effects on the evolution of the Asian summer monsoon. J. Meteor. Soc. Japan, 70 , 319351.

    • Search Google Scholar
    • Export Citation
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Accelerated Iterative Method for Solving Steady Problems of Linearized Atmospheric Models

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  • 1 Faculty of Environmental Earth Science, Hokkaido University, Sapporo, Japan
  • 2 Department of Meteorology, The Florida State University, Tallahassee, Florida, and Department of Meteorology, University of Hawaii at Manoa, Honolulu, Hawaii
  • 3 International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii
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Abstract

A new approach, referred to as the accelerated iterative method (AIM), is developed for obtaining steady atmospheric responses with a zonally varying basic state. The linear dynamical operator is divided into two parts, one associated with the zonally symmetric component and the other with the asymmetric component of the basic state. To ensure an accelerated convergence of the iteration to the true solution, the two parts of the operator are modified by adding and subtracting an identical “accelerating” operator. AIM is shown to be an efficient scheme well suited for computing the higher-resolution, steady atmospheric response of barotropic and more so of baroclinic numerical models linearized about a zonally varying basic state.

A preliminary application of AIM to the T42 baroclinic model linearized about the observed winter (December–February) climatology is presented. A series of steady responses forced by the diabatic heating and transient eddy forcing, both estimated from reanalysis data for individual winters during 1960–2002, captures a certain part of the observed interannual variability associated with dominant teleconnection patterns, such as the North Atlantic Oscillation and the Pacific–North American pattern.

Thus, AIM should be a useful tool for the diagnostic studies of the low-frequency variability of the atmosphere.

* Current affiliation: Department of Land, Air and Water Resources, University of California, Davis, Davis, California

Corresponding author address: M. Watanabe, Faculty of Environmental Earth Science, Hokkaido University, Nishi 5 Kita 10, Sapporo, Hokkaido 060-0810, Japan. Email: hiro@ees.hokudai.ac.jp

Abstract

A new approach, referred to as the accelerated iterative method (AIM), is developed for obtaining steady atmospheric responses with a zonally varying basic state. The linear dynamical operator is divided into two parts, one associated with the zonally symmetric component and the other with the asymmetric component of the basic state. To ensure an accelerated convergence of the iteration to the true solution, the two parts of the operator are modified by adding and subtracting an identical “accelerating” operator. AIM is shown to be an efficient scheme well suited for computing the higher-resolution, steady atmospheric response of barotropic and more so of baroclinic numerical models linearized about a zonally varying basic state.

A preliminary application of AIM to the T42 baroclinic model linearized about the observed winter (December–February) climatology is presented. A series of steady responses forced by the diabatic heating and transient eddy forcing, both estimated from reanalysis data for individual winters during 1960–2002, captures a certain part of the observed interannual variability associated with dominant teleconnection patterns, such as the North Atlantic Oscillation and the Pacific–North American pattern.

Thus, AIM should be a useful tool for the diagnostic studies of the low-frequency variability of the atmosphere.

* Current affiliation: Department of Land, Air and Water Resources, University of California, Davis, Davis, California

Corresponding author address: M. Watanabe, Faculty of Environmental Earth Science, Hokkaido University, Nishi 5 Kita 10, Sapporo, Hokkaido 060-0810, Japan. Email: hiro@ees.hokudai.ac.jp

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