is calculated as a function of the concentration at the previous time step by a mass budget equation:
where is the concentration in ppm and is the flux towards the atmosphere in GtC/year. Note that fluxes are expressed in GtC/year of Carbone. To convert these fluxes in Gt of per year, you need to multiply the fluxes by 44/12. The factor allows us to convert a mass in Gt (t) into a concentration in ppm: is the mass in the present-day atmosphere (750 Gt) and is the present-day concentration (405 ppm).
The flux, , is the sum of several contributions:
We assume that the fluxes leaving the atmosphere by biological
storage and continental alteration are proportional to the
concentration, by analogy with chemical reactions in which
is the reagent:
where is the consumption rate in GtC/ppm/year.
The user chooses the consumption rate of by biological storage and by continental alteration . When the Earth is completely frozen (snowball), these consumption rates are canceled regardless of the choice of the user: in fact, freezing does not allow the consumption of by these processes, which allows the exit of the snowball.
By default, is such that continental alteration balances volcanism for long time scales: . is null by default, because the current biological storage can be neglected. At Carboniferous, =-0.0014 GtC/ppm/year, according to the fluxes reconstructed at that time ([Berner, 2003]).
In nature, the solubility in the ocean depends on the temperature. As a result, an increase in temperature leads to degassing into the atmosphere whereas a decrease in temperature leads to pumping into the ocean. This phenomenon acts on time scales of a few thousand years, and probably played a role in variations observed during glacial-interglacial oscillations (section 3.2.3).
In the model, this is represented by a flux , in GtC/year, written as:
where is the atmospheric concentration in equilibrium with the ocean at temperature and is the relaxation time scale of the concentration towards this equilibrium.
is parameterized according to the temperature according to this equation:
This curve is shown in figure 20. Parameters , , , are chosen according to the following constraints:
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The aim is to represent in a simple way that the superficial ocean and the vegetation absorb some of the emissions: it is estimated, for example, that at present 35% of the current anthropogenic emissions are absorbed by the vegetation and 20% by the ocean. This plays a role especially at small time scales. In the model, we multiplies the fluxes by , where =35% and =20%.