The continuing large traffic on previous threads on the topic of radiative transfer (and increasingly on threads with unrelated topics) has demonstrated the need for a new thread. Here are some posts to start the new discussion over here:
From Arfur Bryant:
In answer to your question; yes, I suppose I do have a problem believing the radiative transfer models as it appears to me that they are based on an assumption. Even the uchicago site states it assumes a deltaT figure in order to run the program. I have gone back over more threads here, and found some excellent information on the ‘best of greenhouse’ thread, although nothing which answers my question in a quantitative sense. maxwell makes a lot of sense but there are some other inputs – mostly regarding adiabatic lapse rates where I think people are confusing the adiabatic lapse rate with the environmental lapse rate. Either way, I can find no real-world measurement of the contribution of CO2 to the GE. This, to me is absolutely crucial to the debate. If one doesn’t know how much effect CO2 has initially (I take ‘initially’ to be circa 1850), how can one know how much effect an increase is likely to have?
Also, there is a very interesting discussion at the end of the thread Confidence in Radiative Transfer Models, between Vaughan Pratt, Fred Moolten, Pekka Perilla, Jan Pompe, Jeff Glassman, and others. Not sure where to pick up this conversation, but here are a few excerpts:
Jeff Glassman | December 21, 2010 at 9:11 am | Reply | Edit
The logarithmic dependence has nothing to do with Beer Lambert. For weakly absorbing lines B-L applies, as the lines become more strongly absorbing (and lines broaden) then the logarithmic regime is entered, even more strongly absorbing and the square root dependence applies. This has been known and used for many years (e.g. by astronomers ) and isn’t peculiar to CO2.
For a weak isolated line with a broad band source, the response is linear with concentration or mass path. That isn’t B-L either. As the center of the line becomes saturated, the response becomes square root as long as the bandwidth of the radiation is much wider than the line wings. But that’s an isolated line with a Lorentz line shape in a homogeneous medium with constant temperature and pressure. The behavior in the wings of the CO2 band in the atmosphere is complex with contribution from different altitudes with different temperature and pressure resulting in different line widths. Below 10 ppmv, the response becomes linear. Above 10 ppmv, the emission is a logarithmic function of partial pressure up to at least 1000 ppmv and possibly much higher.
VP: You do realize you’re picking the frequency peak here and not the more usual wavelength peak, right?
JP: What difference is that supposed to make?
VP: I don’t understand the question. Are you asking whether the frequency and wavelength peaks are different, or whether the color temperature depends on which one you use?
JP: I’m not surprised [that you didn’t understand the question]since you obviously didn’t notice the wavelength scale at the top of the plot.
What I noticed was that the wavenumber scale at the bottom is linear, the wavelength scale at the top is not. Linearizing the latter changes the location of the peak at 270 K from 18.886801383026… microns to 10.73247513517118543… microns, which you may or may not recognize as the more usually given peak for 270 K. (Planck’s law is a mathematical idealization of black body radiation which explains why the frequency and wavelength peaks can be given exactly, taking 270 K to mean 270.000000000… K. Paradoxically this precision is valid even though the universal constants appearing in Planck’s law are only known to a handful of decimal places. In its usual application to stochastic phenomena only the first few digits of these two peak wavelengths are physically significant.)
Thank you, you’ve answered my original question.
JP: I’m wondering if you have worked out yet that it’s the brightness temperature rather than colour temperature that gives us the heating potential.
VP: You may be confusing brightness with heat, they are very different things in general.
JP: What? Like you confuse energy and heat? Not bloody likely.
Ah, then you do agree that brightness is not the same as heat. Good, I was worried for a minute you were going to stick to your guns. Though I see you’re still sticking to your guns for energy and heat. Heat is a form of energy. Heat is not a form of brightness, nor is brightness a form of heat, they’re very different things. Heat is much closer to energy than it is to brightness.
Why don’t you try again when you work out that vectors in general do not have an orthogonal component.
I knew your physics was above my pay grade (I’d have to be paid a lot more before I could understand it), but I see this is also the case for your mathematics. You’ll have to forgive me but I’m unfamiliar with that branch of linear algebra in which a component of a vector can be orthogonal. Please school me.
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What I noticed was that the wavenumber scale at the bottom is linear, the wavelength scale at the top is not.
Hardly surprising given that the one is the reciprocal of the other. So let’s see if we can get on the same page here.
Linearizing the latter changes the location of the peak at 270 K from 18.886801383026… microns to 10.73247513517118543… microns, which you may or may not recognize as the more usually given peak for 270 K
I don’t think so. If you linearise one in a chart the other will be nonlinear but the the relationship remains the same. For instance
1cm-1/530 = .0018.8 = 18.8 micron. This is a measured peak using a Michelson interferometer. You will find that is the ball park for every spectrum obtained that way. The number that you quote is the Wien’s law result 2.9/270 = 10.74 micron. So what is it to be the measured or the computed?I think you’ll find if you look into it that Wien’s law only holds for short wavelengths like Raleigh-Jeans for LW.
Ah, then you do agree that brightness is not the same as heat.
Brightness like luminance, intensity and are indicators of heatingpotential obviously if put into a EMR field of higher brightness or intensity it will be considered cold and the field hot and heat will flow from the field source to the object.
You’ll have to forgive me but I’m unfamiliar with that branch of linear algebra in which a component of a vector can be orthogonal.
Angular momentum and rotational motion has rules where the momentum does not just have orthogonal component but actually is orthogonal to the plane of rotation.
DeWitt Payne 12/21/10 3:51 am,
Where exactly in the HITRAN model or in HAWKS, or elsewhere, are the features you discuss, i.e., line saturation, square root dependence, the Lorentz shape, the CO2 band wings, altitude dependence, linear behavior below 10 ppmv, and logarithmic behavior to at least 1000 ppmv. How is “at least” mechanized or determined?
Previously you were careful to say this information was all in the line-by-line data base, and not in the summing. Now your results depend on the total bandwidth of the application and in the homogeneity of the medium. How is your information stored in the line-by-line data base?
You say the logarithmic function is good “to at least 1000 ppmv and possibly much higher”. That number of 1000 is certainly important because it accounts for IPCC’s essential conjecture about CO2. We need to see the data to be sure your talking about total intensity, I, and not ΔI/ΔC, and that the break doesn’t occur in a lower region, e.g., between about 400 and 600 ppm. What is the standard deviation of the logarithmic fit at 1000 ppmv? Would it be correct to assume you talking about a fit of the logarithmic function to the output of HAWKS or some such calculator? If so, what is the standard deviation of the error between your calculator and the real world, measured absorption? Why do you say, “at least and possibly much higher”? Hasn’t the test been conducted yet?
Where can your data be examined? Or is it to remain secret like the raw data at MLO? Or the temperature data at CRU?