Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 16 1 2009 10.5194/npg-16-65-2009 http://www.nonlin-processes-geophys.net/16/65/2009/ http://www.nonlin-processes-geophys.net/16/65/2009/npg-16-65-2009.html http://www.nonlin-processes-geophys.net/16/65/2009/npg-16-65-2009.pdf 65 76 2009-02-06 Multi-scale analysis of teleconnection indices: climate noise and nonlinear trend analysis C. Franzke chan1@bas.ac.uk British Antarctic Survey, Natural Environment Research Council, Cambridge, UK The multi-scale nature and climate noise properties of teleconnection indices are examined by using the Empirical Mode Decomposition (EMD) procedure. The EMD procedure allows for the analysis of non-stationary time series to extract physically meaningful intrinsic mode functions (IMF) and nonlinear trends. The climatologically relevant monthly mean teleconnection indices of the North Atlantic Oscillation (NAO), the North Pacific index (NP) and the Southern Annular Mode (SAM) are analyzed. <br><br> The significance of IMFs and trends are tested against the null hypothesis of climate noise. The analysis of surrogate monthly mean time series from a red noise process shows that the EMD procedure is effectively a dyadic filter bank and the IMFs (except the first IMF) are nearly Gaussian distributed. The distribution of the variance contained in IMFs of an ensemble of AR(1) simulations is nearly χ<sup>2</sup> distributed. To test the statistical significance of the IMFs of the teleconnection indices and their nonlinear trends we utilize an ensemble of corresponding monthly averaged AR(1) processes, which we refer to as climate noise. Our results indicate that most of the interannual and decadal variability of the analysed teleconnection indices cannot be distinguished from climate noise. The NP and SAM indices have significant nonlinear trends, while the NAO has no significant trend when tested against a climate noise hypothesis. Bengtsson, L., Hagemann, S., and Hodges, K. I.: Can climate trends be calculated from reanalysis data?, J. Geophys. Res., 109, D11111, doi:10.1029/2004JD004536. Cash, B. A. and Lee, S.: Observed Nonmodal Growth of the Pacific-North American Teleconnection Pattern, J. Climate, 14, 1017–1028, 2001. Crommelin, D. T. and Vanden-Eijnden, E.: Reconstruction of Diffusions using spectral data from timeseries, Comm. Math. Sci., 4, 651–668, 2006. Czaja, A., Robertson, A. W., and Huck, T.: The role of Atlantic Ocean-Atmosphere coupling in affecting North Atlantic Oscillation variability, in: The North Atlantic Oscillation: Climatic Significance and Environmental Impact, edited by: Hurrell, J. W., Kushnir, Y., Ottersen, G., and Visbeck, M., Geophysical Monograpgh 134, American Geophysical Union, 147–172, 2003. Duffy, D. G.: The Application of Hilbert-Huang Transforms to Meteorological Datasets, J. Atmos. Oceanic Technol., 21, 599–611, 2004. Feldstein, S. B.: The Timescale, Power Spectra, and Climate Noise Properties of Teleconnection Patterns, J. Climate, 13, 4430–4440, 2000a. Feldstein, S. B.: Is Interannual Zonal Mean Flow Variability Simply Climate Noise?, J. Climate, 13, 2356–2362, 2000b. Feldstein, S. B.: Fundamental Mechanisms of the growth and decay of the PNA teleconnection pattern, Q. J. Roy. Meteorol. Soc., 128, 775–796, 2002a. Feldstein, S. B.: The Recent Trend and Variability Increase of the Annular Mode, J. Climate, 15, 88–94, 2002b. Feldstein, S. B.: The dynamics of the NAO teleconnection pattern growth and decay, Q. J. Roy. Meteorol. Soc., 129, 901–924, 2003. Franzke, C. and Feldstein, S. B.: The Continuum and Dynamics of Northern Hemisphere Teleconnection Patterns, J. Atmos. Sci., 62, 3250–3267, 2005. Hasselmann, K.: Stochastic Climate Models. Part I. Theory, Tellus, 28, 473–484, 1976. Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N.-C., Tung, C. C., and Liu, H. H.: The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis, Proc. R. Soc. Lond. A, 454, 903–995, 1998. Huang, N. E., Shen, Z., and Long, S. R.: A New View of Nonlinear Water Waves: The Hilbert Spectrum, Ann. Rev. Fluid Mech., 31, 417–457, 1999. Huang, N. E., Wu, M.-L. C., Long, S. R., Shen, S. S. P., Qu, W., Gloersen, P., and Fan, K. L.: A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis, Proc. R. Soc. Lond. A, 459, 2317–2345, 2003. Huang, N. E. and Wu, Z.: A Review on Hilbert-Huang Transform: Method and its Applications to Geophysical Studies, Rev. Geophys., 46, 2008. RG2006, doi:10.1029/2007RG000228, 2008. Hurrell, J. W.: Decadal Trends in the North Atlantic Oscillation and Relationships to Regional Temperature and Precipitation, Science, 269, 676–679, 1995. Jones, P. D., Jonsson, T., and Wheeler, D.: Extension to the North Atlantic Oscillation using early instrumental pressure observations from Gibraltar and South-East Iceland, Int. J. Climatol., 17, 1433–1450, 1997. Leith, C. E.: The Standard Error of Time-Average Estimates of Climatic Means, J. Appl. Meteorol., 12, 1066–1069, 1973. Madden, R. A.: Estimates of the Natural Variability of Time-Averaged Sea-Level Pressure, Mon. Weather Rev., 104, 942–952, 1976. Madden, R. A.: A Quantitative Approach to Long-Range Prediction, J. Geophys. Res., 86, 9817–9825, 1981. Majda, A. J., Franzke, C., and Khouider, B.: An applied mathematics perspective on stochastic modelling for climate, Phil. Trans. R., Soc. A, 366, 2429–2455, doi.10.1098/rsta.2008.0012, 2008. Marshall, G. J.: Trends in the Southern Annular Mode from Observations and Reanalyses, J. Climate, 16, 4134–4143, 2003. McDonald, A. J., Baumgaertner, A. J. G., Fraser, G. J., George, S. E., and Marsh, S.: Empirical Mode Decomposition of the atmospheric wave field, Ann. Geophys., 25, 375–384, 2007. Percival, D. B. and Rothrock, D. A.: `Eyeballing' trends in climate time series: A cautionary note, J. Climate, 18, 886–891, 2005. Perlwitz, J., Pawson, S., Fogt, R. L., Nielsen, J. E., and Neff, W. D.: Impact of stratospheric ozone hole recovery on Antarctic climate, Geophys. Res. Lett., 35, L08714, doi:10.1029/2008GL033317, 2008. Rilling, G., Flandrin, P., and Goncalves, P.: On Empirical Mode Decomposition and Its Algorithms, IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03, GRADO(I), 2003. Roscoe, H. K. and Haigh, J. D.: Influences of ozone depletion, the solar cycle and the QBO on the Southern Annular Mode, Q. J. Roy. Meteorol. Soc., 133, 1855–1864, 2007. Thompson, D. W. J. and Wallace, J. M.: Annular Modes in the Extratropical Circulation: Part I. Month-to-Month Variability, J. Climate, 13, 1000–1016, 2000a. Thompson, D. W. J., Wallace, J. M., and Hegerl, G. C.: Annular Modes in the Extratropical Circulation: Part II. Trends, J. Climate, 13, 1017–1036, 2000b. Trenberth, K. E. and Hurrell, J. W.: Decadal Atmosphere-Ocean Variations in the Pacific, Clim. Dynam., 9, 303–319, 1994. von Storch, H. and Zwiers, F., W.: Statistical Analysis in Climate Research, Cambridge University Press, New York, 484 pp., 1999. Wallace, J. M. and Gutzler, D. S.: Teleconnections in the Geopotential Height Field during the Northern Hemisphere Winter, Mon. Rev. Weather, 109, 784–812, 1981. Wu. Z. and Huang, N. E.: A Study of the Characteristics of White Noise using the Empirical Mode Decomposition Method, Proc. R. Soc. Lond. A, 460, 1597–1611, 2004. Wu, Z., Huang, N. E., Long, S. R., and Peng, C. K.: On the Trend, Detrending, and Variability of Nonlinear and Nonstationary Time Series, Proc. Nat. Acad. Sci. USA, 104, 14889–14894, 2007. Wunsch, C.: The Interpretation of Short Climate Records, with Comments on the North Atlantic and Southern Oscillations, B. Am. Meteorol. Soc., 80, 245–255, 1999.