Box model of atmosphere, biosphere, and ocean — simulate anthropogenic perturbation and warming
Global Carbon Cycle Box Model — four reservoirs exchange carbon via first-order fluxes:
dCₐ/dt = E_fossil + E_luc − F_ocean − F_land
F_ocean ≈ α_ocean × (Cₐ − Cₐ,eq) F_land ≈ α_land × NPP × (Cₐ/Cₐ,0) − R_het
Airborne fraction (AF ≈ 45%) is the fraction of emitted CO₂ remaining in the atmosphere after land and ocean uptake. Remarkably stable across emissions scenarios.
TCRE (Transient Climate Response to cumulative Emissions) ≈ 1.5–2°C per 1000 GtC emitted — nearly linear because AF and carbon cycle feedbacks partially cancel.
ΔT ≈ TCRE × ΔCO₂_cumulative / 1000 GtC
Ocean acidification: each GtC → CO₂ + H₂O → H₂CO₃ → H⁺ + HCO₃⁻. pH has dropped 0.1 units since 1750 (30% increase in [H⁺]).
The atmosphere contains ~830 GtC, oceans ~38,000 GtC, land biosphere ~2,600 GtC, fossil reserves ~5,000–10,000 GtC.