Relative Humidity vs Dew point

Definitions:

• \(e\) = actual partial pressure of water vapor in the air (set by how much H2O is there)
• \(e_s(T)\) = saturation vapor pressure at the air temperature \(T\)
• Relative humidity: \(\mathrm{RH} = e / e_s(T)\)
• Dew point \(T_d\): the temperature at which the current vapor pressure would equal saturation, i.e. \(e_s(T_d) \equiv e\)

So the clean relation is:

\[\mathrm{RH} = \frac{e_s(T_d)}{e_s(T)}\]

with \(T_d \le T\) always, and \(T_d = T \iff \mathrm{RH}=100%\).

Physical meaning:

• \(T_d\) is a proxy for absolute moisture content — it doesn't change if you just warm or cool the parcel (no condensation, no mixing).
• RH is a ratio that depends on both moisture and temperature. Heat the air without adding water and RH drops; cool it and RH rises until you hit \(T = T_d\) and dew forms.