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Tim Folkerts: Simple argument supporting a radiative greenhouse effect
My thanks to Tim Folkerts, who braves the generally sceptical stance on the talkshop to fight his corner for the climate mainstream paradigm of the radiative greenhouse effect. Tim has written a pared down synopsis of the fundamental points he believes makes the existence of the radiative effect certain. I suggest we try to restrict ourselves to dealing with the specifics of the article, mentioning in passing those aspects we might feel overly restrict the debate by their omission.
Simplified Greenhouse Effect
by Tim Folkerts – Dec 2012
This is about the simplest, most intuitive, most irrefutable argument I can come up with for why gases like CO2 and H20 in the atmosphere (“greenhouse gases”) must warm the surface.
There are only three fundamental requirements for this argument:
- 1. The ground is a good emitter of thermal IR (ie it is reasonably close to a black body).
- 2. The atmosphere contains gases that can absorb and emit IR radiation (“greenhouse gases” = GHGs).
- 3. The “top of the atmosphere” (TOA) (as related to IR emissions) is cooler than the surface.
Note that all three of these are confirmed by experiment for the Earth: the emissivity of the surface (especially the oceans) is close to 1; GHGs like CO2 and H2O definitely absorb and emit IR in particular wavelength bands; the radiative “top of atmosphere” is near the top of the troposphere, where temperatures are ~ 220 K (or -55 C or -65 F)
Note also that pretty much any other details are not critical. It doesn’t matter why there is a lapse rate; there is no need to calculate averages over the surface of the earth; feedback is irrelevant; exactly where and how the sun shines does not impact the fundamental argument.
For the sake of discussion, let’s look at a specific patch of the surface where the temperature happens to be 290K. Lets further assume that patch has an emissivity of 1.00 (ie it is a perfect black body). The spectrum for the thermal IR emitted from such a patch can be calculated, and is shown by the green curve in the graph below.
If there are no GHGs in the atmosphere, then this green 290 K curve in the graph below would also be the spectrum of the thermal IR leaving the earth. It is relatively easy to determine that the total radiation in this particular case would be 401 W/m^2 — either by integrating the area under the curve on the graph, or by using the Stefan-Boltzmann Law.
If we add some GHGs that absorbs IR in a band near 15 μm but transmits other wavelengths (sort of like CO2), and if this gas is at the top of the atmosphere where the temperature is 225 K, then that gas will emit a spectrum like the blue line on the graph. My hypothetical gas happens to emit 14 W/m^2 at 225. (This value can be found by integrating under the blue curve but again, the exact value is not critical).
So what will the spectrum of the thermal IR leaving the earth look like when the GHG is present? It might be tempting to ADD the two curves, getting a total of 401 W/m^2 + 14 W/m^2 = 415 W/m^2. This would result in a net cooling effect from the extra GHGs, but this it NOT correct. The photons near 15 μm that were emitted by the surface don’t leave the earth, but rather get absorbed on the way up through the greenhouse gas. Instead, the radiation from the gases higher in the atmosphere REPLACES the radiation from the surface. The net radiation will be the dashed line. The area under this curve will be less than the radiation from the surface — 377 W/m^2 vs 401 W/m^2, for a net change of – 24 W/m^2 in our particular case.
The implications should be obvious, but let me spell it out.
For a given surface temperature, less radiation leaves a world with cool greenhouse gases than a world with no greenhouse gases. This applies to each and every patch of surface around earth (at least as long as the three conditions hold). Less radiation leaving means more energy staying. More energy staying means the world with GHGs cools more slowly at night and warms more quickly during the day. This inevitably leads to a warmer world if GHGs are present.
We could also play with the numbers to discover that world with the surface at 295 K and this GHG at 225K would radiate 401 W/m^2. Again the implications are obvious. A warmer world with GHGs can radiate away the same energy as a cooler world with no GHGs. For this particular parcel of surface in this hypothetical world, the warming effect was 5 K. Other parcels at other temperatures in other worlds with other GHGs would have different warming effects, but all parcels in all GHG worlds will have some degree of surface warming due to the presence of GHGs.
QED
A few notes …
1) The specific numbers above are presented simply to have concrete numbers to refer to. As long as the three conditions are met, the general conclusion will hold — ie that a world with GHGs can have a higher surface temperature and still radiate away the same energy as a cooler world with no GHGs.
2) The form of the curve (the bite removed from the black body curve) is confirmed by satellite measurements and by more sophisticated calculations. (NOTE: These are plotted vs wavenumber rather than wavelength, so the shape is a little different).
3) This says nothing about what might happen with MORE GHGs. If more GHGs make the “bite” deeper or wider, then the warming effect would increase, but such details are for a different discussion.
4) Water absorbs over wider bands, but tends to do this at lower altitudes (where it is not as cold). This makes for wider but less deep “bites” in the spectrum. Even if water and CO2 absorb in the same band, the CO2 will still matter because it will tend to be at a higher elevation and a lower temperature, creating a deeper “bite”.
5) Details about evaporation, convection, distribution of sunlight, lapse rate, etc are certainly interesting, and could affect the magnitude of the effect. But none of these can change that fact that GHGs do indeed radiate to space from high in the atmosphere where it is cold.
6) The spreadsheet that calculated all this is available. There are no “instructions”, but there are a few comments that should make the spreadsheet’s set-up reasonably intuitive.
The shapes and values ARE accurately calculated (for the idealized emissivities) You can try playing with the temperatures or emissivities if you are so inclined.
7) “Surface” means the physical surface of the Earth — the land and water. One could also talk about the “effective radiating surface”. The “effective radiating surface”, would be somewhere between the physical surface and the TOA and on earth would have a temperature around 255K. But this level is determined by the GHGs in the atmosphere (with no GHGs the effective radiating surface would BE the physical surface), so even this approach relies on the presence of GHGs to warm the surface.
8.) Nothing here violates any laws of thermodynamics.
I can’t really understand how anyone with even a decent understanding of science could think that GHGs have no effect (or worse yet, that GHGs cool the surface!). The ability of GHGs to warm the Earth is confirmed by multiple lines of reasoning. Furthermore, there is the simple fact that the surface is much too warm to be due to sunlight alone, with no warming from the GHGs.
2012-12-06 14:13:47
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