Since seawater is supersaturated in CaCO3, the dissolution would have to happen on top of the ice, and draw its CO2 from the ambient air above it. That I would think is kinetically limited. To the extent that the ice melts at the bottom of the ice that is exposed to warming seawater in the spring, the carbonate will likely sink to the ocean floor, in effect taking alkalinity away from the ocean water column. (So now we are relying on the CO2 that sank not to return to the surface where it would outgas.) Whether bottom melting or top melting will dominate is difficult to say, but for freshwater melt to dissolve the carbonate requires sufficient exposure time to ambient air to suck up CO2 and dissolve the crystal structure, before the water flows into the sea an gets mixed with seawater to the point that it is supersaturated in calcium carbonate. Your best bet is probably rain hitting the surface of the ice, but even though the pH of rainwater is low, there is very little CO2 available. In any event, to the extent that the freeze/thaw cycle results in carbonate additions to the sediment, the net effect is a reduction in the ocean’s ability to hold CO2.
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Overall, sea ice melt is increasing Arctic water acidification, and sea ice production clearly has the opposite results due to the physical barrier between the water and air. If so, why would sea ice production not be considered an OAE method?
Moreover, why is the brine production, which drags surface GHGs to the seabed, not recognized as a CDR? Sending biomass to the seabed is recognized as such.