“…Hansen (2007) suggested that a 10-year doubling time was plausible pointing out that such a doubling time from a base of 1 mm per year ice sheet contribution to sea level in the decade 2005-2015 would lead to a cumulative 5 m sea level rise by 2095. ”
While we know that in fact the 2005-2015 base to start the doubling from is probably somewhat higher than that.
As with any compounding calculation the final result is very dependent on the starting conditions. Hansen notes in the paper that recent data suggests a 6 to 8 year doubling rather than the 10 year he uses in Figure 7. So his sea level rise in 2100 is very ‘conservative’.
"Since the beginning of the 20th century, the seas have continued to rise at an average rate of 1.7 ± 0.5 mm per year, according to the IPCC (Bindoff et al., 2007). This increase, however, has not happened at a constant rate. The first noted increase was over the period of 1961 to 2003, when the average rate of sea level rise was 1.8 ± 0.5 mm per year (Church et al, 2001; Church and White, 2006; Bindoff et al., 2007). Global mean sea level measurements have become even larger since 1993. According to the IPCC, “For the period 1993 to 2003, the rate of sea level rise is estimated from observations with satellite altimetry as 3.1 ± 0.7 mm yr–1, significantly higher than the average rate.”
So starting at 3.1mm/yr and using that rate doubling in say every 8 years gives over 75 metres rise before 2100, i.e. all grounded ice in the world melted. Most coastal cities (including most of London, Washington, Tokyo, Berlin and Beijing, for example) gone.
Not a good look!
Alternatively, if we use Hansen’s 1.0 mm rise contribution from ice sheets C2010, then we find (as Hansen’s figure 7 shows) we get to 5 metres sea level rise by 2095 with 10-year doubling in the rate of ice sheet loss, by year 2080 with 8-year doubling, and by 2065 with 6-year doubling; and of course the curves just keep on getting steeper after those dates; such is the nature of exponential growth. That is, the melt rate will continue to increase until the volume of ice left to melt starts to diminish, and then the melt will continue until all the ice is gone.
Neither of these approaches yield pleasant outcomes for humanity.