Weather & ClimateWater Vapor

Water Vapor and Saturation

Air is saturated when vapor condenses as fast as water evaporates; the saturation amount climbs steeply with temperature.

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In the water cycle, water evaporates, travels as invisible vapor and condenses into clouds. This unit measures that vapor. Meteorologists count it by the pressure the vapor molecules add to the air, the vapor pressure $e$, in hectopascals. Temperatures here are in Celsius (see temperature scales).

Key idea

Air is saturated when water evaporates and condenses at the same rate, so the amount of vapor stops changing. The vapor pressure at saturation, $e_s$, depends only on the temperature, and it climbs steeply: it roughly doubles for every 10 °C of warming (about 6 to 7% per degree).

Why it works

Picture the surface of a puddle. Water molecules jiggle, and the fastest ones break free into the air: evaporation. Meanwhile vapor molecules flying around hit the surface and stick: condensation. Evaporation depends on how warm the water is; condensation depends on how many vapor molecules there are. When the two rates match, the vapor stops increasing: saturation. Notice what is missing: the nitrogen and oxygen of the air play no part. A sealed jar of water with all the air pumped out reaches the same saturation vapor pressure. Warmer water sends molecules off faster, so it takes more vapor to balance them.
Saturation vapor pressure over liquid water (from the Magnus formula, rounded). Each 10 °C step roughly doubles it near freezing, a little less in hot air.
TemperatureSaturation vapor pressure
−10 °C2.9 hPa
0 °C6.1 hPa
5 °C8.7 hPa
10 °C12.3 hPa
15 °C17.0 hPa
20 °C23.4 hPa
25 °C31.7 hPa
30 °C42.5 hPa
35 °C56.3 hPa
The blue curve is saturation. Drag the air sample: anywhere below the curve the air can take more vapor; on the curve it is saturated; vapor beyond the curve condenses.

Worked example: Room for more vapor?

Air at 20 °C has a vapor pressure of 15.0 hPa. Is it saturated? How much more vapor pressure could it reach?
  1. From the table, saturation at 20 °C is 23.4 hPa.
  2. 15.0 hPa is below that, so the air is not saturated; more water can evaporate into it.
  3. It could gain $23.4 - 15.0 = 8.4$ hPa before evaporation and condensation balance.

Answer: Not saturated; 8.4 hPa more

Worked example: Cooling past saturation

Air at 25 °C has a vapor pressure of 23.4 hPa. Overnight it cools to 15 °C. What happens to the vapor?
  1. At 20 °C the saturation pressure is 23.4 hPa, so the air becomes saturated when it cools to 20 °C.
  2. At 15 °C saturation is only 17.0 hPa, so the vapor pressure can't stay at 23.4.
  3. About $23.4 - 17.0 = 6.4$ hPa worth of vapor condenses into dew or fog.

Answer: It saturates at 20 °C; below that, vapor condenses

Common mistake

Picturing air as a sponge that "holds" water, with warm air holding more. Saturation depends on the temperature of the water and vapor, not on the air; it would happen with no air at all. Saying "warm air can hold more water" gives the right numbers, but the cause is the temperature, not the air. Check: in a vacuum jar at 20 °C, water still evaporates until the vapor pressure reaches 23.4 hPa.
Another way to count vapor is the mass of vapor in each kilogram of air. At sea level, saturated air holds about 3.8 g/kg at 0 °C, 7.6 g/kg at 10 °C, 14.7 g/kg at 20 °C and 27 g/kg at 30 °C: the same steep climb.

Practice

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Sources and further reading

  • OpenStax, College Physics 2e, 13.6 Humidity, Evaporation, and Boiling
  • NOAA National Weather Service, JetStream online school for weather: Humidity
  • Bohren and Albrecht, Atmospheric Thermodynamics (1998), chapter 5, on saturation and the "air holds water" picture
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