A particle tracking model is described and used to explore the role of advection as the source of harmful algal blooms that impact the Shetland Islands, where much of Scotland's aquaculture is located. The movement of particles, representing algal cells, was modelled using surface velocities obtained from the 1.5 km resolution Atlantic Margin Model AMM15. Following validation of model performance against drifter tracks, the model results recreate previously hypothesised onshore advection of harmful algal cells from west of the archipelago during 2006 and 2013, when exceptional Dinophysis spp. abundances were measured at Shetland aquaculture sites. Higher eastward advection of Dinophysis spp. cells was also suggested during 2018. Wind roses explain this higher eastward advection during 2006, 2013 and 2018. The study suggests that the European Slope Current is important for the transport of harmful algal blooms, particularly those composed of dinoflagellates.