The photon gas versus the ideal gas, round 2

As a warmup I thought we could have a look at the following paradoxical behaviour of two reservoirs of ideal gas put in a gravity field and allowed to exchange both energy and matter:

The yellow numbers indicate the kinetic energy of the molecules and the "temperature" standing to the right is simply the ensemble average of the kinetic energy. Now imagine that one of the molecules in the upper reservoir jumps down:

Taking into account that the molecule gains some kinetic energy during the fall we arrive at:

Look what happened! Energy went from lower temperature to higher temperature, thereby equating the temperature of both reservoirs. Pretty queer, huh. But if something is screwing things up here it is certainly not greenhouse gases. In a way this illustrates an important difference between the photon gas and the ideal gas concerning the relationship between internal energy and temperature:

As we can see, for the photon gas the internal energy density is simply a constant times the temperature to the power of four, period. For the ideal gas the situation is different:

Notice the "n", which is the particle density. Hence, in contrast to the photon gas, the ideal gas can have an arbitrarily nonuniform distribution of energy but at the same time be isothermal. Of course this is of no concern for climate science since in their world the atmosphere is a photon gas and an ideal gas at the same time. That is also pretty queer.

Misuses of the complexity argument

In many discussions you encounter the argument "the climate is too complex to be properly understood". But what does it really mean and why do people use it. I think that in many cases it is used to avoid some uncomfortable or difficult question. The more interesting question would be: "What aspects of climate are too complex to be properly understood". Let me give a few examples:

1. Why is it brighter during daytime than during night? Is that complex or simple?

2. Why is it warmer during summer than during winter? Is that complex or simple?

3. Why is the average temperature lower at 5 km altitude than at the surface? Is that complex or simple?

The last question has apparently shown to be too complex for physicists, but maybe it is in fact simple, that we are just too stupid to realize it? Who knows. Maybe the difficulty lies in the fact that the third question posed can under certain circumstances turn almost meaningless. Below I will give two examples of common usage of the complexity argument, one good and one bad.

1. Climatologists claim that the climate is largely determined by the greenhouse effect. They try to prove this hypothesis by running computer simulations and compare them with temperature records of the past, but in reality small temperature variations are too complex to model so the greenhouse hypothesis is still unproven.

2. Nobody has denied the greenhouse effect, but we don't know its future magnitude because climate is so complex. It can be plus 1 or plus 4 or maybe plus 100 degrees or perhaps even -1, who knows, climate is so complex so we shouldn't do anything anyway.

Which one of the above do you think is best?

Can Newton's third law say anything important about the atmosphere?

Here I will expand a little bit on the previous post "Why is something possible in Climate Science that is impossible in Nature?". I thought the most convenient form would be an interview with myself.

A: First question: How is it possible for a spacecraft to leave the earth?

A: It is because of Newton's third law. By spitting out mass and radiation in the downward direction the spacecraft must take the recoil, that is, a force of equal magnitude but with opposite direction. When this force overcomes the gravitational force Mg, where M is the mass of the spacecraft and g the gravitational acceleration the spacecraft leaves the earth. If the recoil is less than Mg after it has left the earth it will fall back again. If you have equality, it will hoover in the air.

A:  So you mean that radiation is a force?

A: Not exactly but almost, radiation carries both momentum and energy. A reformulation of Newton's third law is the law of conservation of momentum. Energy relates to force by the formula E = Fd where d is displacement. Laser is often used nowadays to move small objects.

A:  And when light is absorbed it is converted into heat?

A: Not necessarily, you could say that when it is absorbed it acts as a force, doing work on the absorbing material, and this work can then be dissipated into heat. But dissipation requires an environment.

A: Are you implying that this has importance to climate science.

A: Yes.

A: In what way?

A: For example, Erren and Dietze say the following: "..the Greenhouse effect (GE) is a radiative effect, i.e. warming from back-radiation to ground, which is independent of atmospheric mass.. and thus cannot be governed in its magnitude". That is clearly wrong, just look at the spacecraft. The atmosphere would fly away if the radiation exceeded a certain value.

A: Aren't you beeing somewhat ridiculous right now?

A: A little bit maybe, but we havn't come to my main point yet.

A: What is that?

A: Have a look at the image below, it depicts an air parcel in hydrostatic equilibrium. My point is that for a hoovering air parcel the amount of backspitting of momentum is precisely governed by its mass times gravity, just like the hoovering spacecraft. This momentum can be transferred either by direct molecular collisions or by backradiation, but they must add up to Mg for the parcel to be in mechanical equilibrium.

A: And your point is that the precise nature of this backspitting of momentum is unimportant for the heating impact of an atmosphere?

A: Precisely!

A: Have you talked with anyone else about this?

A: I've tried to.

A: Any results?

A: I don't know, but it seems as if most people prefer to use more advanced laws, such as conservation of energy, molecular spectra, HITRAN and so on. They probably think that Newton's third law is soo 17th century.

A: Ok, thanks for the interview.

A: My pleasure.

A Note: Newton's third law of course also applies to an oscillating force in the horizontal direction.

The Hypothesis of Claes Johnsson and the Rebuttal by Lennart Bengtsson

The story about Claes Johnsson's course litterature Body & Soul and the following media hype is comprehensively covered on his blog. The draft version of his book contained parts discussing atmospheric physics, but these were never included in the numerics course in which the book was used. Nevertheless, Lennart Bengtsson, swedish professor of meteorology at the University of Reading, found himself forced to give a rebuttal in the swedish newspaper Ny Teknik. Bengtsson's attitude towards the IPCC could be described as that he is a little bit for it, but also a little bit against it, whatever suits the circumstances. On the book by Claes Johnsson he is more categorical as you will see. Parts of Bengtssons newspaper article will be quoted, which I will translate to english to the best of my ability.


"..De avsnitt jag inspekterat är förfärande i sin fullständiga brist på relevant atmosfärkunskap. Jag skulle snarare vilja kalla det anti-kunskap.

Kap. 13 försöker på ett märkligt sätt att visa vad temperaturen! är vid atmosfärens övre gräns. Jag kan nämna att tropopausens temperatur ligger mellan -60°C och -80°C och knappast 0. Det man givetvis måste använda är den strålning/ytenhet som träffar atmosfärens övre gräns. Detta kan lätt beräknas och uppgår i årligt medelvärde för hela jorden till just 1/4 av solarkonstanten eller 341W/m2. 102 W/m2 reflekteras (planetärt albedo är 30%). Resten, 239W/m2, återstrålas mot rymden som långvågig strålning. Det inses lätt att den REPRESENTATIVA temperaturen för denna återstrålning är ca 255 K eller -18°C. Detta beror på att strålningen från jordytan absorberas av växthusgaserna som i sin tur strålar vidare från en lägre temperatur osv. Resonemanget i detta kapitel är totalt felaktigt. Vad som händer vid en ökad koncentration av växthusgaser är att den representativa utstrålningen sker från en högre nivå i atmosfären varvid konsekvensen blir en ytterligare förhöjd marktemperatur. Här är det bara att följa den fukt/torradiabatiska temperaturprofilen.....

....Hela det sk strålningsavsnittet vittnar om en total brist på insikt i mekanismerna för atmosfärisk strålning. Det ytterst omfattande arbete som pågått här under de senaste 50-75 åren beaktas överhuvudtaget inte. Författarna borde ta och läsa igenom Richard Goodys senaste utgåva från 1995 tillsammans med Y. L.Yung eller Kuo-Nan Lious bok från 2002. Det är mig en obegriplighet att dylikt nonsens kan skrivas från anställda vid ett av Sveriges främsta lärosäten, åtminstone gällde detta tidigare. Man kunde åtminstone konsulterat någon av de svenska professorerna i meteorologi eller någon utländsk expert på atmosfärstrålning för att undvika de allra värsta tokigheterna. Man kan bara hoppas att eleverna var intelligenta nog för att genomskåda rappakaljan som dessutom presenteras på ett beschäftigt och mästrande sätt...."

Which could be translated as:

"..The chapters I have inspected are appalling in their complete lack of relevant atmospheric physics. I would rather call it anti-knowledge.

In Chapter 13 there is a strange attempt to derive the temperature at the top of the atmosphere. I can inform you that the temperature of the tropopause lies between -60°C och -80°C and not 0. The relevant quantity you need is the amount of radiation/area hitting the upper boundary of the atmosphere. It can easily be calculated and its annual average amounts to 1/4 of the solar constant or 341W/m2. 102 W/m2 is reflected (the planetary albedo is 30%). The rest, 239W/m2, is re-radiated to space in the form of longwave radiation. It is easily understood that the RESPRESENTATIVE temperature for this re-radiation is approximately 255 K or -18°C. This is because the outgoing terrestrial radiation is absorbed by the greenhouse gases which in turn re-radiate from a lower temperature and so on. The reasoning in this chapter is completely wrong. What happens with an increased concentration of greenhouse gases is that the representative outgoing radiation takes place at a higher level in the atmosphere with the consequence that the ground temperature is increased further. Here you only need to follow the moist/dry-adiabatic temperature profile....

....The entire so called chapter on radiation bears witness of a complete lack of insight into the mechanisms of atmospheric radiation. The comprehensive work that has been carried out during the last 50-70 years is completely neglected. The authors should read Richard Goody's latest edition from 1995 coauthored with Y.L. Yung or Kuo-Nan Liou's from 2002. To me it is incomprehensible how such nonsense can be written by people employed at one of Swedens top-ranking universities, at least that was my attitude before. At least they could have consulted some of the swedish professors of meteorology or some foreign expert on atmospheric radiation in order to avoid the worst crazyness. One can only hope that the students were intelligent enough to see through the bullshit, which is also presented in a very obtrusive and patronising manner...."

It is instructive to see how Bengtsson uses the sloppy and dishonest way of reasoning that I have already disected in the post "What is the greenhouse effect". For some reason, even professors of meteorology prefer the sloppy version. Is it perhaps because they have something to hide? In any case I don't think the students became any wiser from reading Bengtsson's pamphlet.

I have a suggestion for you, Professor Bengtsson. Why don't you also comment on the lapse-rate "bullshit" provided by various physicists in the post "4 different descriptions of the lapse rate"?   

How to freeze water under vacuum

According to G&T:

1.2. What is a physical effect?
 
A physical effect consists of three things:
 
(a) a reproducible experiment in the lab;
(b) an interesting or surprising outcome;
(c) an explanation in terms of a physical theory.

In the video above we see (a) and (b), but what is the explanation?

4 different explanations for the lapse rate

Despite the fact that greenhouse speculations (4) have been with us for at least a century, highly trained physicists seem to be awfully uneducated (irony) on this topic. Read and behold:

1. Serways Principles of Physics ISBN 0-534-49143-X,(kap 16.7 s. 520) 'The atmospheric lapse rate':

" ...We can argue conceptually why the temperature decreases with height.
Imagine a parcel of air moving upward along the slope of a mountain. As
the parcel rises into higher elevations, the pressure on it from the
surrounding air decreases. The pressure difference between the interior
and exterior of the parcel causes the parcel to expand. In doing so, the
parcel is pushing the surrounding air outward, doing work on it. Because
the system is doing work on the environment, the energy in the parcel
decreases. The decreased energy is manifested as a decrease in
temperature..."

2. Erren and Dietze, E&E 2003:

"...Upper layers would
be cooler because the vertical component of the thermal molecular speed
is reduced...."

3. M.N. Berbaran-Santos et al. :

".. The fall of temperature with altitude in the troposhere is due to the fact that air is warmed mainly from the surface of the planet. This fall is, however, smaller than could be expected because convection occurs (up to the tropopause). .."

4. Manabe-Strickler:

".. The observed troposheric lapse rate of temperature is approximately 6.5 deg per km. The explanation for this fact is rather complicated. It is essentially the result of a balance between (a) the stabilizing effect of upward heat transport in moist and dry convection on both small and large scales and (b) the destabilizing effect of radiative transfer... "

The Enigma

We now leave theory for a moment to discuss a little what goes on in the real world. Temperature lapse-rates are often expressed in terms of a decline in temperature as a function of altitude. In reality though, it turns out that pressure is a more convenient vertical coordinate to use. From soundings one finds the following approximate relation between temperature and pressure:

The Theta symbol stands for the ground temperature. This is better confirmed by soundings than the dry adiabatic lapse rate expressed in terms of altitude as

dT/dz = -g/Cp.

It is worthwhile to think for a moment what it means.

Some fuel for thought

It seems as if concepts like temperature and the second law of thermodynamics are difficult to apply on the planetary scale. There are a lot of pitfalls, one or two of which probably most of us has fallen into some time. But there is always opportunity to learn from our mistakes. But physics cannot be determined by the human language. Are there any more physical "hands-on" concepts that we can use instead of abstract notions that might lead to confusion?

Imagine that you go to the beach a warm (25 deg C) day with a backpack full of cold beer. You don't want to drink the beer immediately but rather wait a couple of hours until your friends arrive. From experience you know that in the meantime the beer will warm to ambient temperature unless you do something. There are two options: In the bar at the beach there is a refrigerator which you can use. But next to the beach there is also a two kilometer high mountain and a helicopter standing at your disposal. You could if you want take the backpack in the helicopter, fly to the top of the mountain where the temperature is 8 deg C, leave the beer there and then return to pick it up some hours later. Which is more practical? Which is less energy consuming? I think most of us would find the refrigerator more practical, since going up the mountain requires a lot of work against the gravitational field.

Likewise, the gravity field effectively prevents us from constructing a perpetuum mobile from the temperature difference that is beeing maintained for free between the ground and the top of the mountain. So, what do you then think is the cause of this temperature difference?

Roy again

I will let Roy Spencer summarize some of the points made during the last week by quoting parts of two of his blogposts which can be found here and here.

Roy Spencer on the second law of thermodynamics:

"First of all, the 2nd Law applies to the behavior of whole systems, not to every part within a system, and to all forms of energy involved in the system…not just its temperature. And in the atmosphere, temperature is only one component to the energy content of an air parcel."

Roy Spencer on the state of the earth if there were no greenhouse gases:

"....And what happens when there is a temperature difference in a material? Heat flows by thermal conduction, which would then gradually warm the upper atmosphere to reduce that temperature difference. The process would be slow, because the thermal conductivity of air is quite low. But eventually, the entire atmosphere would reach a constant temperature with height."

Yes, that sounds familiar, isn't it the second law of thermodynamics?