In the interests of unfanning (not actually a word, it would seem) the flames, or not fanning them any further, I thought I would write about what seems to be an interesting paper brought to my attention by William Connolley. It’s by Laliberte et al. (2015) called Constrained work output of the moist atmospheric heat engine in a warming climate. It’s also covered in a recent Smithsonian article.
To be quite honest, I’m not sure I quite understand it, so I’m hoping some of my more informed (than me, that is) commenters can elaborate. As I understand it, the idea is that one can think of the atmosphere as some kind of heat engine, with energy transported from the surface, through the atmosphere where it can do some work, and then to the upper atmosphere where it is radiated into space. In this scenario, one ignores the energy lost directly to space from the surface via radiation, and need only consider the energy transported via convection and evaporation. So, one can write that the work done per unit time, , is the difference between the total amount of energy avaliable per unit time and the energy associated with evaporation and then precipitation (water cycle – ). In other words,
What they’ve done in this paper is then use climate models to consider how these quantities will change as we warm. The basic result seems to be that the increase in the water cycle, , exceeds the increase in the total available energy, , and hence the amount of energy available to do work and to drive actual atmospheric circulation goes down. The conclusion they draw is
As the climate warms, the system may be unable to increase its total entropy production enough to offset the moistening inefficiencies associated with phase transitions. This suggests that in a future climate, the global atmospheric circulation might comprise highly energetic storms due to explosive latent heat release, but in such a case, the constraint on work output identified here will result in fewer numbers of such events. Earth’s atmospheric circulation thus suffers from the “water in gas problem” observed in simulations of tropical convection, where its ability to produce work is constrained by the need to convert liquid water into water vapor and back again to tap its fuel.
Therefore, there will be less energy available to do work, with the consequences that there will be fewer storms, but that they could be highly energetic when they do happen.
Although I could embarrass myself by doing this, I thought I might try and understand why this could be the case. In a basic Carnot heat engine, you take energy from a reservoir at temperature , you then do an amount of work , and then transfer the remaining energy, , to a reservoir at temperature . The maximum efficiency is then given by
One of the feedbacks that we expect as we warm is lapse rate feedback. What happens here is that water vapour evaporates from the surface and then condenses in the atmosphere, releasing heat. However, this doesn’t happen uniformly throughout the vertical atmosphere, but preferentially happens at higher altitudes, rather than lower. Consequently, the upper atmosphere warms more than the lower atmosphere/surface, changing the lapse rate (vertical temperature gradient). Therefore, if we think of this as a heat engine, the cool reservoir (upper atmosphere) is warming more than the hot reservoir (surface/lower atmosphere) and therefore the maximum efficiency reduces.
Now, I don’t know if my basic explanation above is correct, or if my understanding of this is correct at all. So, if anyone understands this better than I do (which isn’t hard) feel free to explain it in the comments. This also might be an interesting topic, given the small furore about the recent snowstorm in the NE USA.