Since it looks like fishing will get postponed until tomorrow, a little condensed version for Lucia may be in order.
The Kimoto Equation: dF/dT=4F/T is more elegant than you may think. The 4 is equivalent to using 255K as a reference radiant layer. You can check by using the full S-B 5.67e-8(255)^4-5.67e-8(254)^4 yields 3.74F per T. Exact no, it is an approximation, for more exact, 259K to 260K. In either case, it provides a reference flux to temperature relationship. Heavy emphasis on Reference.
From any other temperature, a variable needs to be included to balance the equation to that reference. Example: 390W/m-2 - 384.7 = 5.31Wm-2 or the change in Wm-2 from 287K to 288K. 4/5.31=0.753 or the approximate ideal emissivity between a point at 287K and a point at 259K. So 0.753F/T = 0.753(390)/288=1.02 meaning the flux at 259K point would increase by 2%. 1.02*255.14=260.2Wm-2 which has an equivalent temperature of 260.25K So a one degree change in surface temperature beginning at 288K would produce a 2% change in emissivity resulting in a 1.2 degree change at a radiant layer initially at 259K. 287K to 260K would of course produces slightly different results. It is an approximation after all.
This would appear to be the classic relationship used to predict that mid tropospheric temperatures would increase by 1.2 degrees per 1 degree change in surface temperature. If the average temperature of the radiant layer in the mid troposphere were 259K, that would be true. Unfortunately, -14.15 degrees C is limited globally as a radiant layer temperature, implying the Arrhenius relationship which appears to be based on 255K, is only valid for temperatures in the range of 255K to 260K for an average radiant layer temperature. If you referred to Arrhenius' 1896 paper, you will note that is estimates by latitude diverge from reality. Please not that in is final table, 0.67K and 1.5K are not temperatures, but changes in CO2 concentration. Assuming 280ppm was the average concentration at the time of his research, 0.67K would be approximately 187ppm and 1.5K would be approximately 420ppm. A quick test of the validity of the Arrhenius equation, since current CO2 levels are approximately 390ppm, would be to compare today's observed temperatures to Arrhenius' predicted temperatures by latitude.
Lucia, I find that the modified Kimoto equation can be a very valuable tool, but only if one realizes that Arrhenius' equation is erroneous since is does not include the require temperature dependance for the average effective radiant layer of the atmosphere in the real world. I believe Angstrom mentioned this to Arrhenius while the Galileo of Global Warming was pondering his role in the master race :)
Just in case Lucia survives the holidays and the skunk invasion.