[QUOTE=jshore]
Just as a break from the sort of contentiousness of the debate and because after noting several times how Santer et al. argues that the magnification of temperature fluctuations with height in the tropical atmosphere is a consequence of what is apparently quite basic physics but without myself knowing the details of what this basic physics is, I thought it might be educational for myself and others to explore “simple moist adiabatic lapse rate (MALR) theory”.
However, because it often leads to deeper understanding if you have to work through it yourself, I decided not to search too hard for the answer but just to get a little guidance and figure it out myself. I will issue the disclaimer that, although I am reasonably confident that I have gotten the basic ideas right, there is no guarantee of this. I did find this general Wikipedia page on lapse rate to be useful in discussing some basic concepts.
Let’s start with the “dry adiabatic lapse rate”. We will consider a parcel of air rising up through the atmosphere. By “dry” it is meant that it is not saturated (i.e., relative humidity < 100%) and the “adiabatic” refers to the fact that we will assume there is no heat exchange with the surrounding atmosphere, a pretty good approximation because of the low thermal conductivity of air. Now, as this air parcel rises, the atmospheric pressure on it drops so it expands. This expansion means it does work on it surroundings, pushing the other air out of the way, which in turn means (along with the adiabatic assumption) that its internal energy…and thus it temperature…decreases. In fact, the “dry air adiabatic lapse rate” (decrease in temperature with height) can be worked out to be about 9.8 C per km…a pretty hefty drop in temperature with height!
Now, let’s consider the lapse rate for “moist”, by which it is meant saturated, air. The story proceeds in the same way. However, now when the air cools, some of the water vapor will condense out because the saturation concentration of water vapor is a strongly increasing function of temperature. This condensation releases “latent heat” which will warm the air. So, moist air will not have as large a lapse rate as dry air. Furthermore, since the saturation concentration of water vapor is not only an increasing function of temperature but also has a positive second derivative, the amount of water vapor that condenses when you drop from say 30 C to 29 C is larger than the amount that condenses when you drop from 29 C to 28 C, so there will be more latent heat released in the former case than the latter. Hence, the moist adiabatic lapse rate decreases with the temperature. (At low enough temperatures that the air doesn’t hold much water vapor, it should approach the dry adiabatic lapse rate.)
So, there you have it, we have derived that the moist adiabatic lapse rate is a decreasing function of the temperature. What are the implications for this when we consider moist air that starts at the surface at two different temperatures and rises up in the atmosphere? Well, the warmer parcel of air not only starts out warmer but it also cools more slowly as it rises because of its lower moist adiabatic lapse rate. Hence, when you consider the same two parcels of air at some point up in the atmosphere, the temperature difference between them will have increased. This is, I believe, the very basic physics behind the idea that the moist adiabatic lapse rate theory predicts a magnification of temperature fluctuations with height in the atmosphere.
Of course, I can think of a lot of questions that one might face in fleshing this out into a full-fledged theory. First of all, one might wonder why this process seems to be said to be particularly important in the tropical atmosphere. My guesses would be that it is because convective processes are important there and because the temperatures there are warm enough that the change in lapse rate with temperature is reasonably large. Second, one might wonder how important the moist adiabatic lapse rate is relative to the dry adiabatic lapse rate (which does not have the same interesting temperature dependence). I am not sure on this one, but it is important to note that even if the air starts out pretty dry, as it rises and cools rapidly at the dry adiabatic lapse rate, it will rapidly approach saturation…at which point the above arguments will start to apply.
So, that is, I believe the basic physics behind the prediction that temperature fluctuations in the tropical atmosphere will be larger as we go up in the atmosphere than they are at the surface. Note that it is a quite general argument and doesn’t make reference to the processes that lead to the temperature differences, i.e., whether they are due to changes in greenhouse gas concentrations, changes in solar irradiance, changes in ocean temperatures, or whatever. It is just a generic consequence of the fact that the moist adiabatic lapse rate is a decreasing function of the temperature.
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As always, jshore, a very interesting piece of research.
Unfortunately, while everything you say is correct, there’s a bit more to the story.
Consider a parcel of air that starts to rise. At some point, condensation starts, and a cumulus cloud forms. More rising air, and we get a thunderstorm.
Now, within the core of the thunderstorm, we have rising saturated air. As you point out, the warmer it starts, the more the condensation warms the rising air.
The missing part in your exposition, jshore, is something linking this to the temperature of the middle troposphere. A thunderstorm converts the heat given off by the condensing water into increased lift, that’s why it is able to drive all the way up through to the upper troposphere.
At the the top, the air finally reaches a zone at which the density is such that it can rise no more. It spreads out and descends to the surface again.
Now, where has the heat gone? Well, it has gone into work, the work of lifting the air parcel.
Where has the heat not gone?
Into the middle troposphere. Inside the core of the thunderstorm, it has bypassed the middle troposphere entirely, and has been converted from heat into work.
This is another example of why we can’t just use “simple physics” to predict the climate. Nature, unfortunately, is rarely simple.
w.