# Units and Terms

## Per Meg Units

We report oxygen measurements as changes in the O2/N2 ratio of air relative to a reference.  We compute

δ = ((O2/N2)sample – (O2/N2)reference)/ (O2/N2)reference)

where (O2/N2)sample is the O2/N2 mole ratio of an air sample and (O2/N2)reference is the O2/N2 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 O2/N2 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 O2/N2 ratio of the air has decreased since the 1980s.

The changes we observe in the O2/N2 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 O2/N2 ratio, we write it as δ(O2/N2).

The O2/N2 ratio can vary due to changes in either O2 or N2.  Air contains roughly 20.9% molecular oxygen (O2) and 78.1% molecular nitrogen (N2).  Because air contains several times more N2 than O2, and because the natural sources and sinks of N2 are much smaller than those of O2, the changes in O2/N2 ratio mostly reflect changes in O2.

## Atmospheric Potential Oxygen (APO)

Atmospheric Potential Oxygen (APO) data, reported on this site, is computed by combining the O2/N2 and CO2 data according to

APO =  δ(O2/N2) + 1.1/0.20946(XCO2-350)

where δ(O2/N2) is the O2/N2 ratio in per meg units and XCO2 is the CO2 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 O2: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 O2 concentration that an air sample would have if the CO2 concentration were adjusted by a typical land plant to exactly 350 ppm through photosynthesis or respiration.