Lefschetz fixed-point theorem

The oxygen cycle.

The oxygen cycle is the biogeochemical cycle that describes the movement of oxygen within its three main reservoirs: the atmosphere (air), the total content of biological matter within the biosphere (the global sum of all ecosystems), and the lithosphere (Earth's crust). Failures in the oxygen cycle within the hydrosphere (the combined mass of water found on, under, and over the surface of planet Earth) can result in the development of hypoxic zones. The main driving factor of the oxygen cycle is photosynthesis, which is responsible for the modern Earth's atmosphere and life on earth (see the Great Oxygenation Event).

Reservoirs

By far the largest reservoir of Earth's oxygen is within the silicate and oxide minerals of the crust and mantle (99.5%). Only a small portion has been released as free oxygen to the biosphere (0.01%) and atmosphere (0.36%). The main source of atmospheric free oxygen is photosynthesis, which produces sugars and free oxygen from carbon dioxide and water:

$\mathrm{6}\mathrm{C}{\mathrm{O}}_{\mathrm{2}}+\mathrm{6}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}\mathrm{⟶}{\mathrm{C}}_{\mathrm{6}}{\mathrm{H}}_{\mathrm{1}\mathrm{2}}{\mathrm{O}}_{\mathrm{6}}+\mathrm{6}{\mathrm{O}}_{\mathrm{2}}$

Photosynthesizing organisms include the plant life of the land areas as well as the phytoplankton of the oceans. The tiny marine cyanobacterium Prochlorococcus was discovered in 1986 and accounts for more than half of the photosynthesis of the open ocean.

An additional source of atmospheric free oxygen comes from photolysis, whereby high energy ultraviolet radiation breaks down atmospheric water and nitrous oxide into component atoms. The free H and N atoms escape into space leaving O₂ in the atmosphere:

$\mathrm{2}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}\mathrm{⟶}\mathrm{4}\mathrm{H}+{\mathrm{O}}_{\mathrm{2}}$

$\mathrm{2}{\mathrm{N}}_{\mathrm{2}}\mathrm{O}+\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}\mathrm{⟶}\mathrm{4}\mathrm{N}+{\mathrm{O}}_{\mathrm{2}}$

The main way free oxygen is lost from the atmosphere is via respiration and decay, mechanisms in which animal life and bacteria consume oxygen and release carbon dioxide.

The lithosphere also consumes free oxygen via chemical weathering and surface reactions. An example of surface weathering chemistry is formation of iron-oxides (rust):

$\mathrm{4}\mathrm{F}\mathrm{e}\mathrm{O}+{\mathrm{O}}_{\mathrm{2}}\mathrm{⟶}\mathrm{2}\mathrm{F}{\mathrm{e}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{3}}$

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Oxygen is also cycled between the biosphere and lithosphere. Marine organisms in the biosphere create calcium carbonate shell material (CaCO₃) that is rich in oxygen. When the organism dies its shell is deposited on the shallow sea floor and buried over time to create the limestone sedimentary rock of the lithosphere. Weathering processes initiated by organisms can also free oxygen from the lithosphere. Plants and animals extract nutrient minerals from rocks and release oxygen in the process.

Capacities and fluxes

The following tables offer estimates of oxygen cycle reservoir capacities and fluxes. These numbers are based primarily on estimates from (Walker, J.C.G.):

Table 1: Major reservoirs involved in the oxygen cycle

Reservoir	Capacity (kg O2)	Flux In/Out (kg O2 per year)	Residence Time (years)
Atmosphere	1.4 * 1018	30,000 * 1010	4,500
Biosphere	1.6 * 1016	30,000 * 1010	50
Lithosphere	2.9 * 1020	60 * 1010	500,000,000

Table 2: Annual gain and loss of atmospheric oxygen (Units of 10¹⁰ kg O₂ per year)

Photosynthesis (land) Photosynthesis (ocean) Photolysis of N2O Photolysis of H2O	16,500 13,500 1.3 0.03
Total Gains	~ 30,000
Losses - Respiration and Decay
Aerobic Respiration Microbial Oxidation Combustion of Fossil Fuel (anthropogenic) Photochemical Oxidation Fixation of N2 by Lightning Fixation of N2 by Industry (anthropogenic) Oxidation of Volcanic Gases	23,000 5,100 1,200 600 12 10 5
Losses - Weathering
Chemical Weathering Surface Reaction of O3	50 12
Total Losses	~ 30,000

Ozone

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${\mathrm{O}}_{\mathrm{2}}+\mathrm{u}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}\mathrm{⟶}\mathrm{2}\mathrm{O}$

$\mathrm{O}+{\mathrm{O}}_{\mathrm{2}}\mathrm{⟶}{\mathrm{O}}_{\mathrm{3}}$

References

• Cloud, P. and Gibor, A. 1970, The oxygen cycle, Scientific American, September, S. 110-123
• Fasullo, J., Substitute Lectures for ATOC 3600: Principles of Climate, Lectures on the global oxygen cycle, http://paos.colorado.edu/~fasullo/pjw_class/oxygencycle.html
• Morris, R.M., OXYSPHERE - A Beginners' Guide to the Biogeochemical Cycling of Atmospheric Oxygen, http://seis.natsci.csulb.edu/rmorris/oxy/Oxy.htm