Detecting Oscillations Hidden in Noise: Common Cycles in Atmospheric, Geomagnetic and Solar Data

In this chapter we present a nonlinear enhancement of a linear method, the singular system analysis (SSA), which can identify potentially predictable or relatively regular processes, such as cycles and oscillations, in a background of colored noise. The first step in the distinction of a signal from noise is a linear transformation of the data provided by the SSA. In the second step, the dynamics of the SSA modes is quantified in a general, nonlinear way, so that dynamical modes are identified which are more regular, or better predictable than linearly filtered noise. A number of oscillatory modes are identified in data reflecting solar and geomagnetic activity and climate variability, some of them sharing common periods.