# Humidity

### Absolute humidity

From the ideal gas law, the density of water, _{w} is given by

_{w}= ( <mw>

_{w}

*f*)/(

_{w}e*R*)

_{*}T
where <mw>_{w} is the molecular weight of water (18.016 gm/mole),
*f _{w}* is a correction factor for non-ideal behavior which can be
taken as

*f*= 1,

_{w}*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*-

*f*)]/(

_{w}e*R*) + (<mw>

_{*}T_{w}

*f*)/(

_{w}e*R*) = [<mw>

_{*}T_{d}· (

*P*- 0.37803

*f*)]/(

_{w}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

*f*) / (

_{w}e*P*- 0.37803

*f*) 0.622

_{w}e*e*/

*P*

Note that

_{w}=

*q*·

and the volumetric mixing ratio, *f*, (*i.e.*, ratio of
water number density, *N _{w}*, to the total number density

*N*) is given by

_{t}

*f*

_{w}*N*/

_{w}*N*= <mw>/<mw>

_{t}_{w}·

*q*

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

_{d}· (1 -

*f*) + <mw>

_{w}_{w}·

*f*

_{w}### Mass Mixing Ratio

*r*=

_{w}/

_{d}= 0.62197 · [(

*f*)/(

_{w}e*P*-

*f*)] 0.62197 ·

_{w}e*e*/(

*P*-

*e*)

*q*

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

*U*100 ·

*r*/

*r*100

_{s}*q*/

*q*100

_{s}*e*/

*e*

_{s}
where *r _{s}*

*r*(

*e*=

*e*) and

_{s}*q*

_{s}*q*(

*e*=

*e*).

_{s}The saturated vapor pressure is approximately given by

*e*6.11 · 10

_{s}^{[(a T)/(b + T)]}mBar

*r*0.62197 ·

_{s}*e*/(

_{s}*P*-

*e*) for

_{s}*e*>

_{s}*P*

*r*0.62197 for

_{s}*e*

_{s}*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*)/(<mw>

_{*}T_{w}

*f*) =

_{w}*e*(

_{s}*T*)

_{dp}
The empirical expression for *e _{s}* can be used or a table
lookup can be utilized after

*e*is calculated.