Prigent, C., F. Aires, and W.B. Rossow, 2006: Land surface microwave
emissivities over the globe for a decade.
So, I 1) attached a surface mount thermocouple to the outside of the twinwall to measure the «actual» surface temperature, and 2) applied a roughly 1.5 by 1.5 inch piece of blue painters tape a few inches below the thermocouple — this is the often used technique of placing a patch of something with know
emissivity over an unknown emissivity surface, and then measure the temperature on the known patch.
Redoing the final calculation of the earth's temperature with a better estimate of
the emissivity over the range of terrestrial wavelengths yields a better estimate.
Not exact matches
And I # is emitted and absorbed by emission and absorption cross sections and
emissivities and absorptivities that are equal for emission into a direction and absorption from that direction at the same location or
over the same path length for the same frequency and polarization.
But
emissivity of a rocky planet would certainly be less than 0.88 and so the temperature would be
over 290K and thus there is actually cooling by greenhouse gases, as empirical data proves to be the case for water vapour.
Now I did use the word «averages
over the planetary surface», but these obviously weighted averages - the effective temperature is weighted by the fourth power of itself, and the effective
emissivity is weighted by the forth power of local temperature.
The only trick is knowing the
emissivity of a surface (and whether the
emissivity is constant
over the wavelength range in question), but that doesn't really seem to be your difficulty.
We have been to some extent been glossing
over this, but
emissivity and absorptivity are functions of wavelength, and even direction.
You are forgetting that
emissivity and absorptivity themselves are not constant
over all wavelengths.
Phil says: «Where do you get your value of 0.2
emissivity from, what range of wavenumber is it for, why haven't you accounted for the variation of energy
over the wavenumber range or the different absorption bands of H2O and CO2?»
The
emissivity of the Earth is
over 0.97 and a perfect black body is 1.0 so, for all intents and purposes, the Watts / m ^ 2 calculated by the Carleton spreadsheet based on Plank's Law may be off by only a small number of Watts / m ^ 2 and my main claim is that there are hundreds of Watts / m ^ 2 streaming down from the Atmosphere, so a few Watts here or there is a drop in a bucket.
The Earth Surface has an
emissivity in the mid - and far - infrared that has been measured at
over 0.98 for the oceans and
over 0.95 for most land areas.
What is actually relevant in figuring out how much the earth is going to absorb is averaging the powers
over the entire planet and what is relevant in figuring out how much it is going to radiate is averaging the temperature
over the entire surface (actually T ^ 4... or, most technically, the
emissivity * T ^ 4 but the
emissivity in the mid - and far - IR is very close to 1 for most surfaces).
For calculating emission, it's more accurate to multiply the
emissivity at each point by the Planck function at that point and sum
over all wavelengths to get the total emission.
Microwave imagery must allow for variations in surface
emissivity and can not act as a surrogate for air temperature
over either snow - covered (Peterson et al., 2000) or sea - ice areas.
How do we know that the radiation absorption and
emissivity of the oceans is not changing
over multi-decadal scales which would affect the heat content of the oceans?
But for real world applications the amount that
emissivity varies with temperature is small enough to not come into play for solid objects
over terrestrial temperatures.