Chapter 7 – Random Processes and Power Spectra

Climatic data and theoretical considerations suggest that a large part of climatic variability has a random nature and can be analyzed using the theory of random processes. In this chapter, we describe the random approach to the study of changes in the climate system, including stationary random processes, calculus of random processes, power spectra, spectrum estimation, and Wiener filter. Moreover, in order to extract intrinsic frequency features from climatic time series, we show how random processes do statistical significance tests by Fourier analysis and wavelet analysis.