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

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The goal of this paper is to explore the potential multistability of the climate for a planet around the habitable zone. We apply our methodology to the Earth system, but our investigation has more general relevance. 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 1510Wm−2 and the CO2 concentration, [CO2], between 90 and 2880ppm. 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). The tipping points of both the transitions (W→SB and SB →W) are located along straight lines in the (S∗,log[CO2]) space. 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 eminently dry climates where heat transport is realised 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 discontinuous decrease at the point of 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. While the specific results presented in this paper depend on some characteristics of the Earth system (e.g. rotation rate, position of the continents), this paves the way for the possibility of proposing efficient parameterisations of complex non-equilibrium properties and of practically deducing fundamental properties of a planetary system from a relatively simple observable. As a preliminary result, we obtain that when reducing the rotation rate of the planet by a factor of two, the multistability properties, the quantitative estimators of the thermodynamics of the system, and the approximate parameterisations in terms of the surface of emission temperature are only weakly affected.