Climate Dynamics

, Volume 50, Issue 9–10, pp 3757–3773 | Cite as

A stochastic model with a low-frequency amplification feedback for the stratospheric northern annular mode

  • Yueyue Yu
  • Ming Cai
  • Rongcai Ren


We consider three indices to measure the polar stratospheric mass and stratospheric meridional mass circulation variability: anomalies of (1) total mass in the polar stratospheric cap (60–90°N, above the isentropic surface 400 K, PSM), (2) total adiabatic mass transport across 60°N into the polar stratosphere cap (AMT), (3) and total diabetic mass transport across 400 K from the polar stratosphere into the troposphere below (DMT). It is confirmed that the negative stratospheric Northern Annular Mode (NAM) and PSM indices have a nearly indistinguishable temporal evolution and a similar red-noise-like spectrum with a de-correlation timescale of 4 weeks. This enables us to examine the low-frequency nature of the NAM in the framework of mass circulation, namely, \(\frac{d}{{dt}}{\text{PSM}}={\text{AMT}} - {\text{DMT}}\). The DMT index tends to be positively correlated with the PSM with a red-noise-like spectrum, representing slow radiative cooling processes giving rise to a de-correlation timescale of 3–4 weeks. The AMT is nearly perfectly correlated with the day-to-day tendency of PSM, reflecting a robust quasi 90° out-of-phase relation between the AMT and PSM at all frequency bands. Variations of vertically westward tilting of planetary waves contribute mainly to the high-frequency portion of AMT. It is the wave amplitude’s slow vacillation that plays the leading role in the quasi 90° out-of-phase relation between the AMT and PSM. Based on this, we put forward a linear stochastic model with a low-frequency amplification feedback from low-frequency amplitude vacillations of planetary waves to explain the amplified low-frequency response of PSM/NAM to a stochastic forcing from the westward tilting variability.


Stratospheric NAM variability Polar stratospheric mass Poleward mass transport Linear stochastic model with a low-frequency amplification feedback 



We are grateful for the two anonymous reviewers’ insightful and constructive comments that led to significant improvements in the presentation. Y. Y. Yu and M. Cai were in part supported by Grants from the National Science Foundation (AGS-1262173 and AGS-1354834), and NASA Interdisciplinary Studies Program Grant (NNH12ZDA001N-IDS). RC Ren was supported by National Science Foundation China (41430533). ERA-Interim data are available from the ECMWF ( and the NAM index is downloaded from


  1. Andrews DG, McIntyre ME (1976) Planetary waves in horizontal and vertical shear: the generalized Eliassen–Palm relation and the mean zonal acceleration. J Atmos Sci 33:2031–2048CrossRefGoogle Scholar
  2. Andrews DG, McIntyre ME (1978) An exact theory of nonlinear waves on a Lagrangian-mean flow. J Fluid Mech 89:609–646CrossRefGoogle Scholar
  3. Baldwin MP, Dunkerton TJ (1999) Propagation of the Arctic Oscillation from the stratosphere to the troposphere. J Geophys Res 104:30937–30946CrossRefGoogle Scholar
  4. Baldwin MP, Dunkerton TJ (2001) Stratospheric harbingers of anomalous weather regimes. Science 294:581–584CrossRefGoogle Scholar
  5. Baldwin MP, Thompson DWJ (2009) A critical comparison of stratosphere–troposphere coupling indices. Q J R Meteorol Soc 135:1661–1672CrossRefGoogle Scholar
  6. Baldwin MP, Stephenson DB, Thompson DWJ, Timothy JD, Andrew JC, Alan O (2003) Stratospheric memory and skill of extended-range weather forecasts. Science 301:636–640CrossRefGoogle Scholar
  7. Black RX and McDaniel BA (2007a) Interannual variability in the Southern Hemisphere circulation organized by stratospheric final warming events. J Amtmos Sci 64:2968–2974CrossRefGoogle Scholar
  8. Black RX and McDaniel BA (2007b) The dynamics of Northern Hemisphere stratospheric final warming events. J Amtmos Sci 64:2932–2946CrossRefGoogle Scholar
  9. Cai M (2003) Potential vorticity intrusion index and climate variability of surface temperature. Geophys Res Lett 30:1119CrossRefGoogle Scholar
  10. Cai M, Ren RC (2007) Meridional and downward propagation of atmospheric circulation anomalies. Part I: Northern Hemisphere cold season variability. J Atmos Sci 64:1880–1901CrossRefGoogle Scholar
  11. Cai M, Shin CS (2014) A total flow perspective of atmospheric mass and angular momentum circulations: Boreal winter mean state. J Atmos Sci 71:2244–2263CrossRefGoogle Scholar
  12. Cai M, Barton C, Shin CS, Chagnon JM (2014) The continuous mutual evolution of equatorial waves and the Quasi-Biennial Oscillation of zonal flow in the equatorial stratosphere. J Atmos Sci 71:2878–2885CrossRefGoogle Scholar
  13. Cai M, Yu YY, Deng Y, van den Dool HM, Ren RC, Saha S, Wu XR, Huang J (2016) Feeling the pulse of the stratosphere: an emerging opportunity for predicting continental-scale cold air outbreaks one month in advance. Bull Am Meteorol Soc 97:1475–1489CrossRefGoogle Scholar
  14. Charlton AJ, Polvani LM (2007) A new look at stratospheric sudden warmings: Part I: climatology and modelling benchmark. J Clim 20:449–469CrossRefGoogle Scholar
  15. Charney JG, Drazin PG (1961) Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J Geophys Res 66:83–109CrossRefGoogle Scholar
  16. Christiansen B (2005) Downward propagation and statistical forecast of the near-surface weather. J Geophys Res 110:D14104CrossRefGoogle Scholar
  17. Christiansen B (2009) Is the atmosphere interesting? A projection pursuit study of the circulation in the Northern Hemisphere winter. J Clim 22:1239–1254CrossRefGoogle Scholar
  18. Cohen J, Salstein D, Saito K (2002) A dynamical framework to understand and predict the major Northern Hemisphere mode. Geophys Res Lett 29:1412CrossRefGoogle Scholar
  19. Dee DP et al (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137:553–597CrossRefGoogle Scholar
  20. Eliassen A, Palm E (1961) On the transfer of energy in stationary mountain waves. Geofys Publ Oslo 22:1–23Google Scholar
  21. Garfinkel, CI, Hartmann DL, Sassi F (2010) Tropospheric precursors of anomalous Northern Hemisphere stratospheric polar vortices. J Clim 23:3282–3299CrossRefGoogle Scholar
  22. Gerber EP, Coauthors (2010) Stratosphere-troposphere coupling and annular mode variability in chemistry-climate models. J Geophys Res 115:D00M06CrossRefGoogle Scholar
  23. Gerber EP, Polvani LM, Ancukiewicz D (2008a) Annular mode time scales in the intergovernmental panel on climate change fourth assessment report models. Geophys Res Lett 35:L22707CrossRefGoogle Scholar
  24. Gerber EP, Voronin S, Polvani LM (2008b) Testing the Annular Mode Autocorrelation Timescale In Simple Atmospheric General Circulation Models. Mon Wea Rev 136:1523–1536CrossRefGoogle Scholar
  25. Gerber EP, Orbe C, Polvani LM (2009) Stratospheric influence on the tropospheric circulation revealed by idealized ensemble forecasts. Geophys Res Lett 36:L24801CrossRefGoogle Scholar
  26. Haynes P (2005) Stratospheric dynamics. Annu Rev Fluid Mech 37:263–293CrossRefGoogle Scholar
  27. Haynes PH, et al (1991) On the “Downward Control” of extratropical diabatic circulations by eddy-induced mean zonal forces. J Atmos Sci 48:651–678CrossRefGoogle Scholar
  28. Holton JR, Haynes PH, McIntyre ME, Douglass AR, Rood RB, Pfister L (1995) Stratosphere–troposphere exchange. Rev Geophys 33:403–439CrossRefGoogle Scholar
  29. Hu JG, Ren RC, Xu HM (2014) Occurrence of Winter stratospheric sudden warming events and the seasonal timing of spring stratospheric final warming. J Atmos Sci 71:2319–2334CrossRefGoogle Scholar
  30. Hu JG, Ren RC, Xu HM, Yang SY (2015) Seasonal timing of stratospheric final warming associated with the intensity of stratospheric sudden warming in preceding winter. Sci China Ser D Earth Sci 58:615–627CrossRefGoogle Scholar
  31. Johnson DR (1989) The forcing and maintenance of global monsoonal circulations: an isentropic analysis. Adv Geophys 31:43–316CrossRefGoogle Scholar
  32. Karpechko AY (2015) Improvements in statistical forecasts of monthly and two-monthly surface air temperatures using a stratospheric predictor. Q J R Meteorol Soc 141:2444–2456CrossRefGoogle Scholar
  33. Kidston J, Scaife AA, Hardiman SC, Mitchell DM, Butchart N, Baldwin MP, Gray LJ (2015) Stratospheric influence on tropospheric jet streams, storm tracks and surface weather. Nat Geosci 8:433–440CrossRefGoogle Scholar
  34. Kolstad EW, Charlton-Perez AJ (2010) Observed and simulated precursors of stratospheric polar vortex anomalies in the Northern Hemisphere. Clim Dyn 37:1443–1456CrossRefGoogle Scholar
  35. Kuroda Y (2002) Relationship between the polar-night jet oscillation and the annular mode. Geophys Res Lett. doi: 10.1029/2001GL013933 Google Scholar
  36. Kushner PJ, Polvani LM (2004) Stratosphere-troposphere coupling in a relatively simple AGCM: the role of eddies. J Clim 17:629–639CrossRefGoogle Scholar
  37. Limpasuvan V, Hartmann DL (2000) Wave-maintained annular modes of climate variability. J Clim 13:4414–4429CrossRefGoogle Scholar
  38. Limpasuvan V, Thompson DWJ, Hartmann DL (2004) The life cycle of the Northern Hemisphere sudden stratospheric warmings. J Clim 17:2584–2596CrossRefGoogle Scholar
  39. Limpasuvan V, Hartmann DL, Thompson DWJ, Jeev K, Yung YL (2005) Stratosphere–troposphere evolution during polar vortex intensification. J Geophys Res 110:D24101CrossRefGoogle Scholar
  40. Lorenz DJ, Hartmann DL (2001) Eddy–zonal flow feedback in the southern hemisphere. J Atmos Sci 58:3312–3327CrossRefGoogle Scholar
  41. Lorenz DJ, Hartmann DL (2003) Eddy–zonal flow feedback in the Northern Hemisphere winter. J Clim 16:1212–1227CrossRefGoogle Scholar
  42. McDaniel BA, Black RX (2005) Intraseasonal dynamical evolution of the northern annular mode. J Clim 18:3820–3839CrossRefGoogle Scholar
  43. Mitchell DM, Gray LJ, Anstey J, Baldwin MP, Charlton-Perez AJ (2013) The influence of stratospheric vortex displacements and splits on surface climate. J Clim 26:2668–2682CrossRefGoogle Scholar
  44. Pauluis O, Czaja A, Korty R (2008) The global atmospheric circulation on moist isentropes. Science 321:1075–1078CrossRefGoogle Scholar
  45. Pauluis O, Shaw T, Laliberté F (2011) A statistical generalization of the transformed Eulerian-mean circulation for an arbitrary vertical coordinate system. J Atmos Sci 68:1766–1783CrossRefGoogle Scholar
  46. Polvani LM, Kushner PJ (2002) Tropospheric response to stratospheric perturbations in a relatively simple general circulation model. Geophys Res Lett 29:1114CrossRefGoogle Scholar
  47. Polvani LM, Waugh DW (2004) Upward wave activity flux as a precursor to extreme stratospheric events and subsequent anomalous surface weather regimes. J Clim 17:3548–3554CrossRefGoogle Scholar
  48. Ren RC, Cai M (2007) Meridional and vertical out-of-phase relationships of temperature omalies associated with the Northern Annular Mode variability. Geophys Res Lett 34:L07704CrossRefGoogle Scholar
  49. Ren RC, Cai M (2008) Meridional and downward propagation of atmospheric circulation anomalies. Part II: Southern Hemisphere cold season variability. J Atmos Sci 65:2343–2359CrossRefGoogle Scholar
  50. Scaife AA, Knight JR (2008) Ensemble simulations of the cold European winter of 2005–2006. Q J R Meteorol Soc 134:1647–1659CrossRefGoogle Scholar
  51. Scaife AA, Knight JR, Vallis GK, Folland CK (2005) A stratospheric influence on the winter NAO and North Atlantic surface climate. Geophys Res Lett 32:L18715CrossRefGoogle Scholar
  52. Shepherd TG (2002) Issues in Stratosphere-troposphere Coupling. J Meteorol Soc Jpn Ser II 80:769–792CrossRefGoogle Scholar
  53. Siegmund P (2005) Stratospheric polar cap mean height and temperature as extended-range weather predictors. Mon Wea Rev 133:24362448CrossRefGoogle Scholar
  54. Simmons A, Uppala S, Dee D, Kobayashi S (2006) ERA-Interim: new ECMWF reanalysis products from 1989 onwards. ECMWF Newsletter, No. 110, ECMWF. Reading, UK, pp 26–35Google Scholar
  55. Smith DM, Scaife AA, Kirtman BP (2012) What is the current state of scientific knowledge with regard to seasonal and decadal forecasting? Environ Res Lett 7:015602. doi: 10.1088/1748-9326/7/1/015602 CrossRefGoogle Scholar
  56. Song Y, Robinson WA (2004) Dynamical mechanisms for stratospheric influences on the troposphere. J Atmos Sci 61:1711–1725CrossRefGoogle Scholar
  57. Thompson DWJ, Wallace JM (1998) The Arctic Oscillation signature in the wintertime geopotential height and temperature fields. Geophys Res Lett 25:1297–1300CrossRefGoogle Scholar
  58. Thompson DWJ, Wallace JM (2000) Annular modes in the extratropical circulation. Part I: month-to-month variability. J Clim 13:1000–1016CrossRefGoogle Scholar
  59. Thompson DWJ, Wallace JM (2001) Regional climate impacts of the Northern Hemisphere annular mode. Science 293:85–89CrossRefGoogle Scholar
  60. Thompson DWJ, Baldwin MP, Wallace JM (2002) Stratospheric connection to Northern Hemisphere wintertime weather: implications for prediction. J Clim 15:1421–1428CrossRefGoogle Scholar
  61. Waugh DW and Rong PP (2002) Interannual variability in the decay of lower stratospheric Arctic vortices. J Meteorol Soc Jpn 80:997–1012CrossRefGoogle Scholar
  62. White LB, Boashash B (1990) Cross spectral analysis of nonstationary processes. IEEE Trans Inf Theory 36:830–835CrossRefGoogle Scholar
  63. Yu YY, Ren RC, Hu JG, Wu GX (2014) A mass budget analysis on the interannual variability of the polar surface pressure in the winter season. J Atmos Sci 71:3539–3553CrossRefGoogle Scholar
  64. Yu YY, Cai M, Ren RC, Van den Dool H (2015a) Relationship between warm air mass transport into upper polar atmosphere and cold air outbreaks in winter. J Atmos Sci 72:349–368CrossRefGoogle Scholar
  65. Yu YY, Ren RC, Cai M (2015b) Dynamical linkage between cold air outbreaks and intensity variations of the meridional mass circulation. J Atmos Sci 72:3214–3232CrossRefGoogle Scholar
  66. Yu YY, Ren RC, Cai M (2015c) Comparison of the mass circulation and AO indices as indicators of cold air outbreaks in northern winter. Geophys Res Lett 42:2442–2448CrossRefGoogle Scholar
  67. Zhang Q, Shin CS, van den Dool H, Cai M (2013) CFSv2 prediction skill of stratospheric temperature anomalies. Clim Dyn 41:2231–2249CrossRefGoogle Scholar
  68. Zhou ST, Miller AJ, Angell JK (2002) Downward-propagating temperature anomalies in the preconditioned polar stratosphere. J Clim 15:781–792CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Nanjing University of Information Science and TechnologyNanjingChina
  2. 2.Geophysical Fluid Dynamics InstituteFlorida State UniversityTallahasseeUSA
  3. 3.Department of Earth, Ocean and Atmospheric SciencesFlorida State UniversityTallahasseeUSA
  4. 4.State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric PhysicsChinese Academy of SciencesBeijingChina
  5. 5.Collaborative Innovation Center on Forecasts and Evaluation of Meteorological Disasters and KLMENanjing University of Information Science and TechnologyNanjingChina

Personalised recommendations