💧 Water Cycle Residence-Time Lab

About this simulation

Rather than just animating evaporation → condensation → precipitation → runoff as a loop, this lab treats the water cycle as a stock-and-flow system: each reservoir (ocean, atmosphere, cloud, land surface, groundwater) holds a stock of water particles, and fluxes move particles between reservoirs. Residence time τ = S / F — stock divided by flux — falls straight out of that bookkeeping, and the panel computes it live for the atmosphere as particles move through it.

How it works

• Evaporation uses a Clausius-Clapeyron-style saturation vapor pressure curve, es(T) = 6.1094 · exp(17.625T / (T + 243.04)) — the same Magnus-form approximation meteorologists use — so warmer water evaporates measurably faster, not linearly faster.
• Condensation growth in the cloud layer accelerates as more droplets crowd together (a simple stand-in for collision-coalescence); once a droplet's accumulated growth crosses the saturation threshold, it precipitates as rain.
• Runoff vs. infiltration — rain landing on the land mass either flows across the surface back to the ocean or infiltrates into the translucent groundwater layer below, where it re-emerges slowly at a spring.
• The stat panel tallies the live stock in each reservoir and an instantaneous evaporation flux, then divides to estimate the atmosphere's residence time in simulated seconds — the same τ = S/F logic that gives the real atmosphere its ~9-day turnover.

Controls

• Sea-surface temperature — drives the Clausius-Clapeyron evaporation flux.
• Wind speed — increases evaporation by replacing saturated air over the ocean, and drifts vapor and clouds downwind.
• Cloud saturation threshold — how much condensation growth a droplet can accumulate before it rains out (a stand-in for the dew-point/updraft balance).
• Soil infiltration fraction — the share of rain on land that soaks into groundwater instead of running off to the ocean directly.

Did you know?

Earth's atmosphere holds only about 12,900 km³ of water at any instant, yet roughly 505,000 km³ pass through it every year as evaporation and precipitation — giving a real residence time of about 9 days. The deep ocean, by contrast, turns over on a timescale of millennia, simply because its stock is so much larger relative to its flux.