METEOROLOGY — THEORY 207 
Example I 
Relative humidity and temperature given. 
Pv = 1,000 (p, is pressure at sea level). 
h* meters 
above 
sealevel (°C RH% H' GA M,' M,' M,' M” 
20 13 60 275.6 0.0 275.6 41.4 3.1 320.1 
70 13 50 274.0 0.0 274.0 34.5 11.0 319.5 
120 15 35 
450 12 30 
1,000 9 20 
5,000 —20 20 
270.5 0.0 270.5 27.1 18.8 316.4 
262.6 0.0 262.6 19.5 70.7 352.8 
248.2 0.2 248.4 10.9 157.0 416.3 
159.0 7.0 166.0 1.2 785.0 952.2 
“Columns for A (meters), t°C, and RH% give the experimentally de- 
termined data. (The heights are measured from sea level.) 
‘Column for H is read from Table 3. 
4@At is obtained by multiplying values of G given in Table 4 by 
At = to —t, where éo is the air temperature at ground level. Interpolation 
is unnecessary in this table. This correction may be omitted except where 
high accuracy is desired. 
§Mq is the sum of H and GAt. (If p0 ~ 1,000 this column should be 
multiplied by 79/1,000 to obtain the true Mg. This, however, is necessary 
only if pp differs appreciably from 1,000 mb, since only the difference of 
refractive index from its value at the ground is of importance and this 
difference is not sensitive to moderate changes of 79.) 
‘Mj is obtained from Table 5. 
1M, is obtained from Table 7 or by multiplying the column for h by 
0.1570. 
“M is the sum of Mg, My and Me. 
M]t should be noted that pp refers to the barometric pressure at sea 
level, not ground level. The difference in these quantities may be appre- 
ciable. 
Table 9, which gives pressure as a function of 
height and temperature, provides a simple method of 
calculating the sea level pressure from a measurement 
of the ground level pressure. For example, suppose 
the elevation of the ground above sea level is 100 m, 
the temperature is 15 C, and pressure at the ground 
is 993.0 mb. Table 9 shows for this height and tem- 
perature, p/p, = 0.9882. In this case, p = 992.0, and 
hence 
p 993.0 
EHzample II 
Vapor pressure and temperature given. 
Po = 1,000 mb at sea level. 
h* meters 
above 
sealevel t¢ Ht Gat Mi f M,' M. M~ 
10 15.0 10.0 274.0 0.0 274.0 4.543 45.4 1.6 321.0 
40 15.2 9.8 273.0 0.0 273.0 4.5387 44.5 6.3 323.8 
75 15.5 9.6 271.5 0.0 271.5 4.527 43.5 11.8 326.8 
150 16.0 9.2 268.6 0.0 268.6 4.511 41.5 23.6 333.7 
300 15.0 9.0 264.7 0.0 264.7 4.543 40.9 47.1 352.7 
1,000 10.0 7.0 247.40.3 247.4 4.706 32.9 157.0 437.8 
“Columns for A, t, and e are the given data. (The heights are measured 
from sea level.) 
{Column for H is read from Table 3. 
4GAt is obtained by multiplying values of G given in Table 4 by 
At = t — t, where & = temperature at ground level. Interpolation is 
unnecessary in this table. 
§Mq is the sum of H and GAt. [If 2) ~ 1,000 this column should be 
multiplied by 79/1,000 to obtain the true Mg. This correction may usually 
be omitted (see Note §, Example I).] 
‘vf, is obtained by taking the product of f, given in Table 6, by e. 
A slide rule gives sufficiently close results here. 
‘1M, is obtained from Table 7 or by multiplying the column for h by 
0.1570. 
“M is the sum of Mg, My, and Me. 
Example III 
Mixing ratio w and temperature given. 
po = 1,000 mb at sea level. 
h* meters 
above sea 
level t w Ft p/po' (p/po)F' M;' M' 
20 15 9 339.0 0.9976 338.2 3.1 341.3 
40 16 8 380.6 0.9953 329.0 6.3 335.3 
100 17 7 322.2 0.9882 318.4 15.7 334.1 
150 17 7 322.2 0.9824 316.5 23.6 340.1 
300 14 6 319.0 0.9650 307.8 47.1 354.9 
500 11 4 307.9 0.9420 290.0 78.5 368.5 
* Columns for h, ¢, and w are the assumed data. w is expressed in grams 
of water vapor per kg dry air. 
1 F is read directly from Table 8. 
1p is read from Table 9. In this table 7 means average temperature 
between ground and height h. 
(If 29 ¥ 1,000 this result should be multiplied by 7) / 1,000. This step may 
usually be omitted.) 
Sip / Po) F is the product of the two previous columns. 
' Mf, may be obtained from Table 7 or by multiplication of h by C=0.1570. 
1 © is the sum of (p/p 9)F and M.. 
Example IV 
Mixing ratio and temperature given. Simplified method 
satisfactory for h < 500 m.** 
h* meters 
above haut 
sea level ¢ w Ft wu} 100 (n—1)10°Mi M 
20 15 9 339.0 0.0 0.0 3381 3.1 341.2 
40 16 8 330.6 1.7 O1 329.0 6.3 335.3 
100 17 7 3222 40 0.2 3184 15.7 334.1 
150 17 7 322.2 60 0.3 316.5 23.6 340.1 
300 14 6 319.0 11.8 06 307.8 47.1 354.9 
500 11 4 307.9 18.7 10 290.2 78.5 368.7 
“Columns for h, ¢, and w are the assumed data. These data are the same 
as in Example III. 
tF is read from Table 8, as before. 
+u is read from Table 10. 
5 Avis read from Table 11. Aw is then to be multiplied by h/100 to give 
the column AAu/100. 7% is the average centigrade temperature from 
ground to h. 
"The column (n—1)108 is given by F — u+ hAu/100. If the average 
temperature ¢ is negative, this column is F — u — (hAu/100). 
1M, is obtained, as before, from Table 7. M is the sum of (n—1)10® 
and Me. 
“This method is not accurate above 500 m. It: will be noted, by com- 
paring the results here with those of Example III, that there are occasional 
differences of 0.1 M units. This is due to rounding off and is not significant. 
Procedure Used in Setting up Tables 
TABLES 3 TO 7 — RELATIVE HuMmMIDITY AND 
TEMPERATURE GIVEN 
Equation 2 may be written 
M=M,+M,+M., (8) 
where 
_ Ap 
Ma ae T? (4) 
M, = fe, (5) 
M, = Ch, (6) 
with 
B D 
a Ce @ 
Tables have been prepared which give the quantities 
