As I mentioned in another post, there is an ideal black body, I think we need an ideal gray body.
The above chart is my idea of an ideal gray body. When the T-value is 0.5 or 50 percent of the surface energy is radiated to space, it is and ideal gray body. I am using T-value and E-value because there is some possible confusion. The E-value is the energy emitted space from the layer or surface and the T-value is the energy transmitted to the next layer. That chart also includes the R-value or the energy transmitted per unit temperature. The R-value is always greater than the E-value because of the conductive energy transfer between molecules in a fluid. The R-value does approach the E-value at extreme temperatures.
Since conductive transfer is unavoidable or we would have a black body, the point where the T-value, E-value and R-value intersect should the the realistic ideal value for a gray body.
In the chart above, the T and E values have been shifted by 0.185 to create the intersect with the R-value. Interestingly, the point of intersection is approximately 0.6 or very close to the TOA emissivity of the Earth. At the surface emission layer, we have the following values:
Flux 335 Temperature 277 R-value 0.349 T-value 0.185 E-value 0.9996
This should indicate that the "Effective" surface radiant layer is 277 degrees K at 335 Wm-2 with an R-value of 0.349 W/K. The T-value of 0.185 should be the Planck response which is not all that useful, but 1 - the Planck response or 1-0.185=0.815 would be the "Effective" emissivity of the surface radiant layer.
As the actual surface characteristics are approximately 288K @ 390 Wm-2, 390-335=55Wm-2 would not be interactive with the atmosphere. That could be the energy emitted through the atmospheric window, latent energy shift or a combination of the two.
The R-value, which is very close to the value determined using the modified Kimoto equation,117Wm-2 which would be the combined conductive flux, which would include some or all of the latent flux from the surface, With latent estimated at 80Wm-2, the conductive sensible value would be 117-80=37Wm-2.
While this is just a first attempt to use a ideal gray body model, it does compare well to observations of the Earth atmosphere. Hopefully, this will somewhat support the modified Kimoto equation which is a lot easier to use. :)
There are of course potential errors and adjustments required, but I will post this now so y'all can have a good laugh while I fine tune my model.
Oh, I nearly forgot, 335Wm-2 from the "effective" radiant layer looking up minus 117Wm-2 equals 218Wm-2, the approximate value of the true down welling long wave radiation :)