Have fun: Balls. Let TSI be ONE foot-ball, falling on the intercepting disk (a). It breaks into 17 tennis balls (b), from which 5 is reflected (albedo 5/17), 12 yellow tennis balls are transmitted (c). 12 are absorbed at the surface, then reemitted as brown tennis balls which are completely absorbed by the atmosphere, and emitted upward and downward equally. Altogether, 24 brown balls are moving there (d). Fine tuning: Let 4 yellow be absorbed in the atmosphere, decreasing the number of the emitted brown balls to 20 (e). Divide by 4, our incoming 12 yellow balls become 3 (f). After division by 4, from our 3 incoming balls 1 will be absorbed in the atmosphere and 2 at the surface, emitted up 5,  atmosphere emnits 3 up and down (g). Then the three tennis balls decay into 9 tabletennis-balls (h), and the final distribution we can experience in global mean energy budgets is there in (i).

Have fun: Albedo.

The consideration here is incomplete and yet unproven, maybe even wrong.

The plane-parallel model albedo, with 51/4 units incoming solar and 15/4 units reflected solar is 15/51 = 5/17, identical to the IPCC AR6 albedo of 100/340 = 0.294. 

We have read in AMS Meteorological Monograph (2019) Chapter 4 that "The CERES flying on the Terra and Aqua satellites confirm that Earth’s albedo is 29.4% (±0.3%) and that the planet emits at an equivalent blackbody temperature of 255 K (±1 K; Wielicki et al. 1996; L’Ecuyer et al. 2015)."

Recent CERES datasets propose only 99 Wm-2 reflection from the same incoming energy, hence their suggested albedo is 99/340 = 0.291 (at the lower boundary of the unceertainty range given above). 

We tried to use a real spherical geometry instead of the stratified, and we found a geometric albedo between the two, α = 1 – sin 45° = 0.293. But we were unable to derive this result from angular distribution models or geometric principles.

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