It is a lazy Sunday. Since I get a little flack over thermal conductivity needing to be considered in Earth atmospheric physics, I thought I might revisit Venus, the granddaddy of greenhouse effects.
Size wise, Venus and Earth are close, atmosphere wise they are two different worlds. Earth has a total solar irradiance of about 1367Wm-2 and Venus about 2614Wm-2 per NASA Planetary Fact Sheet.
Neglecting the difference in rates of rotation, since both are spheres, the average surface irradiance would be 1/4 or 341 Wm-2 for Earth and 653Wm-2 for Venus. Without any reflection or greenhouse effect, the surface temperature of both would be on average about 278K for Earth and about 327 for Venus, using S-B for a perfect black body. If both had the perfect greenhouse effect, I contend that the bond albedo would be 1, or no energy escapes the atmosphere. Since both planets receive sunlight on only one side, perfect insulation would mean that would lose no heat and that the most heat either could gain would be the average solar irradiance. Earth's maximum average temperature would be 556 K and Venus would be 654 K degrees. This, by the way is being a bit generous.
The maximum average irradiance of the sunlit side of the planets would be 682Wm-2 for Earth and 1306Wm-2 for Venus. Their maximum average S-B black body temperatures would be 331K for Earth and 389K for Venus with no atmospheric effect and double, i.e. perfect insulation, or 662K for Earth and 779K for Venus.
Using what I think are the more realistic estimates, since Earth radiates to space about 240Wm-2, it has a black body temperature of about 255K, so 556-255=301K for its maximum GHE, Venus radiates 65Wm-2 for a black body temperature of 184K degrees. 654-184=470K for its maximum GHE. For you doubting Thomases, the absolute maximum would be 779-184=595K degrees for Venus.
The average surface temperature of Venus is about 737K degrees, both estimates are significantly less than the actual average surface temperature. For this reason, I say Venus' surface temperature is enhanced by geothermal energy from its slow cooling core. The amount of enhancement would be between 142K for the impossible case and 267K for the barely possible case.
James Hansen is the authority on Venus. The only possible challenge I have to his Venus Greenhouse theory is the limit of radiant impact of CO2. Given the available solar energy, I contend that the maximum GHE impact on Venus is 470K degrees that could be felt near its surface. Since geothermal energy is likely adding to Venus' surface temperature, I suspect that the concentration, pressure and temperature at the surface cause it to be highly thermally conductive.
This leads me toward two thoughts, there is a limit to CO2 forcing that may be determined from Venus which is significant less than Hansen estimates and that the impact of CO2 enhancement of atmospheric thermal conductivity on Earth is not negligible.
Now, there is something else interesting about Venus. If it truly is experiencing the maximum GHE, it still radiates 65Wm-2 for a black body temperature of 184K degrees. 184K is -89 C degrees, which happens to be the approximate temperature minimum of the Antarctic and the Tropopause. This is where people believe that I have entered the Crackpot Zone. See, I also think that Earth has that limit to its maximum Greenhouse effect.
Since Earth emits about 240Wm-2 at approximately 255K as a black body, the lowest it could emit if I am on the right track is 65 Wm-2. Unfortunately, determining exactly why that limit exists for both Venus and Earth is not all that easy. On Earth I would expect the geomagnetic field plays a role. Venus doesn't appear to have a geomagnetic field of any magnitude. Both are influenced by the Sun's magnetic field and solar winds. Venus has no defense from the solar winds and the Earth's magnetic field somewhat offsets the solar field.
In any case, with a 65Wm-2 limit, albedo would have to increase to maintain the TOA energy balance. Unlikely Venus, Earth still has water in significant quantity. Where that water can have the most impact is in the atmosphere. So water will limit Earth's GHE, not CO2. Since water vapor cannot exist in any significant quantity above the tropopause, the impact of CO2 above the tropopause would be near negligible in the quantities that can be produced on Earth. Unlike Venus, Earth's Greenhouse Effect limit is the tropopause and its odd limit of approximately 65Wm-2.
So just anyone thinks I am running down a rabbet hole, I may be, and it appears to be solar in origin.