# Humidity

### Absolute humidity

From the ideal gas law, the density of water, w is given by w= ( <mw>w fw e)/(R* T)

where <mw>w is the molecular weight of water (18.016 gm/mole), fw is a correction factor for non-ideal behavior which can be taken as fw = 1, e is the partial pressure of water, R* is the universal gas constant, and T is the local temperature.

### Specific humidity

The total density, , is given by the sum of dry and moist densities ( i.e., assumes all other species are included in ``dry''). = d + w = [ <mw>d · (P - fw e)]/(R* T) + (<mw>w fw e)/(R* T) = [<mw>d · (P - 0.37803 fw e)]/(R* T)

where <mw>d is the molecular weight of dry air (28.966), <mw>w/<mw>d = 0.62197, and (<mw>d - <mw>w)/<mw>d = 0.37803. The specific humidity is the ratio of the moist to total density and is dimensionless, but is usually expressed in gm/Kg units.

q = w/ = (0.62197 fw e) / (P - 0.37803 fw e) 0.622 e/P

Note that w = q · and the volumetric mixing ratio, f, (i.e., ratio of water number density, Nw, to the total number density Nt) is given by

fw Nw/Nt = <mw>/<mw>w · q

where the average molecular weight, <mw>, is given by

<mw> = <mw>d · (1 - fw) + <mw>w · fw

### Mass Mixing Ratio

r = w/ d = 0.62197 · [(fw e)/(P - fw e)] 0.62197 · e/(P - e) q

 Alt(km) P(mB) recordlow 1%low midlat.mean 1%high recordhigh sfc 1013.25 0.1 5.0 4,686 30,000 35,000 1 890 24.0 27.0 3,700 29,000 31,000 2 790 21.0 31.0 2,843 24,000 28,000 4 610 16.0 24.0 1,268 18,000 22,000 6 470 6.2 12.0 554 7,700 8,900 8 350 6.1 6.1 216 4,300 4,700 10 265 5.3 43.2 1,300 12 195 1.2 11.3 230 14 140 1.5 3.3 48 16 100 1.0 3.3 38

### % Relative Humidity

U 100 · r/rs 100 q/qs 100 e/es

where rs r(e = es) and qs q(e = es).

The saturated vapor pressure is approximately given by

es 6.11 · 10[(a T)/(b + T)] mBar

rs 0.62197 · es/(P - es)   for es > P

rs 0.62197   for es P

where T is given in °C and a and b are constants.

 a b above water 7.5 237.3 above ice 9.5 265.5

### Dew Point Temperature

The Dew point is the temperature at which the partial pressure of water reaches the saturation value, that is

e = ( w R* T)/(<mw>w fw) = es(Tdp)

The empirical expression for es can be used or a table lookup can be utilized after e is calculated.