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Relative sea-level variations during the late Pleistocene can only bereconstructed with the knowledge of ice-sheet history. On the other hand, theknowledge of regional and global relative sea-level variations is necessaryto learn about the changes in ice volume. Overcoming this problem ofcircularity demands a fully coupled system where ice sheets and sea levelvary consistently in space and time and dynamically affect each other. Herewe present results for the past 410 000 years (410 kyr) from the couplingof a set of 3-D ice-sheet-shelf models to a global sea-level model, which isbased on the solution of the gravitationally self-consistent sea-levelequation. The sea-level model incorporates the glacial isostatic adjustmentfeedbacks for a Maxwell viscoelastic and rotating Earth model with coastalmigration. Ice volume is computed with four 3-D ice-sheet-shelf models forNorth America, Eurasia, Greenland and Antarctica. Using an inverse approach,ice volume and temperature are derived from a benthic δ<sup>18</sup>O stackedrecord. The derived surface-air temperature anomaly is added to thepresent-day climatology to simulate glacial–interglacial changes intemperature and hence ice volume. The ice-sheet thickness variations are thenforwarded to the sea-level model to compute the bedrock deformation, thechange in sea-surface height and thus the relative sea-level change. Thelatter is then forwarded to the ice-sheet models. To quantify the impact ofrelative sea-level variations on ice-volume evolution, we have performedcoupled and uncoupled simulations. The largest differences of ice-sheetthickness change occur at the edges of the ice sheets, where relative sea-levelchange significantly departs from the ocean-averaged sea-level variations

A fully coupled 3-D ice-sheet–sea-level model: algorithm and applications