The analysis of univariate or multivariate time series provides crucial information to describe,
understand, and predict climatic variability. The discovery and implementation of a number …

Climate and weather constitute a typical example where high dimensional and complex
phenomena meet. The atmospheric system is the result of highly complex interactions …

We present a rank reduction algorithm that permits simultaneous reconstruction and random
noise attenuation of seismic records. We based our technique on multichannel singular …

The viewpoint taken in much of this text is that PCA is mainly a descriptive tool with no need
for rigorous distributional or model assumptions. This implies that it can be used on a wide …

Climatology is, to a large degree, the study of the statistics of our climate. The powerful tools
of mathematical statistics therefore find wide application in climatological research. The …

The term singular spectrum comes from the spectral (eigenvalue) decomposition of a matrix
A into its set (spectrum) of eigenvalues. These eigenvalues, A, are the numbers that make …

Singular systems (or singular spectrum) analysis (SSA) was originally proposed for noise
reduction in the analysis of experimental data and is now becoming widely used to identify …

In the late 1970s, the ENSO cycle exhibited frequency change. The oscillation period
increased from 2–4 yr (high frequency) during 1962–75 to 4–6 yr (low frequency) during …

Seasonal signals in GPS time series are of great importance for understanding the evolution
of regional mass fluctuations, ie, ice, hydrology, and ocean mass. Conventionally these …

This book introduces stochastic dynamical systems theory in order to synthesize our current
knowledge of climate variability. Nonlinear processes, such as advection, radiation and …