Topology of Earth's climate indices and phase-locked states

Phase-locked states in Earth's climate system were identified in a study of a set of climate indices by Swanson and Tsonis (2009) [1] (ST). They reported five climate shift events since 1900 based upon features in a phase-locking parameter S. The present study finds that sets of climate indices have important topological properties such as a metric diameter D that describes the magnitude of phase locking among the indices. Minima in D as a function of time are shown to be associated with climate shifts. Eighteen strong events since 1870 are identified, including the five reported by ST. Ten of these minima correspond to reported events such as the well documented “climate shift of the mid-1970s” and the more recent climate shift of 2001–2002. Most climate shifts tend toward radiative equilibrium.