Seasonal gap theory for ENSO phase locking

The life cycle of El Niño–Southern Oscillation (ENSO) typically follows a seasonal march, with onset in spring, developing during summer, maturing in boreal winter, and decaying over the following spring. This feature is referred to as ENSO phase locking. Recent studies have noted that seasonal modulation of the ENSO growth rate is essential for this process. This study investigates the fundamental effect of a seasonally varying growth rate on ENSO phase locking using a modified seasonally dependent recharge oscillator model. There are two phase locking regimes associated with the strength of the seasonal modulation of growth rate: 1) a weak regime in which only a single peak occurs and 2) a strong regime in which two types of events occur either with a single peak or with a double peak. Notably, there is a seasonal gap in the strong regime, during which the ENSO peak cannot occur because of large-scale ocean–atmosphere coupled processes. We also retrieve a simple analytical solution of the seasonal variance of ENSO, revealing that the variance is governed by the time integral of seasonally varying growth rate. Based on this formulation, we propose a seasonal energy index (SEI) that explains the seasonal gap and provides an intuitive explanation for ENSO phase locking, potentially applicable to global climate model ENSO diagnostics.