In something like RCP8.5, where the 8.5 is watts per square meter IIRC, how do you translate that to equilibrium temperature change?
In a 2012 article by James Hansen et al. using an energy balance perspective to describe global warming, they state that each 1 watt/m2 of extra energy translates into about 0.75C warming once temperature has reached equilibrium. But reaching equilibrium takes a long time (more than decades, call it 200 years if you want a number).
RCP8.5 refers to 8.5 watts/m2 by 2100. So based on that ratio the RCP8.5 scenario should lead to ca. 6C warming. But charts by IPCC, Global Carbon project, etc. show the RCP8.5 scenario global average surface temperature anomaly over preindustrial (when CO2 was ca. 278ppm vs ca. 1200ppm at 2100 in RCP8.5) as 3.2 to 5.4C, with a median estimate of 4.3C. That is less than 6 because of the lag. Thus, if CO2e stayed at 1200ppm for a long time, the temperature would gradually approach the +6C level over time.
At least that is how I understand it from a "not a climate scientist" perspective. The immediate temperature response (TCR - transient climate response) is substantially less than the long term equilibrium temperature response (ECS - equilibrium climate sensitivity).
Some things to note - there has been some interesting commentary within the last few weeks about overuse/misuse of the RCP8.5 high end emissions scenario. Hausfather and Peters recently published a commentary, which led to more commentaries by Michael Mann etc. Among other things, RCP8.5 is quite unrealistic with an assumption of rapidly increasing coal consumption out to 2100.
There is consensus that RCP8.5 is an unlikely scenario, and Hausfather and Peters make the point that scientists should not point to that as the basis for future projections. An article last summer also pointed out that RCP8.5 was never intended for how is too often used, i.e. as a prediction of what will happen.
But while there is consensus that RCP8.5 is not a forecast of what will be, there is recognition that it is also still within the realm of plausible outcomes and shouldn't be completely disregarded, especially as new observations and research find reinforcing (aka "positive") feedback mechanisms that are either previously unknown, more vigorous than previously estimated, or not represented in the previous generation of climate models. There is also consensus that reducing the attention given to RCP8.5 in no way argues against the immediacy or severity of the climate crisis. See Michael Mann's short commentary to hear from somebody who actually knows this stuff
http://redgreenandblue.org/2020/02/05/michael-mann-just-bad-climate-change-kept-business-usual/ (note - the chart Mann uses shows upper emissions curve from SSP85 not RCP8.5, with 2100 temperature anomaly at a rounded off 5C instead of the RCP8.5 median temp. of 4.3).
If you want to really freak out, read about the first versions of new batch of CMIP6 climate models generating an ECS much higher than the previous generation. Only a small portion of the CMIP6 models have published output yet, so this is still a developing story. And experts seem to think that it is more likely a bias in the first implementations of the CMIP6 models than a new discovery of much higher sensitivity of the climate system to our CO2 highjinks. But it also suggests that our understanding and best estimate of ECS (as measured by a doubling of CO2 after rising 1% per year) is not likely to go down with the new models.