Comparison of the 30-year running mean of monthly mean September Arctic sea-ice area with cumulative anthropogenic CO2 emissions reveals a linear relationship that implies a loss of 3 ± 0.3 square meters of September sea-ice area per metric ton of CO2 emission.
Based on this simple empirical relationship it is possible to directly estimate that an additional 1000 Gt of CO2 emissions will result in no Arctic summer sea ice. For current emissions of 35 Gt CO2 per year, the limit of 1000 Gt will be reached before mid century. Internal variability causes an uncertainty of around 20 years as to the first year of a near-complete loss of Arctic sea ice.
The results also imply that measures taken to mitigate CO2 emissions will slow down the loss of Arctic summer sea ice. In particular, for cumulative future total emissions corresponding to a 1.5°C global warming target, in other words for cumulative future emissions significantly less than 1000 Gt, Arctic summer sea ice has a chance of long-term survival. Observed Arctic sea-ice loss directly follows anthropogenic CO2 emission, Dirk Notz and Julienne Stroeve, Science, 03 Nov 2016 DOI: 10.1126/science.aag2345