The butterfly flap.....

has spread from Roger Pielke Senior's blog to Stoat and James' Empty Blog and sci.environment and who knows where else. Along the way, we discover that RPS (just lazy, not disrespectful, I save that for RPJ), believes that momentum is not conserved in the atmosphere. Mr. Rabett stuck his oar in briefly, saying that #22

"Dissipative forces exist on a macroscopic level, but then again, so do infinite heat baths. On the other hand, they result not only in the loss of conservation of momentum, but also of conservation of energy. However, as soon as you start looking at the bath in microscopic detail, dissipative forces disappear and you regain the conservation laws.

To the extent that a model treats part of the system as an infinite bath for energy or momentum, you can beat the conservation laws but you have to be careful in the analysis lest you push the assumption too far. It appears to me that the surface of the earth is such an energy bath for atmospheric dynamics models, as the surface of a pipe is for fluid flow. However, as long as the perturbation stays away from the wall it will not dissipate. Since the surface is in all climate models, and since the models show that small perturbations in the atmosphere propagate, for the purposes of this discussion, the butterfly flaps."

 a position that I maintain, and sensible people agree with. Within the atmosphere, momentum IS diffused to larger and larger volumes so that any particular molecule has an infinitely small share, but it IS conserved. Along the way, Eric Swanson in sci.environment raised the point that radiative emission might dissipate momentum. Certainly greenhouse gases in the atmosphere emit photons.

Eli Rabett has intensively consulted with the techno-bunny elite on this point. Along the way, we came up with some wrong answers, drafted a few papers for the journal of last resort, and finally found an answer which was so pleasing that we went out for a few beers to celebrate. My colleagues have designated me to provide the answer to a world waiting with baited breath (have you ever kissed someone who spent the day swallowing worms??).

Momentum is clearly conserved on emission of a photon, it is merely partitioned between the molecule and the photon. De Broglie came up with the idea that photons have momentum, and this is certainly shown by the Compton effect. So what happens in the atmosphere? As usual, there are three cases.

IF the photon is absorbed by another molecule in the atmosphere, momentum is conserved, merely transferred from one molecule to the other. This is boring

IF the photon is absorbed by the surface or in the ocean then momentum is conserved, but since roughly the same number of photons strike the earth going north or south, or east or west, there is no net change in the momentum of the earth and it may be treated as an infinite dissipative sink for momentum. This is uninteresting**

IF the photon is emitted to space, then momentum is transferred from the atmosphere to an infinite sink which is REALLY dissipative. This is both surprising and pleasing (to me, but then again I blog Saturday night, so my standards may not reach yours).

**This is not the case for energy transferred from the atmosphere to the earth by radiation. This is not uninteresting.

This is a tease. What do you think Chris Essex and Ross McKitrick meant when they said .....

"Consider that an ordinary laser pointer, powered by small flashlight batteries, generates peak temperatures of about 10^11 Kelvin. Yet you can shine it on your hand and not feel any warmth! This can happen because temperature represents the distribution of energy across physical states, and the fewer the states the higher the peak temperature, even at low energies.

The laser distributes a small amount of energy across very few states, which allows the temperature peak to get very large, despite not being perceptible by touch. Lasers are idealized in thermodynamics as having infinite temperature because ideally the laser radiation would have all of its energy in one quantum state."

How do you think Essex is defining temperature? Does it have much to do with a temperature measured in the atmosphere? If you are an expert in non-equilibrium thermodynamics, you may have a clue. For extra credit, why is this definition of what useful, and can you think of an interesting counter-example. The answer can be googled.

As for me, I have papers to mark.

Everyman needs a hobby (1)....

I think I may take up Essex and McKitrick, or at least share it with Tim Lambert. I should say at the beginning that I have a very different point of view than Tim, more physically based for one, but Essex and McKitrick sticks in my craw, and keeps on coming up, so I need a place to point to rather than posting the same comments a zillion different times.

Chris Essex and Ross McKitrick have written a book entitled "TAKEN BY STORM
The Troubled Science, Policy and Politics Of Global Warming" in it they make a large number of troubled claims.

The book itself is not on line, but a briefing pamphlet is at http://www.takenbystorm.info/TBSbriefing.pdf. They should know better. The briefing alone is an invitation to a fisking, with so many dubious claims that one hardly knows where to begin. For example, starting at the bottom of page 6 they say:

"Temperature is not energy. It is a thermodynamic variable with some special properties that make it far more interesting than it usually gets credit for."

True enough, but then they start going off the rails

"Consider that an ordinary laser pointer, powered by small flashlight batteries, generates peak temperatures of about 10^11 Kelvin. Yet you can shine it on your hand and not feel any warmth! This can happen because temperature represents the distribution of energy across physical states, and the fewer the states the higher the peak temperature, even at low energies."

Which is absolute garbage. A system with any number of states can have any temperature. You would think Essex would know better. What matters is the distribution of population in the various states. The simplest example is the two level system, which is described at any number of web sites. The temperature is determined by the relative populations in the two states, or alternatively the temperature determines what the relative population in each state is. Chicken/egg.

Here is a neat little applet that lets you play around with a two level system http://physchem.ox.ac.uk/~rkt/tutorials/heatcap/heatcap.html. The energy slider changes the separation between the two states, the temperature slider increases the temperature of the system.

The degeneracy slider is a bit more complicated. If the degeneracy is greater than one, the upper state rather than being composed of a single state, is built out of two or more states with equal energy. Leave that at one for now.

The relative populations in each state are shown by the green bars on top of each level. The blue arrow indicates how much population is shifted into the upper level if the temperature is increased 1 K (same as a 1 C change).

If Essex and McKitrick are right, how come the population of the system can be cooled to ~ 0K if most of the population is in the lower state.

The paragraph above is really a twofer. The statement about the laser temperature is another goody. More about that next time. As homework, go look up what the temperature describing the distribution of energy across states in a system which lases is.

Tea and the stupidity of Starbucks....

Ms. Rabett is a teabag. She never saw a nice cup of tea she did not crave, but the retailers of the world want to sell her flavored excretia that only people who hate tea like. Did you ever notice at Starbucks or wherever that the black tea (in the rare cases they have it) is always sold out, but the strange teas which no sane person drinks are there a plenty. Same thing in restaurants, they bring out this fancy tea case with cyanide flavor aplenty, but no black tea. Oh, they say, no more of that left.

They could reorder and make some money, but that would not be the capitalist way. I say, bring back the Tea Board so we can get some real leaves.

People who tell you that the greenhouse effect has nothing to do with greenhouses,

. . .will tell you that in a greenhouse, the glass windows cut off heat flow caused by air exchange between the inside and the outside of the car. They will also tell you that cutting off the air flow is not what happens in the greenhouse effect. This is the default statement.

What happens in a greenhouse is the same mechanism that heats a car up when you close the windows. The sun’s light (radiation) shines through the glass. The light energy checks in, but it can’t get out because both air flow (most important) and conduction are closed off. The fancy name for air flow is convection. We might fall into the habit of using that below.

That leaves radiation. The wavelength of radiation emitted from a surface depends on the temperature of the surface according to a formula first derived by Max Planck. It turns out that the emission from the sun is peaked in the green which can pass through the glass windows, but the radiation from surfaces at 300 C is peaked at much longer wavelengths in the infrared (IR), which is absorbed by the glass.

The IR radiation inside the car can heat the air inside the car, but, because it is adsorbed by the glass windows and the metal, it cannot get out. OTOH, the surface of the car and the glass is heated from the inside by radiation, conduction and convection.

The surface, in turn, can radiate heat away, but, because the glass has an inside and an outside, half of what is radiated goes back into the car and half out into the air. In short, for cars with closed windows and greenhouses, at first, the rate of radiation into the car exceeds the rate of radiation out of the car and other heat transfer processes are pretty much cut off.

There is another radiation law called the Stefan-Boltzmann law, which says that the rate of emission for radiation from a hot surface is proportional to T^{^4} , (which is T*T*T*T, T being the temperature in Kelvin) so if you heat something up a little, the total amount of energy emitted goes up a lot.

The sun pumps energy into the car at a constant rate. The temperature of the car increases until the surface is hot enough that the energy radiated from the surface per second exactly equals the energy pumped in by the sun. You get one hot car.

With all that in mind, let us talk about the atmosphere.

Again, the sun is the only real source of energy. Heating from the core of the earth is very small by comparison, but that is another story. The emission rate of radiation to space has to equal the rate at which the sun’s radiation reaches the earth. This is called radiation balance. If radiation balance did not exist, the earth would heat up until the surface was hot enough to emit enough energy to restore the balance.

If there was no greenhouse effect, the emitted IR light from the surface would all escape to space. The temperature of the surface necessary to emit enough energy so that the earth would be in radiation balance under those conditions is about 256 K or ~ -17 C. However, some of the light emitted from the surface is absorbed in the atmosphere by the greenhouse gases or clouds. That heats the atmosphere, but it also means that the molecules in the atmosphere will radiate. At the lowest level of approximation, which is good enough for this argument, half of the radiation from the atmosphere escapes upward to space and half is emitted downward to heat the surface. If you want more details google radiation balance.

Since not all of the radiation from the surface escapes to space when there are greenhouse gases, the surface has to emit more energy so that the amount of energy escaping to space per second equals that striking the earth's surface from the sun. In order to emit more energy the surface of the earth has to heat up. That is the greenhouse effect. And that is why the greenhouse effect both is and is not similar to a greenhouse. The atmosphere is not like a blanket, but it is like the glass in the greenhouse, or in your car.

Why doesn't your sock puppet have a Safeway card?

Shopping in the US requires an affinity card, or whatever those annoying things that they ask for at the checkout to give you the discounts they advertise are. We know they are selling the information along with the data they gather on our shopping habits. Lucky for us, when you sign up for the things they don't ask for ID, so Eli Rabett has a full compliment of supermarket/drug store discount cards. Sign your sock puppet up today. The only downside is that you have to pay cash when you use the card so they can't back track.

Explaining the greenhouse effect to your mom....)Part I(

has been a hard thing to do, so don't expect miracles folks. Conventional wisdom, CW says, that it is simple to explain what the greenhouse effect is not, the thing that keeps greenhouses warm and heats up your car in the in the summer. The CW for those two cases is that you cut off convection, exchange of atmospheric gases between the inside and the outside, and as a result the inside of the greenhouse and the car warms as solar energy pours in through the windows. OTOH, says the CW, that ain't the greenhouse effect, the thing that keeps the surface of the earth mostly toasty, or at least about 25 C toastier then it would be without.

I am going to show that what happens in the greenhouse and your car is much like what happens in the earth's atmosphere, and the CW misses something important. This posting will grow and hopefully change under the influence of comments. Eventually we might port it elsewhere, like Wikipedia but I don't want to throw this into that scrum without some preliminary doodling.

Let us start by discussing your car in the summer sun. You have to balance the flow of energy in with a flow of energy out. Assuming the sun is constant, any physicist will tell you that there are only three ways to ditch energy: Conduction, convection, and radiation. A chemist will throw in exothermic phase changes and reactions.

If your car is sitting in the sun with all the windows open, energy from the sun's radiation flows into the car and either is reflected out (off the white seats) or absorbed (off the black ones). For the sake of this thought experiment, assume that the car was sitting in a garage with the garage door opened and had reached an equilibrium temperature with the air around it.

Pull it out of the garage. As seats absorb energy from the sun, they will become warmer and heat the air next to them. The air inside is now a bit hotter than the air outside. The flow of energy into the car is balanced by flows of energy out of the car both from exchange of air and radiation through the open window but also the air inside heats the windows and surface of the car which then radiate faster. For the purpose of this argument we will make the usual spherical elephant assumption and postulate an all glass auto. On net the air in the car will be a bit warmer than that outside in order to maintain the balance.

As the sun's radiation pours in this process heats the windows and body of the car. The wavelength region that the warm seats and the body of the car radiate in is the infrared which cannot pass through the glass, but the glass can radiate back into the car and, on the other side, into the air.

Now close the windows. The rate at which energy flows into the car decreases as convection is cut off. The immediate rate of energy flow out by radiation stays the same, therefore the rate of energy flow into the car exceeds the rate of energy flow out of the car, and....the air in the car warms. As the air in the car warms, the interface between the atmosphere and the car, the glass also warms, as things warm, the rate of radiation increases as the fourth power of the temperature, so the hotter glass radiates at a faster rate. The air in the car stops heating when the temperature is high enough that the energy radiated from the glass surface out into the air (half goes back into the car) exactly balances the energy radiated into the car from the sun.

If you want a hydraulic analogy, imagine a pipe with water flowing through it. Now narrow one part of the pipe. The flow out of the pipe will decrease, but if the flow into the pipe remains constant, the pressure in the pipe will increase until the balance between the flow in and the flow out is restored.

Does anyone see where I am going??