The Science article The average U.S. family destroys a football field's worth of Arctic sea ice every 30 years states:
which carries a link to the abstract of a peer-reviewed Science paper Observed Arctic sea-ice loss directly follows anthropogenic CO2 emission. However the abstract says (in part):
Since climate-model simulations of the sea-ice loss differ substantially, we here use a robust linear relationship between monthly-mean September sea-ice area and cumulative CO2 emissions to infer the future evolution of Arctic summer sea ice directly from the observational record. The observed linear relationship implies a sustained loss of 3 ± 0.3 m2 of September sea-ice area per metric ton of CO2 emission.
My question is about the simplification of linking tons of CO2 to square meters of ice, and without reference to time. The abstract seems to simply say that there appears to be a linear relationship, and since models disagree, then this is a "good enough" way to think about it.
Is it so simple - if in 2017 no CO2 were burned the sea ice would return to normal? No. The summer sea ice would likely continue to decrease for decades. An analogy might be births and deaths of a population. While there might be a rough (or "robust") correlation between birth rate and death rate, a cessation of births in a given year would have almost no impact on death rate for perhaps a half-century.
Is there any mathematics that justifies this simple "robust linear relationship" to be causal? What does "directly follows" mean?
I'm not in any way questioning the causality between CO2 and a wide variety of changes in climate, including reduction in summer sea-ice. I'm only questioning the original quote and the quantitative relationship: 1 metric ton of CO2 costs 3 square meters of summer sea ice.
above x2: Graphics from Science Magazine.