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

Soon-Il An,Fei-Fei Jin

doi:10.1111/j.1600-0870.2010.00482.x

Abstract

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.

Highlights

One of unique features of the El Nino-Southern Oscillation (ENSO) is a seasonal locking of its variance, such that the lowest variability is in boreal spring and the highest variability is in boreal winter (Rasmusson and Carpenter, 1982; Galanti and Tziperman, 2000; An and Wang, 2001)
A somewhat different perspective concerning the annual cycle ENSO interaction is that of An et al (2010), who pointed out that the long-term changes in the relationship between the ENSO and the annual cycle may be due to changes in the annual mean state
We investigated the influences of the annual cycle on the ENSO using a simple linear harmonic oscillator that mimics the ENSO, focusing on the frequency and amplitude modulation of ENSO by the annual cycle

Summary

Introduction

One of unique features of the El Nino-Southern Oscillation (ENSO) is a seasonal locking of its variance, such that the lowest variability is in boreal spring and the highest variability is in boreal winter (Rasmusson and Carpenter, 1982; Galanti and Tziperman, 2000; An and Wang, 2001). This seasonal-locking phenomenon might be understood through the non-linear frequency locking of the ENSO to an annual period (Jin et al, 1994) or the seasonal change in the linear stability of ENSO (Tziperman et al, 1998).

Frequency modulation

Amplitude modulation

Concluding remarks