Weathering

Weathering and burial of carbonates and silicates

Terrestrial weathering of carbonate and silicate rock is represented by F_wc and F_ws, which are the rates of carbon consumed from the atmosphere by the weathering of carbonate and silicate rock, respectively. These rates are dependent on temperature as

$$ \begin{align*} F_{wc} &= F_{wc,0}\, e^{a_c (T_{\mathrm{surf}}-T_{\mathrm{surf},0})} \\ F_{ws} &= F_{ws,0}\, e^{a_s (T_{\mathrm{surf}}-T_{\mathrm{surf},0})} \, , \end{align*} $$

where F_wc,0 and F_ws,0 are the preindustrial weathering rates, T_surf,0 is the preindustrial surface-ocean temperature, and a_c and a_s are the rates of relative change in the weathering rates per degree of warming (set by constants$dFwcdlogT and constants$dFwsdlogT with default values of 0.10/K and 0.02/K, respectively). Since the global mean surface-air temperature is set diagnostically as the surface-ocean temperature plus a fixed increment, these equations are identical to

$$ \begin{align*} F_{wc} &= F_{wc,0}\, e^{a_c (T_{\mathrm{atmo}}-T_{\mathrm{atmo},0})} \\ F_{ws} &= F_{ws,0}\, e^{a_s (T_{\mathrm{atmo}}-T_{\mathrm{atmo},0})} \, . \end{align*} $$

The rate of carbon burial on the ocean floor in the form of calcium carbonate, \eqn{F_{bc}}{F_bc}, is linear in the concentration of deep-ocean carbonate ion,

$$ F_{bc} = F_{bc,0} + a \left([\mathrm{CO}_3^{2-}] - [\mathrm{CO}_3^{2-}]_0\right) \, , $$

where [CO₃^2-] is the concentration (with dimensions of mol/kg) of carbonate ion in the deep ocean, [CO₃^2-]₀ is its preindustrial value, and a is a constant set to 2.5 x 10¹⁷ kg/yr.