Moisture Conversions

Introduction	The amount of water vapor in the air can be expressed in many different ways. Some variables used to quantify and calculate moisture in the air include vapor pressure (e), saturation vapor pressure (e_s), mixing ratio (w), saturation mixing ratio, (w_s), dew point (T_d), and relative humidity (RH).
Defining the variables	Vapor pressure (e): The pressure exerted by water vapor in the air. Atmospheric pressure (p) is the sum of the air pressure and vapor pressure where p>>e. Saturation vapor pressure (e_s): How much water the air can hold at any temperature. Saturation vapor pressure increases with rising temperature. Note that at below freezing temperatures, the saturation vapor pressure is greater over water than over ice. Mixing Ratio (w): The amount of water vapor in a given volume of air. Saturation mixing ratio, (w_s): The amount of water vapor in a given volume of air saturated with respect to a plane surface of water to the mass of the dry air. Dew point (T_d): The temperature to which the air must be cooled at constant pressure in order for it to become saturated with respect to plane surface of water. Also, frost point is the temperature to which the air must be cooled at constant pressure in order for it to become saturated with respect to plane surface of ice. Dew point is also the temperature at which saturation mixing ratio (w_s) with respect to water becomes equal to the actual mixing ratio (w). Relative Humidity (RH): With respect to water, it is the ratio (expressed as a percentage) of the actual mixing ratio (w) to the saturation mixing ratio (w_s) with respect to water at the same temperature and pressure.
Converting Dew Point and Ambient Temperature to Relative Humidity	Since the mixing ratio and saturation mixing ratio are dependent on temperature and pressure, you can use the Goff-Gratch Equation to calculate relative humidity as follows, based on the dew point: Or, to calculate relative humidity based on the frost point: Two examples for dew and frost point: 1) For liquid condensate (i.e. dew), to calculate RH based upon dew point temperature and ambient temperature (measurements in deg C ): Tv = dew point temperature Ta = ambient temperature Assuming the condensate is liquid, fore "dew points": With Tv = 0, and Ta =10 RH= ((6.1078 * exp ((17.7017 * Tv)/(243.7096 + Tv)))/ (6.1078 * exp ((17.7017 * Ta)/(243.7096 + Ta)))) * 100; RH= 49.77% 2) For solid condensate (i.e. frost, Tv=0C or below), for "frost points", change the coefficients to: RH = ((6.1078 * exp ((22.0438 * Tv)/(243.7096 + Tv)))/ (6.1078 * exp ((22.4038 * Ta)/(243.7096 + Ta)))) * 100; For the same Tv and Ta, 0, and 10 as above, but assuming the condensate is frost and not liquid dew, RH = 45.18%, slightly lower.
References	Ahrens, C. D., 1994: Meteorology Today: An Introduction to Weather, Climate, and the Environment, West Publishing Company, 591 pp. Byers, H. R., 1974: General Meteorology, McGraw-Hill, 461 pp. Wallace, J. M. and P. V. Hobbs, 1977: Atmospheric Science An Introductory Survey. Academic Press, 467 pp.