Carbon Cycle Simulator: Box Model of Global Carbon Reservoirs

simulation intermediate ~15 min
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Formula

\frac{dC_{\text{atm}}}{dt} = E - k_{\text{ocean}} \cdot (C_{\text{atm}} - C_{\text{eq}}) - k_{\text{land}} \cdot (C_{\text{atm}} - C_{\text{eq}})
\text{Airborne fraction} = \frac{\Delta C_{\text{atm}}}{\sum E}
\Delta T \approx 3 \cdot \frac{\ln(C/C_0)}{\ln 2} \text{ °C}
C_{\text{atm}} = C_0 + AF \cdot \sum E \cdot \frac{1}{2.124}
The global carbon cycle determines how much of our CO₂ emissions stay in the atmosphere and how much is absorbed by natural sinks. Understanding this cycle is essential for projecting future warming and setting emission reduction targets. This simulator implements a box model with four reservoirs: atmosphere, ocean, land biosphere, and fossil fuels. Carbon flows between reservoirs at rates determined by physical and biological processes. The key equation is dC_atm/dt = emissions - ocean_uptake - land_uptake, where ocean uptake is proportional to the difference between atmospheric CO₂ and a pre-industrial equilibrium. The airborne fraction — the share of emissions remaining in the atmosphere — is one of the most important numbers in climate science. Observations show it has been remarkably stable at ~44% for decades, meaning natural sinks have scaled up proportionally with emissions. But climate models suggest this may not continue: as the ocean warms and its surface layer saturates with CO₂, the ocean sink weakens. Land sinks face threats from drought, fire, and deforestation. Hansen et al. (1988) used early versions of this carbon cycle framework in the seminal paper that brought climate change to public attention through testimony to the U.S. Congress. Their projections for atmospheric CO₂ growth have proven remarkably accurate. Deforestation acts as both a source (releasing stored carbon) and a sink reducer (removing photosynthetic capacity). Tropical forests contain roughly 250 GtC in biomass — comparable to decades of fossil fuel emissions. Their preservation is both a climate and biodiversity imperative.

FAQ

What is the carbon cycle?

The carbon cycle is the biogeochemical process by which carbon moves between the atmosphere, oceans, land biosphere, and geological reservoirs. In the natural cycle, these fluxes are roughly balanced. Human fossil fuel burning and deforestation add ~11 GtC/yr of extra carbon, disrupting the balance and causing atmospheric CO₂ to accumulate.

What is the airborne fraction?

The airborne fraction is the proportion of emitted CO₂ that remains in the atmosphere rather than being absorbed by ocean or land sinks. It has averaged about 44% over the past six decades. The remaining 56% is roughly evenly split between ocean and land uptake.

Why can't the ocean absorb all our CO₂ emissions?

Ocean CO₂ uptake is limited by the rate of surface-to-deep mixing (the 'Revelle buffer factor'). The surface ocean equilibrates with the atmosphere relatively quickly, but mixing with the deep ocean takes centuries. As the surface ocean absorbs more CO₂, its capacity to absorb additional CO₂ decreases due to carbonate chemistry.

How long does CO₂ stay in the atmosphere?

Individual CO₂ molecules cycle in and out of the atmosphere quickly (~5 years), but the perturbation from emissions persists much longer. About 50% of a CO₂ pulse is absorbed within 30 years, 70% within a few centuries, but the remaining 20-25% stays for thousands to tens of thousands of years.

Sources

Other simulations: Climate Science

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View source on GitHub