# How can every ton of CO2 cost 3 square meters of summer sea ice per year - quantitatively?

The Science article The average U.S. family destroys a football field's worth of Arctic sea ice every 30 years states:

Every additional metric ton of carbon dioxide (CO2) puffed into the atmosphere appears to cost the Arctic another 3 square meters of summer sea ice.

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.

• It looks as if they just divided two quantities (output/input) that are related through a chain of actual processes, but ignoring what happens in those processes. That would be very hard to do because input and output differ widely in time and space, so the intermediate steps are diverse. This is almost a case of correlation without causation. Nov 4 '16 at 11:12
• The articles say every metric ton of CO2 reduces about 3 ± 0.3 m^2 of sea ice, you say km in your question. 3 square meters per metric ton of CO2 sounds in the range of plausible. Nov 5 '16 at 7:30
• I worry about giving advice on a site that discourages conversation, but my feeling is leave the check and vote up in the answer, but correct the title, maybe make a footnote that a correction was made. Nov 5 '16 at 8:06
• @userLTK thank you for pointing out the error. I've fixed the title to agree with the units in the quotes - square meters, not square kilometers.
– uhoh
Nov 5 '16 at 10:18