Rates of ice mass loss at the calving margins of tidewater glaciers (frontal ablation rates) are a key uncertainty in sea level rise projections. Measurements are difficult because mass lost is replaced by ice flow at variable rates, and frontal ablation incorporates sub-aerial calving, and submarine melt and calving. Here we derive frontal ablation rates for three dynamically contrasting glaciers in Svalbard from an unusually dense series of satellite images. We combine ocean data, ice-front position and terminus velocity to investigate controls on frontal ablation. We find that frontal ablation is not dependent on ice dynamics, nor reduced by glacier surface freeze-up, but varies strongly with sub-surface water temperature. We conclude that calving proceeds by melt undercutting and ice-front collapse, a process that may dominate frontal ablation where submarine melt can outpace ice flow. Our findings illustrate the potential for deriving simple models of tidewater glacier response to oceanographic forcing.