I don't understand how the Planck function, which is
about black body radiation, affects a greenhouse gas.
Not exact matches
First off, an idealised «
black body» (which gives of
radiation in a very uniform and predictable way as a function of temperature — encapsulated in the Stefan - Boltzmann equation) has a basic sensitivity (at Earth's radiating temperature) of
about 0.27 °C / (W / m2).
Now some energy has already escaped to space by
radiation directly from the surface, and Trenberth insists that is only 40 Watts per square meter, or
about 10 % of the roughly 390 W / m ^ 2 corresponding to a 288 Kelvin
black body spectrum.
That's why I did no assumption
about the precise properties of the
radiation (isotropic, continuous,
black body etc).
It corresponds to a
Black body radiation Temperature of
about +15 deg.
This assumption is absurd, the Earth reflects
about 30 % of the Sun's
radiation, that is why we can see it at all; the Earth can not reflect 30 % and radiate as a
black body at the same time.
We'd need to add the Bond albedo into Equation 2.3 (making this a gray
body instead of a
black body in the process) and so
about 10 % of the
radiation that reaches Venus is actually absorbed by the planet.
In the real world; that being the laboratory where CO2 does its dastardly deed on our climate, the source of the energy that purports to do the heating, is (on average) a
black body like source of Long wave infrared
radiation having a spectral peak at
about 10.1 microns wavelength, and containing
about 98 % of its energy in a range of
about 5.0 to 80 microns wavelength, at an effective Temperature (on average) of 288 Kelvin.
Claim 6: The energy content of the
radiation from the Atmosphere to Space approximates the energy radiated by a
black body at
about 255 K -LRB--18 ºC or -1 ºF).
2) The dipole of water means that unlike linear CO2 and tetrahedral CH4, water has a strong pure rotational absorption spectrum, and this rotational absorption, sitting on top of most of the 277K
black body radiation from a «naked» earth, is what is responsible for the natural warming of
about 20K.
He accurately reported that
about 10 % of the
radiation from a 100 °C
black body was absorbed in his tube, and that at lower pressure at most 9.6 % was absorbed, whereas in fact it must have been
about 9 %.
In practice the
radiation into space is pretty much the
black body spectrum you would expect for a
body at
about 290K with reductions at particular wavelengths particularly between 5 and 8 micron and between 14 and 18 micron as you describe in your text.