The answer in a nutshell : mathematical trickery.
The IPCC equation for the Feedback factor, used to calculate climate sensitivity, is given on AR4, WG1, page 631, footnote 6. It is:
Under these simplifying assumptions the amplification of the global warming from a feedback parameter λ (in W m-2 °C-1) with no other feedbacks operating is
1 ÷ (1 + λ ÷ λp) where λp is the ‘uniform temperature’ radiative cooling response (of value approximately –3.2 W m-2 °C-1; Bony et al., 2006). If n independent feedbacks operate, λp is replaced by (λ1 + λ2 + ... λn).
|- 40% variance||FF[low]||0.18||0.21||0.24||0.27||0.30||0.33||0.36||0.39||0.42|
|+ 40% variance||FF[high]||0.42||0.49||0.56||0.63||0.70||0.77||0.84||0.91||0.98|
Let's consider just how easily we can arrive at a high climate sensitivity value from what looks like a midling feedback factor. The IPCC give their modelers a feedback factor of 0.5 to use
(= λ ÷ λp above, which is a unitless number). Jessica Vial's team were tasked with coming up with (inventing?) this number; as they did. To this central estimate, they add and subtract ±40% (2 standard deviations up or down) because they say they want to cover 95% of eventualities. This is shown in the table (above). Rows 2, 3, and 4 show the feedback factor with -40%, 0%, and +40% adjustments (labeled: FF[low], FF[mid], FF[high]). With a feedback factor of 0.65 (only 0.15 more than their central estimate), the +40% figure for climate sensitivity = 11! That means the equation projects a doubling of CO2 to 560 ppm from pre-industrial times will give an average 11C temperature increase at earth's surface. Don't worry. It's a maths trick it's not real. Unfortunately the likes of Angela Merkel, Ed Miliband, Jeremy Corbyn, countless Tories seem to believe in magic, faeries, and impossible maths equations.
Christopher Monckton has a lot to say on this mathematical trickery here and here. I've yet to read chapter 3 of Bode's "Network Analysis and Feedback Amplifier Design", 1945, from which it looks like the climate modelers stole their feedback ideas. But pray, don't blame Dr. Bode (RIP). The climate modelers did a slight of hand by not using the whole of the forcing in their equation. By only taking the difference in forcing, they created an equation just balanced on the edge of a catastrophe. This has been the climate sensitivity equation since 1979. It predates the IPCC and is used for all 5 IPCC reports. I will elaborate more in another blog. For now: please watch Monckton's talk at the Heartland’s 12th International Conference on Climate Change. After I think I can explain it better, I'll blog it again. I want to show the difference between just using differences (as they do) and what they should do (putting all the forcing in).
How and why does this con work?
You may think the boy that cried wolf story is 'true' of people, in the sense the story chimes with us. That we disbelieve people we know are lying to us. It ain't so. When the liars pose an existential threat to our existence, when they make it a matter of the survival of humanity, then, sadly, we listen to them, again and again. That's why the climate feedback equation is like that. Because with just a bit of tweaking, it can threaten our very existence, and guarantee climate alarmists an audience for their doom-mongering. It's not really about the climate for them. Don't be fooled. It's about putting the brakes on human technological progress. Tying us down, enslaving us to our fears, so we won't be able to harm the environment.