Thermodynamic analysis of snowball Earth hysteresis experiment: Efficiency, entropy production and irreversibility

Abstract

We present an extensive thermodynamic analysis of a hysteresis experiment performed on a simplified yet Earth-like climate model. We slowly vary the solar constant by 20% around the present value and detect that for a large range of values of the solar constant the realization of snowball or of regular climate conditions depends on the history of the system. Using recent results on the global climate thermodynamics, we show that the two regimes feature radically different properties. The efficiency of the climate machine monotonically increases with decreasing solar constant in present climate conditions, whereas the opposite takes place in snowball conditions. Instead, entropy production is monotonically increasing with the solar constant in both branches of climate conditions, and its value is about four times larger in the warm branch than in the corresponding cold state. Finally, the degree of irreversibility of the system, measured as the fraction of excess entropy production due to irreversible heat transport processes, is much higher in the warm climate conditions, with an explosive growth in the upper range of the considered values of solar constants. Whereas in the cold climate regime a dominating role is played by changes in the meridional albedo contrast, in the warm climate regime changes in the intensity of latent heat fluxes are crucial for determining the observed properties. This substantiates the importance of addressing correctly the variations of the hydrological cycle in a changing climate. An interpretation of the climate transitions at the tipping points based upon macro-scale thermodynamic properties is also proposed. Our results support the adoption of a new generation of diagnostic tools based on the second law of thermodynamics for auditing climate models and outline a set of parametrizations to be used in conceptual and intermediate-complexity models or for the reconstruction of the past climate conditions.

Detecting hotspots of atmosphere–vegetation interaction via slowing down – Part 2: Application to a global climate model

“…For example, it may be applied to fluctuations in sea ice cover close to the snowball earth bifurcation (Lucarini et al, 2010;Voigt and Marotzke, 2010).…”

Venus Atmospheric Thermal Structure and Radiative Balance

“…They pointed out that the Carnot cycle efficiency of the Venus heat engine is about twice as large (27.5%) as that for Earth Schubert and Mitchell 2013), suggesting a different distribution for the transfer of energy within the planet's atmosphere as compared to Earth. The Carnot efficiency for Earth has been estimated from an extensive thermodynamic analysis using a climate model (Lucarini et al 2010) and estimated to be considerably less than quoted by Schubert and Mitchell. It is not known whether the discrepancy is due to the approach or due to the use of the model rather than the simplistic definition used previously.…”

Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns

“…[53], can be related to the presence of nearby critical transitions. Indeed, we have recently investigated such an issue in [54], thus providing the statistical mechanical embedding for the classical problem of multistability of the Earth's system, which had been previously studied using macroscopic thermodynamics in [55][56][57].…”

“…PUMA and PLASIM have already been used for several theoretical climate studies, including a variety of problems in climate response theory [2,36], climate thermodynamics [77,78], analysis of climatic tipping points [54,55], and in the dynamics of exoplanets [56,57].…”

“…We wish to emphasise that most state-of-the-art general circulation models feature an imperfect closure of the global energy budget of the order of 1 Wm −2 for standard climate conditions, due to inaccuracies in the treatment of the dissipation of kinetic energy and the hydrological cycle [2,75,79,80]. Instead, PLASIM has been modified in such a way that a more accurate representation of the energy budget is obtained, even in rather extreme climatic conditions [55][56][57]. Therefore, we are confident of the thermodynamic consistency of our model, which is crucial for evaluating correctly the climate response to radiative forcing resulting from changes in the opacity of the atmosphere.…”