A simple theory for the modulation of tropical instability waves by ENSO and the annual cycle

Abstract

Motivated by a recent active period of Tropical Instability Waves (TIWs) that followed the extreme 2015/2016 El Niño, we developed a stochastically forced linear model for TIWs with its damping rate modulated by the annual cycle and El Niño Southern Oscillation (ENSO). The model’s analytical and numerical solutions capture relatively well the observed Pacific TIWs amplitude variability dominated by annual and ENSO timescales. In particular, our model reproduces the seasonal increase in TIWs variance during summers and falls and the nonlinear relationship with the ENSO phase characterised by a suppression, respectively increase of TIW activity during El Niño, respectively La Niña. A substantial fraction of TIWs amplitude modulation emerges from the deterministic nonlinear interaction between ENSO and the annual cycle. This simple mathematical formulation allows capturing the nonlinear rectifications of TIWs activity onto the annual cycle and ENSO through, for instance, TIWs-induced ocean heat transport. Moreover, our approach serves as a general theoretical framework to quantify the deterministic variability in the covariance of climate transients owing to the combined modulation of the annual cycle and ENSO.