Attractors and bifurcation diagrams in complex climate models

TL;DR

This paper explores methods to efficiently construct bifurcation diagrams in complex climate models, aiding understanding of multi-stability and tipping points in Earth's climate system.

Contribution

It introduces two techniques for bifurcation diagram construction in climate models, improving speed and accuracy in identifying stable states and tipping points.

Findings

Random fluctuation method explores phase space broadly.

Reconstruction method precisely locates tipping points.

Combined techniques enhance bifurcation analysis in complex models.

Abstract

The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the possible steady states under different forcing is the bifurcation diagram, that reveals the regions of multi-stability, the position of tipping points, and the range of stability of each steady state. However, its construction is highly time consuming in climate models with a dynamical deep ocean, interactive ice sheets or carbon cycle, where the relaxation time becomes larger than thousand years. Using a coupled setup of MITgcm, we test two techniques with complementary advantages. The first is based on the introduction of random fluctuations in the forcing and permits to explore a wide part of phase space. The second reconstructs the stable branches and is more precise in finding the position of tipping points.