Statistical and Dynamical Analysis and Prediction (SSA)

The analysis of observed – or numerically generated – time series is often a prerequisite for progress in modeling and forecasting the physical system of interest. Two complementary approaches attempt to detect regularities in climate time series, via multiple weather regimes or climatic states, on the one hand, and via harmonic or relaxation oscillations, on the other. Multiple planetary flow regimes have been classified via cluster analysis or estimation of the system dynamics’ probability density function (pdf) and its maxima. Markov chains between such preferred states and and statistical learning method called random forests have been used for long-range forecasting (LRF) of the atmosphere’s LFV.

A team consisting of TCD members and collaborators has developed a technique called Singular-Spectrum Analysis (SSA) which extracts as much reliable information as possible from short, noisy time series without prior knowledge of the dynamics underlying the series. SSA is a form of principal-component analysis applied to lag-correlation structures of uni- and multivariate time series. SSA decomposes a time series by data-adaptive filters into oscillatory, trending, and noise components; generates statistical significance information on these components; and provides reconstructed components. It has been applied to a wide range of data types – from geophysical to financial – for a variety of purposes, including forecast of Niño-3 sea surface temperature anomalies that exhibit both regular and irregular behavior.

References

  • Allen, M. R., and A. W. Robertson, 1996: Distinguishing modulated oscillations from colored noise in multivariate datasets. Climate Dyn., 12, 775-784.
  • Dettinger, M. D., M. Ghil, C. M. Strong, W. Weibel and P. Yiou, 1995: Software expedites singular-spectrum analysis of noisy time series, Eos, Trans. AGU, 76, pp. 12, 14, 21.
  • Dettinger, M. D., M. Ghil and C. L. Keppenne, 1995: Interannual and interdecadal variability in United States surface-air temperatures, 1910-87, Climatic Change, 31, 35-66.
  • Ghil, M., and R. Vautard, 1991: Interdecadal oscillations and the warming trend in global temperature time series, Nature, 350, 324-327.
  • Ghil, M., and P. Yiou, 1996: Spectral Methods: What they can and cannot do for climatic time series, Decadal Climate Variability: Dynamics and Predictability, D. Anderson and J. Willebrand (Eds.), Elsevier, pp. 446-482.
  • Jiang, N., M. Ghil and D. Neelin, 1996: Forecasts of Niño 3 SST anomalies and SOI based on singular spectrum analysis combined with the maximum entropy method. Experimental Long-Lead Forecast Bulletin, Vol. 5, Nos. 2-4. National Meteorological Center, NOAA, U.S. Department of Commerce.
  • Keppenne, C. L., and M. Ghil, 1992: Adaptive filtering and prediction of the Southern Oscillation index, J. Geophys. Res., 97, 20449-20454.
  • Keppenne, C. L., and M. Ghil, 1993: Adaptive filtering and prediction of noisy multivariate signals: An application to subannual variability in atmospheric angular momentum, Intl. J. Bifurcation & Chaos, 3, 625-634.
  • Kravtsov S, Kondrashov D, Ghil M, 2005: Multilevel regression modeling of nonlinear processes: Derivation and applications to climatic variability. J. Climate, 18 (21): 4404-4424.
  • Kondrashov D, Kravtsov S, Robertson AW and Ghil M., 2005: A hierarchy of data-based ENSO models. J. Climate, 18 (21): 4425-4444.
  • Penland, C., and M. Ghil, 1993: Forecasting Northern Hemisphere 700-mb geopotential height anomalies using empirical normal modes, Mon. Wea. Rev., 121, 2355-2372.
  • Penland, C., M. Ghil, and K. M. Weickmann, 1991: Adaptive filtering and maximum entropy spectra, with application to changes in atmospheric angular momentum, J. Geophys. Res., 96, 22659-22671.
  • Plaut, G., M. Ghil and R. Vautard, 1995: Interannual and interdecadal variability in 335 years of Central England temperatures, Science, 268, 710-713.
  • Vautard, R., and M. Ghil, 1989: Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series, Physica D, 35, 395-424.
  • Vautard, R., K. C. Mo, and M. Ghil, 1990: Statistical significance test for transition matrices of atmospheric Markov chains, J. Atmos. Sci., 47, 1926-1931.
  • Vautard, R., P. Yiou, and M. Ghil, 1992: Singular-spectrum analysis: A toolkit for short, noisy chaotic signals, Physica D, 58, 95-126.