Toward quantifying the climate heat engine: Solar absorption and terrestrial emission temperatures and material entropy production

A heat-engine analysis of a climate system requires the determination of the solar absorption temperature and the terrestrial emission temperature. These temperatures are entropically defined as the ratio of the energy exchanged to the entropy produced. The emission temperature, shown here to be greater than or equal to the effective emission temperature, is relatively well known. In contrast, the absorption temperature requires radiative transfer calculations for its determination and is poorly known. The maximum material (i.e., nonradiative) entropy production of a planet's steady-state climate system is a function of the absorption and emission temperatures. Because a climate system does no work, the material entropy production measures the system's activity. The sensitivity of this production to changes in the emission and absorption temperatures is quantified. If Earth's albedo does not change, material entropy production would increase by about 5% per 1-K increase in absorption temperature. If the absorption temperature does not change, entropy production would decrease by about 4% for a 1% decrease in albedo. It is shown that, as a planet's emission temperature becomes more uniform, its entropy production tends to increase. Conversely, as a planet's absorption temperature or albedo becomes more uniform, its entropy production tends to decrease. These findings underscore the need to monitor the absorption temperature and albedo both in nature and in climate models. The heat-engine analyses for four planets show that the planetary entropy productions are similar for Earth, Mars, and Titan. The production for Venus is close to the maximum production possible for fixed absorption temperature.