Bifurcation analysis of delay-induced resonances of the El-Nino Southern Oscillation

TL;DR

This paper analyzes how delays in feedback loops influence the behavior of a simplified climate model for ENSO, revealing delay-induced resonances and stability boundaries through bifurcation analysis.

Contribution

It introduces a bifurcation analysis approach to delay differential equations modeling ENSO, highlighting the role of delays in climate oscillation dynamics.

Findings

Identification of delay-induced resonance regions

Mapping of stability boundaries in the model

Insights into feedback delay effects on ENSO oscillations

Abstract

Models of global climate phenomena of low to intermediate complexity are very useful for providing an understanding at a conceptual level. An important aspect of such models is the presence of a number of feedback loops that feature considerable delay times, usually due to the time it takes to transport energy (for example, in the form of hot/cold air or water) around the globe. In this paper we demonstrate how one can perform a bifurcation analysis of the behaviour of a periodically-forced system with delay in dependence on key parameters. As an example we consider the El-Nino Southern Oscillation (ENSO), which is a sea surface temperature oscillation on a multi-year scale in the basin of the Pacific Ocean. One can think of ENSO as being generated by an interplay between two feedback effects, one positive and one negative, which act only after some delay that is determined by the speed of transport of sea-surface temperature anomalies across the Pacific. We perform here a case study of a simple delayed-feedback oscillator model for ENSO (introduced by Tziperman et al, J. Climate 11 (1998)), which is parametrically forced by annual variation. More specifically, we use numerical bifurcation analysis tools to explore directly regions of delay-induced resonances and other stability boundaries in this delay-differential equation model for ENSO.