ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-12-5691-2012 Understanding and forecasting polar stratospheric variability with statistical models Blume C. 1 2 3 Matthes K. 1 2 3 Helmholtz Centre Potsdam, German Research Centre for Geosciences (GFZ), Potsdam, Germany Institute for Meteorology, Free University of Berlin (FUB), Berlin, Germany now at: Helmholtz Centre for Ocean Research Kiel (GEOMAR), Kiel, Germany 02 07 2012 12 13 5691 5701 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/12/5691/2012/acp-12-5691-2012.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/12/5691/2012/acp-12-5691-2012.pdf

The variability of the north-polar stratospheric vortex is a prominent aspect of the middle atmosphere. This work investigates a wide class of statistical models with respect to their ability to model geopotential and temperature anomalies, representing variability in the polar stratosphere. Four partly nonstationary, nonlinear models are assessed: linear discriminant analysis (LDA); a cluster method based on finite elements (FEM-VARX); a neural network, namely the multi-layer perceptron (MLP); and support vector regression (SVR). These methods model time series by incorporating all significant external factors simultaneously, including ENSO, QBO, the solar cycle, volcanoes, to then quantify their statistical importance. We show that variability in reanalysis data from 1980 to 2005 is successfully modeled. The period from 2005 to 2011 can be hindcasted to a certain extent, where MLP performs significantly better than the remaining models. However, variability remains that cannot be statistically hindcasted within the current framework, such as the unexpected major warming in January 2009. Finally, the statistical model with the best generalization performance is used to predict a winter 2011/12 with warm and weak vortex conditions. A vortex breakdown is predicted for late January, early February 2012.

 References Akaike, H.: A new look at the statistical model identification, IEEE T. Automat. Contr., 19, 716–723, 1974. Ariew, R.: Ockham's Razor: A Historical and Philosophical Analysis of Ockham's Principle of Parsimony, Ph.D. thesis, Champaign-Urbana, University of Illinois, 1976. Avriel, M.: Nonlinear Programming: Analysis and Methods, Dover Publishing, 2003. Baldwin, M. and Dunkerton, T.: Stratospheric harbingers of anomalous Weather Regimes, Science, 294, 581–584, 2001. Baldwin, M. and Thompson, D. W J.: A critical comparison of stratosphere-troposphere coupling indices, Q. J. Roy. Meteor. Soc., 135, 1661–1672, 2009. Baldwin, M., Gray, L J., Dunkerton, T J., Hamilton, K., Haynes, P H., Randel, W J., Holton, J R., Alexander, M J., Hirota, I., Horinouchi, T., Jones, D. B A., Kinnersley, J S., Marquardt, C., Sato, K., and Takahashi, M.: The quasi-biennial oscillation, Rev. Geophys., 39, 179–229, 2001. Baldwin, M P. and Holton, J R.: Climatology of the stratospheric polar vortex and planetary wave breaking, J. Atmos. Sci., 45, 1123–1142, 1988. Basak, D., Pal, S., and Patranabis, D C.: Support Vector Regression, Neural Info. Proc., 11, 203–224, 2007. Bishop, C.: Neural networks for pattern recognition, Oxford: University Press, 1995. Blume, C., Matthes, K., and Horenko, I.: Supervised learning approaches to classify sudden stratospheric warming events, J. Atmos. Sci., 69, 1824–1840, 2012. Burnham, K P. and Anderson, D R.: Model selection and multimodel inference: a practical information-theoretic approach, Springer, 2002. Calvo, N., Giorgetta, M A., Garcia-Herrera, R., and Manzini, E.: Nonlinearity of the combined warm ENSO and QBO effects on the Northern Hemisphere polar vortex in MAECHAM5 simulations, J. Geophys. Res., 114, D13109, http://dx.doi.org/10.1029/2008JD011445doi:10.1029/2008JD011445, 2009. Camp, C D. and Tung, K.-K.: The Influence of the Solar Cycle and QBO on the Late-Winter Stratospheric Polar Vortex, J. Atmos. Sci., 64, 1267–1283, 2007a. Camp, C D. and Tung, K.-K.: Stratospheric polar warming by ENSO in winter: A statistical study, Geophys. Res. Lett., 34, L04809, http://dx.doi.org/10.1029/2006GL028521doi:10.1029/2006GL028521, 2007b. Coughlin, K. and Gray, L J.: A continuum of sudden stratospheric warmings. J. Atmos. Sci., 66, 531–540, 2009. Crooks, S. and Gray, L.: Characterization of the 11-year solar signal using a multiple regression analysis of the ERA-40 dataset, J. Climate, 18, 996–1015, 2005. Delworth, T L. and Mann, M E.: Observed and simulated multidecadal variability in the Northern Hemisphere, Climate Dynam., 16, 661–676, 2000. Deser, C., Alexander, M A., Xie, S.-P., and Phillips, A S.: Sea Surface Temperature Variability: Patterns and Mechanisms, Ann. Rev. Mar. Sci., 2, 115–143, 2010. Franzke, C.,~Horenko, I., Majda, A J., and~Klein, R.: Systematic metastable atmospheric regime identification in an AGCM, J. Atmos. Sci., 66, 1997–2012, 2009. Garfinkel, C I. and Hartmann, D L.: Effects of the El-Nino Southern Oscillation and the Quasi-Biennial Oscillation on polar temperatures in the stratosphere, J. Geophys. Res., 112, D19112, http://dx.doi.org/10.1029/2007JD008481doi:10.1029/2007JD008481, 2007. Gerber, E P., Orbe, C., and Polvani, L M.: Stratospheric influence on the tropospheric circulation revealed by idealized ensemble forecasts, Geophys. Res. Lett., 36, L24801, http://dx.doi.org/10.1029/2009GL040913doi:10.1029/2009GL040913, 2009. Gray, L J., Beer, J., Geller, M., Haigh, J D., Lockwood, M., Matthes, K., Cubasch, U., Fleitmann, D., Harrison, G., Hood, L., Luterbacher, J., Meehl, G A., Shindell, D., van Geel, B., and White, W.: Solar Influences on Climate, Rev. Geophys., 48, RG4001, http://dx.doi.org/10.1029/2009RG000282doi:10.1029/2009RG000282, 2010. Holton, J R. and Tan, H C.: The influence of the equatorial Quasi-Biennial Oscillation on the global atmospheric circulation at 50mb, J. Atmos. Sci., 37, 2200–2208, 1980. Holton, J R. and Tan, H C.: The quasi-biennial oscillation in the Northern Hemisphere lower stratosphere, J. Meteorol. Soc. Jpn., 60, 140–148, 1982. Horenko, I.: On the Identification of Nonstationary Factor Models and Their Application to Atmospheric Data Analysis, J. Atmos. Sci., 67, 1559–1574, 2010. Horenko, I.: Nonstationarity in multifactor models of discrete jump processes, memory and application to cloud modeling, J. Atmos. Sci., 68, 1493–1506, 2011. Jolliffe, I T.: Principal Component Analysis, Springer Series in Statistics, 2002. Kalnay, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M., Saha, S., White, G., Woollen, J., Zhu, Y., Leetmaa, A., Reynolds, B., Chelliah, M., Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K. C., Ropelewski, C., Wang, J., Jenne, R., and Joseph, D.: The NCEP/NCAR 40-year reanalysis project, B. Am. Meteor. Soc., 77, 437–472, 1996. Keerthi, S S. and Lin, C.-J.: Asymptotic behaviors of support vector machines with Gaussian kernel, Neural Comput., 15, 1667–1689, 2003. Kohavi, R.: A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection, vol 2, 1137–1143, Morgan Kaufmann, 1995. Kurkova, V.: Kolmogorov's theorem and multilayer neural networks, Neural Networks, 5, 501–506, 1992. Kuroda, Y.: High initial-time sensitivity of medium-range forecasting observed for a stratospheric sudden warming, Geophys. Res. Lett., 37, L16804, http://dx.doi.org/10.1029/2010GL044119doi:10.1029/2010GL044119, 2010. Labitzke, K.: Sunspots, the QBO, and the stratospheric temperatures in the north polar region, Geophys. Res. Lett., 14, 535–537, 1987. Labitzke, K. and Kunze, M.: Variability in the stratosphere: The Sun and the QBO, 257–278, Climate and Weather of the Sun-Earth System (CAWSES): Selected Papers from the 2007 Kyoto Symposium, Terrapub, Tokyo, 2009a. Labitzke, K. and Kunze, M.: On the Remarkable Arctic Winter in 2008/09, J. Geophys. Res., 114, D00I02, http://dx.doi.org/10.1029/2009JD012273doi:10.1029/2009JD012273, 2009b. Labitzke, K. and Naujokat, B.: The lower arctic stratosphere in winter since 1952, SPARC Newsletter No 15, 11–14, 2000. Labitzke, K. and van Loon, H.: Associations between the 11-year solar cycle, the QBO and the atmosphere. Part I: the troposphere and stratosphere in the northern hemisphere winter, J. Atmos. Terr. Phys., 50, 197–206, 1988. Lu, B., Pandolfo, L., and Hamilton, K.: Nonlinear representation of the quasi-biennial oscillation, J. Atmos. Sci., 66, 1886–1904, 2009. MacDonald, G M. and Case, R A.: Variations in the Pacific Decadal Oscillation over the past millennium, Geophys. Res. Lett., 320, L08703, http://dx.doi.org/10.1029/2005GL022478doi:10.1029/2005GL022478, 2005. Manzini, E., Giorgetta, M., Esch, M., Kornblueh, L., and Roeckner, E.: The influence of sea surface temperatures on the Northern winter stratosphere: Ensemble simulations with the MAECHAM5 model, J. Climate, 19, 3863–3881, 2006. Martius, O., Polvani, L M., and Davies, H C.: Blocking precursors to stratospheric sudden warming events, Geophys. Res. Lett., 36, L14806, http://dx.doi.org/10.1029/2009GL038776doi:10.1029/2009GL038776, 2009. Mitchell, D M., Gray, L J., and Charlton-Perez, A J.: The structure and evolution of the stratospheric vortex in response to natural forcings, Geophys. Res. Lett., 116, D15110, http://dx.doi.org/10.1029/2011JD015788doi:10.1029/2011JD015788, 2011. Montgomery, D C., Peck, E A., and Vining, G G.: Introduction to linear regression analysis, Wiley-Interscience, 2001. Nao, I.,~Naomi, A., and~Sachiko, H.: Estimation of the surface area density of polar stratospheric clouds by using the support vector machines, IPSJ SIG Tech. Reports, Z0031, 2006B. Randel, W J., Garcia, R R., Calvo, N., and Marsh, D.: ENSO influence on zonal mean temperature and ozone in the tropical lower stratosphere, Geophys. Res. Lett., 36, L15822, http://dx.doi.org/10.1029/2009GL039343doi:10.1029/2009GL039343, 2009. Richter, J H., Matthes, K., Calvo, N., and Gray, L J.: Influence of the Quasi-Biennial Oscillation and El Niño-Southern Oscillation on the frequency of sudden stratospheric warmings, J. Geophys. Res., 116, D20111, http://dx.doi.org/10.1029/2011JD015757doi:10.1029/2011JD015757, 2011. Rienecker, M M., Suarez, M J., Gelaro, R., Todling, R., Bacmeister, J., Liu, E., Bosilovich, M G., Schubert, S D., Takacs, L., Kim, G.-K., Bloom, S., Chen, J., Collins, D., Conaty, A., Da Silva, A., Gu, W., Joiner, J., Koster, R D., Lucchesi, R., Molod, A., Owens, T., Pawson, S., Pegion, P., Redder, C R., Reichle, R., Robertson, F R., Ruddick, A G., Sienkiewicz, M., and Woollen, J.: MERRA: NASA's Modern-Era Retrospective Analysis for Research and Applications, J. Climate, 24, 3624–3648, 2011. Robock, A.: Volcanic eruptions and climate, Rev. Geophys., 38, 191–219, 2000. Simmons, A., Uppala, S M., Dee, D., and Kobayashi, S.: ERA-Interim: New ECMWF reanalysis products from 1989 onwards, ECMWF Newsletter, 110, 26–35, 2006. SPARC CCMVal: SPARC Report on the Evaluation of Chemistry-Climate Models, SPARC Report No. 5, WCRP-132, WMO/TD-No. 1526, 2010. Thompson, D. W J.: Stratospheric connection to northern hemisphere wintertime weather: Implications for prediction, J. Climate, 15, 1421–1428, 2003. Trenberth, K E.: The Definition of El Niño, B. Am. Meteor. Soc., 78, 2771–2777, 1997. Vapnik, V.: The Nature of Statistical Learning Theory, Springer-Verlag, New York, 1995. Wallace, J M., Panetta, R L., and Estberg, J.: A phase-space representation of the equatorial stratospheric quasi-biennial oscillation, J. Atmos. Sci., 50, 1751–1762, 1993. Walter, A. and Schönwiese, C.-D.: Attribution and detection of anthropogenic climate change using a backpropagation neural network, Meteorol. Z., 11, 335–343, 2002. Woollings, T. and Hoskins, B.: Simultaneous Atlantic-Pacific blocking and the Northern Annular Mode, Q. J. Roy. Meteor. Soc., 134, 1635–1646, 2008. Zhang, G., Patuwo, B E., and Hu, M Y.: Forecasting with artificial neural networks: The state of the art, Int. J. Forecasting, 14, 35–62, 1998.