Yesterday I collated IPCC AR3 and AR4 “expositions” of the enhanced greenhouse effect, observing that, in my opinion, they were so baby food as to be essentially useless to a scientist from another discipline. Today I’m going to drill a little deeper in the expositions, going to a 1995 journal comment by Houghton and to his text, Global Warming: the complete briefing, to see if either contains a more useful exposition. I’ll also comment on why I find the IPCC heuristic particularly unsatisfying.
Reviewing the bidding briefly, in AR4, I’ve been unable to locate any exposition of the mechanism of the enhanced greenhouse effect that rises above the following in the FAQ:
To balance the absorbed incoming energy, the Earth must, on average, radiate the same amount of energy back to space. Because the Earth is much colder than the Sun, it radiates at much longer wavelengths, primarily in the infrared part of the spectrum (see Figure 1). Much of this thermal radiation emitted by the land and ocean is absorbed by the atmosphere, including clouds, and reradiated back to Earth. This is called the greenhouse effect. … Adding more of a greenhouse gas, such as CO2, to the atmosphere intensifies the greenhouse effect, thus warming Earths climate.
I do not regard this as a satisfactory explanation, but note, as usual, that this does not mean that a satisfactory explanation cannot be provided, only that IPCC elected in AR4 not to provide one. I’ve not been able to locate any other attempts at exposition of the enhanced greenhouse effect in AR4.
AR3 was only a little a better: it mentions a heuristic for the mechanism as to how increased CO2 warms the surface as follows (1.3.1):
These so-called greenhouse gases absorb infrared radiation, emitted by the Earths surface, the atmosphere and clouds, except in a transparent part of the spectrum called the atmospheric window, as shown in Figure 1.2. They emit in turn infrared radiation in all directions including downward to the Earths surface. Thus greenhouse gases trap heat within the atmosphere. This mechanism is called the natural greenhouse effect. The net result is an upward transfer of infrared radiation from warmer levels near the Earths surface to colder levels at higher altitudes. The infrared radiation is effectively radiated back into space from an altitude with a temperature of, on average, -19°C, in balance with the incoming radiation, whereas the Earths surface is kept at a much higher temperature of on average 14°C. This effective emission temperature of -19°C corresponds in mid-latitudes with a height of approximately 5 km. Note that it is essential for the greenhouse effect that the temperature of the lower atmosphere is not constant (isothermal) but decreases with height. …
The increased concentration of greenhouse gases in the atmosphere enhances the absorption and emission of infrared radiation. The atmospheres opacity increases so that the altitude from which the Earths radiation is effectively emitted into space becomes higher. Because the temperature is lower at higher altitudes, less energy is emitted, causing a positive radiative forcing. This effect is called the enhanced greenhouse effect, which is discussed in detail in Chapter 6.
Unfortunately IPCC failed to deliver on its promise for a “detailed” discussion in Chapter 6, where the term “enhanced greenhouse effect” is nowhere in sight. In the TAR exposition, the requirement that temperature decrease with height is specifically mentioned, but they did not provide a diagram showing temperature changes in the atmosphere.
In fact, as shown in the diagram below, the atmospheric temperature profile is not a simple monotonic decrease in temperature as one might presume from the IPCC heuristic – the temperature decreases up to about 10 km (the tropopause) and then increases through the stratosphere (up to the stratopause). There are further interesting features in the very upper atmosphere which are not relevant here. The temperature increase in the stratosphere primarily results from the absorption of UV solar radiation from ozone.
Now it turns out – as I’ll discuss below – that a proportion of CO2 radiation to space occurs in the tropopause and a proportion actually occurs in the stratosphere. For the proportion in the stratosphere, the IPCC heuristic is reversed and increased CO2 would cause radiation-to-space in those lines to occur at a higher temperature, reversing the effect. Now the proportion of radiation-to-space from the stratosphere in practical terms appears to be very small and thus swamped by the tropospheric effect, but there’s no reason not to mention it in an exposition. The proportion of CO2 radiation from the tropopause is very large and important and should not have been passed over even in a heuristic.
Let me now review some comments on this topic by Sir John Houghton, the IPCC WG1 Chairman, in 1995, in response to a comment by skeptic Jack Barrett in Spectrochimica Acta (1995) – a comment that was mentioned in passing in SAR. Houghton stated:
A further point that Barrett makes is to suggest that because most of the absorption by carbon dioxide from the surface occurs within 30 m of the surface, the enhanced greenhouse warming due to increase of carbon dioxide in the lower atmosphere is negligible. In fact, most of the enhanced greenhouse effect occurs not because of changed absorption of radiation from the surface (although some change does occur in the wings of the carbon dioxide band where absorption is weaker), but because as the concentration of carbon dioxide in the atmosphere increases, the average height (around 6 km) from which carbon dioxide emits radiation to space also increases. Since atmospheric temperature in the lower atmosphere falls with altitude, if nothing changes other than the amount of carbon dioxide, the amount of radiation to space is reduced. For atmospheric carbon dioxide, this reduction can be accurately calculated; for doubled atmospheric concentration it is about 4 wm-2. To restore the Earth’s balance the temperature throughout the lower atmosphere has to increase – hence the enhanced greenhouse effect [1- J.T. Houghton, Global Warming: the complete briefing. Lion Publishing, 1984.]
Note that there’s a discrepancy in the effective height between Houghton 1995 (around 6 km) and TAR (about 5 km), both heights safely below the tropopause at about 10 km. Houghton’s argument here (in the “peer reviewed literature”) does not rise above the cartoon discussion in IPCC TAR and AR4. However, he cites his textbook, which we now turn to for possible edification.
Houghton(1984), Global Warming: the complete briefing
At other wavelengths radiation from the surface is strongly absorbed by some of the gases present in the atmosphere, in particular by water vapor and carbon dioxide….Absorbing gases in the atmosphere absorb some of the radiation emitted by the Earth’s surface and in turn emit radiation to space. …
Radiation is emitted out to space by these gases from levels somewhere near the top of the atmosphere – typically between 5 and 10 k high (See Fig. 2.3) [Below is my re-plotting of Houghton's Figure 2.3]. Here because of the convection processes mentioned earlier, the temperature is much colder – 30 to 50 deg C or so colder – than at the surface. Because the gases are so cold, they emit correspondingly less radiation. What these gases have done therefore is to absorb some of the radiation emitted by the Earth’s surface but then to emit much less radiation out to space. They have therefore acted as a radiation blanket over the surface(note that the outer surface of a blanket is colder than inside the blanket) and helped to keep it warmer than it would otherwise be. …
This increased amount of carbon dioxide is leading to global warming of the Earth’s surface because of its enhanced greenhouse effect. Let us imagine that the amount of CO2 in the atmosphere suddenly doubled, everything else remaining the same. What would happen to the numbers in the radiation budget? The solar radiation budget would not be affected. The greater amount of carbon dioxide in the atmosphere means that the thermal radiation emitted from it will originate on average from a higher and colder level than before (Fig 2.3). The thermal radiation budget will therefore be reduced , the amount of reduction being about 4 watts per sq meter.
One quick editorial point: to my knowledge, convection processes warm the upper atmosphere. So when Houghton says “because of the convection processes mentioned earlier, the temperature is much colder – 30 to 50 deg C or so colder”, I don’t get this at all – surely this is a mistake. But the most striking aspect of this particular reference is that it adds virtually nothing to the statement in Houghton (1995) or the cartoon in TAR. In each case, the result is stated, but not derived. I’m not saying that the argument is implausible – obviously it’s not implausible or else it wouldn’t have been relied on so widely. I’m only saying that all we see here are assertions, with no measurements or data. Houghton asserts 4 wm-2 as an impact number, but it just appears out of the blue.
A reader of these heuristics would conclude that CO2 radiation-to-space from the lower troposphere is the most distinctive aspect of CO2 radiation-to-space – radiation from about 5- 6 km. The next figure shows an upwelling spectrum from the Pacific (an image from the 1970s downloaded from John Daly’s site – a more up-to-date image should be around somewhere, but won’t change the main observations here):
The large notch or “funnel” in the spectrum is due to “high cold” emissions from tropopause CO2 in the main CO2 band. CO2 emissions (from the perspective of someone in space) are the coldest. (Sometimes you hear people say that there’s just a “little bit” of CO2 and therefore it can’t make any difference: but, obviously, there’s enough CO2 for it to be very prominent in these highly relevant spectra, so this particular argument is a total non-starter as far as I’m concerned. )
So when I look at spectra like this, I take away the impression that a very large proportion of CO2 radiation-to-space is from the tropopause (10 km) area. While a lot of radiation-to-space may come from 5-6 km altitude, the proportion of CO2 radiation-to-space coming from such altitudes looks like a relatively small proportion of the total. Because the temperature at the tropopause is more or less invariant with altitude, incremental CO2 will have a relatively small impact on any radiation within this funnel – which is the most important part of CO2 emissions. (You notice a little peak in the center of the funnel. The odd thing about this is that the center of the funnel is where CO2 absorption is the greatest and I wonder whether that might actually indicate some emissions from the stratosphere above the tropopause (but in any event, this is a very secondary feature.)
This seems very fundamental to me for the potential derivation of the logarithmic relationship. Most/all of the “explanations” of the logarithmic relationship volunteered here ignore the fact that the “forcing” depends on the atmospheric temperature profile – this is one of the reasons that I discourage these “bright ideas” unless the people have read the literature. The way that one would go about trying to establish a logarithmic relationship for additional CO2 around present levels is plausible would be to show that the combination of:
1) negligible forcing for CO2 radiation from the tropopause;
2) linear forcing for CO2 in the wings in the troposphere.
As temperature goes up, the “width” of the funnel would increase and the proportion of linear forcing to total forcing would decrease sort of as 1/n, yielding a logarithmic relationship. To some extent, that’s probably what’s done in the 1-D models, but the description of these models is very opaque and they don;t bother trying to explicate the mathematical properties of the model.
Now the Houghton back-of-the-envelope argument relies heavily on the fact that nothing else changes with additional CO2; it is my impression that this is also the case with Lacis et al 1981 and the 1-D studies. But it sure seems like a curious coincidence that the CO2 “funnel” just happens to be at the tropopause. Presumably the tropopause is where it is, at least in part because of CO2 radiation. Thus the whole premise of changing CO2 levels without changing the atmosphere temperature profile does not seem to me like a relevant method of modeling CO2 impacts, as higher CO2 levels would surely change the height of the tropopause and related atmospheric profiles. The assumptions on atmosphere temperature profiles intrigue and will be what I look at closely if and when I ever find a study that is on point to these issues.
Houghton, J. Spectrochimica Acta A 51, 1391-1392.
J.T. Houghton, Global Warming: the complete briefing. Lion Publishing, 1984.