🌎
Community request
Requested by u/tenderhart on Reddit — “I'd love some environmental ones like the carbon cycle…”

The Carbon Cycle — Interactive 3D Model

🌍 Tier: AP Environmental Science / IB ESS / Early Undergraduate

Watch carbon flow between four great reservoirs — atmosphere, biosphere, oceans, and fossil reserves. Burn fossil fuels, plant a forest, kill the phytoplankton: every slider tilts the planet's carbon balance in real time.

1 · Interactive 3D Simulation

👁 See It Clearly
🌍 3D Earth
🔀 Reservoir Flow
📈 CO₂ vs Time
Pre-industrial baseline
Atmosphere ≈ 280 ppm CO₂. Photosynthesis and respiration are roughly balanced. Move the sliders to disturb the equilibrium.
Year 0
Atmospheric CO₂
410 ppm
Ocean C (PgC)
38,000
Vegetation (PgC)
550
Soil (PgC)
1,500
Fossil reserves (PgC)
4,000
ΔT vs 1850 (°C)
+1.1
Year
2025
▶ Playback
📖 Story Walkthrough
Auto-advance
⚙ Scenario
🎚 Anthropogenic Forcings
🌿 Biospheric Parameters
⏱ Simulation
🎛 Display
Flow particles
Reservoir labels
Auto-rotate Earth
Clouds

2 · The Whole Thing in One Sentence

🛁 The bathtub analogy

Think of the atmosphere as a bathtub. The tap is everything that adds CO₂ — factories, cars, deforestation. The drain is everything that removes CO₂ — forests photosynthesising, oceans dissolving it. For 10,000 years the tap and drain were balanced, so the water level stayed around 280 ppm. Since 1850 we've opened the tap much wider than the drain can handle, and the level keeps rising. The hotter the bath gets (the higher the level), the worse the climate gets. That's the whole story.

What each slider does, in plain words

SliderReal-world meaning
Fossil-fuel burningHow much coal/oil/gas humanity is burning per year. Bigger = tap wide open.
DeforestationCutting forests releases stored carbon. Negative values = planting forests (drain bigger).
Cement / industryMaking cement chemically releases CO₂ even before fuel is burned.
Photosynthesis kPHow efficiently plants soak up CO₂. Healthier biosphere = bigger drain.
Respiration kRHow fast plants/soil release CO₂ back. Warmer Earth = bigger leak back into the tub.
Ocean uptake kOHow quickly the ocean dissolves atmospheric CO₂. Slow but steady drain.

3 · The Idea, Step by Step

Picture carbon as money that never gets created or destroyed — it only moves between accounts. There are four accounts: the air (a small checking account you spend from every day), living things and soil (a medium savings account), the ocean (a huge, slow vault), and fossil fuels underground (an old safe nobody touched for millions of years). For thousands of years the same amount flowed into the air account as flowed out, so its balance held steady near 280 ppm. Then humanity cracked open the old safe and started shovelling its carbon into the air faster than the savings and vault accounts can take it back.

To put numbers on it, think of one simple rule: change equals what comes in minus what goes out. Over a year the air's carbon $A$ changes by

$$\Delta A \;=\; (\text{sources} - \text{sinks}) \times \Delta t.$$

Right now humans add about $11$ PgC each year (fossil fuels $\approx 10$ + deforestation $\approx 1$), while forests and oceans together pull back roughly $5.5$ PgC. So about $5.5$ PgC stays in the air per year. Multiply by the conversion $0.471$ ppm per PgC and you get $\approx 2.3$ ppm/yr — exactly the climb measured at Mauna Loa. That single subtraction is the whole crisis in one line.

The deeper, AP-level picture replaces those two lumps with one balance equation for every account. For the atmosphere,

$$\frac{dA}{dt} = \underbrace{E_{ff} + E_{lu}}_{\text{human sources}} \;-\; \underbrace{P}_{\text{photosynthesis}} \;+\; \underbrace{R_V + R_S}_{\text{respiration}} \;-\; \underbrace{k_O\,(A - A_{eq})}_{\text{ocean uptake}}.$$

Each slider in the panel above is one term here: Fossil-fuel burning sets $E_{ff}$, Deforestation sets $E_{lu}$ (negative values plant forests instead), Photosynthesis $k_P$ scales $P$, Respiration $k_R$ scales the leak-back $R_V$, and Ocean uptake $k_O$ controls how fast the vault drains the air toward its equilibrium $A_{eq}\approx 280$ ppm. Notice the ocean term only pulls while $A > A_{eq}$, and it pulls slowly — which is why the air stays high for centuries even after the sources stop.

Try this in the sim above. First press Run as-is and watch CO₂ and ΔT climb together. Then drag Fossil-fuel burning to $0$: the curve flattens but does not fall — proof that stopping emissions only stops the rise, it doesn't undo it. Finally set Deforestation negative (reforestation) and raise Ocean uptake $k_O$, and watch how much harder the sinks have to work just to bend the line back down.

4 · The Physics & Chemistry (the equations behind the cartoon)

Carbon is conserved. It does not disappear; it merely moves between four major reservoirs: the atmosphere (as CO₂ & CH₄), the terrestrial biosphere (plants & soils), the oceans (dissolved inorganic carbon), and lithospheric reserves (fossil fuels, carbonate rock). Burning fossil fuels and deforesting land take carbon out of slow reservoirs and dump it into the fastest one — the atmosphere — where it warms the climate until the slower reservoirs catch up.

4.1 · State variables & conservation

Let A, V, S, O, F be carbon (in PgC = petagrams = 10¹⁵ g) in atmosphere, vegetation, soil, ocean, and fossil reserves. Mass conservation:

$$\frac{dA}{dt} = -P + R_V + R_S - \Phi_{O\leftrightarrow A} + E_{ff} + E_{lu}$$ $$\frac{dV}{dt} = P - R_V - L - D$$ $$\frac{dS}{dt} = L - R_S$$ $$\frac{dO}{dt} = \Phi_{O\leftrightarrow A}$$ $$\frac{dF}{dt} = -E_{ff}$$
SymbolMeaningTypical value
PPhotosynthesis (gross primary productivity)kP·A ≈ 120 PgC/yr
RVAutotrophic (plant) respirationkR·V ≈ 50 PgC/yr
RSHeterotrophic (soil) respirationkS·S ≈ 50 PgC/yr
LLitterfall (V → S)kL·V ≈ 50 PgC/yr
ΦO↔ANet ocean → atmosphere fluxkO·(A − Aeq)
EffFossil-fuel + cement emissions10 PgC/yr (2025)
EluLand-use change (deforestation)~1 PgC/yr

The ocean–atmosphere exchange is approximated as a relaxation toward chemical equilibrium with partial pressure of CO₂:

$$\Phi_{O\leftrightarrow A} = -k_O \left(A - A_{eq}\right), \qquad A_{eq} \approx 280\ \text{ppm-equivalent}$$

4.2 · From PgC to parts-per-million

One petagram of atmospheric carbon corresponds to about 0.471 ppm (because the mass of dry air is ≈ 5.15 × 10¹⁸ kg and CO₂'s molar mass is 44 g/mol). So when emissions push A up by 10 PgC, ppm rises by ~4.7 — and if the ocean & biosphere together soak up half, we measure ~2.3 ppm/yr at Mauna Loa.

4.3 · Climate sensitivity (toy)

To turn CO₂ change into a temperature, the simulation uses the logarithmic forcing law and a 3 °C-per-doubling sensitivity:

$$\Delta T = \lambda \cdot \frac{\ln(C/C_0)}{\ln 2}, \qquad \lambda = 3\ \text{K}, \qquad C_0 = 280\ \text{ppm}$$

5 · How the Simulation Works — Step by Step

  1. Initialize reservoirs. The default scenario starts at 2025: A = 870 PgC (~410 ppm), V = 550, S = 1500, O = 38 000, F = 4000.
  2. Each tick (Δt = 0.05 yr by default) we compute flows. Photosynthesis P = kP·A scales with atmospheric CO₂ — this is the famous CO₂ fertilisation effect.
  3. Respiration + soil decomposition return carbon to the atmosphere. Warmer soils respire faster (Q₁₀ ≈ 2), but the simulator keeps the rate constants user-controllable for clarity.
  4. Ocean exchange is slow. The ocean equilibrium constant kO ≈ 0.02/yr means a CO₂ pulse takes decades to relax — explaining the long tail of climate damage.
  5. Fossil emissions and land-use change add carbon. Both come straight out of geological storage; the planet has no way to put them back on human timescales.
  6. The 3D Earth visualises the budget: dim orange particles = fossil flux, green = photosynthesis, brown = respiration, blue = ocean exchange. Particle count is proportional to the flow rate.
  7. The flow tab shows the box-and-arrow diagram. The chart tab plots CO₂ ppm against year.

6 · Worked Example

If we burn the remaining 4 000 PgC of known reserves

Set fossil emissions to 30 PgC/yr (extreme growth) and press Run. The atmospheric reservoir balloons from ~870 to ~2 000 PgC in about a century. That converts to roughly 945 ppm — high enough for ΔT ≈ +5.4 °C above pre-industrial. Ocean uptake clips it slowly: even after 2 000 simulated years, ~30 % of the pulse is still in the atmosphere. Try it: set the sliders, press Run, and watch.

7 · FAQ

Why does CO₂ stay in the atmosphere for so long?
Because the major sinks (ocean carbonate chemistry, rock weathering) are slow. A pulse of CO₂ added today decays roughly exponentially with several time constants: ~10 % of it is essentially permanent on human timescales (re-equilibration with the deep ocean & lithosphere takes 100 000+ years), ~25 % is gone within a thousand years, and the remaining ~65 % decays with time constants between 5 and 500 years.
What is the CO₂ fertilisation effect — and is it saving us?
Higher CO₂ boosts photosynthesis in C3 plants up to a point (it's the very effect commercial greenhouses use). Globally this currently absorbs ≈ 30 % of human emissions. But it saturates — nitrogen, phosphorus, water and temperature become limiting — and warming itself increases plant respiration. The land sink is expected to plateau and possibly reverse later this century.
Why is the ocean called both a carbon sink and a problem?
It absorbs ~25 % of emissions, which slows surface warming — but the dissolved CO₂ forms carbonic acid, dropping ocean pH by ~0.1 since 1850. That's a 30 % increase in [H⁺]. Shell-building organisms (corals, pteropods, coccolithophores) struggle to precipitate CaCO₃ in more-acidic water. So the ocean buys us climate time at the cost of marine ecosystems.
Is planting trees enough to fix this?
Reforestation is necessary but not sufficient. The global potential is roughly 200 PgC over a century — about 20 years of current emissions. It also requires the trees to actually stay alive: fire, drought and pests can flip a forest from sink to source within a single bad year. Halting fossil emissions is the primary lever.
What's the difference between gross and net primary productivity?
GPP = total CO₂ photosynthesised. NPP = GPP − autotrophic respiration (what's left for growth). NEE (Net Ecosystem Exchange) = NPP − soil respiration (what the atmosphere actually loses). In this sim, P is GPP, and RV + RS sum to the rest. Real ecosystem flux towers report NEE.

8 · References

Friedlingstein, P. et al. (2023). Global Carbon Budget 2023. Earth System Science Data, 15, 5301–5369.
IPCC, 2021. Climate Change 2021: The Physical Science Basis. Working Group I contribution to the Sixth Assessment Report. Cambridge University Press.
Archer, D. (2005). Fate of fossil fuel CO₂ in geologic time. JGR Oceans 110, C09S05.
Sarmiento, J.L. & Gruber, N. (2006). Ocean Biogeochemical Dynamics. Princeton University Press.