The following units are in use:

Volume units: mainly used for gases, such as volume % or % (v), and ppm (v)

80% (v) N₂ in the atmosphere means that 1 liter of air contains 0.8 liter of pure N₂ gas

360 ppm (v) CO₂ = 360 10^-6 liter of pure CO₂ per liter of pure air.

Mole % are equivalent to volume % and are expressed as moles of N₂ per total number of moles (80 moles N₂ out of 100 moles of air)

Partial pressures (expressed in bar, millibar, or atmosphere) are also equivalents to volume % and mole %: for N₂, 80 % (v) translates into a partial pressure of N₂ that is 80% of the total pressure. The total atmospheric pressure at sea level is 1 atmosphere, so the partial pressure of N₂ is 0.8 atmosphere.

Mass (weight) based units: %, ppm

When we want to express the amount of a substance in water or in a solid, we use by convention weight based units.

20 ppm of gold (Au) in water is the equivalent of 20 10^-6 g Au / g water. We could also say 20 g Au/ m³ water, because a m³ = one million grams (or a metric ton). When we calculate chemical equilibria, we use molar units, mainly the molality (# moles/kg water). To convert from molar units to ppm values we have to multiply with the molar or atomic weight and divide by thousand. The latter is necessary to go from kg of water to g of water. So 10^-5 moles of H₂CO₃/kg water equals 10^-5 x 62 / 1000 = 10^-8 x 62. When we express this in ppm, we have to multiply by a million (10⁺⁶) and we obtain 62 10^-2 ppm H₂CO₃ (or 0.62 ppm). This signifies that we have 0.62 10^-6 g H₂CO₃ / g water.

We convert from volume units to mass units and obtained that 360 ppm (v) CO₂ in the atmosphere is the equivalent of 765 Gt C (giga ton carbon), knowing that the mass of the atmosphere is 5.14 10²¹ g air. We also calculated that a seasonal wobble in the atmospheric CO₂ levels equates to a net transfer of about 12.7 Gt C from the atmosphere to other reservoirs (mainly the biosphere) over a whole year.

In the short carbon cycle, CO₂ exchanges between air, water (ocean), soil, and biosphere. The ocean biomass is about 3 Gt C and the terrestrial living biomass about 550 Gt C. Both the oceanic and the terrestrial biomass pull roughly 100 Gt C / year out of the atmosphere by photosynthesis, and give back a significant fraction through respiration and direct decay. This implies that the annual withdrawal of CO₂ from the atmosphere by the biosphere is close to 200 Gt C (or less depending on how you count ongoing respiration in plants), whereas the seasonal oscillation is about 12 Gt C. Much of that atmospheric extraction of CO₂ must thus be damped by simultaneous release of CO₂, which may be related to the large biomass in the non-seasonal tropics. I have put a table with 'amount of biomass' by vegetation type, rate of productivity and Net Primary Productivity (NPP) per vegetation belt at the end here. The NPP takes into account the rate of CO₂ assimilation minus the rate of respiration. This distribution takes some of the edge of the difference (~ 50%), but still, seasonal CO₂ exchange in the oceans must play an important role as well to explain the relatively small northern hemispheric atmospheric CO₂ oscillation.

The marine carbon cycle is an extended and complex version of the terrestrial carbon cycle. On land, plants live, die and/or get eaten and/or end up in soils. The soils will slowly regenerate CO₂ from the dead twigs and leaves, which is a CO₂ flux back to the atmosphere. Many "plant" remnants in the ocean are oxidized right next to where they lived and their CO₂ is respired locally, which will ultimately escape to the atmosphere. Part of the photosynthate escapes to deeper levels and is thus temporally wtihdrawn from direct interactions with the atmosphere (mixing time oceans about 800 years)

A difference between the oceanic and terrestrial biospheres is the lack of a soil environment in the former: plant-like organisms live in the photic zone, and when they die, they may fall a few kilometers before they arrive at the bottom of the sea. During their fall, they may get re-oxidized by dissolved O₂ in seawater, and then turn into dissolved CO₂. In that case, they will never reach the ocean floor and the CO₂ is given back to the atmosphere once that parcel of seawater has reached the surface again (ocean currents), which may take many100's of years. This is called the biological carbon pump, where Carbon is "pumped down" into the deep sea by biota.

MPP - mean net primary production NPP - total net primary productivity

The organisms in the photic zone can be subdivided into a group with SiO₂ skeletons (diatoms - primary producers; radiolaria - heterotrophs) and those with carbonate skeletons (picoplankton and nano plankton - primary producers with calcite tests; foraminifera, ostracods - heterotrophs with calcite tests; larger organisms like bivalves - heterotrophs with calcite or aragonite shells). They all either produce (photosynthesis) or consume (heterotrophs) organic carbon and the latter recycle the organic matter rapidly and free up part of the nutrients for the next cycle of photosynthesis. About 90 % of primary productivity in the photic zone is recycled almost instantaneously (scale of months to years) and about 10 % "escapes" to deeper levels in the ocean. Only about 1-3 % of the organic matter reaches the sea floor, and of that amount, only a small fraction is preserved. The oxidation of organic matter in the water column is largely the result of the reaction C_org + O₂ è CO₂

The oxygen in seawater thus will become used, and may be even used up, leading to an oxygen minimum zone and in extreme cases to anoxic waters (e.g., the Black Sea, Long Island Sound). Once carbon is buried in the sediment, it may still react with the pore waters (water in between grains of clay and sand, which may amount to 60-70 % in some sediments), making the pore waters anoxic. The next reaction of Corg toward CO₂ then uses sulfate as an electron acceptor (oxidizer) with the reaction

2C_org + SO₄⁼ + 2H₂O è 2HCO₃^- + H₂S

The reduced sulfur gas (hydrogen sulfide) has the familiar smell of rotten eggs and is extremely toxic, both for humans and animals (remember the spaghetti worms along the hot spouter vents in the deep sea). The human nose can detect H₂S at the low ppb level! (but can not detect high levels - the nose "blanks out"). A fraction of the H₂S escapes from the pore waters and is re-oxidized back to sulfate in sea water. Another fraction may react with Fe²⁺ and forms the mineral pyrite ("fools gold"). It is for that reason that many sediments rich in organic matter carry little cubes of pyrite. Some rare environments (restricted basins) crystallize pyrite right from the water (the Black Sea).

The oxidation of organic carbon in seawater influences the CO₂ contents of the deep ocean, which has an almost unlimited appetite for this gas. The infamous carbonate equations (see earlier notes) come into play and the dissolution of CO₂ will make water more acidic and corrosive with respect to carbonates according to the 'master reaction' of carbonate chemistry:

As a result of the dissolution of C_org in deep waters (consuming O₂), the carbonate becomes unstable and dissolves again. So many "beastie bodies" never make it to the bottom and their demise leads to the dissolution of their former homes as well. So the record of their existence gets wiped off the face of the earth è through their own death their life time of work is destroyed as well è think about that!

The effects of carbonate precipitation in the surface waters is complex as well:

Carbonate formation leads to the reversed reaction above, which implies that the crystallization of carbonate leads to a flux of CO₂ to the atmosphere. So the primary productivity of nano and picoplankton is both a source and sink for atmospheric CO₂. The crystallization of carbonate by heterotrophs and their subsequent burial as limestones is of importance for the long carbon cycle, but is only a source of atmospheric CO₂ for the short carbon cycle. In conclusion, primary productivity is a sink for atmospheric CO₂, which is simple for opaline skeleton builders and more complex for carbonate synthesizing organisms. The short carbon cycle is further complicated by the recycling of carbon and carbonate in the deep oceans. This CO₂ travels with deep currents and provides a flux of CO₂ to the atmosphere in areas of upwelling.