Skip to comments.Do greenhouse gases warm the planet by 33°C? Jinan Cao checks the numbers.
Posted on 09/08/2012 9:49:28 AM PDT by Ernest_at_the_Beach
Jinan Cao has been dissecting the nature of the greenhouse effect and a key calculation that I normally just accept without questioning. This will set a few pigeons loose, but it will be interesting to see where they land. The claims analyzed here are the oft repeated ones that the Earths greenhouse effect already warms us by 33°C and that a doubling of CO2 directly causes a 1.1°C rise (thats with no feedbacks taken into account).
Jinan points out that these numbers, repeated as fact, are merely a result of misuse of the Stefan-Boltzmann equation. If Earth is not a perfect black body, but has an emissivity of 0.7 (as satellites suggest), then the temperature of the planets surface without any greenhouse effect would not be -18°C, but more like 5°C. That would mean the entire warming due to the greenhouse effect is only around 10°C, not the more impressive 33°C that is usually claimed. It means the greenhouse effect is probably less important than implied.
The 1.1°C direct rise that is predicted from doubling CO2 without feedbacks would also need to be recalculated. This paper does not try to do that, but if Jinan is right, that figure would be significantly lower too. Jinan looks at how that figure was derived. David Evans has been helping review Jinans work and writes the introduction below. Jo
The Stefan-Boltzmann equation describes how much radiation (energy) is given off by a body, such as a planet or a layer of air. It figures extensively in climate science, especially in simple calculations of where energy is flowing on average as the earth radiates heat into space as infrared radiation.
The Stefan-Boltzmann equation is used to obtain known nostrums of the climate debate, such as it would be 33C cooler without greenhouse gases and the direct (no feedbacks) effect of doubling the CO2 levels is to raise the surface temperature by about 1.1C. The equation is a standard one in physics. Its application to radiation from the earth can be done by any physicist or scientist; only a very rudimentary knowledge of climate science is required. (No mystical climate science secret knowledge relevant here; the laws of arithmetic and physics are sufficient.)
Jinan Cao clinically dissects several of these applications of the Stefan-Boltzmann equation and finds it has been sloppily applied. Do you think the errors in application by the climate science community work in the direction of understating, or overstating, the role of CO2? Jinans article, although technical, is not difficult.
This paper will ruffle a few feathers and deserves a fair hearing. It brings up valid points, and challenges the application of the SB equation that are, by everyones admission, somewhat unsatisfactory.
Todays climate scientists will attempt to laugh off these criticisms by saying that their models are much more sophisticated and accurate than the crude 0-D models considered when applying the SB equation. (A 0-D model treats the earth as a point, with zero dimensions. A 1-D model takes account of one dimension, either height in the atmosphere or latitude. A 3-D model treats the earth as having latitude, longitude, and height.)
But there are two problems with this defense. The first is authority. We dont know what goes on inside these models, so are we supposed to just take the word of their modelers, that they have got it right? The models are too opaque and not open to public scrutiny, so this amounts to argument by authority. As the motto of the Royal Society says, take the word of nobody. The second problem is that todays climate science community have demonstrated a habit of exaggerating issues even as straightforward as death threats, so how might they handle issues as vital to their funding as the importance of greenhouse gases to our well-being?
Common errors in the use of the Stefan-Boltzmann equation
Download the full paper here 8 page PDF
Climate scientists frequently make technical errors in their use of the Stefan-Boltzmann equation.
The Stefan-Boltzmann equation is simple: a black-body object with surface temperature, T, emits energy per unit time and unit surface area, J, the energy flux density:
J = σ T4 (1)
where σ is the Stefan-Boltzmann constant equal to 5.67 x 10-8 (W/m2K4).
When the Stefan-Boltzmann law is applied to the Earth-Atmosphere system, climate scientists often make one or more of these technical errors:
i) a coefficient ε in the range 0 to 1, called emissivity should multiply the right hand side, but not when applied to objects that are not black bodies;
ii) a failure to specify correctly the surface and surface temperature of the Earth-Atmosphere system;
iii) a failure to specify whether or not a layer of air is a single object or a cluster of objects.
These errors can be easily demonstrated by examining several statements (methodologies) most popular in current climate research:
1) the 33°C greenhouse warming effect for the Earth;
2) the 390 W/m2 surface radiation in the Earth Energy Budget;
3) the 1˚C CO2 non-feedback climate sensitivity; and
4) the formula for emission by a layer of air.
they are in the PDF however.
See my note at #3.
This is a subject on which I have posted several articles in the past. I agree with some but not all of Jinans claims.
Firstly, the warmists derive the -33C by assuming an albedo for earth of 0.3 as Jinan mentions however one needs to recognize that most of this albedo is due to clouds which are water vapour. Without green house gases ie: without water vapour earths albedo would be more like that of the moon (0.12) so the received radiation would be higher (390 * .88) leading to a surface temperature of 279K or +6C.
Now Jinan makes the point that the surface emissivity is much less than 1, in fact more like 0.7 derived from the albedo. I have to disagree with this, the albedo comes from reflection of visible light by clouds. The liquid water surface which comprises 70% of earths surface has an emissivity in the thermal infrared of about 0.96 which is indeed very close to 1. Land may have a somewhat lower emissivity but even there, surface covered by vegetation has a high emissivity in the thermal infrared.
Jinan makes the point that one must consider each wavelength region separately and here I totally and absolutely agree with him. This is to me is a fundamental error make by warmists when the talk about an equivalent radiation altitude. In the atmospheric window the atmosphere is transparent and the emission comes directly from the surface (or from cloud tops where the surface is covered by clouds). At green house gas absorption wavelengths the atmosphere is opaque and emission comes from the top of the green house gas column exactly as Jinan claims, and as he correctly states the temperature of the gas at this altitude is more like -50C (basically the tropopause or very low stratosphere) certainly not +14C. If anyone has any doubt about this point, I invite them to look at Earths emission spectrum as seen from space (Nimbus satellite). At these wavelengths the emissivity of the atmosphere is exactly 1. This comes about because emissivity always equals absorptivity. If the gas column absorbs all the energy radiated form the surface it has an absorptivity of 1 hence an emissivity of 1 as well.
It is Jinans point 2.4 which I disagree with most. It is not necessary to consider the emission of each molecule separately. For a layer of air thick enough to absorb all energy radiated up from below the layer as a whole has an emissivity of 1 (at that wavelength of course) and can be treated as a black body emitter at that wavelength (which means one can apply Planks law which defines energy emitted at a particular wavelength NOT Stefan Boltzman law which defines emission for an object which is a black body at all wavelengths).
As to the sensitivity to doubling CO2; we know there is a logarithmic relationship between ghg concentration and energy retained. We know how much energy CO2 currently retains simply by looking at the emission spectrum of Earth as seen by the Nimbus satellite. Without CO2 the emission temperature at around 14.7 microns would be that of the surface +14C instead of what it actually is -50C. We can either integrate Planks law over the wavelength absorption range of CO2 or graphically look at the reduction in area under the curve of the emission spectrum to space the result is 27 watts/sqM. We also know the total absorbance of the CO2 column at 280 PPM and it is about 2000 abs. That represents 10-11 doublings from the point at which the line center saturates (which is where the logarithmic relationship starts) so the incremental effect of doubling CO2 is 2.7 watts/sqM (I disagree with the warmists 3.7 watts/sqM figure). My calculation ignores the impact of clouds. If this is taken into account the 2.7 watts/sqM figure is reduced somewhat because cloud tops are cooler than the surface thus without CO2 the emission to space would be less than a surface at +14C would imply.
This comment is already too long so let me finish by re-iterating, I agree with much but not all of what Jinan states but my conclusions do indeed agree with his.
Thanks again Ernest!