But if this was due to Lambert’s cousin (just kiddin ;)), or including it respectively, then radiation would have dropped sharply at an angle 45° (to below 0.7), right?

Then if you take the emissivity as drawn under “Henderson et al – 2003”, this is almost exactly the counterpart to water reflectivity as shown here:

So .. I may be wrong, but given that this emissivity profile can not include Lambert’s law and is in fact only the same reflectivity (which it was to do on a given wavelength btw.), then it is still true, that hemispherical emissivity is lower than total “absobidity”, roughly by a ratio of 0.84 to 0.925.

That of course would be a simple “mechanic” consequence. Let me explain it like this: Half of solar radiation hits the surface at an angle of less than 45° because sin(45°) = 0,7071 = 0,5 ^0,5. However half of hemispherical emission goes to angle of below 60°. So with regard to emissions, the lower angles are much more significant. And because that is so, oceans should actually be the significant “greenhouse” factor. Which is reflected by that any land-based place on earth is the warmer, the closer it is to the ocean. I mean just compare Trondheim to Irkutst..

]]>Erich: I think this is a case where Lambert’s cosine law is being applied. A detector viewing a surface rom an angle a receives W*cos(a) and W when the detector is looking normal to the surface (a=0). So relatively little power is transmitted at large angle (near 90 degrees). So the reduced emissivity at high angles applies to a smaller fraction of the emission than one might expect if you didn’t apply Lambert’s cosine law.

]]>Of course, we need to think in 3 dimensions here, and total hemispheric emmissivity would thus be around 0.85 (note that the section 60-90° is making up for half of hemisphere surface, and low emmissivity at flat angles play an overproportionate role).

So should the hemispheric emmissivity of water not be around 0,85, rather than 0.96 or whatever else was named here ??? ]]>

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E.G., In the longwave, the surface is assumed to have an emissivity of 1.0 within the radiation model. However, the radiative surface temperature used in the longwave calculation is derived with the Stefan-Boltzmann relation from the upward longwave surface ﬂux that is input from the surface models. Therefore, this value may include some representation of surface emissivity less than 1.0, if this condition exists in surface models (e.g. the land model).

from documentation of the Community Atmosphere Model http://www.cesm.ucar.edu/models/cesm1.0/cam/