The "small wave" in the fast feedback that Hansen & Sato 2012 are referring to is the bump in their Figure 7 that shows that that as the increase in radiative forcing (above pre-industrial) approaches 3 W/sq m [...]
This is a misunderstanding. Here is Hansen and Sato's quote regarding a "small wave":
The fast-feedback climate sensitivity is a reasonably smooth curve, because the principal fast-feedback mechanisms (water vapor, clouds, aerosols, sea ice) do not have sharp threshold changes. Minor exceptions, such as the fact that Arctic sea ice may disappear with a relatively small increase of climate forcing above the Holocene level, might put a small wave in the fast-feedback curve.
This quote has nothing to do with the large bump (peak) in the center of the Fast Feedback + Surface Albedo curve (just to the right of the Holocene conditions). In fact, the latter bump is due to the "possibility of a hysteresis effect that makes demise of the Antarctic ice sheet difficult, thus stretching out toward larger forcing the ice sheet addition to the fast-feedback sensitivity".
See also the following SkepticalScience comment by Tom Curtis:
http://www.skepticalscience.com/hansen-and-sato-2012-climate-sensitivity.html#80362
While I agree with jai's response to Steven's post, that Hansen & Sato 2012 are hindcasting using approximate GCM projections that were calibrated primarily by paleo records, and that as H&S's Figure 7 does not adequately differentiate between various slow, intermediate and fast feedback factors, it is difficult to interpret exactly what they mean, and thus it would be good if the ACME Earth System Model project were to put out some early results of their findings (which includes any possible Antarctic hysteresis). Unfortunately, as the final ACME ESM results may not be available for 10 years or so, we are left with commenting about the information at hand. Therefore (not to beat H&S 2012 to death), I provide the addition quote from H&S 2012:
Quote form Hansen & Sato 2012: "The equilibrium climate sensitivity for a positive (warming) from the Holocene state depends on the magnitude of the forcing. Hansen et al. (2008) conclude that the mean sensitivity over the entire range from the Holocene to a climate just warm enough to lose the Antarctic ice sheet is almost 6°C for doubled CO2, but most of the surface albedo feedback in that range is caused by loss of the Antarctic ice sheet. The decreasing amplitude of glacial-interglacial temperature oscillations between the late Pleistocene and Pliocene (Fig. 4b) suggests that the sensitivity is smaller as climate warms from the Holocene toward a Pliocene-like climate."
Therefore, it is reasonable to conclude that the 6 C "wave" on H&S Fig 7 is associated with the Antarctic ice sheet, and while I do agree with jai that Arctic amplification must contribute to this 6 C "wave"; all of my prior comments were predicated on polar amplification (both Arctic and Antarctic amplification), as Hansen and Sato project a sea-level rise of up to 5m by 2100; which in my book means that they must believe that a collapse of a significant portion of the West Antarctic Ice Sheet, WAIS, is probably by 2100. In this regards the National Research Council, NRC, (2013), "Abrupt Impacts of Climate Change Anticipating Surprises", The National Academies Press, Washington D.C. makes the following statements:
"However, a large part of the West Antarctic Ice Sheet (WAIS), representing 3-4 m of potential sea-level rise, is capable of flowing rapidly into deep ocean basins. Because the full suite of physical processes occurring where ice meets ocean is not included in comprehensive icesheet models, it remains possible that future rates of sea-level rise from the WAIS are underestimated, perhaps substantially. Improved understanding of key physical processes and inclusion of them in models, together with improved projections of changes in the surrounding ocean, are required to notably reduce uncertainties and to better quantify worst-case scenarios. Because large uncertainties remain, the Committee judges an abrupt change in the WAIS within this century to be plausible, with an unknown although probably low probability.
...
A retreat of Thwaites Glacier in West Antarctica could give a much wider and deeper calving front than any observed today, so the "speed limits" suggested by Pfeffer et al. (2008) may not apply (Parizek et al., 2013)."
Furthermore, Eric Rignot (2014) makes the following statements on the topic of the WAIS stability:
"We announced that we had collected enough observations to conclude that the retreat of ice in the Amundsen sea sector of West Antarctica was unstoppable, with major consequences – it will mean that sea levels will rise one metre worldwide. What's more, its disappearance will likely trigger the collapse of the rest of the West Antarctic ice sheet, which comes with a sea level rise of between three and five metres. Such an event will displace millions of people worldwide.
Two centuries – if that is what it takes – may seem like a long time, but there is no red button to stop this process.
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Thwaites glacier started to accelerate after 2006 and in 2011 we detected a huge retreat of the glacier grounding lines since 2000. Detailed reconstructions of the glacier bed further confirmed that no mountain or hill in the back of these glaciers could act as a barrier and hold them up; and 40 years of glacier flow evolution showed that the speed-up was a long story.
At the current rate, a large fraction of the basin will be gone in 200 years, but recent modelling studies indicate that the retreat rate will increase in the future.
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Controlling climate warming may ultimately make a difference not only about how fast West Antarctic ice will melt to sea, but also whether other parts of Antarctica will take their turn. Several "candidates" are lined up, and we seem to have figured a way to push them out of equilibrium even before warming of air temperature is strong enough to melt snow and ice at the surface.
Unabated climate warming of several degrees over the next century is likely to speed up the collapse of West Antarctica, but it could also trigger irreversible retreat of marine-based sectors of East Antarctica. Whether we should do something about it is simply a matter of common sense. And the time to act is now; Antarctica is not waiting for us."
Furthermore, the first attached image of the Amundsen Sea Sector ice mass loss rates (from the European Space Agency - GOCE satellite 2014), shows that ice mass loss from this area has been (2009-2012) contributing an average of 0.51 mm/year (out of 3.2 mm/year) to global sea-level rise. Furthermore, the second attached image (from Mouginot, J., E. Rignot, and B. Scheuchl, (2014), "Sustained increase in ice discharge from the Amundsen Sea Embayment, West Antarctica, from 1973 to 2013", Geophys. Res. Lett., 41, doi:10.1002/2013GL059069) shows the evolution of ice mass loss from the Amundsen Sea Embayment marine glaciers, that shows particularly that ice mass loss from the Thwaites Glacier is continuing to accelerate. Therefore, if Rignot points-out that without the acceleration of ice mass loss from the WAIS glaciers that it could take as much as 200-years for the WAIS to partially collapse, then it is not unreasonable to assume that as the acceleration of ice mass loss from the WAIS is likely to continue, that the partial collapse of the WAIS is probable (or at least as the NRC states plausible) by 2100.
I will post more on the topic of significant polar amplification by 2100 shortly (or if you do not want to wait you can look at the threads in the Antarctic folder)