Earth thermal feedback effects

Looking at some apparently widely accepted data, I understand:

- CO2 mass change => direct "greenhouse" heating is approx linear over ranges considered
- Doubling CO2 (i.e. adding same again) would give 1C change for direct greenhouse.
- CO2 change x1.5 since pre-industrial times (half added), hence direct greenhouse would be 0.5C
- delta T has been observed to be 1C in same period, and attributed to CO2 increase.
- this suggests feedback gain around 1 => nearly unstable heat in-> heat out loop
- heat may generate some net CO2 directly e.g. by warmed sea out gassing
- this would suggest the thermal loop (even without any external forcing) is unstable, gain>1

An unstable Earth might change between 2 saturating temperatures, with little external "forcing". Saturating regions could have loop gains just below 1.
I expect there are flaws in the above, but it would be interesting to find out where.

You are assuming the system is linear.
If there is a tipping point, the system will be non-linear.

I am not clear that that is so. A loop gain becoming >1 would generate exponential increases i.e. a "tipping point", in an otherwise linear system (e.g. microphone howl).
Non linear, second order, effects are what would change the loop gain, and create stable "saturation" levels.
What non linearities are you suggesting?

I see a "tipping point" as being a point where the gain of the system changes. It does not need to become greater than +1, it could just change sign, inducing a change in the trajectory of the system state.

Our replies crossed. The observed T and CO2 changes and (I am told) agreed direct CO2 heating effect together suggest that there is a purely thermal loop gain close to 1, required to amplify the CO2 "forcing" change from 0.5C to the observed 1C.

I made a foolish mistake: feedback effectively generates a geometric series, so if the result is to double the input, the feedback gain is 1/2, not 1. i.e. factor=1/(1-gain).

Did you read the chapter 7 from the IPCC report AR6 - WG1?
https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Chapter07.pdf

CarbonBrief provided a good summary of the concepts and definitions used by the IPCC:
https://www.carbonbrief.org/explainer-how-scientists-estimate-climate-sensitivity/

Edit: I saw a dead link inside the CarbonBrief article, it is referencing this article: https://pubs.giss.nasa.gov/abs/ha07600n.html

Thanks for the links. I'll work my way through this stuff.