First off, here’s a fantastic link (with references in the slides – pages 8 and 10 especially) for how albedo is mathematically defined according to astrophysicists. It appears not only that Wikipedia is wrong (and they’re usually pretty good on raw science), but you and I have been using the wrong definition as well. Albedo is clearly defined as the ratio of total emergent flux (ie reflected plus emitted energy) to total incident flux. Ultimately, though, it doesn’t matter. The black-body temperature of a body is clearly altered by the ratio of the body’s effective absorptivity over the body’s effective emissivity, and so the temperature of the body can vary from the ideal according to that ratio.

Second, I’m not trying to accurately model clouds et al. I don’t need to go to that level of detail to illustrate the errors in your equations.

Third, it appears that there are two competing definitions of a gray body. Here’s a few definitions from scattered places around the Web:

“any body that emits radiation at each wavelength in a constant ratio less than unity to that emitted by a black body at the same temperature.” Source: Dictionary.com (emphasis mine)

“An energy radiator which has a blackbody energy distribution, reduced by a constant factor, throughout the radiation spectrum or within a certain wavelength interval. Also known as nonselective radiator.” Source: TheFreeDictionary.com (emphasis mine)

“An energy radiator which has a blackbody energy distribution, reduced by a constant factor, throughout the radiation spectrum or within a certain wavelength interval. The designation “gray” has no relation to the visual appearance of a body but only to its similarity in energy distribution to a blackbody.” Source: accessScience Encyclopedia (emphasis mine)

“A hypothetical body which absorbs some constant fraction, between zero and one, of all electromagnetic radiation incident upon it, which fraction is the absorptivity and is independent of wavelength. As such, a gray body represent a surface of absorptive characteristics intermediate between those of white body and a black body. No such substance are known in nature.” Source: NASA Goddard Space Flight Center definition

“Bodies that emit less thermal radiation than a blackbody have surface emissivities ε less than 1. If the surface emissivity is independent of wavelength, then the body is called a “gray” body, in that no particular wavelength (or color) is favored.” Source: Efunda.com

So NASA says it’s a flat spectrum while the McGraw-Hill accessScience Encyclopedia of Science and Technology online says it’s a black-body spectrum. I’m using the the blackbody energy distribution definition, as it more closely models reality than a flat spectral response gray body does. Here’s an updated explanation in .pdf, based on the same data, but reformatted (since I didn’t explain myself well enough the first time around).

Fourth, that’s actually not where I got my 6000K thing – The average temperature of the Earth’s surface (which isn’t the Earth’s black body radiation temperature, by the way – I’ll illustrate this below, with my discussion on your problem with Venus) only matches your T_sun/21 if you boost the temperature up from 5778K to about 6000K. Still, though, the difference is so small that it’s within the noise when using four significant digits, so it’s actually a small quibble.

Fifth, the University of East Anglia’s Climate Research Unit may or may not get tax money from the UK government – I don’t know. But it’s not the same as the Met Office, which is the UK equivalent to the U.S. National Weather Service. Also, neither you nor anyone else I’ve read across has pointed out even a single scientific paper that the CRU emails invalidate. It’s put up or shut-up time on this one, Bob.

And finally, your errors with regard to Venus are included in this .pdf. In summary, there are two possible ways that Venus’ surface could be as hot as it is – internal heating from either Venus’ core or a collision millions to hundreds of millions of years ago, or the greenhouse effect. I disprove the internal heating hypothesis as the source of anywhere near enough energy to maintain the output energy, leaving the greenhouse effect as the only viable hypothesis.

The sentence :
“As you indicate , it is the ratio between the values for the half millionth of the sky from which we absorb heat from the sun , and the entire sky to which we emit at the earth’s average temperature .”
Should be :
As you indicate , it is the ratio between the values for the half millionth of the sky from which we absorb heat from the sun , and the entire sky to which we emit at the earth’s average temperature which matters .

I invite any readers of this blog to study my implementation at http://cosy.com/Science/TemperatureOfGrayBalls.htm to compare approaches . It’s clear that both produce the same numbers , but understanding our temperature in terms of the difference between our absorption from the small disk of the sun , and the entire rest of space reflects the reality more realistically .

By the way ( 0 ) , Brian , I see where you got the idea that I was using 6000k . It’s just a starting parameter for K’s search routine to keep the floating point from exploding . The answer would be the same with any starting point , eg , 5500 , so long as the calculations don’t overflow , which does happen with a starting point of , eg , 0 .

By the way ( 1 ) , the tax funded Met office’s behavior is inexcusable , but not that uncommon . It simply shows what I’ve always argued ( from experience ) , that peer review is just an “old boys” network and it’s the deifying of it by the Statist alarmists has been the real religious fraud .

Also, I failed to point out that I was assuming that the Earth was a uniform, ideal material for those graphs. However, my point was to illustrate that effective absorption and effective emission were NOT the same, and so the ratio would not be 1, even for a uniform ideal gray body. And since a uniform ideal gray body has different effective absorption and emission coefficients, non-ideal bodies will also have different effective absorption and emission coefficients.

I’ll see if I can’t crank out the math for your Venus problem too.

At this point there’s no proof that any of the science has been manipulated. It’s about the science, people, and the science hasn’t changed as a result of this. Even if a few dozen papers are found to be seriously flawed (and don’t you think that we’d have heard about that by now? All I hear on the science front is crickets), those papers would barely scratch the surface of the overwhelming scientific evidence and fundamental physics underlying climate disruption.

It doesn’t matter if the same data is available to anyone — CRU doesn’t say how the massages the data (though it admits it does) and then demands you take their results as gospel and if you don’t you can’t get in the peer club. That’s not science and you should be offended.

CRU gets free weather station data from nations around the world who sell that data to anyone else who asks for it. CRU was contractually obligated to not release the data for that reason.