SPECTRAL METHODS: WHAT THEY CAN AND CANNOT
DO FOR CLIMATIC TIME SERIES
MICHAEL GHILl and PASCAL YIOU 2
Ecole N ormale Superieure
Paris, France
Contents
1 Wherefrom: Introduction and Motivation
1.1 Analysis in the time vs. the spectral domain.
1.2 Time series and nonlinear dynamics . . . . .
2 SIN Enhancement: Singular Spectrum Analysis
2.1 Motivation . . . . . . . . . . . . .
2.2 Decomposition and reconstruction
2.3 Monte Carlo SSA . . . . .
3 Spectral Analysis Methods
3.1 Blackman-Tukey spectral estimate
3.2 Maximum Entropy Method (MEM) .
3.3 Multi-Taper Method (MTM)
4 M-SSA and Other Examples
5 Whereto next?
Abstract
The analysis of time series - uni- or multivariate - is one of the high roads to
our understanding of climatic variability. This classical field of study has recently
been revitalized by the discovery and implementation of a number of new methodologies for extracting useful information from time series, as well as for interpreting
the information so obtained in terms of dynamical systems theory. In this chapter,
we describe the connections between time-series analysis and nonlinear dynamics,
discuss signal-to-noise enhancement, and present some of the novel methods for
spectral analysis. The various steps, as well as the advantages and disadvantages of
these methods, are illustrated by their application to a well-known climatic time series, the Southern Oscillation Index. Open questions and further prospects conclude
the chapter.
lalso at: Institute of Geophysics and Planetary Physics, Los Angeles, USA
2Laboratoire de Modelisation du Climat et de l'Environnement, Saclay, France
NATO AS! Series, Vol. ! 44
Decadal Climate Variability
Dynamics and Predictability
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Edited by David L. T.Anderson and Jiirgen Willebrand
© Springer-Verlag Berlin Heidelberg 1996