# Units and Terms

## Per Meg Units

We report oxygen measurements as changes in the O_{2}/N_{2} ratio of air relative to a reference. We compute

δ = ((O_{2}/N_{2})_{sample} – (O_{2}/N_{2})_{reference})/ (O_{2}/N_{2})_{reference})

where (O_{2}/N_{2})_{sample }is the O_{2}/N_{2} mole ratio of an air sample and (O_{2}/N_{2})_{reference} is the O_{2}/N_{2} mole ratio of our reference. Our reference is based on tanks of air pumped in the mid 1980s which we store in our laboratory.

The quantity δ is zero if the sample has the same O_{2}/N_{2} ratio as the reference and negative if the sample has a lower ratio than the reference. δ values of air samples collected today are negative because the O_{2}/N_{2} ratio of the air has decreased since the 1980s.

The changes we observe in the O_{2}/N_{2} ratio are tiny. Typical air in 2008 had δ a value of around -0.000400. The decrease from year to year is around -0.000020. We could multiply δ by 100 and report δ in percent units, or multiplying by 1000 and report in permil units. But because the changes in δ are so small, we instead multiply δ by 1000000 and express δ in “per meg” units. Thus -0.000400 equals -400 per meg. One per meg equals 0.001 permil or 0.0001 percent.

Similar δ units are used to report changes in isotopic abundance. To indicate that δ refers to changes in the O_{2}/N_{2} ratio, we write it as δ(O_{2}/N_{2}).

The O_{2}/N_{2} ratio can vary due to changes in either O_{2} or N_{2}. Air contains roughly 20.9% molecular oxygen (O_{2}) and 78.1% molecular nitrogen (N_{2}). Because air contains several times more N_{2} than O_{2}, and because the natural sources and sinks of N_{2} are much smaller than those of O_{2}, the changes in O_{2}/N_{2} ratio mostly reflect changes in O_{2}.

## Atmospheric Potential Oxygen (APO)

Atmospheric Potential Oxygen (APO) data, reported on this site, is computed by combining the O_{2}/N_{2} and CO_{2} data according to

APO = δ(O_{2}/N_{2}) + 1.1/0.20946(X_{CO2}-350)

where δ(O_{2}/N_{2}) is the O_{2}/N_{2} ratio in per meg units and X_{CO2 }is the CO_{2} mole fraction in ppm units_{, }and 1/0.2095 is a conversion factor from ppm to per meg, 1.1 is an estimate of the average O_{2}:C ratio for land photosynthesis or respiration, and 350 is an arbitrary additive constant. APO is reported in per meg units.

APO is a measure of the O_{2} concentration that an air sample would have if the CO_{2} concentration were adjusted by a typical land plant to exactly 350 ppm through photosynthesis or respiration.