Humidity
Absolute humidity
From the ideal gas law, the density of water, w is given by
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'').
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.
Note that
and the volumetric mixing ratio, f, (i.e., ratio of water number density, Nw, to the total number density Nt) is given by
where the average molecular weight, <mw>, is given by
Mass Mixing Ratio
Alt (km) | P (mB) | record low | 1% low | midlat. mean | 1% high | record high |
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
where rs r(e = es) and qs q(e = es).
The saturated vapor pressure is approximately given by
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
The empirical expression for es can be used or a table lookup can be utilized after e is calculated.