Water isotope ratios in ice cores and marine sediments are a key indicator of past temperature and global ice volume. Quantitative interpretation of these ratios requires understanding of the storage capacity and exchanges among the ocean, atmosphere, and cryosphere. We combine numerical models of ice dynamics and tracer transport to predict bulk ice properties by simulating the fine layering of ice sheets locally validated at ice core sites. The 18O/16O content of ice sheets is found to vary between the present and 20 kyr ago from -34? to -37? for Greenland, from -41? to -42.5? for West Antarctica, and always remained near -56.5? for East Antarctica. Their combined effect on sea-water 18O/16O is a 0.08--0.12? increase 20 kyr ago, a 1.11? decrease if ice sheets were to vanish. We confirm that ice volume changes in Antarctica and Greenland linearly affect ocean composition, though at different rates.