Water Cycle Simulation: Evaporation, Condensation and Mass Conservation

Five reservoirs, one conserved quantity

The water cycle is not really a cycle so much as a set of storages exchanging a strictly conserved mass: ocean, atmosphere, land surface (rivers, lakes, soil moisture), groundwater and ice. Every arrow between them — evaporation, condensation, precipitation, runoff, infiltration — moves mass out of one box and into another; nothing is created and nothing disappears. A correct simulation has to track that mass explicitly, which makes the water cycle a genuinely good teaching example of a conservation law you can watch in real time.

d(mass_i)/dt = sum of inflows to reservoir i - sum of outflows

sum over all 5 reservoirs of mass_i  =  constant, always

Clausius-Clapeyron: why warm air holds more water

Evaporation and condensation are governed by the Clausius-Clapeyron relation, which says the saturation vapour pressure of water rises roughly exponentially with temperature. The practical form used in weather and climate models is the Magnus (Tetens) approximation:

e_s(T) = 6.1094 * exp( 17.625*T / (T + 243.04) )     // hPa, T in °C

// rule of thumb: the atmosphere's water-holding capacity rises
// about 7% for every 1°C of warming

That 7%-per-degree scaling is why a warmer atmosphere doesn't just feel more humid — it can hold measurably more water before it saturates, which is one of the clearest, most quantitative links between global temperature and the intensity of both droughts (more evaporative demand) and heavy rainfall (more moisture available to condense out at once).

Condensation, precipitation and the dew point

Air becomes saturated when its actual vapour pressure equals e_s(T) — equivalently, when temperature falls to the dew point. Push moist air upward (over a mountain, along a front, inside a thunderstorm updraft) and it cools adiabatically until it crosses that threshold; condensation nuclei (dust, sea salt, pollution) then let droplets nucleate, and once droplets are heavy enough to overcome updraft and drag, precipitation falls.

Where rain goes once it lands: infiltration versus runoff

On the ground the water cycle forks again. Water either infiltrates into the soil column, eventually recharging groundwater, or it runs off overland into the drainage network — the same partition the flash-flood Curve Number method above is built to estimate. Soil moisture that doesn't drain or run off is returned to the atmosphere by evapotranspiration, closing the loop over land the way open-ocean evaporation closes it over the sea.

Residence times: the cycle runs at wildly different speeds

atmosphere        ≈ 9 days
rivers             ≈ 2-6 months
soil moisture      ≈ 1-2 months
lakes              ≈ years to decades
groundwater        ≈ years to tens of thousands of years
ice sheets         ≈ thousands to hundreds of thousands of years
ocean              ≈ ~3,000 years (mean)

A molecule of water spends most of its existence locked in ice or ocean and only a fleeting nine days, on average, in the atmosphere between evaporating and precipitating out — which is also why weather forecasts lose skill after roughly a week: the atmospheric moisture that drives it is turning over almost that fast.

Frequently asked questions

Try it live

Everything above runs in your browser — open Water Cycle Simulation and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.