Module moist 

Moist air: saturation vapour pressure, and the density and speed of sound of humid air.

Air is treated as an ideal mixture of dry air (the 1976 standard’s M₀, γ = 1.4) and water vapour (see docs/physics/atmosphere.md):

x_v = e / p                                         vapour mole fraction (Dalton)
M   = (1 − x_v) M₀ + x_v M_v                        mixture molar mass
ρ   = p M / (R* T)  =  p / (R_d T_v)                density
T_v = T / (1 − x_v (1 − M_v/M₀))                    virtual temperature (WMO-No. 8 eq. 12.18)
γ   = C_p / (C_p − R*),  C_p = (1 − x_v) (7/2) R* + x_v 4 R*
a   = (γ R* T / M)^½

Water vapour’s molar heat capacity is taken as 4 R*, the rigid nonlinear molecule (33.26 J/(mol·K)); the ideal-gas value near 300 K is about 1% higher, which moves a by 0.009% at 30 °C and saturation. Viscosity stays dry air’s: by Wilke’s mixing rule, water vapour lowers it by 2.1% at 30 °C and saturation, which changes turbulent skin friction by about 0.4%.

Saturation vapour pressure over liquid water follows WMO-No. 8, Guide to Instruments and Methods of Observation, Vol. I (2023), Annex 4.B, eq. 4.B.1, at every temperature: radiosonde relative humidity is always reported relative to water, even below 0 °C.

Constants

WATER_VAPOUR_MOLECULAR_WEIGHT_KG_PER_KMOL

Molar mass of water vapour M_v, kg/kmol (A. Picard et al., “Revised formula for the density of moist air (CIPM-2007)”, Metrologia 45, 149–155 (2008), section 2.1).

Functions

moist_air

The state of moist air at temperature_k and pressure_pa with water vapour at partial pressure vapour_pressure_pa. The vapour mole fraction is capped at 1.

saturation_vapour_pressure_pa

Saturation vapour pressure of pure water vapour over a plane surface of liquid water, Pa, at temperature temperature_k. WMO-No. 8 (2023), Vol. I, Annex 4.B, eq. 4.B.1, with t in °C:

vapour_pressure_pa

The vapour pressure, Pa, of air at temperature_k with relative humidity relative_humidity (a fraction, relative to liquid water): e = U e_w(T).