Multistability in a Coupled Ocean-Atmosphere Reduced Order Model: Non-linear Temperature Equations

TL;DR

This study demonstrates multistability in a reduced order coupled ocean-atmosphere model when non-linear temperature equations are numerically solved, revealing multiple stable states and different variability behaviors.

Contribution

It introduces a numerical implementation of the full non-linear Stefan-Bolzmann law in a reduced model, showing how non-linear temperature equations affect system dynamics and stability.

Findings

Multiple stable solutions with distinct flow patterns

Observation of different Low Frequency Variability behaviors

Impact of coupling strength and greenhouse effects on stability

Abstract

Multistabilities were found in the ocean-atmosphere flow, in a reduced order ocean-atmosphere coupled model, when the non-linear temperature equations were solved numerically. In this paper we explain how the full non-linear Stefan-Bolzmann law was numerically implemented, and the resulting change to the system dynamics compared to the original model where these terms were linearised. Multiple stable solutions were found that display distinct ocean-atmosphere flows, as well as different Lyapunov stability properties. In addition, distinct Low Frequency Variability (LFV) behaviour was observed in stable attractors. We investigated the impact on these solutions of changing the magnitude of the ocean-atmospheric coupling, as well as the atmospheric emissivity to simulate an increasing green-house effect. Where multistabilities exist for fixed parameters, the possibility for tipping between solutions was investigated, but tipping did not occur in this version of the model where there is a constant solar forcing. This study was undertaken using a reduced-order quasi-geostrophic ocean-atmosphere model, consisting of two atmosphere layers, and one ocean layer, implemented in the Python programming language.