Mixed mode oscillations in a conceptual climate model

• Published in: Physica. D 2015-02, Vol.292-293, p.70-83
• Main Authors: Roberts, Andrew, Widiasih, Esther, Wechselberger, Martin, Jones, Christopher K.R.T.
• Format: Article
• Language: English
• Subjects: Atmospherics; Carbon; Climate; Climate models; Fast/slow; Folded node; Glacial cycle; Mathematical models; Mixed-mode oscillations; MMO; Oscillations; Oscillators; Paleoclimate; Relaxation oscillations; Stores
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2014.11.003

Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data are often more complicated than what can be described by such mechanisms. This paper examines complex oscillatory behavior in climate data through the lens of mixed-mode oscillations. As a case study, a conceptual climate model with governing equations for global mean temperature, atmospheric carbon, and oceanic carbon is analyzed. The nondimensionalized model is a fast/slow system with one fast variable (corresponding to ice volume) and two slow variables (corresponding to the two carbon stores). Geometric singular perturbation theory is used to demonstrate the existence of a folded node singularity. A parameter regime is found in which (singular) trajectories that pass through the folded node are returned to the singular funnel in the limiting case where ϵ=0. In this parameter regime, the model has a stable periodic orbit of type 1s for some s>0. To our knowledge, it is the first conceptual climate model demonstrated to have the capability to produce an MMO pattern. •A conceptual model for Pleistocene glacial cycles is developed.•The model is analyzed using geometric methods for multiple time-scale systems.•For certain parameters the model exhibits mixed-mode oscillations.