If you truly knew that I was incorrect on this matter you would not need to use these tactics to make me appear stupid. I am not an expert on the matter, however I am able to respond to your statements:
Make that infra red radiation, not light.
Light does leave the earth, otherwise how would we be able to see it from space? I am speaking of reflection and emittance. You are probably correct that most emittance is infra red, which IS light though we cannot see it.
Things are a bit different thatn that, considering that the variation in solar energy output is rather low and diminishes even more when the fourth root is drawn from it, according to the Stefan Bolzman law. What really makes a big difference is Earth Albedo, changing reflectivity mainly due to variation in cloud cover.
Firstly, irradiation is incoming light. Secondly, for emittance it is a power of 4, not a root (so a change in Earth temperature by a couple degrees will have a fairly large effect on emittance).
If we speak of the heat transfer between the Earth and space, the change in the Earth's energy (incl. atmosphere) = heat in - heat out. Heat in is light entering the atmosphere and heat out is light leaving the atmosphere. Light coming into the atmosphere can either be absorbed by the atmosphere or reach the surface of the Earth (or as you mention, reflected by clouds). Upon reaching the surface of the earth, it is either absorbed or reflected. Light that is reflected by the Earth surface and that which is emitted by the Earth surface is then either absorbed by the atmosphere or passes into space (or reflected by clouds). My statement:
The effect of CO2 on the Earth's temperature is insignificant compared to the effect that the variation in solar irradiation has.
was simply stating that while CO2 increases the amount of solar energy absorbed by the atmosphere, the effect is insignificant compared to how much the variation of light entering the atmosphere affects the Earth temperature. I'm sure, as you state, cloud cover does have some effect since from memory (correct me if wrong): there is much more water vapour in the atmosphere than CO2, and it has more global warming effect.
The odd thing though is that the bulk of the CO2 in the oceans are stored in the deep where the temperature ranges between 0 and 2 degrees Celcius all the time, regardless if it is in the Arctic ocean or around the equator, only the upper 6-800 meters are warmer. So when atmospheric tempeature changes not a lot of the ocean is affected, hence variation in the CO2 storage capacity of the ocean may be sufficient to explain the variation in atmospheric CO2 during the "ice age" to "interglacial" transitions.
Yes, most CO2 is deep in the oceans and it takes a LONG time to warm these depths and release CO2 (~600 year delay). As you said, only the 6-800 meters varies significantly and this is where CO2 is presently coming from. Note that large warming periods in the past have seen CO2 levels a lot higher than today (~10 times?) because these have had the time to release CO2 from deep in the ocean. We have just been through a short warming stage and CO2 levels have increased, we are now entering a short cooling stage and CO2 levels will decrease. Again I am referring to solar cycles, to which you said:
Can it? But how? Things are still unclear,
As I said earlier, I am not an expert on this matter but the sun experiences a 22 or 11 year cycle during which the amount of light it emits significantly varies. There are also other cosmic effects which are still being studied.
I would like to conclude by saying: the amount of CO2 in the atmosphere remains to be directly related to the ocean temperature (whether we talk of the great depths or 6-800m). Evidence shows that CO2 levels in the past have been significantly higher than they are today. A CO2 global warming analogy: a CO2 increase is similar to putting on a shirt when you are outside; yes it will make you slightly warmer, but how warm you are really depends on your surroundings.