I'm not sure I understand your question correctly. It is not a question of time but of system parameters.
I just dug through the literature to get this right. The only study I found that actually modelled the feedback of the rising temperature due to emitted greenhouse gases (CO2 and CH4 - methane) on the permafrost says that any model they ran with a climate sensitivity above 3°C (how the system reacts to a doubling of CO2 or equivalent in the atmosphere [1]) produced a runaway effect, that is, atmospheric CO2 content keeps rising even if anthropogenic emissions stop in 2013 (which, as you know, they didn't). The current state on climate sensitivity is 3°C +-1.5°C.
They estimated some parameters conservatively too. So it could be worse. Or better - there are still a lot of uncertainties.
- The way carbon is released into the atmosphere can happen in different ways, and that can lead to different ratios of carbon in the air and other reservoirs like water or soil in bound form, as well as different ratios of methane and CO2 (they have vastly different atmospheric lifetimes and warming potential, so this matters).
- The total amount of carbon stored in permafrost soils is unclear. Permafrost can be very thick and deep, and large areas are hard to access. edit: Estimations are that the reservoir holds about twice that of the current atmosphere. Some of that will definitely go into the ocean and biosphere, but it's still a lot.
- Permafrost has a range of interesting behaviour during the freeze-thaw cycle (if you're interested, check it out, the features it produces are really neat). It is unclear how they change with temperature differences, and it influences the melting and release of carbon.
- Other climate-related effects such as flooding, increased vegetation etc have an influence. How much? Hard to say.
- Once the permafrost starts melting, carbon is released with a time delay, which is also not clear.
.. and so on. Non-linear effects, effects highly dependent on topography, micro-climate, vegetation... very hard to model in a consistent way. So.. it might be wrong too. Let's hope so.
The new balanced state will need years to centuries to be reached too, since thawing takes time. There is permafrost beneath the northern oceans. How? It's still there from the last ice age.
A note on time: The numbers I found for increased temperature due to permafrost melting by 2100 are in the 0.1°C-0.7°C range [2]. So we're probably fine. The ones after us.. well. There are some other feedback mechanisms that still require research. It would be great if something there helped us.. or we are all horribly wrong. That would be brilliant.
I'd argue that it's happening now. On February 17, it was 81F in my back porch in Albany, NY. That is an all time record.
Right now, at 6PM EST, its 64F. It hasn't been below 20 in a week. Our average high is about 28F. We've had fewer snow events in the last 5 years than we had in any year in the 90s.
It's been warm here in Michigan also, but there were also record lows just 2 years ago, and while this year as been extraordinary, there are years in the late 1800s with big melt ups and so on.
Which I'm just saying that it is difficult to take a season of weather and be sure it fits into a broader context. I'm arguing against drawing conclusions from short periods of observation.
The parent specifically asked about "the runaway," not merely climate change. The term "runaway" refers to a feedback effect, so that climate change breeds more climate change rather than relying on our carbon emissions to fuel it.
"Now" still seems like a very good answer. I doubt that if we stopped emissions today, we'd see any positive changes for decades, and that's if we're very very lucky.
Yeah, "now" seems a good answer. A couple decades ago, I would have said "no clue, really". But now, it seems pretty clear.
And yes, even without positive feedback, it would take several decades for forcing to relax after carbon emissions ceased. Which is very unlikely.
So I really do think that it's time to consider active mitigation. But I'm not even very optimistic about that, given the likely positive feedbacks. Requisite mitigation requirements would also be going exponential. And where will the energy for that come from?
