The Dynamics of ENSO Phase Locking in a Spatiotemporal Oscillator Model

Abstract

Abstract The ENSO phase locking to the annual cycle is investigated by applying a spatiotemporal oscillator (STO) model, in which the annual cycle of the climatological thermocline depth and its associated parameter are introduced. It is easy to derive its analytic solution, which demonstrates a harmonic oscillation of a combined variable. The ENSO phase locking can be theoretically proven by discussing the distribution of the calendar months of the peak time of the sea surface temperature anomaly (SSTA) time series. The calendar months of the peak time can be divided into two parts. The first part can evenly distribute in any a month of a year and hence has no phase locking feature whereas the second part, directly associated with the annual cycle, adds an increment onto the first part to make it move toward the phase of the annual cycle to realize the phase locking feature. This is the physical mechanism of the ENSO phase locking. With observed seasonal variation of the climatological thermocline depth, the Niño-3.4 index time series approach to extreme values in November was calculated with higher probability, reproducing the observed phase locking phenomenon quite well. The maximum probability of the calendar month that the ENSO peak time occurs is directly determined by the phase of the annual cycle and the stronger the annual cycle is, the larger the maximum probability is. Significance Statement El Niño–Southern Oscillation (ENSO) events tend to be strongest in the boreal wintertime. This phenomenon is called ENSO phase locking. This study investigates the dynamics of ENSO phase locking to the annual cycle by introducing the annual cycle to a spatiotemporal oscillator (STO) model that can deal with the complex spatial and temporal variations in SSTAs. The analytic solution can be obtained and then the phase locking feature can be theoretically proven and numerically testified. Therefore, the dynamics and the mechanism of ENSO phase locking can be comprehensively understood. It may be beneficial for the community to have a better understanding of this complex phenomenon.