first a word of caution. Clive Best is an AGW 'skeptic', and while he is more mathematically sophisticated than most AGW 'skeptics', he still breathlessly writes about the lack of warming over the last twelve years, and predicts cooling temperatures for the next decade because the lower uncertainty bound of the HadCM2 model short term climate forecast permits it. Any recommendation of one blog post by Clive Best should not be construed as a recommendation of any other blog post by Best, or the quality of his blog in general.
More importantly,
Clive Best's attempt to calculate the effective altitude of radiation clearly fails on empirical grounds. Specifically, this is his calculated "effective altitude of radiation":
Clearly he shows the effective altitude of radiation on either sides of the spikes at 620 and 720 cm-1 as being between zero and 1000 meters. In contrast, as can be seen in the real spectrum he shows, at those wave numbers, the effective altitude of radiation is closer to 6000 meters {calculated as (ground temperature - brightness temperature)/lapse rate}:
As can be seen from his
graph of the predicted IR spectra, he clearly gets the 660 cm-1 spike wrong as well, showing it as a dip (?!) for 300 ppmv, and as a barely discernable spike at 600 ppmv. That is so different from the obvious spike in the real world spectrum (at approx 390 ppmv) that you know (and he should have known) that he has got something significantly wrong.
Before addressing that specifically, I will note two minor things he omitted (perhaps for simplicity). The first is that he has not included a number of factors
that broaden the absorption lines. Broadening increases the width of the lines, but also reduces the peak absorbance of the lines. In any event, he has not included doppler broadening, possibly does not include collissional broadening, and probably does not include some of the other minor forms of broadening.
The second factor is that he has not allowed for the difference in atmospheric profiles between the US Standard atmosphere and
actual tropical conditions. Specifically, the atmosphere is thicker at the equator due to centrifugal "force", and also has a higher tropopause due to the greater strength of convective circulation. That later should reduce CO2 density, and might be accepted as the cause of the discrepancy except that mid latitude and even polar spectra show the same reduce absorbance relative to his calculated values (and hence higher effective altitude of radiation in the wings, and for the central spike).
Although these factors are sources of inaccuracy, they do not account for the major error in calculation. That is
probably a product of his definition of effective altitude of radiation, which
he defines as the highest altitude at which "... the absorption of photons of that wave length within a 100m thick slice of the atmosphere becomes greater than the transmission of photons". That is, it is the altitude of the highest layer at which less than half of the upward IR flux at the top of that altitude comes from that layer.
This definition is superficially similar to
another common definition, ie, the lowest altitude from which at least half of the photons emitted upward from that altitude reach space. Importantly, however, this later definition is determined by the integrated absorption of all layers above the defined layer. Specifically, it is the layer such that the integrated absorption of all layers above it = 0.5. I think the layer picked out by Best's method is consistently biased low relative to that picked out by this later definition.
There are two other common definitions of the effective layer of radiation around.
The most common is:
"Here the effective emission level is defined as the level at which the climatological annual mean tropospheric temperature is equal to the emission temperature: (OLR/σ)1/4, where σ is the Stefan–Boltzmann constant."
(
Source, h/t to
Science of Doom)
That definition can be generalized to specific wave numbers, or spectral lines, and is used by Best
in an earlier blog post specifically on the subject. It also needs to be modified slightly to allow for the central spike (which comes from the stratosphere). The difficulty of such a modification, plus a certain circularity in this definition makes others preferable. The third definition is the one I give above of "the temperature weighted mean altitude from which the radiation comes". I take it that the three common definitions pick out the same altitude, at least to a first order approximation. In contrast, Best's definition in the blog post to which you refer is of by (in some portions of the spectrum) at least 6 kms.
Despite this flaw, Best's blog post does give a good idea of the methods used in radiative models. However, his detailed results are inaccurate, in a way that does not reflect the inaccuracy of the radiative models used by scientists. This also applies to the graph shown by scaddenp @55 above, which was also created by Best. It is very indicative of the type of profiles likely to be seen, but should not be considered an accurate source. I discuss the accuracy of actual models
briefly here, and
in more detail in the comments.