# Revelle factor

The Revelle factor (buffer factor) is the ratio of instantaneous change in carbon dioxide (CO$_2$) to the change in total dissolved inorganic carbon (DIC), and is a measure of the resistance to atmospheric CO$_2$ being absorbed by the ocean surface layer. The buffer factor is used to examine the distribution of CO$_2$ between the atmosphere and the ocean, and measures the amount of CO$_2$ that can be dissolved in the mixed surface layer. It is named after the oceanographer Roger Revelle. The Revelle factor describes the ocean's ability to uptake atmospheric CO$_2$, and is typically referenced in global carbon budget analysis and anthropogenic climate change studies.
Revelle factor = ⁠Δ[CO$_2$]/ [CO$_2$]⁠ / ⁠Δ[DIC]/[DIC]⁠ where Δ[CO$_2$] / [CO$_2$] is the instantaneous change in pCO$_2$ and Δ[DIC] / [DIC] is the instantaneous change in dissolved inorganic carbon at the oceans surface.

## Thermodynamics

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.

## DIC

The species of DIC present in ocean waters are dependent on the pH of the system, and are illustrated by the Bjerrum plot below (Figure 1). Carbonate is dominant in higher pH (basic) environments, whereas carbon dioxide is dominant in lower pH (acidic) environments. Bicarbonate ions are abundant in relatively mid-pH waters. As the pH decreases, most of the DIC will be present as CO$_2$ and hence increases its partial pressure (pCO$_2$), and the buffer factor will increase. An increased buffer factor results in a decreased buffering effect, which could lead to the uptake of more CO$_2$ from the atmosphere, and decreasing the pH even more.
Figure 1: Curves illustrating the molar fraction of carbonate species present in seawater across pH, with salinity set at 5,000ppm, and temperature set to 25 degrees Celsius. Note temperature and salinity affect carbonate species present, and vary with location and season.
DIC and alkalinity govern carbonate and acid-base chemistry in the world's oceans, and their effects on the Revelle factor is no exception. The ratio of DIC to total alkalinity, and the changes in pCO$_2$ are the main cause of Revelle Factor variability. Higher levels of DIC result in a lower Revelle factor, and consequently a larger buffering effect. Higher levels of pCO$_2$ results in a higher Revelle factor, a positive feedback loop, and consequently a smaller buffering effect. Typically, the buffer factor ranges between 8 and 13.

## Anthropogenic CO$_2$

The capacity of the ocean waters to take up surplus (anthropogenic) CO$_2$ is inversely proportional to the value of the Revelle factor. Hence, in modern-day oceans, it is possible to see the concentrations of anthropogenic CO$_2$ by measuring the Revelle factor; the lower the Revelle factor, the greater the amount of anthropogenic CO$_2$. 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 of the North Atlantic. The North Pacific has higher Revelle factors, and has lower anthropogenic CO$_2$. This is due to the fact that the alkalinity values in the North Pacific are as much as 100μmol/kg lower than those in the North Atlantic.

## The Revelle effect

The Revelle effect describes how only a small fraction of pCO$_2$ is present in ocean water when much larger amounts are added to the atmosphere. Depending on the alkalinity of the water, DIC is either present as CO$_3$, HCO$_3$, or CO$_2$. When the pH is high (basic) the buffering effect is greatest, causing much of the DIC to exist as HCO$_3$ or CO$_3$, and not CO$_2$. So, the greater the buffering effect (low Revelle Factor) the more DIC occurs as CO$_3$ or HCO$_3$, effectively lowering the pCO$_2$ levels in both the atmosphere and ocean.