Phase Synchronization of the El Niño-Southern Oscillation with the Annual Cycle

The El Niño-Southern Oscillation (ENSO) is the largest global climate signal on the interannual time scale. ENSO events occur irregularly, yet individual events follow a similar pattern of developing during boreal summer or fall and peaking during boreal winter. This characteristic of ENSO is often referred to as “phase locking” of ENSO with the annual cycle. However, no observational evidence of phase interaction between the two phenomena has thus far been presented. In this study, we analyze sea surface temperature observations and find the first evidence of partial phase synchronization of ENSO with the annual cycle.

Figure 1

The magnitudes (${\mathbf{q}}_n$, ${\sigma }_n(t)$) and phases (${\mathbf{r}}_n$, ${\varphi }_n(t)$) associated with the first two modes obtained from a CEOF analysis of HadISST data. The contour plots show the spatial maps of ${\mathbf{q}}_n$, ${\mathbf{r}}_n$, with contour intervals indicated on the top right. The corresponding time series ${\sigma }_n(t)$ (blue line, left ordinate) and ${\varphi }_n(t)$ (green x’s, right ordinate) are shown below. The first mode (a) captures the seasonal cycle while the second mode (b) captures ENSO.

Figure 2

Probability distributions of the phase difference $\delta {\varphi }_{1,2}(t)$ mod $2\pi$, from the first two CEOF modes of HadISST observations (a), from surrogate time series (b), and from a synthetic time series based on a simple ENSO model (c). The error bars indicate the 95% confidence intervals calculated from the surrogate time series (b). The monthly variance of the synthetic temperature series and the HadISST mode 2 time series are shown for comparison (d).

Figure 3

Scatter plot of the mode 1 time series (${\alpha }_1$) with marker size proportional to the magnitude of the mode 2 time series (${\sigma }_2$). Highlighted in red are points where the mode 2 temporal phase is near zero, corresponding to El Niño events ($-\frac{\pi }{9}\le {\varphi }_2\le \frac{\pi }{9}$). The figure is divided into seasonal quadrants, based on the monthly averages of the mode 1 temporal phase (${\varphi }_1$). The interpolated composite seasonal cycle is shown as a dashed circle.