Increasingly, models of surface mass loads are used either to correct geodetic time coordinates by removing seasonal and other noise, or for comparison with other geodetic parameters. However, models of surface loading obtained by simply combining the mass redistribution due to individual phenomena will not in general be self-consistent, in that (i) the implied global water budget will not be mass-conserving, and (ii) the modelled sea level will not be an equipotential surface of Earth's total gravity field. We force closure of the global water budget by allowing the passive ocean to change in mass. This medium-term passive ocean response will not be a uniform change in non-steric ocean surface height, but must necessarily be spatially variable to keep the passive ocean surface on an equipotential. Using existing load models, we demonstrate the effects of our consistency theory. Geocenter motion is amplified significantly, by up to 43%.