This doesn’t change anything - sure it includes some infrared light which may be absorbed and radiated in both directions while the light is entering the atmosphere. I’m talking exclusively about the broad spectrum of light that is able to enter the atmosphere as it is sent from the Sun to the Earth, but which is then converted into infrared when it is absorbed and radiated by the Earth. This means that on its return journey back to space, the energy that was once UV/visible is now infrared, and thus it can be absorbed and radiated back by the atmosphere.
So by your math it would look like this (sun radiation is comprised of 50% infrared/50% visible and UV, and 30% of UV/visible reflected before entering atmosphere):
First, let’s model the actual IR absorption rate of our atmosphere which is around 70% with 30% direct passthrough.
- Sun
- Radiation into space
- Atmosphere
- Radiation to Earth
- Earth
Sun Sends:
(100 = 50 IR + 50 UV/Visible) 0 0 0 0
Atmosphere absorbs infrared/UV is reflected:
100 (15 UV/visible reflected back) (35 IR) 0 (15 IR + 35 UV/Visible)
Atmosphere radiates Infrared:
100 (17.5 IR) 0 (17.5 IR) (15 IR + 35 UV/visible)
End state of initial absorption:
100 0 0 0 (32.5 IR + 35 UV/visible)
Essentially 100% of the UV/visible is converted to infrared and radiated by Earth back into the atmosphere which looks like this:
Earth converts all energy to IR and radiates to atmosphere which absorbs 70% and 30 % exits to space:
100 (20.25 IR) (47.25 IR) 0 0
Radiates outward and back to Earth:
100 ~23.6 0 ~23.6 0
100 0 0 0 ~23.6
Now, running the same example but increasing to 80% atmospheric absorption of infrared with 20% passthrough:
(100 = 50 IR + 50 UV/Visible) 0 0 0 0
Atmosphere absorbs infrared/UV is reflected:
100 (15 UV/visible reflected back) (40 IR) 0 (10 IR + 35 UV/Visible)
Atmosphere radiates Infrared:
100 (20 IR) 0 (20 IR) (10 IR + 35 UV/visible)
End state of initial absorption:
100 0 0 0 (30 IR + 35 UV/visible)
Earth converts all energy to IR and radiates to atmosphere which absorbs 80% and 20% exits to space:
100 (13IR) (52 IR) 0 0
Radiates outward and back to Earth:
100 26 0 26 0
100 0 0 0 26
As you can see, because there is additional infrared energy being radiated out from Earth after the UV/visible is converted compared to the initial amount of IR coming in, this leads to increased atmospheric radiation as the atmospheric IR absorption increases. The impact of higher absorption is not equal in both directions due to this variable, which results in more heat being passed to Earth as more IR is retained.



