adb said:
It is not a "bath" of IR radiation. According to greenhouse, there is a hemispherical emitter (the sky) providing as much radiation to the top of the sunbather, as the sun was, before she was put in the shade.
The notion of a "bath" of radiation is standard, and it applies here because there are large flows in both directions. Any IR detector is going to see radiation coming from all sides, and that is called a bath of radiation.
If you want to know what occurs according to the greenhouse, use the description of the greenhouse you've provided already. Here it is again, inserted visually.
http://www.climateprediction.net/images/sci_images/ipcc_fig1-2.gif
(Source: http://www.climateprediction.net/content/basic-climate-science at climateprediction.net.)
Remember, that is averaged over night and day, summer and winter, poles and equator, clear and cloudy. If you want to get concrete numbers for the sunbather, you'll have to adjust the numbers for some typical daylight sunbathing.
OK. Let's do some physics! I'll welcome corrections to my numbers; but they have to stay consistent with basic physics.
You can skip over this indented section at first reading. It's only here because I want to use more realistic daytime numbers. The real answer to the puzzle is simply that you can't block the backradiation without trapping the upwards radiation also.
We're looking at transfers at the beach. The 198 W/m
2 (168+30) sunlight coming down will be roughly 1000 W/m
2. This is a scaled up by four for the sun being overhead; plus a bit more for clear sky and reduced atmospheric reflection. This corresponds well to measurements of summer sunlight at midday on a clear day. The ground reflection scales the same way, up from 30 to 150.
The surface radiation upwards relates to ground temperature. 390, by Stefan-Boltzmann, corresponds to about 15C. But in the day, when sunbathing, it will be more like 30C, which would be radiation of about 480. To stick with rough figures, I'll use 500 W/m
2 upwards, which is a surface temperature of 33C (or 92F if you like Fahrenheit). This also has the benefit of keeping temperatures close to body skin temperature; because we want to ignore complications of body heat.
The radiation down from the atmosphere tends to remain roughly in proportion to surface air temperature. (See the paper I cited previously on measurements of backradiation.) So we can scale the 324 backradiation to roughly 400.
What's left? 850 in from the sun, 400 in from the atmosphere, and 500 out from the surface; we have 750 W/m
2 unaccounted for. This will be divided between absorbed energy heating up the surface (which will be given back again at night time, so it doesn't show up in the diagram) plus convection and latent heat from the surface (which is 102, on average, in the diagram).
Grabbing the back of an envelope: air has heat capacity of about 1000 J/kg/K. At night, you can get an "inversion", or reversal of the atmospheric temperature gradient, up to about 500m or so. This is the air giving heat back to the surface at night. Density is about 1.2 kg/m^3. Hence the upper 500m of the atmosphere is about 6e5 J/K/m^2. Assuming a temperature difference of about 20 degrees from night to day, we get about 1.2e7 J/m^2 stored energy difference. Assuming a transfer of this over 8 hours, or about 2.9e4 seconds, I get a bit over 400 W/m
2 flux. That sounds plausible as about the flux of excess energy up into the daytime sky to heat the air, storing energy that is given back at night. So in the daytime, there's about 400 W/m
2 energy actually being soaked up in the air. The 350 still unaccounted for needs to show up as convection and latent heat… and this looks a credible value also, because the average over night and day is given in the diagram as 102. If anyone has actual measurements of daytime energy balance, I'd love to see them for comparison with this guesstimate for division of the remaining 750.
Final numbers I propose for the midday sunbather, all in W/m
2.
- 1000 downwards as sunlight.
- 400 downwards as infrared backradiation.
- 150 upwards as reflected sunlight.
- 500 upwards as infrared surface emission.
- 350 upwards as convection and special heat.
- 400 excess being absorbed to heat up the air.
[/size]
OK. The real question is, can't we make the sunbather feel cold by shielding her from the 400 Wm
2 backradiation? The answer is… no, because there's no physical way to remove that without trapping the radiation she emits herself.
Radiation shields are used everywhere. Your car exhaust is fitted with radiation shields.
Right; and this is useful, because the exhaust pipe is so much hotter than the air outside. What you CAN'T do is make a shield that keeps all the thermal heat inside at the exhaust pipe, but still let's in heat from the other direction. If you could make such a shield, you could take a warm brick, which is cooler than the exhaust pipe, put it next to the radiation shield, and have heat from the brick flowing in through the barrier, while heat from the exhaust pipe was prevented from flowing the other way. You could use such a shield to heat up a hot object from a colder one, in violation of the second law.
As I said previously, we CAN block infrared radiation with glass. It does make a very good shield for IR radiation. So what happens if we put a glass sheet over the sunbather?
Sure enough, we've blocked out the 400 W/m
2 atmospheric backradiation. But the sunbather, who is at a nice comfortable 33C, is radiating herself, upwards, at 500 W/m
2! And we've trapped that inside! She gets HOTTER as a result. You simply cannot block out the 400 W/m
2 down without also blocking the 500 W/m
2 going up.
All your examples of cooling something by blocking radiation work because they are shielding you from something hotter than you are. But in the greenhouse effect, the surface (and the sunbather) is hotter than the atmosphere. If you put in a block, you're actually making it harder for the sunbather to shed the thermal radiation she needs to emit to keep cool.
It's the same problem in all these discussions. All the attempts to portray greenhouse, or backradiation, as some kind of violation of thermodynamics or perpetual motion are ignoring the energy flows in the other direction.
The paper by G&T is just the same. It may look superficially plausible, but it's not going to take in anyone who works with atmospheric thermodynamics for a second. If they were first year physics students, we'd simply say that they need to learn a bit more about basic physics. But these clowns have had their errors pointed out to them at length, for years. The paper came out ages ago in arxiv, and the errors were identified quickly and publicly. Recently, they actually managed to get their paper into a small mainstream journal, bypassing the normal technical review by appearing in an "invited" category. Whichever editors made the invitation have slipped up badly, and G&T are plainly pseudoscientific cranks – on this topic, at least. Neither one of them has any publication record in climate or basic thermodynamics, nor indeed do they have much of a publication record at all. They are very minor players in real science, with a sideline in gibberish. It's not unheard of, and there are plenty of other isolated examples in other fields of science. From time to time such individuals do manage to get some of their stuff into the scientific literature, because editors are not infallible.
------
And also, in response to your next post:
adb said:
We're both intelligent people and I'd like to tie things down. I don't work in the industry and have nothing to gain whether greenhouse exists or not.
Thanks muchly; I feel the same way. I'll add that there's no animosity between us either, as far as I am concerned, and I'm sure you feel the same. We're just having an "energetic" discussion of points of physics.

It's fun, and hopefully it's educational. I expect we'll be able to tie most of it down. The point about radiation shields working in both directions will be crucial.
… It is also interesting that you agree that greenhouse does not have a significant effect on atmospheric temperature profiles. This agrees with what Thieme suggests.
Sure. Thieme's errors – and his essay is full of them – are on other matters. His comments on convection are merely a distracting non-sequitur. He might as well point out that greenhouse has no effect on atmospheric scattering of light, and the consequent colour of the sky.
Cheers -- Sylas