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Home/Biophysics, Fluids & Geoscience/Carbon Cycle (4-Box Model)

Carbon Cycle (4-Box Model)

Four carbon reservoirs — atmosphere, ocean mixed layer, deep ocean, and land biosphere — exchange mass through first-order fluxes proportional to the donor pool (Gt C yr⁻¹). The default coefficients are approximately balanced at the initial inventories, so zero emissions starts near steady state; moving sliders deliberately creates drift. Fossil emissions enter only the atmospheric box; pulses can be added for idealized experiments. The toy highlights why most emitted carbon does not remain airborne indefinitely: mixing and terrestrial uptake draw the perturbation into large ocean and land inventories on multi-decadal to centennial scales. Parameters are not tuned to reproduce IPCC airborne fractions; the goal is qualitative intuition about residence times, linear box mathematics, and the bookkeeping of cumulative emissions.

Who it's for: Introductory climate, biogeochemistry, or systems-dynamics courses.

Key terms

  • Carbon cycle
  • Box model
  • Airborne fraction
  • Ocean uptake
  • Land sink

IPCC-style inventories use many more boxes and nonlinear chemistry; this page is for intuition about residence times, partitioning, and why emissions do not remain 100% in the air.

Live graphs

Deep ocean holds most carbon but turns over slowly; after a pulse, part of the fossil carbon remains airborne until mixing and land uptake catch up — a toy airborne fraction.

Exchange rates (yr⁻¹)

0.042
0.035
0.0028
0.000077
0.017
0.00672

Flux from pool i to j is kᵢⱼ·Cᵢ (Gt C yr⁻¹). Defaults are approximately balanced at the initial inventories, so zero emissions starts near steady state; changing rates intentionally creates drift. Numbers are pedagogical, not a calibrated IPCC inversion.

Emissions & run

0 GtC/yr
1.2 ×

Measured values

Atmosphere850 GtC
Ocean mixed layer1020 GtC
Deep ocean37100 GtC
Land biosphere2150 GtC
Total inventory41120 GtC
Model time0.0 yr
Cumulative emissions0 GtC
Airborne fraction ≈ ΔCa / cum. emit—

How it works

Four linearly exchanging carbon reservoirs with fossil emissions to the atmosphere illustrate how airborne fraction drops as the ocean and land absorb CO₂ — a box-model cartoon of the modern carbon cycle.

Frequently asked questions

Why is deep-ocean carbon plotted separately?
Its inventory is much larger than the other pools, so sharing one vertical axis would visually flatten the atmosphere and land curves.
Does the airborne fraction match observations?
No. The linear kinetics and four boxes are a teaching scaffold; real models add nonlinear carbonate chemistry, spatial structure, and many more processes.