Observations and an ocean box model are combined in order to test the adequacy of the freshwater forcing hypothesis to explain abrupt climate change given the uncertainties in the parameterization of vertical buoyancy transport in the ocean. The combination is carried out using Bayesian stochastic inversion, which allows us to infer changes in the mass balance of Northern Hemisphere (NH) ice sheets and in the meridional transports of mass and heat in the Atlantic Ocean that would be required to explain Dansgaard-Oeschger Interstadials (DOIs) from 30 to 39 kyr B.P. 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. The inversion suggests that the duration of the DOIs should be directly related to the growth of land ice. Our results are unaffected by uncertainties in the representation of vertical buoyancy transport in the ocean. However, the solutions are sensitive to assumptions about physical processes at polar latitudes.