However the next question, in modern global warming theories the effect of solar radiation variances due to sun spot cycles is considered inconsequential. CO2 ppm takes more focus for modern (settled…) global warming theories. So how is paining a roof white effecting CO2 production (clue; it is not) and why is this effect being compared with tons of CO2? Clearly the cooling effect from painting a roof white it is a result of reducing the absorption of solar radiation?

So it’s not the cars eh, it’s the black roads and dark roofs we have been building like crazy for generations.

Well no actually

See if it is reflecting energy then the spectral distribution of the energy reflected will have the same spectral distribution as the incident energy – of course.

If we are talking about emitting energy then of course it is a entirely different matter. Any body regardless of surface color that is in thermal equilibrium with its environment will be emitting energy in an amount exactly equal the incident energy falling upon it. In the real world any object will be reflecting portion of the incident energy and absorbing another portion. The absorbed portion will be re-emitted with a spectral distribution described by Max Plank’s Black body radiation formula which depends upon the temperature of the body in question but is “favors” if you will the longer wavelengths ie infra red.

Now of course it is the shorter wavelengths which find it “easier” to escape the planet while the longer wavelengths are absorbed by the atmosphere warming it (the greenhouse effect).

but the whole purpose of this exercise is to keep the planet cool by reflecting the suns incident energy back into space rather than have it absorbed and re-emitted in the longer wavelengths

Here endith the physics lesson

Ever had snow blindenss?

Can you imagine driving on a white reflective road on a bright sunny day?

On the boffins flying around the world a well spotted trend, wonder how much CO2 goes on conference travel?

I wonder what difference that makes to the carbon footprint of this house and its inhabitants, by using the most efficient coloured roof (black) to trap heat than by using a white roof.

Does that trade off the savings to the individual carbon emissions by painting the roof white, as your post suggests. I know that little heating (via a heat pump) is only required to keep the house warm.
In summer of course, the roof cavity gets up to more than 50 degrees but insulation in the ceiling mitigates that. As the roof cavity cools after sundown, faster than does the house, cooler air is transferred into the house to force out hotter air. I do not know whether the colour of the roof has any effect on the radiation of heat away from the roof cavity.