Actually the results based on the empirical data show an ECS of about 2 C.
With other papers coming in as low as .8 C, but many showing an ECS of about 1.8 C.
https://www.ethz.ch/content/dam/eth...documents/group/climphys/knutti/otto13nat.pdf
When we look at the idea of how AGW is supposed to work, we see where the high estimates fall apart.
The warming from CO2 forcing, is supposed to be amplified by various climate feedbacks to produce additional warming,
once the long latency equilibrium period has occurred.
Thankfully we have a period of warming in the record (1910 to 1940) where temperatures rose by .2 C and never went back down.
We can use this input, to see how much unaccounted for warming exists.
If we assume the high end of the IPCC range of 4.5 C, the climate amplifier would have to apply a gain factor
of 4.09 to the input warming of 1.1C to arrive at 4.5C.
Since the climate system cannot discriminate the source of the warming, the 1910 to 1940 warming is an input as well.
So .2 C times the gain factor of 4.09 equals .818 C.
This sounds like the 4 C range is plausible, until you subtract out the physics based forcing by CO2 since 1940.
This would be defined by the equation of 1.58 X ln(409/311)= .432 C.
The most gain factor that the observable evidence supports is one that causes .2 C to gain to .386, or about 1.93.
This would be an ECS of about 2.1 C.
But we still have not taken into account the up to .3 C increase from the solar input.
As you can see the climate does appear to have an amplification factor, it just happens to be at the low end of the IPCC range.