Entropy production rates of the climate

There is ongoing interest in the global entropy production rate as a climate diagnostic and predictor, but progress has been limited by ambiguities in its definition; different conceptual boundaries of the climate system give rise to different internal production rates. Three viable options are described, estimated and investigated here, two of which -- the material and the total radiative (here planetary) entropy production rates -- are well-established and a third which has only recently been considered but appears very promising. This new option is labelled the transfer entropy production rate and includes all irreversible processes that transfer heat within the climate, radiative and material, but not those involved in the exchange of radiation with space. Estimates in three model climates put the material rate in the range $27$-$48$ mW/m$^2$K, the transfer rate $67$-$76$ mW/m$^2$K, and the planetary rate $1279$-$1312$ mW/m$^2$K. The climate-relevance of each rate is probed by calculating their responses to climate changes in a simple radiative-convective model. An increased greenhouse effect causes a significant increase in the material and transfer entropy production rates but has no direct impact on the planetary rate. When the same surface temperature increase is forced by changing the albedo instead, the material and transfer entropy production rates increase less dramatically and the planetary rate also registers an increase. This is pertinent to solar radiation management as it demonstrates the difficulty of reversing greenhouse gas-mediated climate changes by albedo alterations. It is argued that the transfer perspective has particular significance in the climate system and warrants increased prominence.