I saw a claim today that without the greenhouse effect, Earth's surface would be on average at a chilling -18°C (note: this is not a climate change thread).(adsbygoogle = window.adsbygoogle || []).push({});

I set about trying to reproduce this result, so at first I assumed that Earth was a perfect blackbody, and that in order to be in equilibrium, it would have to radiate away as much power as it received. So I took the solar irradiance of ~1400 W/m^{2}and divided it by 2 (since I figured that the surface area over which it could be radiated away again would be twice the surface area over which it was received). Then I took this irradiance (or 'flux' in astronomy parlance) and divided it by the Stefan-Boltzmann constant in order to get the fourth power of the surface temperature that the Earth would have to have in order to have this surface flux (as a blackbody). The resulting surface temperature was T = 60°C.

Then I decided it was silly to assume that all of the incident solar radiation was absorbed, so I looked up the Albedo (reflectivity) of Earth on Wikipedia. Two numbers were stated: geometric Albedo of 0.367 and Bond Albedo of 0.306. Being too lazy to read more about them, I just tried them both. Assuming them to be the fraction of radiation reflected, I scaled my required output flux by (1-Albedo) and got results of 30°C and 22°C for the lower and higher albedos respectively. Neither of these is -18°C. What am I missing (aside from the obvious that Earth is not a blackbody). Shouldn't this method give something reasonably close? I assumed that an equally crude estimate was applied to arrive at the -18°C in the first place.

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# Earth as a Blackbody

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