Error Theory

Does gravity induced atmospheric pressure warm the atmosphere going down? On the one hand, this would seem to be the mechanism behind the adiabatic lapse rate (the temperature change of a parcel of air as it rises through the atmosphere in the absence of any heat exchange with surrounding air parcels):

As air descends through the troposphere it experiences increasing atmospheric pressure. This causes the parcel volume to decrease in size, squeezing the air molecules closer together. In this case, work is being done on the parcel. As the volume shrinks, air molecules bounce off one another more often ricocheting with greater speed. The increase in molecular movement causes an increase in the temperature of the parcel. This process is referred to as adiabatic warming.

[This website does not relate the temperature gain to the loss of potential energy from descending the gravity well, but I think they should be equal.]

On the other hand, Willis Eschenbach over at Watts Up With That has offered a proof that gravitational warming of the atmosphere would violate conservation of energy:

I hold it can be proven that there is no possible mechanism involving gravity and the atmosphere that can raise the temperature of a planet with a transparent GHG-free atmosphere above the theoretical S-B temperature.

"The theoretical S-B temperature" is the theoretical equilibrium temperature of the planet's surface in the absence of an atmosphere. Thus Willis is claiming that an atmosphere can only cause warming through the mechanism of heat trapping green house gases (GHGs), and his argument seems airtight. (Check it out here.)

I have a few naive comments to offer, but my immediate purpose is just to make a 2003 paper on the pressure-warming side of the debate more available. Tallbloke has the whole thing posted but Willis, feeling that Tallbloke has engaged in censorship of contrary views, just censored MY link to Tallbloke's posting of Hans Jelbring's 2003 paper. (Hellooo Froma Harrop!)

If Han's gives me permission, I'll post his full paper. (Done. Thank's Hans.) Here is his abstract:

The Greenhouse Effect as a function of atmospheric mass
JELBRING Hans
Abstract

The main reason for claiming a scientific basis for Anthropogenic Greenhouse Warming (AGW) is related to the use of radiative energy flux models as a major tool for describing vertical energy fluxes within the atmosphere. Such models prescribe that the temperature difference between a planetary surface and the planetary average black body radiation temperature (commonly called the Greenhouse Effect, GE) is caused almost exclusively by the so called greenhouse gases. Here, using a different approach, it is shown that GE can be explained as mainly being a consequence of known physical laws describing the behaviour of ideal gases in a gravity field. A simplified model of Earth, along with a formal proof concerning the model atmosphere and evidence from real planetary atmospheres will help in reaching conclusions. The distinguishing premise is that the bulk part of a planetary GE depends on its atmospheric surface mass density. Thus the GE can be exactly calculated for an ideal planetary model atmosphere. In a real atmosphere some important restrictions have to be met if the gravity induced GE is to be well developed. It will always be partially developed on atmosphere bearing planets. A noteworthy implication is that the calculated values of AGW, accepted by many contemporary climate scientists, are thus irrelevant and probably quite insignificant (not detectable) in relation to natural processes causing climate change.

Journal Title
Energy & environment ISSN 0958-305X
2003, vol. 14, no2-3, pp. 351-356


UPDATE: My earlier comment exchange with Hans Jelbring

The lapse rate is a well established real phenomenon, but I've always had a little trouble squaring it with my own experience with altitude and temperature. Riding up Windy Hill near sunset, it always gets much colder towards the bottom when I'm going back down, not warmer. This "temperature inversion" (where the temperature gradient is opposite of the lapse rate) is a ground effect. Local topology creates local cold spots from which cold air flows into local cold air sinks.

I've thought a little about these things while mountain biking, but I never sat down before and tried to figure out how the lapse rate and local ground effects combine to explain my own experience. That is, until about a week ago, when I first saw Han's Jelbring's 2003 paper at Tallbloke's. Reading his paper prompted me to try to figure out the Windy Hill to Portola Valley temperature dynamics, and I left my rumination on the subject as a comment on Tallbloke's Jelbring post.

Han's very nicely left me a reply that filled in a key point. I surmised that the sun dropping behind the ridge of the Santa Cruz Mountains was creating create a local cold spot on the east slope of the mountains. At the same time, the sun would still be heating the western slope on the east side of Portola Valley, and since the difference in afternoon sun exposure can be a couple of hours, it seemed that a pretty big east-west temperature differential could develop, creating a U-shaped flow of cold air streaming down the shaded slope towards the valley floor, pushing warm air up on the still lit side of the valley.

This would explain why the warmest location in such an area will be well up from the valley floor, but in his reply Hans added another crucial element to this story, explaining why these warmest locations can be surprisingly warm: it is because when the cold air flows down the shaded mountainsides, it doesn't just push air up on the other side of the valley, but it also pulls air down from up above the shaded hillside, and as this air is pulled down, its potential energy is converted into heat energy at the adiabatic lapse rate.

Of course the question arises: shouldn't this air have been colder by the adiabatic lapse rate before it got pulled down? Why would this air from above be warmer than what it displaces? But there could well be reasons for that, maybe convection of air from local hot spots during the day tends to accumulate a certain distance above the hilltops. In any case, there is an empirically documented phenomenon of an especially warm layer that can often be found a few hundred meters above a valley floor.

Not this leads me now to a further speculation: that the warm elevation on the western side of a valley (the east facing slope) might turn out to be substantially warmer than the warm elevation on the east side of the valley, or at the least there could tend to be a systematic difference between the temperature on the two side, because the source of the evening warm-belt air on the two sides will tend to be very different. On the west side of the valley, it will be air that is pulled down from above, replacing the down-slope cold air that is sliding to the valley floor. On the east side of the valley, it would be air from below, pushed up by the cold air coming in from the west side of the valley. As this air gets pushed up from the valley floor it will cool at the adiabatic lapse rate, and if it had already lost its hot-spot air to convection, it might end up on the cool side.

Or maybe the fact that the east side is in sunlight longer offsets, or more than offsets, any such effect, leaving the east-side warm-belt as warm as, or warmer than, the west-side warm-belt. Just the fact that there is a glaring asymmetry in the sources of these warm-belts makes it an interesting empirical question whether there tends to be any systematic temperature differential between east and west side warm-belts.

If there is, it might even be important to know. Current survival advice is for people caught out at night to get themselves well up off of a valley floor should it it be easy enough to do so. If it is actually more advantageous to be up on one side of a valley than the other, serious outdoorsmen might want to know that too.

In any case it could be an interesting exercise for amateur naturalists, if they live in an area where some data points could be collected.


UPDATE II: Jelbring vs. Eschenbach

I also collected some thoughts on Eschenbach's "proof" that gravity induced atmospheric pressure cannot be a source of surface warming. In short, I think he is right, and that the explanation for how this can be squared with the fact of the adiabatic lapse rate is pretty simple: the lapse rate implies a temperature gradient, but it does not by itself imply anything about the level at which this gradient is set. It can shift up or down, and its position is determined by the surface temperature. To think that atmospheric pressure is creating the surface temperature is backwards. It is surface temperature that creates atmospheric pressure by causing the atmosphere to evaporate up from the oceans, at least in the special case world under consideration.

Anyone who wants to bother with this might want to read Willis' post first. Here is my comment. Willis asked for an account of Jelbring's theory that can be summarized in an elevator conversation. I offered instead:

A maintenance elevator story FOR Willis' QED

He already provided a simple enough argument (an express elevator story) but the following working-through of the history of a liquid planet dropped into a uniformly irradiated environment might help flesh it out a bit:

Assume the liquid is just like water, except that it does not freeze, and its gaseous form is not a GHG. Instead of water, call it fauxter. Assume that the incoming radiation levels are such that the SB equilibrium temperature of the planet Fauxter is below the boiling point of fauxter, and that when it pops into existence, Fauxter is entirely liquid and is colder than the SB equilibrium temperature.

When incoming radiation starts to strike Fauxter's ocean, the ocean will begin to warm and some of the surface fauxter molecules will transition to vapor. Evaporation will cool the oceans as energy gets pumped into the atmosphere, but the overall effect will be warming. Both the oceans and the atmosphere will gain heat content, and the more the planet warms, the more readily the surface fauxter will transition to fauxter vapor, building the atmosphere.

In this initial phase, incoming radiation exceeds outgoing radiation. The difference is stored both in the rising heat content of the ocean and the atmosphere, and in the increased potential energy of the atmosphere as it gets lifted up through the planet's gravity well.

Conduction should tend to bring the surface temperature of the ocean together with the near-surface atmospheric temperature. If they are brought fully together then the temperature above would lapse from the ocean surface temperature according to ideal gas law, decreasing with decreasing atmospheric pressure as altitude increases.

This seems to me to be the crux of the issue. The heat content of the atmosphere is all determined by the ocean surface, both through the warming of fauxter into fauxter vapor, and by heat conduction between ocean and atmosphere. If we assume no convection, then the temperature profile from the surface on up just follows the lapse rate, and it is the surface that determines the LEVEL of this profile. The temperature profile can be stepped up or stepped down but the level of the profile is driven from the bottom of the atmosphere, not the top.

This is why atmospheric pressure cannot warm the surface. The causality goes the other way, at least in this GHG-less-atmosphere example. It is surface heat that lifts the atmosphere in the first place and is responsible for the level of the temperature profile going up. That result of the surface temperature cannot in turn be the cause of the surface temperature. The push only goes one way. Atmospheric mass does determine the lapse rate, but not the level of the temperature profile.

Once the ocean surface temperature reaches the SB equilibrium temperature, the system does not gain or lose energy. Solar radiation will still pry fauxter vapor from the ocean, but an equal amount of fauxter should be phase transitioning back to liquid.

The upshot is that atmospheric pressure will not drive surface temperatures above the SB equilibrium surface temperature because the causality goes the other way. It is surface temperature, not atmospheric pressure, that determines the level of the atmospheric temperature profile.

You have now arrived at the Fawlty Towers penthouse. How's the view?