Edit to correct the spelling of Stephens
Note that OLR absorbed is 22% of the total absorbed by the atmosphere. Increased CO2 would increase that value by 3.7 Wm-2 to 56.7 Wm-2. Then the total absorbed by the atmosphere would be 243.7 and the surface energy would eventually increase from 385 to 388.7 Wm-2 with +/- 17 Wm-2 margin of error for the whole shebang. That additional 3.7 Wm-2 would increase latent by ~ 3 Wm-2 cooling the surface but adding to the atmospheric absorption. That could cancel most of the CO2 impact or add up to 3 Wm-2 to the impact producing 391.7 Wm-2 of surface energy( using my 385) at some point in the future. The high end would be 6.7Wm-2 increase which at an average surface energy of 385Wm-2 would be roughly 1.24 degrees increase in average surface temperature. That is below the minimum 1.5 Estimated by the IPCC and very close to the range estimated by several "skeptics". More warming that than would require feedbacks that are not evident so far. That warming would also require warming of the oceans surface which would require warming to some depth in the oceans which requires an undermined time to fully equalize if it in fact could ever equalize. So the estimated range of warming due to a doubling of CO2 is almost nada to 1.24 C degrees. Not exactly the alarming number tossed about by climate activists.
Is Stephens and gang's Budget THE Budget? I have no idea. It does though more accurately resemble what climate has done of the past 40% of a doubling after considering other factors.
UPDATE 2: Since I found another misspelling I may as well add this. When I put in the separation, it is to simplify understanding of what is going where. Trying to include both the day and night modes will always result in something that looks like it violates the laws of thermodynamics. The budget cartoon is just that, a cartoon trying to get as much information as possible on one fairly simple drawing. Someone noticed that the All-sky downwelling longrange is greater than it should be. That is why I used the net and separated the atmosphere. At night, the actually altitude of the source of DWLR would be lower than in the day and the amount of surface energy emitted would be less. I estimated that night Fmin would be about 380Wm-2 and that day Fmax would be about 414Wm-2. So the 240 Wm-2 I use in the split would be a rough 24 hour average with somewhere in the ballpark of 33Wm-2 variation on an annual daily average. Like a said before, there Stephens and gang budget is not perfect, but a lot better than all the past budgets I have seen.