Bistability of the climate around the habitable zone: a thermodynamic investigation

Abstract

The goal of this paper is to explore the potential multistability of the climate of a planet around the habitable zone. A thorough investigation of the thermodynamics of the climate system is performed for very diverse conditions of energy input and infrared atmosphere opacity. Using PlaSim, an Earth-like general circulation model, the solar constant S* is modulated between 1160 and 1510 Wm-2 and the CO2 concentration, [CO2], from 90 to 2880 ppm. It is observed that in such a parameter range the climate is bistable, i.e. there are two coexisting attractors, one characterised by warm, moist climates (W) and one by completely frozen sea surface (Snowball Earth, SB). Linear relationships are found for the two transition lines (W\rightarrowSB and SB\rightarrowW) in (S*,[CO2]) between S* and the logarithm of [CO2]. The dynamical and thermodynamical properties - energy fluxes, Lorenz energy cycle, Carnot efficiency, material entropy production - of the W and SB states are very different: W states are dominated by the hydrological cycle and latent heat is prominent in the material entropy production; the SB states are predominantly dry climates where heat transport is realized through sensible heat fluxes and entropy mostly generated by dissipation of kinetic energy. We also show that the Carnot efficiency regularly increases towards each transition between W and SB, with a large decrease in each transition. Finally, we propose well-defined empirical functions allowing for expressing the global non-equilibrium thermodynamical properties of the system in terms of either the mean surface temperature or the mean planetary emission temperature. This paves the way for the possibility of proposing efficient parametrisations of complex non-equilibrium properties and of practically deducing fundamental properties of a planetary system from a relatively simple observable