Geologic records and climate model simulations suggest that changes in the meridional heat transport in the Atlantic Ocean were involved in the abrupt warming events – the so-called Dansgaard-Oeschger Interstadials (DOIs) – that punctuated an otherwise cold Greenland climate during the last glacial period. However, the role of Northern Hemisphere (NH) ice sheets in these events remains a subject of controversy. Here we report on the first attempt to combine quantitatively a paleo-temperature proxy with simplified ocean models, with the specific purpose of extracting information about the changes in mass balance of the NH ice sheets during the last glaciation. A Greenland paleotemperature record is combined with the climate models using Bayesian Stochastic Inversion (BSI) in order to estimate the changes that would be required to alter the Atlantic Ocean mass and heat transports between ~30 and 39 thousand years ago. The mean sea level changes implied by changes in NH ice sheet mass balance agree in amplitude and timing with reconstructions from the geologic record, which gives some support to the freshwater forcing hypothesis. Our results are unaffected by uncertainties in the representation of vertical buoyancy transport in the tropical ocean, in large part because the global adjustments to high latitude freshening bypass the tropics and affect sinking rate in the opposite pole. However, the solutions are sensitive to assumptions about physical processes at polar latitudes. We find that the inversion reproduces the gradual changes in sea level and Antarctic temperature inferred from the independent evidence provided by proxy records. The Greenland warm event lasting over 3000 years (DOI 8) can be explained by sustained growth of NH ice sheet and reduced supply of icebergs to the North Atlantic. Our results indicate a more involved role of the NH ice sheets than previously thought, in which both collapse and subsequent growth would be required to explain the full series of the long (> 3000 years) warm events recorded in Greenland ice. / text