### The Sceptic or the Skeptic

In the last couple of weeks Eli has been toe-nailling about one of those incestuous ideas that creep into a bunny's mind. Something potentially very important, unnoticed, but upsetting to the normal way of thinking about the greenhouse effect. Now, let his Bunnyship get this out at the front, the idea, as the imminent readers will see, has nothing to do with the global effect, that is absolutely nailed by radiative transfer codes matched against emissions to space. And no, it is not Viscount Rabett's maundering about how there is no such thing as nasty hominids warming the planet, but to continue

Now, for some, not Eli to be sure, but maybe, Willard Tony,, the title of this post would be

## Rabett Run publishing suspended – major announcement coming

Something’s happened. From now until Sunday February 30th, around Noon RRST, Rabett Run will be suspending publishing except for what Brian says and maybe John. At that time, there will be a major announcement that I’m sure will attract a broad global interest due to its controversial and unprecedented nature.But, then again, all remember the resulting damp squib. That and the fact that Ms. Rabett has put Eli on a carrot free diet till he loses some have perhaps deepened the hallucination.

Media outlets be sure to check in to Rabett Run every half hour. Hits are needed

On the other hand were Eli Tamino he would think about his thoughts and ask others for their take

That’s what scientists do. When we don’t agree on what’s happening, we try to understand it. If a lot of different possibilities are investigated, well that’s the way it always happens. Eventually, we’ll sort through which arguments are most persuasive and reach at least some measure of agreement. That’s how science works. And it works, bitches.As discussed above, bun fun, at least Eli's, and he is a very dull and old bunny indeed, sometimes includes thinking about usual things in different ways. About a week ago the Rabett got into it with someotherbunny who knows what he is blathering about, who uttered the usual idea that the greenhouse effect works, because emission from greenhouse molecules is isotropic, not unidirectional, certainly not in the upwards direction and stuck there

OK, let's think about this a bit Eli thought. Hmm, when you think about it the hallmark of emission and absorption from greenhouse gases is that locally (key word that) they really don't connect with each other. Absorption is driven by radiation in the right wavelength region from the ground or other greenhouse gas molecules. Emission is a function of local thermal collisional excitation. Molecules excited by absorbing a photon, thermalize that energy within a few microseconds so we need to think about where the heat energy released from collisional vibrational de-excitation flows. If the energy is localized, for example if transport is limited to diffusion which is quite slow at atmospheric pressures, then we can model emission and absorption of photons as coming from the same point in space. On the other hand, if the energy is transported a great distance before it excites a molecule which emits or hits the ground, then the process is transport limited and the direction of the emission really does not matter much.

One of the interesting things is that at say 280 ppm, the distance at which the absorption is 1/e ~ 37%, in the R branch (the bunch of lines to higher frequency, which represent transitions from rotational levels with quantum numbers j" of the ground state to those with quantum number j'=j"+1)of the CO2 absorption is about 2 m. For the Q branch (the structure in the middle, where j"=j') the 1/e distance is about 35 cm

..

At 400 ppm, the 1/e distance in the R/Q branch is ~ 1.3/0.2 m and at 600 ppm R/Q 1/e is ~0.9/0.15 m.

For one thing this shows that the level from which emission from greenhouse gases reaches the surface is about zilch. But wait, there is more. We now have a scale for absorption height and emission rate, the inverse of the radiative lifetime of 1.1 sec for the bending mode of CO2 at 670 cm

^{-1}. That gives a rate of 0.9 sec

^{-1}, call it 1 Hz. The ratio of the rate to the mixing rate is equivalent to a set of parameters called Damkohler numbers.

Damkohler numbers are ratios of reaction rates to mixing rates, handy things for ChemEs If the Damkohler number is greater than unity it means that reactions are faster than the ability to mix, and the reaction is mixing/flow controlled, and if it is less than one, then conversely the reaction is kinetically limited. To decide which is the case, we need a rate or characteristic time for thermal transport on both calm and windy days, specifically for vertical mixing.

Finding this actually turns out to be harder than you would think because folks who do fluid dynamics don't really measure this, and if they do it is as ratios to various scale lengths that are obscurely buried in obscure equations as functions of things that are obscure constants but never clearly stated. Even my modeler friend can't give a simple answer, but it is clear that a few m/s for eddy diffusion is not unreasonable near the ground and in urban canyons, which implies that the greenhouse effect in the boundary layer and maybe higher up in those huge up and downdrafts that bump planes is driven by atmospheric flow, not radiation, and that it is only in the limit of the Damkohler number going to zero (high up) that the process becomes completely radiative.

Given how good the radiative transfer codes are at predicting emission it is unlikely that this mechanism makes a global difference at the TOA, but the implications especially for high/low CO2 situations with major eddies, like urban canyons and tree canopies, are Eli thinks potentially interesting.

Consider this a provocation.

## 11 comments:

I'm not quite getting the subtlety of your post. I think I understand the first half. When a photon is absorbed but a CO2 molecule, the molecule thermalises quickly, meaning the energy is localised. Hence, when that energy is re-emitted, it's re-emitted very close to where it was absorbed. At least I think that's what you're saying :-)

What I'm failing to get is the significance of the latter part of your post. I had assumed that the processes you describe and the timescales/lengthscales would be related to the lapse rate. The lapse rate presumably depends on how far a photon can travel before being re-absorbed. Is that the case and is that what you're getting at in the second half of your post, or am I missing something here (quite likely, to be honest).

A few years back I provisionally decided that outgoing energy transport was dominated by convection at ground level and radiation at high levels. Even found a paper describing aviation measurements in tropical storms with some modelling.

Never got to the bottom of it and figured i needed to run some computer codes with modelling of all the transport factors to get a proper handle on the contributions of the different transport mechanisms vs altitude.,

The Climate Ferret

No, it has very little to do with the lapse rate. As a matter of interest, the adiabatic lapse rate has nothing to do with the greenhouse effect EXCEPT that the ghe sets the surface temperature.

Perhaps more clearly, the absorption length is a local scaling factor for the Damkohler number.

One can define a wind transport rate as the ratio of the vertical wind speed to the scaling factor.

If that rate is faster than the emission rate, the recirculation of thermal energy in the greenhouse effect at that location is controlled by the vertical winds.

Since vertical wind velocity in eddys, updrafts, downdrafts, etc can easily exceed 1 m/s, corresponding to a Damkohler number of 1/2 s-1, this is at least important, and when the vertical wind speed exceeds 10 m/s (D#= 5) controlling.

Eli, thanks. I think I get it a bit more than I did, but not quite :-)

Ferret, the beauty of Damkohler numbers is that it give OOM estimates with little effort. Eli favors little effort:)

ATTP, the lapse rate is set by conservation of energy together with gravity.

As gas molecules rise in the atmosphere, they gain gravitational potential energy. By conservation of energy they lose velocity in the vertical access sufficiently to lose a corresponding about of kinetic energy. However, they are subject to collisions, which result in the other forms of kinetic energy (two horizontal axis plus energy in their vibrational modes) being redistributed so that all are equal on average across the population. Hence translation kinetic energy falls not with the gain in velocity falls not with gain in potential energy, but with that gain divided by the number of forms of kinetic energy in the gas, ie, by the heat capacity.

To slightly complicate things, kinetic energy can also be supplied from latent heat of condensation from water vapour, which lowers the lapse rate. It can also be supplied by absorption of radiation, as in the stratosphere where the absorption is sufficient to reverse the lapse rate.

The lapse rate is normally explained in terms of convection, which explains the lapse rate in the troposphere, but not the mesophere. I believe that explanation reduces to the one above, which then explains the lapse rate at all levels of the atmosphere. I say I believe, because deriving the lapse rate from the above principle gives a a lapse rate based on the heat capacity per unit mass, while that derived using convection gives you a lapse rate based on the heat capacity per unit volume. I am unsure how much difference that makes, if any.

Eli, I'm not sure, but it looks to me like you have just shown that within the troposphere, energy transfer is governed by convection, whereas above the troposphere it is governed by radiation. I thought that relation was well known, having seen it expounded by Chris Colose. He explained it in terms of characteristic times of energy transfer, with the tropopause being the location where (on average) radiative transfer overtakes convection or diffusion as the dominant form of energy transfer in the atmosphere.

Unfortunately, I am unsure precisely what you were saying, so I may have simply misunderstood you.

I saw a note that may touch on similar, er, stuff in today's mail, Physics Today (Feb.2014 at 18): "Many planets, similar tropopauses" citing Robinson and Catling, Nat. Geosci. 7, 12, 2013, about which I know nothing.

Tom (and probably And), it is actually quite different, sort of the difference between micro and macroeconomics.

On the macro level Chris was writing about the movement of energy in the Trenberth picture sense, net energy averaged over time and not including absorption of energy from photons by greenhouse gases.

Eli is talking about micro, the movement of energy from a single photon absorbed by greenhouse gases from radiation in both directions, up and down and over very short times.

One interesting effect would be if the scale length of the vertical transport exceeded that of the IR absorption (which it easily could), that the transport of energy due to ghg absorption would be longer than radiative transfer theory modeled. Another would be more efficient transfer of energy from the atmosphere to the surface

At the most basic level, your post highlights a point often skipped over in simple accounts of the radiative GHE: a given radiatively active GHG molecule that absorbs an IR photon will not typically just re-emit another photon of the same wavelength.

Instead--correct me if I'm wrong here--one molecule absorbs one IR photon, but the vibrational state that induces is typically quenched by collisions with other molecules, both GHGs and others. Thermal energy gets distributed across the whole population of molecules. Some bit of that thermal energy can put *other* GHG molecules into a vibrational state which can be lost by IR emission (in any direction.) Changing the concentration of GHG molecules in the mixture changes … something about this, but I can't articulate exactly what. Just the mean altitude of emission to space?

Increasing the mean altitude of emission to space means (until the concentration gets huge) that the temperature at which the emission to space takes place is colder, which means the emission rate is slower, which means the whole damn thing has to heat up to restore radiative balance. Eli had a nice puzzler on that.

But no, that is not the point here. The point is that near the surface the radiative part of the greenhouse effect may not be important, the absorptive is tho.

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