How much Arctic fresh water participates in the subpolar overturning circulation?

Fresh Arctic waters flowing into the Atlantic are thought to have two primary fates. They may be mixed into the deep ocean as part of the overturning circulation, or flow alongside regions of deep water formation without impacting overturning. Climate models suggest that as increasing amounts of fresh water enter the Atlantic, the overturning circulation will be disrupted, yet we lack an understanding of how much fresh water is mixed into the overturning circulation's deep limb in the present day. To constrain these fresh water pathways, we build steady-state volume, salt, and heat budgets east of Greenland that are initialized with observations and closed using inverse methods. Fresh water sources are split into oceanic Polar Waters from the Arctic and surface fresh water fluxes, which include net precipitation, runoff, and ice melt, to examine how they imprint the circulation differently. We find that 65 mSv of the total 110 mSv of surface fresh water fluxes that enter our domain participate in the overturning circulation, as do 0.6 Sv of the total 1.2 Sv of Polar Waters that flow through Fram Strait. Based on these results, we hypothesize that the overturning circulation is more sensitive to future changes in Arctic fresh water outflow and precipitation, while Greenland runoff and iceberg melt are more likely to stay along the coast of Greenland.