On short timescales of <104 years, the cycling between the atmosphere/ocean and surface pools such as organic carbon can have significant impact on atmospheric carbon dioxide levels (e.g., the glacial/interglacial cycles of the last 2 million years, anthropogenic impacts), the long-term cycle (>10 years) is controlled by the silicate-carbonate geochemical cycle. This cycle entails transfers of carbon to and from the solid Earth, that is, the crust and mantle. In the modern era, this cycle was first described by Harold Urey over 50 years ago:
The reaction to the right corresponds to chemical weathering of Ca silicates on land (CaSiO3 is a simplified proxy for the diversity of rock-forming CaMg silicates such as plagioclase and pyroxene which have more complicated formulas, for example, Ca plagioclase: CaAl2Si2O8), while the reaction to the left corresponds to metamorphism ('decarbonation') and degassing returning carbon dioxide to the atmosphere.
This cycle is really biogeochemical. While decarbonation and outgassing is surely abiotic, taking place at volcanoes associated with subduction zones and oceanic ridges, chemical weathering involves active biological participation. Chemical weathering requires a flow of water and carbon dioxide through a layer of soil, with a high reactive surface area of CaMg silicates if consumption of atmospheric carbon dioxide is to occur at a rate similar to that on today's Earth. Thus, most chemical weathering occurs on vegetated continental surface in temperate and tropical climates because of moderate to high rainfall and temperatures. Naturally, higher temperatures, with other conditions constant, mean higher rates of reaction, because of the normal temperature effect on chemical reactions. In general, rocks that formed at high temperatures from cooling magma, such as basalt, weather fastest with respect to atmospheric carbon dioxide consumption. Taking in carbon dioxide and water in the weathering equation for a very common rock-forming mineral in basalt, Ca-rich plagioclase (simplifying by leaving out the Na component), gives the following:
Al2Si2O5(OH)4 is kaolinite, a clay mineral. The products include dissolved Ca cations and bicarbonate anions, which ultimately wind up in the ocean from river input, and kaolinite, left in the soil.
Only the reaction of calcium and magnesium silicates with carbonic acid results in a carbon sink via the formation of bicarbonate, its transfer to the ocean, and the precipitation of CaCO3; the weathering of limestone produces no net change in carbon dioxide in the atmosphere/ocean system, nor as a first approximation at least does the weathering of NaK silicates, since no Ca or Mg is supplied to the ocean. On land:
CaSiO3 + H2O + 2CO2 ! 2HCO- + Ca2+ + SiOz  In ocean:
CaCO3 I+CO2 + H2O
(reverse reaction is weathering of limestone on land).
Note that for each mole of CaSiO3 reacting, there is a net consumption of 1 mole of CO2, which is buried on the ocean floor as limestone.
Surface temperature is stabilized because of the dependence of the weathering rate on surface temperature, itself controlled by carbon dioxide in the atmosphere. This rate increases with increasing temperature because of two main effects: the speedup of chemical reactions and the increase in rainfall and therefore river runoff with increasing temperature. These effects are empirically supported by global studies of weathering rates and solute levels in rivers, as well as theoretically by models. Negative feedback resulting in temperature stabilization is obtained because the carbon sink increases as temperature (carbon dioxide) increases.
Steady-state levels of carbon dioxide in the atmosphere are achieved on timescales of the order of 10 -10 years, since as a first approximation, the time needed to reach steady-state level is the residence time of carbon in the atmosphere/ocean pool with respect to the volcanic source, or (40 000/0.1) = 4 x 105 years. Note that carbon rapidly equilibrates within the atmosphere/ ocean pool (<103 years), with about 50 times as much carbon in the present ocean as in the atmosphere. Short times are also entailed for the achievement of equilibrium between the atmosphere/ocean and the carbon in the biota and soil, so that for the long-term C cycle, the atmosphere/ocean/biota/soil C can be considered as one pool at equilibrium.
Departures from the carbon dioxide steady state in the atmosphere/ocean pool can occur as a result of Earth's orbital variations, fluctuations in organic carbon burial, pulses in volcanic outgassing, etc.
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