In other words, 95% is initially absorbed and some of that reaches the Earth through convection.
Just on a simple math level, your contention doesn't add up.
The Cambridge Atlas says of all available solar radiation, 49% reaches the surface of the planet. Therefore, 51% never reaches the surface of the planet, and best I can tell, is never accounted for in THIS balance.
The balance doesn't account for 51% of the energy. How do you know that the 51% "is initially absorbed"?
FWIW, a clinical view of "convection" has it transferring energy "up" as a column of warm fluid rises through cooler, more dense fluid. You may instead be thinking of diffuse (vs. direct) radiation, and conduction.
You're kidding right? You guys will argue anything to be right! Did you read the part about "available" radiation? Obviously the remaining percent was not ignored. Perhaps that's the reflected light, I don't know, but I doubt Cambridge made THAT big of an error.
Why is it so hard for some people to accept readily verifiable facts? Go to a library and read the Atlas. It's all there. Just be sure you read it correctly and you look at RADIATIVE sunlight reaching the surface as that's what's relevant for the laser discussion.