An analysis of the periodically forced PP04 climate model, using the theory of non-smooth dynamical systems

TL;DR

This paper analyzes the PP04 climate model's behavior under periodic forcing using non-smooth dynamical systems theory, revealing complex bifurcations and synchronized solutions relevant to climate change and ice-age transitions.

Contribution

It introduces a novel application of non-smooth dynamical systems theory to the PP04 climate model, uncovering complex bifurcation structures and synchronized solutions.

Findings

Discontinuous bifurcations influence climate state transitions.

Periodic forcing leads to synchronized oscillations.

Rich dynamical structures depend on forcing amplitude and frequency.

Abstract

In this paper we perform a careful analysis of the forced PP04 model for climate change, in particular the behaviour of the ice-ages. This system models the transition from a glacial to an inter-glacial state through a sudden release of oceanic Carbon Dioxide into the atmosphere. This process can be cast in terms of a Filippov dynamical system, with a discontinuous change in its dynamics related to the Carbon Dioxide release. By using techniques from the theory of non-smooth dynamical systems, we give an analysis of this model in the cases of both no insolation forcing and also periodic insolation forcing. This reveals a rich, and novel, dynamical structure to the solutions of the PP04 model. In particular we see synchronised periodic solutions with subtle regions of existence which depend on the amplitude and frequency of the forcing. The orbits can be created/destroyed in both smooth and discontinuity induced bifurcations. We study both the orbits and the transitions between them and make comparisons with actual climate dynamics.