74 



METEOROLOGY— THEORY 



these ralciilatioiis to be carried out quickly and accur- 

 ately. M is a luimber of the order of 300 to 500. 

 Physically, the important quantity is the slope of M, 

 i.e., dU/dh. This often calls for calculating M at fairly 

 close height intervals. 15 ni or even less. The values of 

 M at such heights may differ l)y only two or three M 

 units. Hence, to obtain even two significant figures 

 for this quantity, the il/'s must be computed to four 

 significant figures, that is, to tenths of an M unit. 

 It is with a view to this situation that tables were 

 computed. 



These tables fall into two groups, depending upon 

 how the moisture in the atmosphere is evaluated. In 

 the first group (Tables 3 to 7) the moisture is given 

 in terms of relative humidity or vapor pressure ; in the 

 second (Tables 8 to 11) the mixing ratio is used. 



6.5.2 



Use of Tables 



The following examples explain the mechanics of 

 using these tables. The first two examples use the first 

 group of tables : Tables 3 to 7 inclusive. The quantities 

 // and G which appear in these examples are auxiliary 

 functions which are fully explained in the appendix. 

 Examples III and lY use Tables 8 to 11. 



Fj. ram pie I 



Relative humidity and temperature given. 



Po 



1,000 (po is pressure at sea level). 



h* meters 



above 

 sea level 



t°C RH^ 



H' GAt'- Mi M„ M: M" 



'Columns for h (meters), l°C, and RH% give the experimentally de- 

 termined data. (The heights are measured from sea level.) 



^Column for H is read from Table 3. 



'ffA( is obtained by multiplying values of G given in Table 4 by 

 A< = iQ — t, where /o is the air temperature at ground level. Interpolation 

 is unnecessary in this table. This correction may be omitted except where 

 high accuracy is desired. 



^Md is the sum of H and GA(. (If po ?< 1,000 this column should be 

 multiplied by Po/1,000 to obtain the true Md- This, however, is necessary 

 only if Po 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 Po-) 



"itfu, is obtained from Table 5. 



''Mc is obtained from Table 7 or by multiplying the column for h by 

 0.1570. 



"M is the sum of Md, Mw and Mc. 



'^It should be noted that Po refers to the barometric pressure at sea 

 level, not ground level. The difference in these quantities may be appre- 

 ciable- 



Table '■>, 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 pi'essure at the ground 

 is 993.0 nib. Table 9 shows for this height and tem- 

 perature, p/p^, = 0.9882. In this case, p = 993.0, and 

 hence 



p 993.0 



Po 



0.9882 0.9882 



= 1004.9. 



Example II 



Vapor pressure and temperature given. 

 Po = 1,000 mb at sea level. 



Columns for h, t, and e are the given data. (The heights are measured 

 from sea level.) 



'Column for H is read from Table 3. 



*GAt is obtained by multiplying values of G given in Table 4 by 

 At ~ t(t — t, where /o = temperature at ground level. Interpolation is 

 unnecessary in this table. 



^Md is the sum of H and GAt. [If Po ^ 1,000 this column should be 

 multiplied by Po/1,000 to obtain the true Md- This correction may usually 

 be omitted (see Note §, Example I).] 



Mu, is obtained by taking the product of /, given in Table 6, by e. 

 A slide rule gives sufficiently close results here. 



' Mc is obtained from Table 7 or by multiplying the column for h by 

 0.1570. 



"M is the sum of Md, Mw, and Mc. 



Ea-am,ple III 



Mixing ratio w and temperature given. 

 Po = 1,000 mb at sea level. 



h* meters 



above sea 



level 



t w 



P/Pc {p/po)F' Mc' M' 



20 

 40 

 100 

 150 

 300 

 500 



* Columns for h, t, and w are the assumed data, w is expressed in grams 

 of water vapor per kg dry air. 



^ F is read directly from Table 8. 



^ p is read from Table 9. In this table t means average temperature 

 between ground and height h. 



(If Po '^ 1,000 this result should be multiplied by Po/1,000. This step may 

 xjsually be omitted.) 



^ (p/Po)^ is the product of the two pre\'ious colunms. 



' M^ may be obtained from Table 7 or by multiplication of h by 0^0.1570. 



^ M 13 the sum of (p/Pu)f and M^- 



