Симуляція Водного Циклу: Випаровування, Конденсація та Збереження Маси

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 live demo · evaporation, condensation and runoff moving mass between reservoirs● LIVE 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).

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

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.

Де куди йде після того, як впав: проникнення проти відтоку

На землі цикл води знову розгалужується. Вода або просочується у ґрунтову колонну, зрештою поповнюючи рівень підземних вод, або стікає поверхнею в дренажну мережу — та ж подільність, що й метод Flash Flood Curve Number вище, призначений для оцінки. Волога ґрунту, яка не дренується і не стікає, повертається в атмосферу, замикаючи цикл на суші так само, як відкриття океану замикає його над морем.

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 iced 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.

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)

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Усе, що вище, працює прямо у вашому браузері — відкрийте Water Cycle Simulation і змінюйте параметри під час роботи. Нічого не встановлюється, нічого не завантажується на сервер, уся модель живе в одній вкладці.