The Revelle factor is a measure of the resistance to atmospheric carbon dioxide being absorbed by the ocean surface layer posed by bicarbonate chemistry. It is named after the oceanographer Roger Revelle.
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In order to enter the ocean, carbon dioxide gas has to partition into one of the components of carbonic acid: carbonate ion, bicarbonate ion, or protonated carbonic acid, and the product of these many chemical dissociation constants factors into a "back-pressure" that limits how fast the carbon dioxide can enter the surface ocean.
The capacity of the ocean waters to take up surplus (anthropogenic) CO2 is inversely proportional to the value of the Revelle factor. Hence, in modern day oceans, it is possible to see the concentrations of anthropogenic CO2 by measuring the Revelle factor; the lower the Revelle factor, the greater the amount of anthropogenic CO2[1]. Low Revelle factors are typically found in the warmer tropical to subtropical waters, whereas higher Revelle factors are found in the colder high latitude waters. The North Pacific has much greater Revelle factors due to its greater alkalinity, and hence has lower anthropogenic CO2.
If CO2 in the atmosphere is increased by one part per million, the CO2 in the ocean is increased by only a tenth of a part per million, because of the way that the carbon dioxide in the water is partitioned between carbonate ions and bicarbonate ions and free CO2. As additional CO2 is added, it tips the equilibrium between these three kinds of carbon dioxide, so because of the Revelle Factor, it means that you can add a large amount of CO2 to the air without adding much to the water. This is known as the Revelle Effect[2].