Rising Carbon Dioxide Levels Don’t Increase Earth’s Temperature

vanesch

Right. I had understood from his post - maybe erroneously - that it couldn't "get higher up from the surface than a few meters".

What I wanted to point out is that even if the atmosphere is "totally black 20 times over", there is STILL emission of this radiation ; only it will come from the highest layers. And if you double that, the emission will not alter much, but still a bit because the emission must now come from still somewhat higher up - although I grant that the difference in temperature of these two layers will not be much. However, they also don't represent much in the outgoing radiation balance. Even though the "black" parts represent important chunks of the spectrum, they don't represent a large part in the OLR, so saying that they won't change much, doesn't affect the fact that the parts that DO have strong emissions in the OLR spectrum can change notably.

Maybe I misunderstood his post, and was this already understood.

sylas

I think he is referring to "mean path length" of a photon; and he also speaks also of "secondary photons" emitted from the atmosphere itself. Doubling concentrations does tend to halve the mean path lengths, as he describes.

In fact, quoting the end of his post:
This is actually quite correct... and it really IS those parts of the spectrum where the mean path length is of the order 2 to 20 km which are the ones that are most important for each increment of additional heating as concentrations rise.

What bellatti misses is that this is not the 15 micron band, but a region somewhere between the maximum and the minimum of absorption; and there are always some parts of the spectrum where this is the case, at least for atmospheres with anything from 10 to 10000ppm CO2.

Here is figure 4.12 from "Principles of Planetary Climate" again:


15 microns corresponds to a wavenumber of 667 cm^-1. Now the bottom half of the figure shows the absorption co-efficient of CO2 for each frequency, and the vertical lines show which absorption co-efficient gives optical depth of unity for a given CO2 concentration in Earth's atmosphere. The 1 kg/m² line is of the order of Earth's atmosphere. The spectrum looks like a very solid black line because in fact there are very fine absorption lines compressed together on this scale. If you have the book downloaded, look also at figure 4.7 on page 182 to see what the spectrum looks like when you zoom in.

Cheers -- sylas

vanesch

Well, that's what I thought too. But when you look at the text output, I don't think that MODTRAN alters any temperature profile. (I'm talking here about the only MODTRAN calculation I have access to, which is the web interface by Archer).

So I'm not so sure anymore what MODTRAN does, and does not. It seems that MODTRAN takes a user-given temperature and composition profile and calculates the emissions (based upon that temperature profile) and absorptions (as "deletion of radiation"), in other words, a radiation transport calculation in a fixed medium with fixed thermal properties, upward and downward, but doesn't do any energy balance. That's apparently the responsability of the user, to introduce a good T-profile. I thought before that MODTRAN re-calculated the temperature profile based upon a new energy balance, but apparently no.

You can see this when, all else equal, you add a temperature offset. This is bluntly added to the temperature profile up to 10 km or so, and higher up, things are unchanged.

So MODTRAN looks like a radiation transport code in a "frozen-in" atmosphere (worse, frozen-in with thermostats for each layer), where thermal emission and emissivity is taken into account and absorption is taken into account, but that's it.

So, given what you said before, I don't think that the full Planck response (including the "temperature profile adaptation" of which it was explicitly argued that this is not an "added feedback" but inherent in the Planck response) is calculated by MODTRAN, if the user didn't take the responsibility to change the temperature profile. Maybe more evolved versions of MODTRAN can do this, I don't know.

BTW, do you know what the "water vapor scale" parameter means ?

EDIT: oops, you said "Planck radiation" and not "Planck response". Makes my point moot, because I argue exactly that.

sylas

Just to show the context, I have included here nested quotes, including also the remark to which I was responding. The tool we are all referring to is MODTRAN web interface, as supplied by David Archer of the Uni of Chicago.

I don't see that we are in disagreement; and I certainly still maintain the remark you have quoted. My understanding is the same as yours. The MODTRAN tool used does not alter the temperature profile. You can specify a temperature increment, which then is applied all the way up the whole column before the calculation starts, using the given profile for whatever atmosphere you pick from the pull down list.

I think you have described it correctly. Basically, they hold the lapse rate fixed... and that is what you should expect from the effects of convection and energy balance. What is a bit more problematic is that you can alter the humidity -- but it STILL does not alter the lapse rate. That's not so realistic, and so you couldn't use this tool to look at water vapour feedbacks.

As for energy balance... with this style of calculation, I think the procedure is this. At each level, and for each frequency, you calculate the flux of radiation up, and down; and also what fraction is absorbed, and emitted. When you integrate over all the frequencies at a given level, you find that there is an excess of energy, as radiation effects are either heating or cooling the atmosphere at that level. By maintaining the lapse rate, you are effectively taking convection to give the necessary energy balance; and this is indeed what happens in our troposphere.

This is physically realistic as a measure of how much energy convection is delivering into any level -- at least for the troposphere. In the stratosphere, this becomes inaccurate, because there is no convection, and you actually should expect the temperature profile of the stratosphere to alter in response to radiant heating or cooling, until you have a pure radiative energy balance. But in the troposphere the profile remains as given by the lapse rate.

This is why I have often advised putting the sensor altitude at about the tropopause, to get a better idea of the actual forcings from changes in CO2. The plots I provided in message 7, for example, used 20km as the sensor altitude, and this is reported in my post. I didn't really explain why in this thread, but I have explained it in a bit more detail in msg #69 of thread "Physics of Global Warming", where we also discussed this calculator.

With a frozen in lapse rate, you mean, which is not the same as an atmosphere with fixed immovable slabs and a purely radiative equilibrium. This is in fact the normal way to calculate Planck response for the atmosphere, and it DOES take convection into account because it takes the constant lapse rate into account. It's fairly standard to use the tropopause level for defining Earth's energy balance, since there's effectively no convective transport above that level, and so this technique works well. In full detail you would also allow for non-uniform temperature changes, but this would only make a difference in the stratosphere, and has minimal effect on the total energy balance at the tropopause. The more general method is described in "Principles of Planetary Climate" page 256.

Here, for example, is the description from a widely cited reference (link to 3.2Mb pdf):

• Bony, S., et al (2006) "How Well Do We Understand and Evaluate Climate Change Feedback Processes?", in Journal of Climate, Vol 19, 1 Aug 2006, pp 3445-3482.

Here is an extract from pages 3474-3475 which describes precisely what you have noted with the way temperature is handled (my bold):

The most fundamental feedback in the climate system is the temperature dependence of LW emission through the Stefan–Boltzmann law of blackbody emission (Planck response). For this reason, the surface temperature response of the climate system is often compared to the response that would be obtained (ΔT_s,P) if the temperature was the only variable to respond to the radiative forcing, and if the temperature change was horizontally and vertically uniform...

No, in fact what is occurring here is the correct way to do Planck response, and the correct way to take into to account the effects of energy transport from convection and energy balance. What I said before is that there isn't a temperature profile adaption, because convection works to maintain the adiabatic lapse rate.


It seems to multiply the humidity by this constant factor at all altitudes. The only difference this makes is in the calculation of radiative absorption and emission. In reality, of course, you would expect all kinds of other effects on lapse rate and cloud formation; these are not considered with this tool.

Yes; in my description of how the calculator works, I indicate that it uses the frequency dependent Planck radiation. It seems to step through a series of atmospheric levels (1km intervals) and through every frequency of radiation (wavenumbers at intervals of 2 cm^-1).

Your comments are still relevant, because I do also believe this the right way to calculate Planck response in the troposphere; and it's worth explaining the additional detail. The Bony (2006) reference gives a confirmation of this.

Cheers -- sylas

vanesch

I didn't realize that the lapse rate was essentially independent of temperature or composition, but I guess it is a good approximation. What is done in MODTRAN is keeping the dT/dz constant, and this is given for a dry adiabat to be:

[tex]-\frac{dT}{dz} = \frac{m g}{R} \frac{\gamma - 1}{\gamma} [/tex]

which, indeed, shouldn't alter much if m and gamma remain about the same.

At first I thought that the adiabat was to be a curve, depending on initial (surface) temperature AND composition, and hence also its derivative, but that seems to be largely independent of it (a constant slope), so an adiabat at a different temperature is just the old adiabat, translated. Didn't realize that. As you say, indeed, then, if you start out with an adiabat, you can play around but the adiabat remains valid, so this IS the full Planck response.

At least, as long as we remain on the adiabat. The stratospheric response must be wrong in this way.

However, there's something strange in MODTRAN: the delta-T is added up to 11 km or so, and not beyond. There's a jump in temperature at that level (at least when looking at the text output).

Maybe the authors of MODTRAN (or better, of the web interface to MODTRAN) consider that it is a better approximation to keep the stratospheric temperature constant instead of also applying a delta-T to it.

sylas

That is strange! I had never noticed that and I have no idea why it is like that. It looks wrong to me. If you put a negative temperature offset, you even get an inversion. It would be worth emailing Professor Archer to ask. I may do that.

Thanks -- sylas

vanesch

Check it yourself first, I could be mistaken...

sylas

I did. And I have sent the email to ask about it. I'll let you know if I get a response.

Cheers -- sylas

sylas

I have received a very prompt reply, as follows:

Hello Chris,

The temperature adjustment that I put into MODTRAN was very ad-hoc, just a toy for teaching undergraduates. No doubt you are correct that the change in temperature with altitude would be more complicated than this. If you think it's a serious error I can probably dig my way back into that code and the web interface to fix it. But I am guessing that the impacts should be pretty small, at least for the purposes that the model was designed for.

Feel free to quote me in your discussion thread.

regards,

David Archer

I'm happy with this at present. The text "Principles of Planetary Climate" explains more about how to do a detailed calculation. The references for more thorough forcings calculations are readily available and have been cited in various threads. I continue to think the MODTRAN web interface is a useful tool for explaining some of the principles of the physics involved. I don't think any change is likely to make much difference for people who don't recognize the basic physics of the matter anyhow.

As I understand it... the calculator handles the radiative transfers aspect of the problem, and gives a rough handing of temperature processing. vanesch has identified a genuine shortcoming in this tool; well done. I'll take it on board as well when using the tool. Since this is not intended as a full blown model, a quick fix would probably still be less than ideal in any case.

So there you have it. Caveat Emptor. This is a useful tool for exploring some of the ideas, but not a replacement for what is found in texts or professional literature.

BTW. My real name is "Chris Ho-Stuart", and I used that in my email.

Cheers -- sylas

ViewsofMars

I was going through my notes for another topic when I ran across this article that I think is excellent, remembering this topic from a while back, so I thought others might enjoy reading it as well.Here’s a snippet from it, but I suggest reading the whole article, The ups and downs of global warming, published by NASA on September 22, 2009.

Xnn

Here's a link to the article along with some other excerpts:

http://www.nasa.gov/topics/earth/fea...alWarming.html

ViewsofMars

Thanks Xnn. I love NASA! They have a wonderful website to explore for information about Global Climate Change – Eyes on the Earth. You can find the latest information on Signs of the Planet (Ice, Carbon Dioxide, Sea Level, Global Temperature, and Ozone Home) and experience Earth satellites in 3D.
http://climate.nasa.gov/