Humidity

050-03-01Pablo Asensio Martínez2026-04-012 min

Humidity is the measure of the amount of water vapor present in the air.

Key Concepts

1. Relative Humidity (RH)

It is the ratio between the amount of water vapor the air contains and the maximum amount it could hold at that temperature, expressed as a percentage.

  • Approximate Formula: $RH \approx 100 - 5 \times (T - T_d)$ Where $T$ is the air temperature and $T_d$ is the dew point.
  • Exact Formula (based on Mixing Ratio): $RH = \frac{\text{Humidity Mixing Ratio (HMR)}}{\text{Saturation Mixing Ratio (SMR)}} \times 100$
  • Relationship with Temperature:
    • If the temperature increases (and the water content remains constant), the air's capacity to hold water increases, therefore, the Relative Humidity decreases.
    • If the temperature decreases, the capacity decreases, and the Relative Humidity increases.
  • Diurnal Variation:
    • Maximum RH: At sunrise (minimum temperature).
    • Minimum RH: In the early afternoon (maximum temperature).

2. Dew Point ($T_d$)

It is the temperature to which air must be cooled (at constant pressure) to reach saturation (RH = 100%).

  • The dew point can never be higher than the air temperature ($T_d \le T$).
  • If $T = T_d$, the air is saturated.
  • Changing the air temperature does not change the dew point (unless the temperature drops below the dew point, causing condensation).

3. Saturation

Occurs when the air contains the maximum amount of water vapor possible for its temperature and pressure.

  • RH = 100%.
  • T = Td.
  • Any further cooling or addition of water vapor will cause condensation (clouds, fog, dew).

Ways to saturate the air:

  1. Add water vapor (e.g., evaporation of rain).
  2. Cool the air (e.g., adiabatic ascent, nocturnal radiation cooling).

Vapor Pressure over Ice vs Water

The saturation vapor pressure over ice is lower than over liquid water at the same temperature.

  • This means that air saturates faster over ice than over water.
  • It favors the growth of ice crystals at the expense of water droplets (Bergeron-Findeisen Process).
  • The "Frost Point" is higher than the Dew Point when the temperature is below freezing.

Global Distribution of Water Vapor

  • Poles: ~0 g/m³ (very cold air, low capacity).
  • Equator: ~25 g/m³ (warm air, high capacity).
  • Water vapor is concentrated in the lower troposphere (0-5% of air volume).

Practical Calculations

Example 1:

  • Temperature ($T$): 18°C
  • Dew Point ($T_d$): 12°C
  • $RH = 100 - 5 \times (18 - 12) = 100 - 30 = 70\%$

Example 2:

  • Current content (HMR): 10 g/kg
  • Maximum capacity (SMR): 15 g/kg
  • $RH = (10 / 15) \times 100 = 66.7\%$