Monday, January 18, 2010

Another damn puzzler

The lapse rate is the rate of cooling with altitude based on the compression of the atmosphere by gravity. Here is a short derivation of the adiabatic lapse rate
Of course, it's not as simple as that, but to first order it predicts a constant decrease in temperature with altitude. The graph to the right is a represents that with a few twists and turns.

One of the bleats of denial, based on such graphs is that "the temperature profile of the atmosphere has nothing to do with the greenhouse effect", but this is not true.


Eli already gave the answer elsewhere, so they who should not be named should be still for a short while.

Eli promises to link to the answer given by Pieter Vermeesch who wrote the New Years Puzzler. Several have already spotted it. You may, of course, choose to differ


carrot eater said...

What's the purple line? I don't see a label. Could just be me.

Jim Bouldin said...

I'll assume the decrease in absolute amount of GHGs with altitude is not what you're looking for, and respond confidently that I have no idea.

Anyway, do one that's really useful: explain the memory lapse rate of deniers if you really want to compete with Click and Clack.

Webmaster said...

"Earth's Greenhouse Effect is constant and does not rise with human CO2 emissions. That is the main point of Dr Miskolczi's results, called to the attention of the EPA in the 'Endangerment Finding' evaluation process. The EPA could not disprove this or Miskolczi’s results."

Jim Bouldin said...

Mark, taking advice is not your strong suit is it?

carrot eater said...

Which direction is the puzzler? Are we being asked whether global warming would affect the lapse rate, or whether the lapse rate is important for understanding the greenhouse effect?

Arthur said...

carrot - I'm pretty sure the question is the first, whether greenhouse gases have some effect on the atmosphere's temperature profile (given the rather rigid adherence to lapse rates that the figure demonstrates - but surely it's a theory graph? :), and what the nature of that effect is.

I don't recall seeing what Eli has written on this elsewhere, but I think I'm a little too close to being a usual suspect and will defer my answer till others have had a chance to speculate a bit more...

carrot eater said...

Hmm. I think the second question is more important.

I don't know whether I'm a usual suspect or not, but I'll hold my tongue as well.

jre said...

The lapse rate is indeed central to the greenhouse effect. To my mind, the best concise discussion of why this is so is David Archer's. To paraphrase:
1) Once you know insolation, emissivity and albedo, you can ring up Stefan and Boltzmann and know the earth's skin temperature.
2) Skin altitude is determined by absorption, reflection and re-radiation by wavelength at all altitudes. In general, higher IR opacity results in higher skin altitude.
3) Surface temperature may be found by taking the skin temperature (known from radiative equilibrium) and the skin altitude (known from atmospheric radiative properties), then sliding down to the surface at a constant lapse rate. Higher skin altitude + constant lapse rate -> higher surface temperature.

Armed with these few concepts and a clear mental picture of the atmospheric temperature profile, such as the one you have kindly provided, anyone can explain the greenhouse effect to a climate skeptic. For all the good it will do you.

Arthur said...

Alright, jumping in now because jre has really just answered both questions anyway.

The one thing that might be a remaining query is why does the lapse rate apply from surface to skin altitude, but not (much) above? The answer I've become comfortable with is that, in an atmosphere without convection, the temperature gradient would be *higher*. The reason for that higher temperature gradient is the concentration of greenhouse gas molecules, and the resulting infrared absorption in the atmosphere. The more infrared absorption, the higher the temperature gradient that a convection-free atmosphere could support. There's enough in Earth's atmosphere that the gradient (absent convection) is higher than the lapse rate.

That leads to instability and initiates vertical convection in the real atmosphere, and brings the actual gradient close to the adiabatic rate.

But with a lower concentration of GHG's you might have a situation where the radiatively forced gradient was lower than the lapse rate. And with no GHG's at all, the skin altitude goes to zero...

EliRabett said...

More bluntly put, the temperature in the troposphere can be fit ~ by

T = To - b x

Where T is the temperature, To, the surface temperature, b the lapse rate and x the altitude.

To is determined by the greenhouse effect. The discussion about the skin temperature runs this backwards from the top.

carrot eater said...

For a secondary effect, would changes in absolute humidity due to warming mess with your slope b in any significant way? The moist and dry lapse rates are quite different, after all.

Something I'll well capable of answering myself, but I'm feeling lazy.

Anonymous said...

Little Mouse is way out of his depth here but wants a guess anyway.

Higher surface temp, same lapse rate equals higher tropopause. Do we not have a higher tropopause?

Arthur said...

carrot - yes, that lapse rate change is what the tropical troposphere "hot spot" business is about. The moist lapse rate change (the gradient decreases with increasing surface temperature) is actually a small negative feedback on warming, closely correlated with the (positive feedback) increase in water vapor levels.

Little Mouse - yes, the troposphere height has increased, or at least as far as IPCC AR4 WG1 was concerned:

"The combination of a warming troposphere and a cooling stratosphere has likely led to an increase in the height of the tropopause."

(Ch. 9, p. 665)

Anonymous said...

Hmmm, as the skin altitude increases, the surface we're considering also increases. Does that slow things down (compared to a cylindrical world)?

Hank Roberts said...

Well, Blogger just barfed on a post.

I'll put the links in because there's lapse rate in there, a couple jumps removed. Clever, droll, and other commentary, gone, forget it.

So I read this (good!, recent)

Followed a link to this (good!, four years back)

Found that author had been Pielke'd, Peiser'd, Bahner'd and Hemphilled -- slapped around with lapse rate arguments, with no help from anybody, over at shall we call it "Where Else?"

Blogger choked up and spat out a page ending with:

"... See if anyone else is having the same problem: Search the Blogger Help Group for bX-fktnrk .... Please make sure to mention bX-fktnrk in your message."

Well, I never!

Arthur said...

Rumor has it that today (Jan 21) is Eli's birthday - wish him well, all!

carrot eater said...

I'll have an extra carrot for dinner, just to celebrate.

Marco said...

Congrats to the bunny! That he may bother the deniosphere for many more years to come.

Unknown said...


Timothy Chase said...

JRE's explanation sounds right on target. However, I was wondering what is the difference between the skin temperature and the effective temperature -- where the latter is the apparent temperature of the earth as measured at a distance based upon its thermal radiation. As a matter of fact, I believe it was in terms of the latter that Tamino explained the relationship between the lapse rate and the greenhouse effect maybe three or so years ago. But if the effective radiating altitude (which I believe has a temperature equal to the effective radiating temperature -- which would be the temperature of the earth essentially in the absence of a greenhouse effect ~-18°C) is the altitude of the "skin" I would assume that the skin temperature and the effective radiating temperature are the same.

Or am I missing something? Or several things, for that matter?

Timothy Chase said...

Here is Tamino's:

Lapse Rate
July 16, 2007 · 14 Comments

However, I brought in the effective radiating altitude. (Called it "height" at the time.)

Rachel said...

Thank you very much all of you, I had a take-home test in oceanography and "skin altitude" is NOWHERE on the Internet except for on this forum, and I needed the definition for a high point question. So thank you, and a very interesting discussion.

EliRabett said...

Ray P sends a note and a publication date:

Note that there is some confusion floating around regarding "skin temperature" vs. "radiating temperature," especially because as often applied to solids the term "skin temperature" is actually the "radiating temperature." David sometimes uses skin temperature as synonymous with radiating temperature, but in usual atmospheric parlance the skin temperature is the temperature of a two-sided blackbody (i.e. optically thin slab) in equilibrium with the outgoing radiation -- the temperature of the skin of the atmosphere. That differs from the radiating temperature by a factor of 1/2**(1/4). If you google "radiating temperature" you'll find a lot more on that. There's an extensive discussion of all this in my climate book (on track to go on sale in December!) for those who don't mind "death by theoretical physics," as Eli so kindly puts it.


Anonymous said...