Spectral analysis of climate data

Abstract

The complexity of climate variability on all time scales requires the use of several refined tools to unravel its primary dynamics from observations. Indeed, ideas from the theory of dynamical systems have provided new ways of interpreting the information contained in climatic time series. We review the properties of several modern time series analysis methods. Those methods belong to four main classes: Fourier techniques (Blackman-Tukey and Multi-Taper), Maximum Entropy technique, Singular-spectrum techniques and wavelet analysis. Their respective advantages and limitations are illustrated by numerical experiments on synthetic time series. As climate data can be irregularly spaced in time, we also compare three interpolating methods on those time series. Those tests are aimed at showing the pitfalls of the blind use of mathematical or statistical techniques on climate data. We apply those methods to ‘real” climatic data from temperature variations over the last century, and the Vostok ice core deuterium record over the last glacial cycle. Then we show how interpretations on the dynamics of climate can be derived on those time scales.