204 Table 48 (continued) 



DETERMINATION OF HEIGHT BY THE BAROMETER AND REDUCTION OF 

 PRESSURE TO FIXED LEVELS 



REDUCTION OF PRESSURE 



If the pressure p2 and geopotential <*> 2 at a given level are known and it is desiredto 

 obtain the pressure pi at some other given level $1, use is made of the following expression 

 derived from equation (5), 



A$.i = A$. 2 - A* -J?- = A<P J2 - A* ;[ (6) 



1 mv * ~T" *mv 



Considering the independent variables in the right-hand member of equation (6), the 

 values of A$,2 corresponding to the station pressure /> 2 can be found from Table 48 B; 

 A* is equal to (* a — *i) ; and methods for determining t mv are outlined in the following 

 paragraphs. After computing A$,i by means of this equation the corresponding pressure 

 Pi can be obtained from Table 48 B. In the case of reduction of pressure to sea level, 

 *i = and A* = 4> 2 (see Table 50). If <i> 2 < *,, A* < 0. 



Mean adjusted virtual temperature. — To solve (6) it is necessary to estimate t'mv for 

 the stratum between <Pi and <p 2 . If this stratum is in the free air and temperature sound- 

 ings are available the customary procedures may be used. 3 If no soundings are available 

 or reduction must be made through a fictitious air column (the usual case in reducing 

 pressure to sea level) a reasonable estimate of the temperature lapse rate and moisture 

 conditions between $1 and $2 must be made. 4 



The mean adjusted virtual temperature of an air column t' mv can be considered to be 

 the algebraic sum of three terms: 



(a) a representative station temperature t,, 



(b) a correction for lapse rate, L, 



(c) a correction for humidity, C, 



t' mv = t. + L + C. (7) 



We now consider t,, L, and C in order: 



(a) t,: In the United States t. is usually taken to be the mean of the current and the 



12-hour previous air temperature, although this practice is not world-wide. 



(b) L: If we assume that the lapse rate is one-half of the dry adiabatic, i.e., 1 °C./200 



gpm., and that the mean temperature of the air column occurs at a point A<p/2 

 geopotential meters below the station elevation * 2 , then L = A$/400, in °C. 

 Some meteorological services make different assumptions in determining L. 

 (The sign of L depends on the lapse rate assumed and on the sign of A*.) 



(c) C: In the case of reducing pressure to sea level, a satisfactory estimate of C 



can be made from Table 48 A, using current dew-point temperature and station 

 elevation as arguments. Table 48 A is based on two assumptions: (1) that 

 pressure varies with altitude in accordance with the U. S. Standard Atmosphere, 

 and (2) that the vapor pressure varies with height in accordance with Hann's 

 empirical formula 5 



e/eo = 10-*' 6300 (8) 



where e is the vapor pressure at a height of h meters above sea level, and e<> 

 is the vapor pressure at sea level. An alternative method of obtaining C where 

 no other information is available is to use Table 72 after making reasonable 

 estimates of the temperature, relative humidity, and_ pressure at the midpoint 

 of the column. The temperature at this point is approximately given by (t, + L). 

 (C is always positive.) 



The method for determining t'mv in reducing pressure to sea level outlined above will 

 in general give a value slightly different from that used by the U. S. Weather Bureau, 

 which employs a system developed by Bigelow 6 based on representative lapse rates and 

 humidity conditions differing for each station. Other countries generally use still different 

 procedures. 7 



8 See U. S. Weather Bureau Circular P, Instruction for modulated audio frequency radiosonde 

 observations, January 1945, p. 63. See also Table 72. 



* See U. S. Weather Bureau forms 1154 A and B. 



B Hann, J., Lehrbuch der Meteorol. 3d ed., p. 230, 1915. 



•Bigelow, F. H., Report on the barometry of the U. S., Canada, and the West Indies, Report of 

 the Chief of the Weather Bureau, 1900-1901, vol. 2, Washington, 1902. 



'Report of the International Meteorological Conference at Innsbruck, September 1905, app. Ill, 

 p. 60. Meteorol. Off. Publ. No. 195, London, 1908. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



