I am getting this from the alarmist sites like the GISS and the IPCC.
NASA GISS: Science Briefs: Taking the Measure of the Greenhouse Effect
I realize that the GISS data is dated, but they claim that doubling the CO2 level would cause an energy imbalance of
4 W/m2 (now revised down to 3.71 W/m2). This imbalance would force warming of about 1.1C.
This 1.1°C of warming would then cause feedbacks, that would amplify the warming by a feedback factor.
If the ECS were actually 3°C, then the feedback factor would have to be output divided by the input, or 3/1.1=2.72.
The entire concept of the greenhouse effect is based on the idea that Earth is 33°C than it would be if the atmosphere
were completely transparent.
This 33°C is claimed to be the result of an energy imbalance of 150 W/m2.
This is all documented in many sites,
Climate Sensitivity - American Chemical Society
For those who are counting, the difference between 255 K and 288K is ...33°C.
So if we double the CO2 level, it forces warming of about 1.1°C, But in theory there are positive feedbacks that push the warming much higher.
Any warming perturbation would activate the feedbacks, so we can see how past warming events have reacted.
The GISS site says that CO2 is responsible for 20% of the 150 W/m2 of imbalance, or ~30W/m2.
But wait, the GISS site also says,
Consider why the idea that 20% of 150W/m2 causing 33°C of warming, is not comparable
with the idea that a single doubling of CO2 would equal 20 W/m2 of imbalance?
It would take 8 doubling s of CO2 to reach pre industrial levels.
Were each doubling worth 20 W/m2, the energy imbalance would need to be at 160 W/m2,
when 20% of 150W/m2 is only 30 W/m2!
There may well be net positive feedbacks, but they cannot be at anywhere near the level suggested!