Asymptotic analysis of internal relaxation-oscillations in a conceptual climate model
Abstract
We construct a dynamical system based on the KCG (K\"all\'en, Crafoord, Ghil) conceptual climate model which includes the ice-albedo and precipitation-temperature feedbacks. Further, we classify the stability of various critical points of the system and identify a parameter which change generates a Hopf bifurcation. This gives rise to a stable limit cycle around a physically interesting critical point. Moreover, it follows from the general theory that the periodic orbit exhibits relaxation-oscillations which are a characteristic feature of the Pleistocene ice-ages. We provide an asymptotic analysis of their behaviour and derive a formula for the period along with several estimates. They, in turn, are in a decent agreement with paleoclimatic data and are independent of any parametrization used. Whence, our simple but robust model shows that a climate may exhibit internal relaxation-oscillations without any external forcing and for a wide range of parameters.
Keywords
Cite
@article{arxiv.1902.03467,
title = {Asymptotic analysis of internal relaxation-oscillations in a conceptual climate model},
author = {Łukasz Płociniczak},
journal= {arXiv preprint arXiv:1902.03467},
year = {2019}
}