Weird Relationship?

While setting up a spreadsheet to compare the solar irradiance and temperatures for a few of our neighbors I hit one of those odd things that just drive you nuts.

What I was trying to do was compare the actual temperatures after adjusting for the weird 65Wm-2 oddity I noticed in the Antarctic. Since the rotation of the planets vary considerably, I was just going to use the lit face TSI minus the 65Wm-2 for the not lit face. So for the Earth, 1367.7 Wm-2 minus the 65 would be 1307.7Wm-2.

After plugging in the formula to convert surface flux to temperature, things looked pretty normal. Only I noticed that I had used albedo, the reflected energy instead of the absorbed.

1302.7*0.306=396.63 Wm-2, which I plugged into the S-B (396.63/5.67e-8)^.25 and got 289.33K as my surface temperature. Obviously, I had not expected the values to be so close to the actual. I had mistakenly used just the reflected portion of the TSI, not adjusted for geometry and not even adjusted for day/night. I was just setting up a baseline value for maximum surface temperature to compare with the other planets, but forgot to use (1-albedo) for the absorbed TSI. Not my first dumb mistake throwing a spreadsheet together. The numbers came out so close though, I thought I might use it sometimes just to mess with somebody.

Now if I had not subtracted the odd 65Wm-2, the numbers would have been 394.1Wm-2 and 291.8K degrees. Because of the geometry of a sphere, the 1367.7 would have been divided by 4 yielding 341.9Wm-2 TOA, then I could go through the standard PITA estimates, used the calculated average surface temperature and come up with nearly the same values.

Odd coincidence? I did the same thing with Mars and came up with a surface temperature of about nine K warmer than the blackbody temperature. If the oddity Flux on Mars were 145, then the temperatures would have matched using Mars albedo of 0.25. For Mercury, it doesn't work. With the moon I get an average surface temperature of 224K.

It is probably just a weird situation, but there are a few questions about just how elastic photon reflection might be. If nothing else, it may be fun for doing quick estimates of surface temperature with back of the envelope calculations.

I may go back to the Postma paper to see what he did though. He could have been close to something after all?

The Bond Albedo does take into account the geometry and there is a disagreement between the Mars references for Bond Albedo versus the visual albedo. This may be more than a coincidence. Venus of course is warmer than would be indicated by the solar irradiantion. I have theorized that is due to iso-conductivity at the surface atmosphere boundary so core energy is being more efficiently transferred to the surface and lower atmosphere. This quirk may be a quick way to do what ifs on the effective radius of the energy absorption layer.