Is it possible to have an oceanic limnic eruption?
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I don't think so, because for a limnic eruption to occur, excessive gas needs to be involved. In the acidic zone there is no gas to my understanding.
The article says that this is being caused by the increase of carbon dioxide in the water.
But it's emphasis is on that increase coming from the surface, so I'd still support your reply, since the limbic eruption requires that the source of the carbon dioxide be beneath the water, and not come from the surface.
Based on my amateur understanding, it actually seems possible if climate change gets bad enough. When the calcium carbonate of plankton, seashells, and limestone reacts with the carbonic acid that defines the acidic zone, you do get an increase of gaseous carbon dioxide in the water.
The main chemical reaction is
CaCO3 + 2 H2CO3 -> Ca(2+) + 2 HCO3(-) + CO2 + H2O
The chemical reaction by which seashells and limestone dissolve, releasing CO2 and increasing the gas pressure. The CO2 can be dissolved back into the water via
CO2 + H2O <-> H2CO3 (<-> H(+) + HCO3(-))
While dissolving limestone and seashells neutralize the acid in the short term, this just means that more CO2 will be pulled in from the atmosphere and from the freshly produced CO2 to increase the acidity again. Luckily this isn't an infinite loop - half the CO2 gets stuck in HCO3- each time - so this would actually be a carbon sink from a purely chemical perspective. Ecologically, the dissolving of plankton would take away a carbon sink and so accelerate climate change.
As for the limnic eruption, while shellfish and plankton live in shallow enough water that them dissolving would probably be able to outgas into the atmosphere quickly enough that there is never a toxic concentration, limestone deposits can be found at great depths and can be over a kilometer thick. Just because the ocean can dissolve a 0.2mm plankton shell quickly enough for it to die doesn't mean it can eat through 2km of limestone at an appreciable rate. It seems possible that ocean acidification would increase fast enough that the limestone isn't yet all gone by the time it erodes fast enough to form a convective plume, sucking in fresh acidic ocean from the surrounding water while carbonated but less acidic water quickly rises to the ocean's surface, outgassing the carbon dioxide like a limnic eruption.
While on average the dissolution of limestone would be a carbon sink, a lot of the ocean floor is not limestone, and so these places would draw in CO2 while places that do have limestone deposits would vent CO2. I don't know if it would be fast enough to produce a toxic concentration of CO2. I also don't know if by the time oceanic limestone gets eaten away at this rate the earth would still be habitable by humans.