Radiation entropy flux and entropy production of the Earth system

Abstract

The study of the Earth's radiation entropy flux at the top of the atmosphere is reviewed with an emphasis on its estimation methods. Existing expressions for calculating radiation entropy flux scattered in different disciplines are surveyed, and their applicabilities are examined. It is found that the Earth's net radiation entropy flux estimated from these various expressions can differ substantially, more than the typical value of the entropy production rate associated with the atmospheric latent heat process. Comparison analysis shows that the commonly used expression of radiation entropy flux as the ratio of radiation energy flux to absolute temperature underestimates the Earth's radiation entropy flux by >30%. Theoretical analysis reveals that the large difference in the Earth's reflected solar radiation entropy flux among the different expressions arises mainly from the difference of the Earth's reflection properties (i.e., Lambertian or specular) assumed in these expressions. For the Earth system with typical shortwave albedo of 0.30 and longwave emissivity between 0.50 and 1.00, the Earth's net radiation entropy flux derived from the most accurate Planck's spectral expression ranges from 1.272 to 1.284 W m-2 K-1, amounting to the overall Earth's entropy production rate from 6.481 × 1014 to 6.547 × 1014 W K-1. Copyright © 2010 by the American Geophysical Union.