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  • Borges, M. D., and P. D. Sardeshmukh, 1995: Barotropic Rossby wave dynamics of zonally varying upper level flows during northern winter. J. Atmos. Sci, 52 , 3779–3796.

    • Search Google Scholar
    • Export Citation

  • Branstator, G. W., 1992: The maintenance of low-frequency anomalies. J. Atmos. Sci, 49 , 1924–1945.

  • Branstator, G. W., 1995: Organization of storm track anomalies by recurring low-frequency circulation anomalies. J. Atmos. Sci, 52 , 207–226.

    • Search Google Scholar
    • Export Citation

  • Branstator, G. W., and S. E. Haupt, 1998: An empirical model of barotropic atmospheric dynamics and its response to tropical forcing. J. Climate, 11 , 2645–2667.

    • Search Google Scholar
    • Export Citation

  • Cai, M., J. S. Whitaker, R. M. Dole, and K. L. Paine, 1996: Dynamics of systematic errors in the NMC medium range forecast model. Mon. Wea. Rev, 124 , 265–276.

    • Search Google Scholar
    • Export Citation

  • Cherry, S., 1996: Singular value decomposition analysis and canonical correlation analysis. J. Climate, 9 , 2003–2009.

  • DelSole, T., 2000: A fundamental limitation of Markov models. J. Atmos. Sci, 57 , 2158–2168.

  • DelSole, T., and A. Y. Hou, 1999: Empirical stochastic models for the dominant climate statistics of a general circulation model. J. Atmos. Sci, 56 , 3436–3456.

    • Search Google Scholar
    • Export Citation

  • Farrell, B., 1988: Optimal excitation of neutral Rossby waves. J. Atmos. Sci, 45 , 163–172.

  • Farrell, B., 1989: Optimal excitation of baroclinic waves. J. Atmos. Sci, 46 , 1193–1206.

  • Farrell, B., and P. J. Ioannou, 1993: Stochastic dynamics of baroclinic waves. J. Atmos. Sci, 50 , 4044–4057.

  • Feldstein, S., 1998: The growth and decay of low-frequency anomalies in a GCM. J. Atmos. Sci, 55 , 415–428.

  • Ferranti, L., T. N. Palmer, F. Molteni, and E. Klinker, 1990: Tropical–extratropical interaction associated with the 30–60 day oscillation and its impact on medium and extended range prediction. J. Atmos. Sci, 47 , 2177–2199.

    • Search Google Scholar
    • Export Citation

  • Gardiner, C. W., 1985: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Springer-Verlag, 442 pp.

  • Haltiner, G. J., and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology. John Wiley and Sons, 477 pp.

  • Hasselmann, K., 1976: Stochastic climate models. Part I. Theory. Tellus, 28 , 474–485.

  • Hendon, H. H., B. Liebmann, M. Newman, and J. D. Glick, 2000: Medium-range forecast errors associated with active episodes of the Madden–Julian oscillation. Mon. Wea. Rev, 128 , 69–86.

    • Search Google Scholar
    • Export Citation

  • Higgins, R. W., and K. C. Mo, 1997: Persistent North Pacific circulation anomalies and the Tropical Intraseasonal Oscillation. J. Climate, 10 , 223–244.

    • Search Google Scholar
    • Export Citation

  • Hoskins, B. J., and D. J. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci, 38 , 1179–1196.

    • Search Google Scholar
    • Export Citation

  • Hoskins, B. J., and T. Ambrizzi, 1993: Rossby wave propagation on a realistic longitudinally varying flow. J. Atmos. Sci, 50 , 1661–1671.

    • Search Google Scholar
    • Export Citation

  • Johnson, S. D., D. S. Battisti, and E. S. Sarachik, 2000: Empirically derived Markov models and prediction of tropical Pacific sea surface temperature anomalies. J. Climate, 13 , 3–17.

    • Search Google Scholar
    • Export Citation

  • Kiladis, G. N., and K. M. Weickmann, 1992: Circulation anomalies associated with tropical convection during northern winter. Mon. Wea. Rev, 120 , 1900–1923.

    • Search Google Scholar
    • Export Citation

  • Klinker, E., 1990: Investigation of systematic errors by relaxation experiments. Quart. J. Roy. Meteor. Soc, 116 , 573–594.

  • Lau, K-M., and T. J. Phillips, 1986: Coherent fluctuations of extratropical geopotential height and tropical convection in intraseasonal timescales. J. Atmos. Sci, 43 , 1164–1181.

    • Search Google Scholar
    • Export Citation

  • Lau, N-C., 1983: Midlatitude wintertime circulation anomalies appearing in a 15-yr GCM experiment. Large Scale Dynamical Processes in the Atmosphere, B. J. Hoskins and R. P. Pearce, Eds., Academic Press, 111–125.

    • Search Google Scholar
    • Export Citation

  • Liebmann, B., and C. A. Smith, 1996: Description of a complete (interpolated) outgoing longwave radiation dataset. Bull. Amer. Meteor. Soc, 77 , 1275–1277.

    • Search Google Scholar
    • Export Citation

  • Lo, F., and H. H. Hendon, 2000: Empirical extended-range prediction of the Madden–Julian oscillation. Mon. Wea. Rev, 128 , 2528–2543.

    • Search Google Scholar
    • Export Citation

  • Mo, K. C., 1999: Alternating dry and wet episodes over California and intraseasonal oscillations. Mon. Wea. Rev, 127 , 2759–2776.

  • Mo, K. C., and R. W. Higgins, 1998: Tropical convection and precipitation regimes in the western United States. J. Climate, 11 , 2404–2423.

    • Search Google Scholar
    • Export Citation

  • Newman, M., and P. D. Sardeshmukh, 1995: A caveat concerning singular value decomposition. J. Climate, 8 , 352–360.

  • Newman, M., and P. D. Sardeshmukh, 1998: The impact of the annual cycle on the North Pacific/North American response to remote low-frequency forcing. J. Atmos. Sci, 55 , 1336–1353.

    • Search Google Scholar
    • Export Citation

  • Newman, M., P. D. Sardeshmukh, and C. Penland, 1997: Stochastic forcing of the wintertime extratropical flow. J. Atmos. Sci, 54 , 435–455.

    • Search Google Scholar
    • Export Citation

  • Newman, M., M. A. Alexander, C. R. Winkler, J. D. Scott, and J. J. Barsugli, 2000: A linear diagnosis of the coupled extratropical ocean atmosphere system in the GFDL GCM. Atmos. Sci. Lett, 1 , 1–12.

    • Search Google Scholar
    • Export Citation

  • Newman, M., P. D. Sardeshmukh, and C. R. Winkler, 2001: A linear model of wintertime low-frequency variability. Part II: Diagnosis of covariance statistics. J. Climate, submitted.

    • Search Google Scholar
    • Export Citation

  • Opsteegh, J. D., and H. M. Van den Dool, 1980: Seasonal differences in the stationary response of a linearized primitive equations model: Prospects for long-range weather forecasting? J. Atmos. Sci, 37 , 2169–2185.

    • Search Google Scholar
    • Export Citation

  • Papanicolaou, G., and W. Kohler, 1974: Asymptotic theory of mixing stochastic ordinary differential equations. Commun. Pure Appl. Math, 27 , 641–668.

    • Search Google Scholar
    • Export Citation

  • Penland, C., 1989: Random forcing and forecasting using principal oscillation pattern analysis. Mon. Wea. Rev, 117 , 2165–2185.

  • Penland, C., 1996: A stochastic model of IndoPacific sea surface temperature anomalies. Physica D, 98 , 534–558.

  • Penland, C., and M. Ghil, 1993: Forecasting Northern Hemisphere 700-mb geopotential heights using principal oscillation patterns. Mon. Wea. Rev, 121 , 2355–2372.

    • Search Google Scholar
    • Export Citation

  • Penland, C., and T. Magorian, 1993: Prediction of Niño-3 sea surface temperatures using linear inverse modeling. J. Climate, 6 , 1067–1076.

    • Search Google Scholar
    • Export Citation

  • Penland, C., and L. Matrosova, 1994: A balance condition for stochastic numerical models with application to the El Niño–Southern Oscillation. J. Climate, 7 , 1352–1372.

    • Search Google Scholar
    • Export Citation

  • Penland, C., and P. D. Sardeshmukh, 1995: The optimal growth of tropical sea surface temperature anomalies. J. Climate, 8 , 1999–2024.

  • Penland, C., and L. Matrosova, 1998: Prediction of tropical Atlantic sea surface temperatures using linear inverse modeling. J. Climate, 11 , 483–496.

    • Search Google Scholar
    • Export Citation

  • Qin, J., and W. A. Robinson, 1995: The impact of tropical forcing on extratropical predictability in a simple global model. J. Atmos. Sci, 52 , 3895–3910.

    • Search Google Scholar
    • Export Citation

  • Qin, J., and H. M. Van den Dool, 1996: Simple extensions of an NWP model. Mon. Wea. Rev, 124 , 277–287.

  • Sardeshmukh, P. D., 1993: The baroclinic chi problem and its application to the diagnosis of atmospheric heating rates. J. Atmos. Sci, 50 , 1099–1112.

    • Search Google Scholar
    • Export Citation

  • Sardeshmukh, P. D., and B. J. Hoskins, 1984: Spatial smoothing on the sphere. Mon. Wea. Rev, 112 , 2524–2529.

  • Sardeshmukh, P. D., and B. J. Hoskins, 1985: Vorticity balances in the tropics during the 1982–1983 El Niño–Southern Oscillation event. Quart. J. Roy. Meteor. Soc, 111 , 261–278.

    • Search Google Scholar
    • Export Citation

  • Sardeshmukh, P. D., and B. J. Hoskins, 1988: The generation of global rotational flow by steady idealized divergence. J. Atmos. Sci, 45 , 1228–1251.

    • Search Google Scholar
    • Export Citation

  • Sardeshmukh, P. D., M. Newman, and M. D. Borges, 1997: Free barotropic Rossby wave dynamics of the wintertime low-frequency flow. J. Atmos. Sci, 54 , 5–23.

    • Search Google Scholar
    • Export Citation

  • Sardeshmukh, P. D., M. Newman, and C. R. Winkler, 1999: Dynamically consistent estimates of diabatic heating. Proc. 24th Annual Climate Diagnostics and Prediction Workshop, Tucson, AZ, 172–175.

    • Search Google Scholar
    • Export Citation

  • Sardeshmukh, P. D., G. P. Compo, and C. Penland, 2000: Changes of probability associated with El Niño. J. Climate, 13 , 4268–4286.

  • Schemm, J. E., H. M. Van den Dool, and S. Saha, 1996: A multi-year DERF experiment at NCEP. Preprints, 11th Conf. on Numerical Weather Prediction, Norfolk, VA, Amer. Meteor. Soc., 47–49.

    • Search Google Scholar
    • Export Citation

  • Simmons, A. J., 1982: The forcing of stationary wave motion by tropical diabatic heating. Quart. J. Roy. Meteor. Soc, 108 , 503–534.

  • Simmons, A. J., J. M. Wallace, and G. W. Branstator, 1983: Barotropic wave propagation and instability, and atmospheric teleconnection patterns. J. Atmos. Sci, 40 , 1363–1392.

    • Search Google Scholar
    • Export Citation

  • Smith, C. A., and P. D. Sardeshmukh, 2000: The effect of ENSO on the intraseasonal variance of surface temperatures in winter. Int. J. Climatol, 20 , 1543–1557.

    • 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 , 907–918.

    • Search Google Scholar
    • Export Citation

  • Van den Dool, H. M., 1983: A possible explanation of the observed persistence of monthly mean circulation anomalies. Mon. Wea. Rev, 111 , 539–544.

    • Search Google Scholar
    • Export Citation

  • von Storch, H., and J-S. Xu, 1990: Principal oscillation pattern analysis of the 30–60-day oscillation in the tropical troposphere. Part II: Definition of an index and its prediction. Climate Dyn, 4 , 175–190.

    • Search Google Scholar
    • Export Citation

  • von Storch, H., and D. P. Baumhefner, 1991: Principal oscillation pattern analysis of the tropical 30–60-day oscillation. Part II: The prediction of equatorial velocity potential and its skill. Climate Dyn, 6 , 1–12.

    • Search Google Scholar
    • Export Citation

  • Whitaker, J. S., and P. D. Sardeshmukh, 1998: A linear theory of extratropical synoptic eddy statistics. J. Atmos. Sci, 55 , 237–258.

  • Xie, P., and P. A. Arkin, 1997: Global precipitation: A 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs. Bull. Amer. Meteor. Soc, 78 , 2539–2557.

    • Search Google Scholar
    • Export Citation

  • Xu, J-S., and H. von Storch, 1990: Predicting the state of the Southern Oscillation using principal oscillation pattern analysis. J. Climate, 3 , 1316–1329.

    • Search Google Scholar
    • Export Citation

  • Zhang, C., and H. H. Hendon, 1997: Propagating and standing components of the intraseasonal oscillation in tropical convection. J. Atmos. Sci, 54 , 741–752.

    • Search Google Scholar
    • Export Citation
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Research Article

A Linear Model of Wintertime Low-Frequency Variability. Part I: Formulation and Forecast Skill

Christopher R. WinklerNOAA–CIRES Climate Diagnostics Center, University of Colorado, Boulder, Colorado

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Matthew NewmanNOAA–CIRES Climate Diagnostics Center, University of Colorado, Boulder, Colorado

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Prashant D. SardeshmukhNOAA–CIRES Climate Diagnostics Center, University of Colorado, Boulder, Colorado

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Print Publication:
15 Dec 2001
DOI:
https://doi.org/10.1175/1520-0442(2001)014<4474:ALMOWL>2.0.CO;2
Page(s):
4474–4494
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Abstract

A linear inverse model (LIM) suitable for studies of atmospheric extratropical variability on longer than weekly timescales is constructed using observations of the past 30 years. Notably, it includes tropical diabatic heating as an evolving model variable rather than as a forcing, and also includes, in effect, the feedback of the extratropical weather systems on the more slowly varying circulation. Both of these features are shown to be important contributors to the model's realism.

Forecast skill is an important test of any model's usefulness as a diagnostic tool. The LIM is better at forecasting week 2 anomalies than a dynamical model based on the linearized baroclinic equations of motion (with many more than the LIM's 37 degrees of freedom) that is forced with observed (as opposed to the LIM's predicted) tropical heating throughout the forecast. Indeed, at week 2 the LIM's skill is competitive with that of the global nonlinear medium-range forecast (MRF) model with nominally O(106) degrees of freedom in use at the National Centers for Environmental Prediction (NCEP). Importantly, this encouraging model performance is not limited to years of El Niño or La Niña episodes. This suggests that accurate prediction of tropical diabatic heating, rather than of tropical sea surface temperatures per se, is key to enhancing extratropical predictability.

The LIM assumes that the dynamics of extratropical low-frequency variability are linear, stable, and stochastically forced. The approximate validity of these assumptions is demonstrated through several tests. A potentially limiting aspect of such a stable linear model with decaying eigenmodes concerns its ability to predict anomaly growth. It is nevertheless found, through a singular vector analysis of the model's propagator, that predictable anomaly growth can and does occur in this dynamical system through constructive modal interference. Examination of the dominant growing singular vectors further confirms the importance of tropical heating anomalies associated with El Niño/La Niña as well as Madden–Julian oscillation episodes in the predictable dynamics of the extratropical circulation. The relative contribution of initial streamfunction and heating perturbations to the development of amplifying anomalies is similarly examined. This analysis suggests that without inclusion of the effects of tropical heating, extratropical weekly averages may be predictable about two weeks ahead, but with tropical heating included, they may be predictable as far as seven weeks ahead.

Corresponding author address: Matthew Newman, NOAA–CIRES Climate Diagnostics Center, Mail Code R/CDC, 325 Broadway, Boulder, CO 80305-3328. Email: matt@cdc.noaa.gov

Abstract

A linear inverse model (LIM) suitable for studies of atmospheric extratropical variability on longer than weekly timescales is constructed using observations of the past 30 years. Notably, it includes tropical diabatic heating as an evolving model variable rather than as a forcing, and also includes, in effect, the feedback of the extratropical weather systems on the more slowly varying circulation. Both of these features are shown to be important contributors to the model's realism.

Forecast skill is an important test of any model's usefulness as a diagnostic tool. The LIM is better at forecasting week 2 anomalies than a dynamical model based on the linearized baroclinic equations of motion (with many more than the LIM's 37 degrees of freedom) that is forced with observed (as opposed to the LIM's predicted) tropical heating throughout the forecast. Indeed, at week 2 the LIM's skill is competitive with that of the global nonlinear medium-range forecast (MRF) model with nominally O(106) degrees of freedom in use at the National Centers for Environmental Prediction (NCEP). Importantly, this encouraging model performance is not limited to years of El Niño or La Niña episodes. This suggests that accurate prediction of tropical diabatic heating, rather than of tropical sea surface temperatures per se, is key to enhancing extratropical predictability.

The LIM assumes that the dynamics of extratropical low-frequency variability are linear, stable, and stochastically forced. The approximate validity of these assumptions is demonstrated through several tests. A potentially limiting aspect of such a stable linear model with decaying eigenmodes concerns its ability to predict anomaly growth. It is nevertheless found, through a singular vector analysis of the model's propagator, that predictable anomaly growth can and does occur in this dynamical system through constructive modal interference. Examination of the dominant growing singular vectors further confirms the importance of tropical heating anomalies associated with El Niño/La Niña as well as Madden–Julian oscillation episodes in the predictable dynamics of the extratropical circulation. The relative contribution of initial streamfunction and heating perturbations to the development of amplifying anomalies is similarly examined. This analysis suggests that without inclusion of the effects of tropical heating, extratropical weekly averages may be predictable about two weeks ahead, but with tropical heating included, they may be predictable as far as seven weeks ahead.

Corresponding author address: Matthew Newman, NOAA–CIRES Climate Diagnostics Center, Mail Code R/CDC, 325 Broadway, Boulder, CO 80305-3328. Email: matt@cdc.noaa.gov

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