We report on the strong enhancement of tropical winds in the martian atmosphere during the Global Dust Storm of Martian Year 34, as revealed by an assimilation of temperature and dust observations into a martian global climate model. We demonstrate that global super-rotation almost doubled at the peak of the dust storm period, as compared to Mars Year 33, which did not have a Global Dust Storm. The enhanced westerly jet played a key role in the initial stages of the dust storm, transporting dust across the planet and between different lifting centers. By tracking the progression of dust plumes, we derive estimates of wind speeds in the lower tropical atmosphere of 10-15 m/s below 10 km. The tropical region was dominated by diurnal and semi-diurnal tides, with a significant amplification of the gravest Kelvin mode during the onset of the storm.