absolute_humidity#

hydrometlib.meteorology.absolute_humidity(ta, rh)[source]#

Calculate absolute humidity Q [g m-3]

A measure of the actual amount of water vapor in the air.

\[Q = \frac{6.112 \, \exp\!\left( \dfrac{17.67 \, T_a}{T_a + 243.5} \right) \times 2.1674 \times RH} {T_a + 273.15}\]

with \(T_a\) in Celsius and \(RH\) as a percentage. The derivation of the constants is set out step by step below.

References

  • Saturation vapour pressure (step 1): Bolton, D. (1980). The computation of equivalent potential

    temperature. Monthly Weather Review, 108(7), 1046-1053, eq. 10 https://doi.org/10.1175/1520-0493(1980)108%3C1046:TCOEPT%3E2.0.CO;2

  • Absolute humidity from vapour pressure (steps 3-4): WMO Guide to Instruments and Methods of

    Observation (WMO-No. 8), Volume I, Chapter 4 “Measurement of humidity” - Annex 4.A

Steps to derive Q:

  1. Saturation vapour pressure [Bolton 1980, eq. 10], in hPa (The vapour pressure when air is fully saturated (RH = 100%)) Psat = 6.112 exp((17.67 Tc) / (Tc + 243.5))

  2. Actual vapour pressure at any relative humidity (RH): P = 6.112 exp((17.67 Tc) / (Tc + 243.5)) * RH/100

  3. Apply the ideal gas law: PV = nRT, => n = PV/RT [where P = Pressure of the gas, V = Volume occupied by the gas, R = universal gas constant, T = Temperature]

    Set V=1 to get density per cubic metre n = P / RT

    Multiply by molecular weight of water = 18.02 grams/mol Q = 18.02 * P / RT

    Substitute P from step 2, scaling it from hPa to Pa (x100) so it matches the units of R:

    Q = (18.02 * 100 * 6.112 * exp((17.67 Tc) / (Tc + 243.5)) * RH/100) / (R Tk)

  4. Plug in the constants R = 8.314 J mol-1 K-1 18.02 / 8.314 = 2.1674

    The hPa -> Pa scaling (x100) cancels the RH percentage (/100), so RH enters as a percentage and no factor of 100 survives:

    Q = 6.112 * exp((17.67 Tc) / (Tc + 243.5)) * RH * 2.1674 / Tk

    where Tc is air temperature in Celsius and Tk = Tc + 273.15 is the same temperature in Kelvin.

Parameters:

  • ta (Expr) – Air temperature [Celsius]

  • rh (Expr) – Relative humidity [%]

Return type:

Expr

Returns:

Expression or Series computing absolute humidity, Q [g m-3]