Friday, December 11, 2009

Answering a question of CO2

I have to post this as a post rather than a comment because blogger won't accept it as a comment:

To address Steve's main question (see first comment), when you've reached almost 100% absorption of ground based (blackbody) energy from water, there's very little additional energy that the 2.7um and 15um absorption lines of CO2 can absorb. The key to interpreting all this data is to translate to *integrated* ground energy absorbed in the atmosphere. The scientific graphs are very deceiving in this regard. First, it is almost meaningless to focus on the absorption of one species like CO2. You must focus on total atmospheric absorption across the entire blackbody spectrum of the Earth. You have to multiply the absorption percent times the energy at each wavelength and add them all up to get total energy absorbed by the atmosphere. It is this energy that is radiated isotropically, and therefore only this that contributes to "greenhouse" effect.
To assess the relative impact of CO2, you modify the total atmospheric absorption curve to exclude the CO2 lines. As I noted, the 2.7um line is completely negligible -- water vapor completely dominates and in the absence of the CO2, the same energy would be absorbed by the atmosphere. The 15um line (the broadest) is almost as bad -- looking at the water vapor absorption curves, it appears to absorb about 70% of the energy at this wavelength. That means there's only 30% of the energy left at this wavelength for the CO2 to absorb. This diminishes the significance of CO2 absorption at this wavelength by about 3:1. The only spectral line left for CO2 to absorb energy from is the middle 4.3um wavelength. There's no other atmospheric species that absorbs much at this wavelength, so you can assume CO2 dominates.
So now you add up all the energy that *only* CO2 would absorb, in the *presence* of water vapor and all other atmospheric gases. Then you divide by the *total* ground energy that is absorbed by the atmosphere. This is the relative percent significance of the CO2. I haven't done the calculation, but it is relatively simple. Anyone care to try? I believe from the data I've seen that CO2 is going to come out much less than the 8% figure quoted in that older data, and probably less than the 2% figure that Connolley was using.
Regarding the data itself, I have seen much more than I put in the blogpost, and without going into the gory details, I think the absorption curves are accurate. The blackbody spectrums of the first graph are somewhat deceptive, however, because they are relative amplitudes. Search for "atmosphere Earth blackbody spectrum" and you'll come up with some of it. For the blackbody spectrum of the Earth, you can either calculate it approximately from Planck's formula, using mean temperature of between 255K to 288K, or you're looking for curves with a vertical axis of "Irradiance" in units of watts per square meter per micron wavelength (or per hertz).
When you look for atmospheric absorption, be careful to distinguish "absorption" curves versus "transmission" curves. Transmission = 1 - Absorption. That is, a transmission of 0 is the same as an absorption of 1.0 (100%). Both provide the same information in different form.
I have access to other data in different forms -- there's a lot of research going on right now in military electronics for Terahertz transmission through the atmosphere. These guys put the data into attenuation curves, decibels per kilometer (or meter) of distance through which the radiation passes at a given frequency. (Frequency is the inverse of wavelength, multiplied by the speed of light constant, of course.) This data essentially confirms the other data, albeit in a different and more precise form. Most important however, is to get data for vertical transmission through the atmosphere because horizontal transmission is very altitude dependent. For instance, water vapor is much more concentrated in Bangkok than in Boulder, Colorado. A big factor in all this data is the relative humidity, and they usually have different curves for 0, 50%, 100% humidity, etc.
The vertical data (transmission straight up or down through the atmosphere) also has the merit of including the full distance traveled by the energy, though you do have to know the endpoint. Some of my curves extend from space to the top of Mauna Kea in Hawaii -- 14,000 feet up. The same as Pikes Peak. Very dry! This is why the observatory is there. For greenhouse effect you've got to go from space to sea level.
Regarding the point of heating of the air above the ground, this is a simple one, relatively speaking. If air is transparent to most wavelengths from the sun, they can only be stopped by one thing -- the Earth. The ground warms up, and then radiates at lower infrared wavelengths. The air above absorbs energy according to those absorption curves and re-radiates isotropically -- in all directions, so 50% of the energy goes back to Earth. Mathematically, you can model it accurately as 50% straight up, 50% straight down, and then make up an equation for the distribution of this absorption and re-radiation, and integrate it numerically on a computer. Believe it or not, this is *not* hard to do, and from this you'll get a distribution of air temperature from the layers of "thermal blankets" of the absorbing species -- assuming a fixed ground temperature. To say the air heats up above the ground is no different than saying you'll stay warm by putting a sweater on.
What is the effect of hotter air above the ground? Primarily in a slight broadening of the absorption lines of the atmospheric energy absorbers. Random thermal motion of molecules of water and O2 and O3 and CO2, etc, makes them absorb across a wider range of wavelengths. My recollection is that the broadening has a Lorentzian distribution, but don't hold me to that. The point is, molecules with a velocity see energy doppler shifted up or down in frequency. Figure out the probabilities yourself if the velocities are in all directions with a gaussian magnitude distribution.

The most important point in my post is simply that the influence of absorption lines in CO2 is greatly diminished by water. Water simply absorbs most of the energy at most wavelengths -- and then throw in the effect of reflecting sunlight from the Earth's (albedo).

I agree that the details of the greenhouse effect are complicated, if you want a really accurate answer, but the principles are fairly simple. In fact, what is amazing me more and more as I've learned about this is how easy it is to understand the basic science and how transparently bad the reasoning behind CO2 warming is, if you simply try to understand the effect analytically and don't rely on hand-waving arguments.

Since I'm posting this as a blogpost rather than comment, I will add some of the data I'm referring to, without much comment on how to interpret it -- most notably, much of the data is at wavelengths that are too long relative to the Earth's blackbody spectrum. but they are still indicative of the influence of water. The most important fact you can get from this is the overwhelming effect of water vapor on absorption. Simple humidity changes alone (without clouds) overwhelm any other effect, even a lower frequencies (longer wavelengths) and climate "modelers" who simply assume water is "X" percentage of the the absorption of energy at the CO2 15um linewidth are wildly wrong.

This shows the spectrum of solar radiation received on the Earth:





Yet another very old curve of atmospheric absorbers:


This shows energy absorbers in relation to the solar radiation on the Earth and the radiation coming up from the warmed Earth:



More accurate blackbody spectra for relative amplitude of incoming solar radiation versus Earth's radiation:



Horizontal transmission through the atmosphere:


The next graph is transmission through the atmosphere from space down to Mauna Kea (a 14,000 foot mountain in Hawaii) at 3 different humidities (not 0% to 100%! -- these are humidities that occur at 14,000 feet!). Even at such a dry altitude, note how water can cut transmission down by 30 - 40%! This illustrates that those simple "H2O absorption" curves from the previous graphs are extremely deceiving. There *is* no single H2O absorption curve for the atmosphere.


Note the effect of altitude on absorption, even at lower frequencies (Note: 3dB attenuation equals a 50% increase in absorption, 6dB is a 75% increase in absorption, etc. -- it doesn't take many dB or many kilometers of propagation distance to get almost 100% absorption!):



Note the enormous effect of rain:



And here, the effect of simple humidity, up to 30um wavelength. Even at a measily 100GHz frequency (3mm wavelength) the difference in humidity between Bangkok and Boulder causes the attenuation (absorption) to increase by 6dB per kilometer -- over 1km distance (less than the altitude difference -- Boulder is at 6000feet) over 75% of the energy is absorbed for every kilometer the radiation propagates!:




Again, the effect of water vapor on transmission -- but this is only 100 meters of distance:



"Channel capacity" is data bandwidth for wireless communications through the atmosphere... it goes to hell if there's any water, even at such long wavelengths.


The message here, over and over again (and there's lots more data): Water dominates, utterly, totally, absolutely in defining any greenhouse effect. Now you know why climate "researchers" have failed over and over again to correctly predict the Earth's temperature from CO2 influences.

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