Consequences of glacial cycles for magmatism and carbon transport at mid-ocean ridges

Submarine and subaerial volcanism transfers carbon from the solid Earth into
the atmosphere. Volcanic activity may be modulated by glacial/interglacial
cycling of water between continental ice sheets and oceans. It has been argued
that the consequent fluctuations in volcanic carbon emission could have paced
Pleistocene glacial cycles. This depends on the amplitude and lag of the
mid-ocean ridge response to sea-level changes. Here we develop and analyse a
new model for that response, eliminating the questionable assumptions made in
previous work. Our model accounts for the thermodynamic effect of mantle
carbon: reduction of the solidus temperature and a deeper onset of melting. We
discuss models forced by idealised, periodic sea level to conclude that
fluctuations in melting rate are the prime control on magma and carbon flux (in
contrast to previous work). Our models predict lags of less than 10 kyr between
peaks in the rate of sea-level change and peaks in mid-ocean ridge emissions.
We also discuss a model forced by a reconstruction of eustatic sea level over
the past 800 kyr. It indicates that peak-to-trough variations of magma and
carbon flux are up to about 20% and 10% of the mean flux, respectively.