348 Table 93 (continued) 



DEFINITIONS AND SPECIFICATIONS OF WATER VAPOR IN THE 



ATMOSPHERE 



(11) The thermodynamic frost-point temperature Tf of moist air at temperature T, 

 pressure p and mixing ratio r is the temperature to which the air must be cooled 

 in_ order that it shall be saturated with respect to ice at the initial pressure p and 

 mixing ratio r. 



(12) The dew- and frost-point temperatures, so defined, are related with the mixing 

 ratio and total pressure p by the respective equations : 



e'„(7\0 = 



0.62197 + r r 



e ' i(T,) = 0.62i r 97 + r P 

 (13)* The relative humidity U (in percent) of moist air is defined by: 



U = 10Q — 

 r«, 



where r is the mixing ratio of moist air at pressure p and temperature T and r« 

 the saturation mixing ratio at the same pressure and temperature. 



Note. — At the Philadelphia meeting (May 6, 1950) of the International Joint Committee on 

 Psychrometric Data, resolutions were adopted giving definitions of relative humidity different 

 from the above. These may be paraphrased as follows: 



(a) In regard to a mixture of air and water vapor under given conditions of barometric 

 pressure and temperature at which saturation of air is possible, relative humidity is the ratio 

 of the mol fraction of water vapor in the mixture to the mol fraction of water vapor in a mass 

 of air saturated with water vapor at the given barometric pressure and temperature. 



_(b) In regard to a mixture of air and water vapor or a sample of pure water vapor unad- 

 mixed with any other substance under given conditions of barometric pressure and temperature 

 at which saturation is impossible, relative humidity is the ratio of the partial pressure of water 

 vapor in the mixture or sample to the saturation pressure of pure water at the given tempera- 

 ture. 



The Committee adopted (b) subject to verification. The mol fraction of water vapor in any 

 mixture is the number of mols, or molecules, of water vapor in the mixture divided by the 

 total number of mols, or molecules, of all constituents in the mixture. 



Mol fraction of water vapor : 



r -f- (mw/m) 



(14) Relative humidity at temperatures less than 0°C. is to be evaluated with respect 

 to water. The advantages of this procedure are as follows : 



(a) Most hygrometers which are essentially responsive to the relative humidity 

 indicate relative humidity with respect to water at all temperatures. 



(b) The majority of clouds at temperatures below °C. consist of water, or 

 mainly of water. 



(c) Relative humidities greater than 100 percent would in general not be ob- 

 served. This is of particular importance in synoptic weather messages, since 

 the atmosphere is often supersaturated with respect to ice at temperatures 

 below °C. 



(d) The majority of existing records of relative humidity at temperatures below 

 °C. are expressed on a basis of saturation with respect to water. 



(15)* The thermodynamic wet-bulb temperature Tw of moist air at pressure p, tempera- 

 ture T and mixing ratio r is the temperature which this air assumes when water 

 is introduced gradually by infinitesimal amounts at the current temperatures and 

 evaporated into the air by an adiabatic process at constant pressure until saturation 

 is reached. 

 Tv, is determined by the equation 



log' /-•"( ■* ") __ c P c — Cvb j Cp -f- c pv r 



L V (T) c P v Cp + c pv r w ( Tw ) 



where : 



Lr(T) = heat of vaporization of water at temperature T, 

 Lv(T w ) = heat of vaporization of water at temperature T w , 



c w = specific heat of liquid water, 

 TviTw) = saturation mixing ratio with respect to water at pressure p and 

 temperature T*,, 

 Cp = specific heat of dry air at constant pressure, and 

 Cpv = specific heat of water vapor at constant pressure. 



Here c p and c pv are assumed to be independent of temperature in the interval T w 

 to T . . . 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



