This is a genuine five-box mass-balance model of the carbon cycle — it splits the ocean into a fast-mixing surface layer and a slow deep layer, instead of treating the ocean as one box. Every arrow below is a real flux computed from the current reservoir sizes, not a fixed decoration.
Air-sea gas exchange (Revelle-buffered):
F(atm→surf) = G · (1 + (Atm−590)/590)
F(surf→atm) = G · (1 + R·(Surf−900)/900)
net = F(atm→surf) − F(surf→atm) R ≈ 10 (Revelle factor)
Surface↔deep mixing (concentration-gradient driven):
mix = M · [(Surf−900)/900 − (Deep−37100)/37100] · 900
Land uptake (CO2-fertilized photosynthesis):
P = P0 · (1 + β·ln(Atm/590))
land net = P·(1−r) − deforestation r tuned so land balances at Atm=590
CO2 ppm:
ppm = 280 + (Atm − 590) / 2.13
- Ocean mixing rate — turn it down and the surface ocean saturates quickly (it can only exchange with a small box), slowing the whole ocean sink; turn it up and the effectively infinite deep ocean keeps pulling carbon out of the surface layer, keeping air-sea exchange running longer.
- CO2 fertilization β — controls how much extra photosynthesis kicks in as atmospheric CO2 rises. At β=0 the land reservoir just sits near its pre-industrial balance; raise it and the land biosphere becomes a growing carbon sink as CO2 climbs, exactly as observed (though real forests saturate this effect at high CO2, which this simple model does not capture).
- Fossil fuel emissions — the only human-controlled input; every other flux is the system's own response to how far the atmosphere has drifted from its five reservoirs' shared pre-industrial equilibrium.
Because the ocean is split into two layers with genuinely different exchange physics, this model behaves differently from a single-ocean-box version: carbon can pile up in the surface layer faster than the deep ocean can absorb it, which is exactly the real-world bottleneck that limits how fast the ocean can buffer rising CO2.