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.
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.
| Slider | Real-world meaning |
|---|---|
| Fossil-fuel burning | How much coal/oil/gas humanity is burning per year. Bigger = tap wide open. |
| Deforestation | Cutting forests releases stored carbon. Negative values = planting forests (drain bigger). |
| Cement / industry | Making cement chemically releases CO₂ even before fuel is burned. |
| Photosynthesis kP | How efficiently plants soak up CO₂. Healthier biosphere = bigger drain. |
| Respiration kR | How fast plants/soil release CO₂ back. Warmer Earth = bigger leak back into the tub. |
| Ocean uptake kO | How quickly the ocean dissolves atmospheric CO₂. Slow but steady drain. |
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
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,
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.
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.
Let A, V, S, O, F be carbon (in PgC = petagrams = 10¹⁵ g) in atmosphere, vegetation, soil, ocean, and fossil reserves. Mass conservation:
| Symbol | Meaning | Typical value |
|---|---|---|
| P | Photosynthesis (gross primary productivity) | kP·A ≈ 120 PgC/yr |
| RV | Autotrophic (plant) respiration | kR·V ≈ 50 PgC/yr |
| RS | Heterotrophic (soil) respiration | kS·S ≈ 50 PgC/yr |
| L | Litterfall (V → S) | kL·V ≈ 50 PgC/yr |
| ΦO↔A | Net ocean → atmosphere flux | kO·(A − Aeq) |
| Eff | Fossil-fuel + cement emissions | 10 PgC/yr (2025) |
| Elu | Land-use change (deforestation) | ~1 PgC/yr |
The ocean–atmosphere exchange is approximated as a relaxation toward chemical equilibrium with partial pressure of CO₂:
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.
To turn CO₂ change into a temperature, the simulation uses the logarithmic forcing law and a 3 °C-per-doubling sensitivity:
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.