Figure 3

A schematic representing the seasonal evolution of the variance with the two-season stability structure (a). During the period in which a(t) is positive destabilising processes dominate the dynamics, amplifying fluctuations, N(t)ξ(t). As a(t) changes sign stabilising processes dominate, suppressing the fluctuations. There are two transition points between them. When a(t) is positive (negative) noise generated variability is accumulated (suppressed) up to the transition point. Hence, the maximum variance occurs at the transition point from positive to negative stability. We show this dynamics using our time series analysis on three major climate indices; the Nino3 SST index (b), the Atlantic Niño index (c) and the Dipole Mode Index (d). In each pair of panels we plot on the top the monthly standard deviation calculated from the data (blue line) and from the stochastic model of equation 1 (red line), and in the bottom panel the a(t) (blue line) and N(t) (green line) constructed by our time series method. All indices exhibit a variance maximum proximal to the transition from destabilising to stabilising dynamics and the stochastic model produces monthly standard deviations in excellent agreement with the observations alone without the need to include long-term variability, f(τ). Therefore, it appears that the monthly stability a(t) and the accumulation of noise–memory effect–are sufficient to capture phase locking as observed in seasonal climate dynamics.