💧
Community request
Requested by u/tenderhart on Reddit — “…the water cycle.”

The Water Cycle — Interactive 3D Model

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

Watch how the Sun lifts ocean water into the sky, the wind blows it inland, mountains squeeze rain out of the clouds, rivers carry it back to the sea — and feel what happens when you turn the thermostat up.

1 · Interactive 3D Simulation

👁 See It Clearly
🌍 3D Earth
🔀 Reservoir Flow
📈 Fluxes vs Time
Normal hydrologic balance
≈ 500,000 km³ of water cycles through the atmosphere every year. Evaporation ≈ precipitation. Move the sliders to upset the balance.
Year 2025
Atmos vapor (km³)
13,000
Ocean (10⁶ km³)
1,338
Ice / snow (km³)
24,000,000
Surface water (km³)
178
Precip (km³/yr)
486,000
Global ΔT (°C)
+1.1
Year
2025
▶ Playback
📖 Story Walkthrough
Auto-advance
⚙ Scenario
🌡 Climate
🌿 Land Surface
⏱ Simulation
🎛 Display
Flow particles
Cloud opacity
Auto-rotate Earth

2 · The Whole Thing in One Sentence

☀️ The conveyor-belt analogy

The water cycle is a giant solar-powered conveyor belt. The Sun heats the ocean → water evaporates into the sky → wind carries the vapour inland → it condenses into clouds → falls back as rain or snow → rivers, glaciers, and groundwater move it back to the sea. Globally about half a million cubic kilometres of water make this round trip every year. The crucial fact: warm air holds about 7 % more water vapour per °C (Clausius–Clapeyron). So when you crank the temperature slider, the whole conveyor belt speeds up — more evaporation, more intense rain, longer droughts, and a faster cycle overall. That's the whole story.

What each slider does, in plain words

SliderReal-world meaning
Global ΔTWarmer atmosphere = more water vapour per cubic metre + faster evaporation. Cooler = ice ages, less rain everywhere.
Solar intensityHow much sunlight reaches the surface. Low values mimic large volcanic eruptions (Mt. Pinatubo dropped global temps for years).
Forest coverTrees pump water from soil to sky via transpiration. Cutting forests kills that pump — the Amazon "flying river" is a real, measurable effect.
Soil moisture kSHow readily the land surface gives up moisture. Wetter soils evaporate faster; bare desert hardly evaporates at all.

3 · The Idea, Step by Step

Start simple. Leave a wet towel on a sunny windowsill and come back later — it's dry. The water didn't disappear; the Sun quietly lifted it into the air. Now do that to an entire ocean, let the wind carry the moisture inland, let it fall as rain, and let rivers run it back to the sea. That round trip, powered entirely by sunlight, is the water cycle. Nothing is created or destroyed — the same water just keeps moving.

Now name the pieces. Water leaving a surface as vapour is evaporation $E$ (from plants we call it transpiration); water returning as rain or snow is precipitation $P$. Over a whole year the planet is in balance, so $E \approx P$. The surprising part is how little water the sky holds at once: only about $13{,}000\ \text{km}^3$. Yet roughly $486{,}000\ \text{km}^3$ rains down each year. Dividing the flow by the stock, $486{,}000 / 13{,}000 \approx 37$, tells you the air's entire water content is swapped out about 37 times a year — once every 9 to 10 days. A tiny bucket can move an ocean if you empty and refill it fast enough.

Go deeper. The atmospheric store changes at the rate vapour comes in minus the rate it falls out:

$$\frac{dV_a}{dt} = E - P$$

What sets the pace is temperature. The Clausius–Clapeyron relation says warmer air can hold about 7 % more water vapour for every $1\,^\circ\text{C}$, a factor of $1.07^{\Delta T}$. That single factor is the engine behind the sliders: Global ΔT multiplies every flux by $1.07^{\Delta T}$, Solar intensity scales how hard the Sun drives ocean evaporation, Forest cover turns the transpiration pump up or down, and Soil moisture $k_S$ sets how willingly the land gives water back. Warm the world and the whole conveyor belt speeds up: fiercer downpours, but longer dry spells in between.

🔬 Try this in the sim above

1. Drag Global ΔT to +4 °C and press Run — watch the CC factor climb and precipitation rise. 2. Pull Forest cover down to 30 % and see land evaporation and runoff collapse while the ocean keeps evaporating. 3. Set Solar intensity to ~80 % (a "volcanic winter") and watch the whole cycle slow as the air cools and dries.

4 · The Physics

4.1 · Reservoirs & the global budget

The Earth holds roughly 1.386 × 10⁹ km³ of water. Almost all of it (97 %) sits in the oceans; another 2 % is locked up in ice. The atmosphere holds only ~13 000 km³ at any moment — less than 0.001 % of the total — yet that tiny pool turns over in just ~9 days, because precipitation and evaporation flows are huge.

$$\frac{dV_a}{dt} = E - P, \qquad E = E_{\text{ocean}} + E_{\text{land}}, \qquad P = P_{\text{ocean}} + P_{\text{land}}$$
ReservoirVolume (km³)Mean residence time
Oceans1 338 000 000≈ 3 200 yr
Ice caps & glaciers24 000 0001 000–100 000 yr
Groundwater23 000 000days–10 000 yr
Lakes & rivers178 000weeks–years
Atmosphere~ 13 000≈ 9 days
Biosphere~ 1 100~ 1 week

4.2 · Clausius–Clapeyron: the master equation

Saturation vapour pressure of water roughly doubles for every 10 °C of warming. To good approximation:

$$e_s(T) = 6.112 \cdot \exp\!\left(\frac{17.67 \, T}{T + 243.5}\right)\ \text{hPa}, \quad T\ \text{in °C}$$

So when ΔT = +2 °C, atmospheric water capacity rises by ~ 14 %. Heavy-rain events scale even faster (~ 2× C-C ≈ 14 %/°C) because storms concentrate the available moisture.

4.3 · Simplified model used in this simulator

To keep the simulation responsive, we use first-order kinetics for each flux scaled by current temperature and surface state:

$$E_{\text{ocean}} = E_0 \cdot \frac{S}{S_0} \cdot 1.07^{\Delta T} \cdot f(T_\text{ocean})$$ $$E_{\text{land}} = E_{L0} \cdot k_S \cdot f_{\text{forest}} \cdot 1.07^{\Delta T}$$ $$P = E \quad\text{(global, on annual mean — atmospheric pool is tiny)}$$ $$\text{Runoff} = P_{\text{land}} - E_{\text{land}}$$

5 · How the Simulation Works — Step by Step

  1. Sun heats the ocean. Solar slider sets incoming flux; ΔT raises sea-surface temperature.
  2. Evaporation = ocean E + land ET. Both scale as 1.07ΔT (Clausius–Clapeyron).
  3. Vapour condenses into clouds when air is lifted by mountains, fronts, or convection. The intuitive view shows this with rising water droplets and forming clouds.
  4. Precipitation falls back as rain (warmer regions) or snow (colder, high-altitude). In the simulation, snow accumulates if ΔT < −1 °C and melts if > +1 °C.
  5. Runoff & rivers carry land precip back to the ocean at ~ 40 000 km³/yr globally — about 0.1 % of the ocean per year.
  6. The conveyor belt speeds up with warming — global precipitation rises ~ 1–3 % per °C of warming (less than C-C because energy, not moisture, is the bottleneck).

6 · Worked Example

If we deforest the entire tropics

Set Forest cover to 30 % and run for 30 years. Land evaporation drops dramatically (less transpiration), the Amazon and Congo "flying-river" moisture flux fails, and the downwind rainfall (parts of southern Brazil, central Africa, southwest U.S.) collapses by 20–40 %. Total global precip falls ~ 3 % because the ocean still evaporates the same amount — but rainfall is now concentrated near coasts. Try it: set forest cover to 30, press Run, and watch land precipitation in the readouts.

7 · FAQ

How can warming cause both droughts AND floods?
Same physics, different timescales. A warmer atmosphere holds more vapour, so when it does rain, it can dump much more at once → flash floods, intense storms. But between storms, the same thirsty atmosphere pulls more water out of soil and plants → droughts. The wet places get wetter and the dry places get drier — that's the canonical climate-change signature.
If the atmosphere only holds 13 000 km³, where does all the rain come from?
From rapid turnover. The atmospheric reservoir is replaced ~ 40 times per year. Picture a tiny bucket that's being constantly emptied and refilled. The flow is enormous (500 000 km³/yr) even though the stock is small.
What is a "flying river"?
Large forests (Amazon, Congo) pump huge water vapour fluxes through transpiration. The Amazon transports more water through the atmosphere than the Amazon river itself — roughly 20 trillion litres/day. Downwind countries depend on it for rainfall. Cut the forest, lose the river.
Why doesn't the atmospheric water vapour cause runaway warming like CO₂?
Water vapour is the strongest greenhouse gas — but its concentration is controlled by temperature, not human emissions. Add water to the air and it rains out in days. Add CO₂ and it stays for centuries. So water vapour amplifies CO₂ warming (a feedback) but cannot start warming on its own.
How long does a single water molecule spend in each reservoir?
A molecule that evaporates today spends ~ 9 days in the air, may then fall as rain on land and infiltrate to groundwater (where it could stay for thousands of years), or splash into a river and reach the sea in days. Across the ocean it can spend up to 3 000 years before evaporating again. The cycle is a slow shuffle on average, but with very fast express lanes.

8 · References

Trenberth, K.E. et al. (2011). Atmospheric Moisture Transports from Ocean to Land and Global Energy Flows. J. Climate, 24, 4907–4924.
Oki, T. & Kanae, S. (2006). Global Hydrological Cycles and World Water Resources. Science, 313, 1068–1072.
Held, I.M. & Soden, B.J. (2006). Robust Responses of the Hydrological Cycle to Global Warming. J. Climate, 19, 5686–5699.
IPCC, 2021. AR6 WGI, Ch. 8 — Water Cycle Changes.