Raff,

I looked up your original comment to find the context.
Your comment of Jul 31, 2014 at 6:14 PM is a concise and clear explanation of the "greenhouse" effect.

But I wasn't sure I understood your first point: "if at height h in the stratosphere the concentration of CO2 molecules is some nominal X, do you accept that after doubling the % CO2 in the atmosphere h will increase for the same X?"

It might be the wording, I might have missed some earlier context that makes this clear, I might be having a slow day..

What units is X? I'm picturing X in units of ppmv.

Martin A, I see.
What's the altitude of the space station? The mixing ratio of CO2 (ppmv) is constant above the boundary layer, through the troposphere and into the stratosphere. There is a height where the mixing ratios start changing due to molecular weight but it's above the point where it affects radiative transfer equations for the troposphere. I can't remember what that height is, I'd have to go and find a paper.

Raff, the wording confused me in the revised version. But if I understood correctly, of course.
I think your wording was, using a concrete example, if there are 6x10^21 /m^3 CO2 molecules at 5km height, then after doubling CO2 concentration the height, h', where we find 6x10^21 /m^3 CO2 molecules is say 10km.
The number of molecules in 1m^3 depends on p/T so the new height h' is not usually exactly equal to 2xh.

SoD, yes thanks. Your concrete example is much better:

if there are 6x10^21 /m^3 CO2 molecules at 5km height, then after doubling CO2 concentration the height, h', where we find 6x10^21 /m^3 CO2 molecules is say 10km.

The idea that h' should be 2xh did occur to me but I thought I was probably being naive and that there would be confounding factcors - so I didn't mention it.

Anyway, the upshot is that the important question is whether people accept that h' is greater than h. If not they have to come up with some explanation for what seems (naively) self evident. If one does accept that h' is greater than h, then consequetly the average height of effective IR emission to space must increase with increasing CO2. As temperature decreases with height, it is unavoidable that after working back to ground level the temperature must rise with increasing CO2 **unless** the magnitude of the lapse rate decreases.

So essentially if you want to argue against the greenhouse effect of rising CO2 you have to argue that the magnitude of the lapse rate decreases (and hopefully propose a mechanism).

Martin:

"..essentially rhoda asks, in other threads her over the past few years, what is the actual best evidence that increased atmospheric CO2 increases overall atmospheric temperature (if I have got it right) .

Not calculations from lab measurements of CO2's property of absorbing IR when in a plastic bottle, not estimates from GCMs, not calculations from radiative forcing, but actual best direct evidence. [I hope I've expressed it right]."

There's only one planet and one set of observations.

So if the question is: how can we tell that increased CO2 increases global mean surface temperatures from climate observation then any evidence is going to be weak. There are 100s of different factors at work. The only way a scientific experiment on the planet could disentangle these factors would be to isolate and change one condition and "rerun" the last 150 years.

Likewise you can't tell anything about any factors. Can you prove that the earth's rotation is what causes the geostrophic winds? Not tests in a lab, not mathematical equations, actual direct evidence. Where is it? There isn't any. Maybe the winds all rotate in a certain way because of other reasons. The only direct evidence would be to stop the planet rotating and see what happens. Or find a similar planet that wasn't rotating and investigate. Of course, the geostrophic equations are pretty simple and rely on the fundamental laws of mechanics that everyone accepts..

I might have misunderstood what was allowed to be put forward as evidence. The question seemed quite restrictive.

On the other hand if you believe the first law of thermodynamics, and that can be used, then the question might become, how can we tell that more GHGs reduce outgoing longwave radiation (OLR)? If that is the more restrictive question then it becomes easier.

If the question is accepting a) the first law of thermodynamics, b) that more GHGs in one spot reduce OLR, what evidence is there for more CO2 over 100 years changing global mean surface temperature then the evidence is weak as it relies on GCMs.

So maybe the "what's allowed and not allowed" factors need to be made crystal clear.

Generally when people are concerned about using the results of lab experiments and equations - from anecdotal experience only in dealing with such questions - they have a conceptual problem understanding the relevance of these for the atmosphere, or just conceptually struggle to see how more GHGs reduce OLR. If that's the issue you just have to look at the satellite data. Hot places with lots of water vapor have a lower "brightness temperature" = low OLR. Hot places with no water vapor have a higher "brightness temperature" = high OLR. And the maths works every time. The maths is used to calculate many climate variables - SSTs, lower, mid and upper tropospheric temperature, humidity fields, concentrations of GHGs..

More GHGs reducing OLR is as non-controversial in the field of atmospheric physics as Kepler's law of motion in the field of astronomy.

On the other hand, the overall consequence for the climate system with 100s of interacting variables, of reducing OLR by a few W/m^2 over a century timescale is a very challenging problem.

"More GHGs reducing OLR is as non-controversial in the field of atmospheric physics as Kepler's law of motion in the field of astronomy. "

I'm not quite sure what SoD means by that line. Is that a 'lab' measurement where IR can't gens t through lots of GHG's? What happens in the limiting case in the atmosphere to OLR when it is fully opaque to IR?

More GHGs reducing OLR is as non-controversial in the field of atmospheric physics as Kepler's law of motion in the field of astronomy.

Which if true would be the proof of AGW. However, it would seem SoD comes to this conclusion, stated on his own site, from;

If the place of emission of radiation – on average – moves upward for some reason then the intensity decreases. Why? Because it is cooler the higher up you go in the troposphere.

Which is cart before horse: as the place of emission rises it takes its temperature with it as dictated by the background temperature of space. The bottom of atmosphere temperature increases by working that back down the lapse rate (AOTBEqual).

Aug 10 2014 at 9:17 AM | Registered CommenterRichard Drake

A very simple model will demonstrate the existence of something like winds caused by rotation. I was just asking for clarification on the bit I didn't understand. I assum I'm just missing something basic there though. I don't quite understand your response either.

What happens in the limiting case in the atmosphere to OLR when it is fully opaque to IR?

What do you think being "fully opaque to IR" means? What effect do you expect it to have?

Rob Burton asked:

"I'm not quite sure what SoD means by that line. Is that a 'lab' measurement where IR can't gens t through lots of GHG's? What happens in the limiting case in the atmosphere to OLR when it is fully opaque to IR?"

Theory and experiment match up. Nobel prize winner Subrahmanyan Chandrasekhar wrote the book on radiative transfer in the 1950s. The theory derives from the fundamental physics of absorption and emission. The Beer-Lambert law of absorption was figured out in the mid 1800s.

The lab experiments confirm the theory. So do the experiments through the whole atmosphere. I gave some examples in Theory and Experiment – Atmospheric Radiation.

This isn't something new, created by "climate science" in the 1980s. This is fundamental physics. There's a whole set of observing systems, well validated against "traditional" measurements, that calculate SST, lower tropospheric temperature, humidity profiles & GHG concentrations - all from satellite measurements of radiance in different wavelengths. They all rely on this theory.

"What happens in the limiting case.."

..when OLR is fully opaque to IR - interesting question. Current atmospheric conditions are a long way from that.

For example, we have an atmospheric window between 8-12um, with a little absorption at the ozone wavelength around 10.5um. This atmospheric window is not such a great window when we get very high water vapor concentrations, as a result of the water vapor continuum. And CO2 absorbs very strongly at 15um, but not so much at 12um.

What do you mean by "fully opaque"?

Do you mean "absorptivity as a function of wavelength = 0 at all wavelengths for path length = 1m"?

And why is this important?

Well, please clarify the conditions.

Aug 10, 2014 at 9:27 AM | Registered CommenterRichard Drake

I think you will find you are wrong there. I'd be surprised there isn't a mathematically analytically solved version of something like rotation and wind, when given reasonable assumptions and linearising the solution being it is such a trivial case. I assume no one else would pick up on this as it seemed a bit out of place compared to rest of SoD's good argument. As I said I just reallly didn't understand his OLR argument and would just like it explained to me, by anyone.

Rob Burton:

"..A very simple model will demonstrate the existence of something like winds caused by rotation.."

A very simple model will demonstrate the reduction in OLR due to GHGs.

In fact, mathematically speaking the changing OLR from changing GHGs is simpler. I find the maths of geostrophic winds to be quite complex. You have to calculate conservation of momentum in a rotating frame of reference. That's not very intuitive.

However, the key difference is - no one questions conservation of momentum because everyone was brought up with it, and most people have some limited experience of it in a non-rotating frame.

Most people have not been brought up with the laws of absorption and emission. Plus the "final answer" requires a numerical calculation - a double integral - across all wavelengths and up through all altitudes.

Anyway, it was an analogy. All analogies are wrong. But some are useful illustrations. If it was a useful illustration that is wonderful. If not, shoot the analogy bringer.

Rob Burton,

Our latest comments have crossed.

If we want to keep working the analogy, I picked up the best textbook I have on basic atmospheric circulation: "Atmosphere, Ocean and Climate Dynamics", Marshall & Plumb (2008).

It's many pages starting from the conservation of momentum through to geostrophic rotation.

For non-physics people who were skeptical of the phenomenon, how would this equation be accepted:

Du/Dt + 1/ρ∇p+gz=-2Ω x u + -Ω x Ω x r + F

where D/Dt is the Lagrangian operator, u = velocity vector (u,v,w), ∇p is the gradient of pressure, Ω x Ω x r is the vector cross product not "times"..

then there is a whole set of assumptions about the relative magnitude of each parameter in the equation, that's after you have placed the set of equations on a sphere.

By contrast: change in intensity of radiation with respect to optical thickness (think "height") = emission - absorption

dI(λ)/dτ = I(λ) – B(λ,T)

Let's explain this equation, which is much simpler than the Lagrangian formulation of the conservation of momentum in a rotating frame of reference..

Intensity at a given wavelength changes due to [source temperature - local temperature] x amount of GHGs

Or, even more vernacular - if the atmosphere gets colder as you go up, then the more GHGs you have the more the outgoing radiation reduces. Likewise the more GHGs you have the more the DLR (aka "back radiation") increases.

ssat:

" However, it would seem SoD comes to this conclusion, stated on his own site, from;
If the place of emission of radiation – on average – moves upward for some reason then the intensity decreases. Why? Because it is cooler the higher up you go in the troposphere.

Which is cart before horse: as the place of emission rises it takes its temperature with it as dictated by the background temperature of space. The bottom of atmosphere temperature increases by working that back down the lapse rate (AOTBEqual)."

The total emission to space from some way up in the troposphere is balanced by incoming solar radiation mostly absorbed at the surface.

The lapse rate x the effective height of emission determines the difference between the surface temperature and the "effective radiating temperature" of the climate system.

The background temperature of space has nothing to do with it.

SoD

The total emission to space from some way up in the troposphere is balanced by incoming solar radiation mostly absorbed at the surface.

To which I would add: The temperature (effective radiating) at that equilibrium is governed by the background temperature of space.

The lapse rate x the effective height of emission determines the difference between the surface temperature and the "effective radiating temperature" of the climate system.

Firstly, we don't know what the surface temperature is for we don't measure the land surface temperature: we measure the BOA temp at Stevenson screen height with results ignoring whether the air is from an ascending or decending source. We do attempt to measure SST the result of which is currently agreed as being higher than the BOA and S-B average. That itself should be sufficient to suggest that actual average surface temperatures of ice and terrain are lower than the Stevenson average. That aside, my disagreement is principally with your contention that the "background temperature of space has nothing to do with it". It is that sink that sets the effective radiating temperature, not the planet surface (try a sink temperature of 100K in S-B). Effective radiating temperature x lapse rate = BOA temperature.