Surface water inventory of 228Ra

The ²²⁸Ra inventory in surface waters was calculated using 10 stations in the central basin (bottom depth >1000 m) where water column data for the upper 500 m were available (table S1). Two stations with bottom depths of >1000 m were excluded from the inventory calculation due to poor sampling resolution. A depth threshold of 500 m was chosen because ²²⁸Ra released from deep sea sediments is unlikely to reach the top 500 m (21); thus, any ²²⁸Ra present in this layer must be from one of the margin sources included in the mass balance (rivers, ice-rafted sediments, advection, and continental shelves). Depth-integrated inventories were calculated for each station by summing the products of the average activity of two consecutive samples and the depth interval between those samples.