Global Carbon Cycle

Five boxes. Carbon moves between the air (1 ppm of CO₂ is 2.124 PgC), land vegetation (550 PgC), soil and litter (1,500 PgC), the surface ocean (900 PgC of dissolved inorganic carbon) and the deep ocean (37,100 PgC). In 1850 every box was in balance at 280 ppm.

Land. Photosynthesis is GPP = 120 (1 + β ln(C/280)) PgC/yr, where β is the CO₂ fertilisation factor. Half of it is lost at once by plant respiration, the other half (NPP) feeds the vegetation, which turns over in about 9 years into litter and soil. Soil respiration is (60/1500) S · Q₁₀^ΔT/10 with Q₁₀ = 2, so warmer soils release more CO₂; the warming is ΔT = ECS · ln(C/280)/ln 2.

Ocean. Seawater chemistry makes the surface ocean a stiff buffer: the CO₂ pressure of the surface water rises about ξ = 10 times faster than its carbon content (the Revelle factor), pCO₂ = 280 (1 + ξ ΔOs/Os₀). The air-sea flux is 0.32 PgC/yr per ppm of difference, and the surface water slowly mixes into the deep at 45 (ΔOs/Os₀ - ΔOd/Od₀) PgC/yr. The pH change shown is the empirical fit ΔpH = -0.28 ln(pCO₂/280), which gives about -0.11 today.

What the model reproduces. Driven by approximate 1850-2023 fossil and land-use emission tables, the five-box model gives about 422 ppm in 2023 (Mauna Loa: 420.6), an ocean sink near 2.8 PgC/yr (Global Carbon Budget: about 2.9) and an airborne fraction near 0.45. These numbers come from tuning two ocean parameters on that history, so the match is a calibration, not an independent proof.

Honest simplifications. Global box model with constants: no seasons, no regions, no ocean circulation geometry, no carbonate chemistry beyond the Revelle factor, no permafrost, fires or nitrogen limitation, no weathering or sediment burial (those act over thousands of years). The land sink is a single pool pair with a fixed turnover. The emission tables for 1850-2025 are rounded approximations of published budgets. The 1,500 PgC fossil reserve is an illustrative round number (estimated resources are larger and uncertain). In the 3D scene, particle counts are proportional to the fluxes, except burning and land use which are drawn ten times larger so they stay visible; tree size follows the vegetation pool and the leaf colour warms with temperature.

• Pick Emissions stop in 2026 and press Jump 200 years ahead: the air does not return to 280 ppm, because the ocean and land share the pulse between boxes.
• Set CO2 fertilisation to 0 and climate sensitivity to 5 K: the land sink weakens and the airborne fraction rises.
• Compare the arrow widths: natural flows of 60 to 90 PgC/yr dwarf the 10 PgC/yr we add, yet the small imbalance accumulates.