Abstract
Abstract. This article presents the results of a bifurcation analysis of a simple energy balance model (EBM) for the future climate of the Earth. The main focus is on the following question: can the nonlinear processes intrinsic to atmospheric physics, including natural positive feedback mechanisms, cause a mathematical bifurcation of the climate state, as a consequence of continued anthropogenic forcing by rising greenhouse gas emissions? Our analysis shows that such a bifurcation could cause an abrupt change to a drastically different climate state in the EBM, which is warmer and more equable than any climate existing on Earth since the Pliocene epoch. In previous papers, with this EBM adapted to paleoclimate conditions, it was shown to exhibit saddle-node and cusp bifurcations, as well as hysteresis. The EBM was validated by the agreement of its predicted bifurcations with the abrupt climate changes that are known to have occurred in the paleoclimate record, in the Antarctic at the Eocene–Oligocene transition (EOT) and in the Arctic at the Pliocene–Paleocene transition (PPT). In this paper, the EBM is adapted to fit Anthropocene climate conditions, with emphasis on the Arctic and Antarctic climates. The four Representative Concentration Pathways (RCP) considered by the IPCC (Intergovernmental Panel on Climate Change) are used to model future CO2 concentrations, corresponding to different scenarios of anthropogenic activity. In addition, the EBM investigates four naturally occurring nonlinear feedback processes which magnify the warming that would be caused by anthropogenic CO2 emissions alone. These four feedback mechanisms are ice–albedo feedback, water vapour feedback, ocean heat transport feedback, and atmospheric heat transport feedback. The EBM predicts that a bifurcation resulting in a catastrophic climate change, to a pre-Pliocene-like climate state, will occur in coming centuries for an RCP with unabated anthropogenic forcing, amplified by these positive feedbacks. However, the EBM also predicts that appropriate reductions in carbon emissions may limit climate change to a more tolerable continuation of what is observed today. The globally averaged version of this EBM has an equilibrium climate sensitivity (ECS) of 4.34 K, near the high end of the likely range reported by the IPCC.
Highlights
Today, there is widespread agreement that the climate of the Earth is changing, but the precise trajectory of future climate change is still a matter of debate
The present paper presents an energy balance model (EBM) with more accurate diagnostic equations than the early EBMs, built upon the basic laws of geophysics and including nonlinear feedback processes that amplify anthropogenic CO2 forcing
Can a bifurcation leading to a warmer and more equable climate state be expected in the EBM if it is allowed to evolve along one of the four Representative Concentration Pathways (RCP) in Fig. 4? In Fig. 5b, this bifurcation would correspond to crossing the line of fold bifurcations separating the green and yellow regions on increasing μ and possibly FO
Summary
There is widespread agreement that the climate of the Earth is changing, but the precise trajectory of future climate change is still a matter of debate. One advantage of an EBM over a more complex GCM is that it facilitates the exploration of specific cause and effect relationships, as particular climate forcing factors are varied or ignored Another advantage of an EBM is that rigorous mathematical analysis often can prove the existence of certain behaviours, such as bistability and bifurcations, that could only be surmised from numerical evidence, or missed, in more complicated models. The EBM of this paper has been kept as simple as possible, while incorporating the nonlinear physical processes that are essential to our exploration of bifurcation behaviour In that sense, it follows in the tradition of simple energy balance models of Budyko (1968), Sellers (1969), North et al (1981), and others.
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