We present for the first time an assimilation of Thermal Emission Spectrometer (TES) water vapour column data into a Mars global climate model (MGCM). We discuss the seasonal cycle of water vapour, the processes responsible for the observed water vapour distribution, and the cross-hemispheric water transport. The assimilation scheme is shown to be robust in producing consistent reanalyses, and the global water vapour column error is reduced to around 2-4 pr-μ m depending on season. Wave activity is shown to play an important role in the water vapour distribution, with topographically steered flows around the Hellas and Argyre basins acting to increase transport in these regions in all seasons. At high northern latitudes, zonal wavenumber 1 and 2 stationary waves during northern summer are responsible for spreading the sublimed water vapour away from the pole. Transport by the zonal wavenumber 2 waves occurs primarily to the west of Tharsis and Arabia Terra and, combined with the effects of western boundary currents, this leads to peak water vapour column abundances here as observed by numerous spacecraft. A net transport of water to the northern hemisphere over the course of one Mars year is calculated, primarily because of the large northwards flux of water vapour which occurs during the local dust storm around LS=240°-260°. Finally, outlying frost deposits that surround the north polar cap are shown to be important in creating the peak water vapour column abundances observed during northern summer.