Fortunately those 3°C or more "use to be happening" by about 2800 a.d.
I got the reply I expected. In a nutshell, if fosil fuel related emissions ceased right now -CO2, methane from coal mining and fracking, sulphates- models show a drop of 6 to 8 ppmv of CO2 in a decade as calculated from their modules modelling natural sinks and sources. He thinks the final value will be a bit more, not as optimistic as me -10 to 12 ppm-. This comes from different reasons, including a concern we share which I'll explain below.
Those 6 to 8 (or more) ppmv during the first decade seem to drop slower than I expected for the following decades. This has little variation in spite of transient effects of previous emissions: the still-to-rise temperatures are not enough to induce great changes in sources and sinks.
A different picture comes if we wait until we reach 500 or 600 ppmv. In that case there is a change of the ocean as a sink and permafrost emissions activate as a consequence of the transient effects. In such cases, CO2 concentration drops slowly. Any inference about what happens with 850 or 1100 ppmv is pretty much useless.
The concern we share is about how different models do when they estimate the ocean mixed layer. Basically they can be either pretty bad, bad or worse at it. As the ocean mixed layer and the role of oceans as carbon and heat sinks are closely related, conclusions in the long term are to be taken with a pinch of salt.
A lesson comes from
the paper by Yu Kosaka & Shang-Ping Xie that was mentioned before. The title says it all: "Recent global-warming hiatus tied to equatorial Pacific surface cooling" and the content, in a nutshell, refers they taking a coupled model and modifying it to get about 8% of the ocean surface to be a temperature input and not a state. The area chosen was all the equatorial Pacific from the American coasts to longitude 180°, that is, the ENSO area. As a result they got the "pause" pretty well [figure 1 - black line, observed global temperatures; purple line, global temperatures got with the original model; red line, global temperature got with the modified model]. But both models got similar results for ocean heat content [extended data figure 3] but they got more realistic values for the net radiative imbalance with the modified model.
In certain scientific website an interesting debate arose between a climatologist and a Finnish gentleman who objected both the blatant violation of conservation laws and the amount of OHC exceeding the real estimates for the period. The answer to that is both valid and revealing: the model understands what happens between the ocean surface and outer space, the differences in heat for that 8% of the global oceans is something that doesn't affect the outcome, and it's pretty valid because the area chosen is one of upwelling, so you have the heat difference temporarily ditched. Of course, it'll arrive the point that heat is gonna come back and haunt you, meaning, at some point in the timeline the model renders itself invalid, and by force that is to happen earlier than later.
For me this story makes easier to explain how a model is to be valued. Models are basically tools for research and control, and they give some orientation about what the future may hold. The fact that some items researched, like the equilibrium climate sensitivity, need models run for thousand of years doesn't make them a prediction tool.