  Magmatism and volcanism transfer carbon from the solid Earth into the climate
system. This transfer may be modulated by the glacial/interglacial cycling of
water between oceans and continental ice sheets, which alters the surface
loading of the solid Earth. The consequent volcanic-carbon fluctuations have
been proposed as a pacing mechanism for Pleistocene glacial cycles. This
mechanism is dependant 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 some questionable assumptions made in previous work. Our
model calculates the carbon flux, accounting for the thermodynamic effect of
mantle carbon: reduction of the solidus temperature and a deeper onset of
melting. We analyse models forced by idealised, periodic sea level and conclude
that fluctuations in melting rate are the prime control on magma and carbon
flux. 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. Peaks
in mid-ocean ridge emissions lag peaks in sea-level forcing by less than about
20 kyr and the lag could well be shorter. The amplitude and lag are sensitive
to the rate of melt segregation. The lag is much shorter than the time it takes
for melt to travel vertically across the melting region.
