A yardstick for global entropy‐flux

The flux of entropy carried from the planet by radiation was estimated, from Earth Radiation Budget Experiment data, by Stephens and O'Brien. the present paper provides the numerical context for Stephens and O'Brien's results by deriving: (1) the maximum possible flux of entropy, subject only to the constraint that the planet be in energy balance with incoming solar radiation; (2) the latitude profiles of albedo and brightness temperature that maximize the entropy flux for a planet without horizontal transport of energy; (3) the entropy flux for a planet with such efficient transport that the brightness temperature is uniform from equator to pole. In each case, the entropy fluxes are computed as functions of the planetary albedo. the entropy fluxes in models (2) and (3) are found to be almost indistinguishable numerically. the result is extended to a family of latitude profiles for albedo and brightness temperature which interpolate between the dynamical extremes represented by models (2) and (3), and it is shown that all members of the family have essentially the same entropy‐flux. This suggests that measurements of the planetary entropy‐flux derived from satellite radiances may not enable us to distinguish easily between different atmospheric and oceanic circulations. the entropy flux for planet earth reported by Stephens and O'Brien is observed to lie close to the maximum.