Linear solutions for the frequency and amplitude modulation of ENSO by the annual cycle

We obtained linear solutions for the frequency and amplitude modulations of the El Ni˜no-Southern Oscillation (ENSO) by the annual cycle using a modified harmonic oscillator equation. The frequency modulation by the annual cycle was capable of changing the ENSO phases and dominant frequency, but could not modify the ENSO amplitude. On the other hand, the amplitude modulation by the annual cycle intensifies the ENSO variability and also induces seasonal amplitude locking. The intensification rate of the ENSO amplitude with respect to the annual cycle becomes less sensitive in low-frequency regime of ENSO.

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