# Moisture Conversion Calculations

## A. Variables which are used to quantify the Actual Amount of Moisture

1. vapor pressure (e)
The pressure exerted by water vapor molecules.
Common atmospheric pressure (p) is measured as the sum of the air pressure and vapor pressure and p >> e.
2. mixing ratio (w)
• The ratio of the mass of the water vapor to the mass of the dry air.

• Mixing ratio is a dimensionless quantities. However, since mass of water vapor is much less than the mass of dry air in typical atmospheric condition, mixing ratio is more commonly expressed in g/kg.

where is the ratio of the molecular weight of water vapor to dry air.

3. specific humidity (q)
The ratio of the mass of the water vapor to the mass of the total air.

and
4. absolute humidity or density ( )
The mass of the water vapor to the volume of the water vapor. It is also commonly referred as the density of the water vapor.
5. Dew point Temperature (Td)
The temperature at which the amount of water vapor will become saturated.

## B. Saturation

• When liquid water and water vapor reaches thermodynamic equilibrium, that is evaporation is the same as condensation, it is referred to as saturation.
• Saturation can be interpreted as the maximum amount of water vapor that can exist in a stable condition.  Under normal circumstances, excessive water vapor will condense into liquid water.  Supersaturation in typical atmospheric condition is possible but rare.
• The variables describing the saturation is the same as in (A) and all the equations in (A) remain the same as long as the subscript (s) is on both side of the equation.
1. saturation vapor pressure (es)
2. saturation mixing ratio (ws)
3. saturation specific humidity (qs)
4. saturation absolute humidity
5. temperature (T)
• Saturation of water vapor (es) is a function of temperature only and does not depend on the air.  Equations of es(T) can be found at  http://hurri.kean.edu/~yoh/calculations/satvap/satvap.html
• However, saturation mixing ratio (ws or qs) will depend on total atmospheric pressure (p) since a change of atmospheric pressure means a change of mass of the dry air, and mixing ratio depends on the mass of the dry air.

• Temperature (T) describes Saturation (es).

• Dew Point Temperature (Td) describes the actual amount of water vapor (e), which  is the saturation value at dew point temperature.

Note that the form of the equations are the same (in this case, Bolton (1980) and temperature is measured in Celcius) in both cases.

## C.    Relative Humidity (Rh)

Relative humidity will only depend on temperature if vapor pressured is used in the definition.  WMO has also adopted the definition

which will have a slight pressure dependence.  The two definition only differ slightly in typical atmospheric condition.

## D.    Wet Bulb Temperature (Tw)

where p is the total atmospheric pressure,
cp is the specific heat capacity of dry air (1005 J kg-1 deg-1)
Lv is the latent heat of vaporization (2.5*106 J kg-1 deg-1 at 0C)

• For any given pressure, this equation involves three variables (T, Td and Tw).  By given any two of them, the third one can be determined.