It seems difficult to determine what scientists have done with regards to modeling permafrost carbon emissions in CMIP5. However, to me the linked reference seems to indicate that CMIP5 used land models that did not represent carbon emissions from permafrost very well (and thus they have low confidence in the projected emissions); and that scientists will try to do a better job in CMIP6. ...
That's my impression as well. Here is another very nice paper that comes pretty much to the same conclusion.
Schuur etal (including Schaefer, McGuire, ...), Climate change and the permafrost carbon feedback, Nature 2015 (doi:10.1038/nature14338
, free copy here
The paper is based on research that was published after AR5. On page 177 it says:
Next steps for model–data integration
The Earth system models analysed for the IPCC AR5 did not include permafrost carbon emissions, and there is a need for the next assessment to make substantive progress analyzing this climate feedback. It is clear, even among models that are currently capable of simulating permafrost carbon emissions, that improvements are needed to the simulations of the physical and biological processes that control the dynamics of permafrost distribution and soil
More on the shortfalls of the current permafrost carbon models (same page).
The bad news are outlined on page 176:
There is uncertainty, but the vulnerable fraction does not appear to be twice as high or half as much as 5%–15%, based on this analysis. Ten per cent of the known terrestrial permafrost carbon pool is equivalent to, 130–160 Pg carbon.
If my math is correct, that equates to 475 to 590 Gt CO2
to the end of this century. The only good news: According to them, most of it will be released constantly in form of CO2-carbon. An abrupt release is not likely, they conclude:
projected emissions of CO2 and CH4 from thawing permafrost are unlikely to occur at a speed that could cause abrupt climate change over a period of a few years to a decade
The sad thing is. Pretty much all of the carbon budget estimates and mitigation pathways (at least those I am aware of) are base on the AR5-framework. Consequently, most of them do ignore the emissions from permafrost carbon feedback.
Taking into account that the best estimate for these emissions is 475 to 590 Gt CO2 (until 2100), most of these budget-estimates and pathways are imho based in an alternative reality, or in la la land (with a lot of arctic sea ice left in the summers after 2050?). What is the best guess for the 2C-carbon budget 1.000 Gt CO2?
Of course this is not news to you guys ... but it gets constantly ignored elsewhere. And even than most of the 2C-pathways require absurd amounts of negative emissions. What a mess ...
Ah, all will be fine. Let's simple built a billion E-SUVs, just under 2 tones each - those who enable us to finally enjoy our wonderful nature & stop - en passant - the ongoing mass extinction (needs a cool app of course)