Heat Transport and Lapse Rate

Over at RealClimate we find a post entitled A Simple Recipe for GHE by someone called Rasmus. The post is an attempt to explain the greenhouse effect, and to convince us that a doubling the CO2 concentration will raise the Earth's surface temperature by a few degrees Centigrade. We have already claimed that all explanations of the greenhouse effect we encountered on the web violated at least one law of physics or thermodynamics. The manner in which this new explanation violates the laws of thermodynamics is interesting enough to merit a short discussion.

The author agrees with our conclusion that the Earth's atmosphere radiates its heat at an altitude where it becomes transparent. And so he brings the atmospheric temperature lapse rate to our attention in his section (iv). The lapse rate is the drop in temperature with altitude. In Atmospheric Convection we found that the drop in temperature with altitude is the result of the adiabatic expansion of gas during during the transport of heat by convection to the upper atmosphere. If there were no greenhouse gases in the atmosphere, there would be no radiation of heat by the upper atmosphere, and no heat to transport. With no heat to transport, there would be no convection, no adiabatic expansion, and therefore no atmospheric lapse rate. To suggest that a convection cycle can exist in a viscous fluid without the transport of heat and without any source of physical work, such as a paddle, is to believe in a perpetual motion machine. In the comments of Motl on CO2 Sensitivity you will see us debating this same issue with a reader. The reader claims that convection will take place even in a transparent atmosphere without any machines to move the air and without any upward heat transport. Rasmus appears to share our reader's belief, because he makes no mention of the relationship between heat transport and atmospheric lapse rate. He refers to hydrostatic balance, but such balance in no way requires a drop in temperature.

When we ignore the dependence of the atmospheric lapse rate upon heat transport, we conclude that the atmosphere keeps cooling as we go up, so that there is no layer in the atmosphere where the lapse stops. In short, Rasmus's understanding of the lapse rate implies that there is no tropopause, even though the existence of the tropopause in the Earth's atmosphere is well-established. In the first comment following the post, we see a reader asking some cogent questions about the tropopause, and Rasmus answering that the tropopause is above the highest altitude of heat radiation by the atmosphere. But this cannot be true, because without vertical heat flow, the temperature of the atmosphere would not be dropping. The tropopause must mark the upper limit of the atmospheric heat transport away from the Earth.

Rasmus's argument requires that we set aside the law of conservation of energy, which is the First Law of Thermodynamics. We prefer explanations that adhere to established laws, so we feel justified in dismissing his post.

PS. Originally spelled "lapse" without the "e", but corrected spelling in title and text after Chuck pointed out my error, see comments.