Table 48 203 



DETERMINATION OF HEIGHT BY THE BAROMETER AND REDUCTION OF 

 PRESSURE TO FIXED LEVELS 1 



DETERMINATION OF HEIGHT 



The geopotential $2 at a level of pressure p* is given by 



$2 ==#! + A* (1) 



where $1 is the geopotential at a level of pressure pi and A* is the difference in geo- 

 potential between the levels of p 2 and pi. If pi is station pressure, $1 can be found from 

 Table 50 provided the latitude and station elevation are known. To ascertain $2 by means 

 of equation (1) it is necessary to make a calculation of A3>, a method for which is given 

 below. 

 According to equation (4a), page 224, A* in geopotential meters is given by 



A* = 67.442 7"». log h 



T'r, 



( 67.442 To log A - 67.442 To log tt \ (2) 

 \ P* pi J 



T, 



where T'mv is the mean adjusted virtual temperature 2 of the stratum (°K.),. To is the 

 temperature of the ice point, 273.16 °K., and p, is an arbitrary reference pressure. 



We choose p, = 1100 millibars, a value not likely to be exceeded in the atmosphere, in 

 order to avoid negative values in (3) and (4). Defining A<£,i as the geopotential difference 

 between the level of p\ and the 1100-millibar level when T'mv = To, then 



A*.! = 67.442 To log (1100/fc), (3) 



and similarly, 



A$, 2 = 67.442 To log ( 1 lOO/^) . (4) 



Equation (2) may be written 



A$ = Zj5! (A$,2 — A*,0 

 To 



= (A<J>. 3 - A*.,) + Tmv ~ To (A*.i - A*.x) 

 1 



= (A$.» - A$n) + ~- (A#.i — A$.i) (5) 



1 



where t'mv = T' mv — To = mean adjusted virtual temperature in °C. 



Table 48 B gives values of 67.442 Tolog (1100//)) as a function of p, and Table 48 C 

 gives values of (t'mv/To) (A<£> t2 — A<i>.i) as a function of (A$ J2 — A*»i) and of t'mv. 



To calculate A<I> given pi, p 2 , and tmv. — 



1. Determine A$ S i and A3> s2 corresponding to pressure pi and pi from Table 48 B. 



2. Take the difference (A$, 2 — A<i>,i). 



3. Compute or estimate the mean adjusted virtual temperature between pi and pi. (See 



Table 72.) 



4. Determine (t'mv/To) (A$, 2 — A*,i) from Table 48 C corresponding to the value 



of t'mv between pi and p 2 and the value of (A<£,2 — A$,i) found in step 2. 

 (Note. — (t'mv/To) (A$, 2 — A<i>,i) is linear in (A$, 2 — A$ 5l ) for a given t'mv 

 and the result for any value of (A>l>,2 — A$,i) can be found by a linear combi- 

 nation of the values in Table 48 C. For example if (A#, a — A<i>,i) = 1793 gpm. 

 and t'mv = 19 °C, Table 48 B gives for 19 °C. the following values: for 1000 

 gpm., 69.6; for 700 gpm., 48.7; for one-tenth of the value for 900 gpm., 6.3; 

 and for one-hundredth of the value for 300 gpm., 0.2. The sum 69.6 + 48.7 + 

 6.3 + 0.2 = 124.8 gpm. is the desired value of Uv/To (A$. a — A*.i). // t' m , < 

 °C. a minus sign must be prefixed to the result.) 



5. Add algebraically the value of ( t' mv /To) (A4>,2 — A*,i) found in step 4 to the 



value of (A<i>,2 — A^^) found in step 2. The sum is the required A$, in accord 

 with equation (5). 



1 This table involves relationships between pressure, geopotential and virtual temperature in the 

 atmosphere. The unit of geopotential used herein is the "geopotential meter." The relationship of 

 geometric height to geopotential is explained in Table 49. In this section, all logarithms are to the 

 base 10. 



3 See Table 72. 



(Continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



