Irreversible processes in phase transitions and radiative transfer

The two main climate processes contributing to the entropy budget are radiative interactions and phase changes in the climate system. The foundations for estimating the entropy production rate by radiative interactions had been laid down in the last two decades of the 20th century. However, in the first decade of the present century wrong formulae have been proposed and used regarding absorption and emission of radiation in the atmosphere and the ocean. We saw it as our duty to point out those failings, which was done in the paper by Pelkowski (2012) for the atmospheric science community. Moreover, in the last years many attempts at proving or substantiating the so-called hypothesis of maximum entropy production have been published, but few definitive advances seem to have surfaced. The paper of Pelkowski (2014), developed on rigorous theoretical grounds, sheds light on the whole issue. It suggests the Earth’s climate to be operating nearly at maximum entropy production rate, whatever the temperature distributions in the atmosphere (Figure 1). However, scattering has not been included, which could have been done but we did not consider it for lack of time. The issue of entropy production by phase changes we develop from thermodynamic principles. The investigation is nearly closed for evaporation of water from the oceans. Phase changes and the entropy production rate in cloud formation, on the other hand, has turned out to be far more difficult to estimate, because the equations describing nucleation and droplet growth could not yet be solved analytically (and doing so numerically is not illuminating to our minds). Entropy production due to evaporation turns out to be about 10% of the total global rate. This value is not negligible but it has been, and still is, most often neglected. We plan to publish an article about it very soon.

Participating researchers: Joachim Pelkowski and Thomas Frisius



Figure 1: Total steady-state entropy production rates of the climate of a system with uniformly warm atmosphere and a different surface layer of temperature Ts for different optical depths.