76 



METEOROLOGY— THEORY 



Table 4 gives G{T,li). The term GU in equation 

 (11) is very small at altitudes less than 500 m and 

 for this range of altitudes may be safely neglected. 



Since it is assumed in these tables that i\, = 1.000, 

 the value of Ma read from the tables should be multi- 

 plied by po/1,000, where p^ is the actual air pressure 

 at sea level. This step may, however, be eliminated in 

 most cases, particularly as the physically important 

 quantity is not M Init differences in M at various 

 heights. 



Wet Term. Since 



e = (RH)e' 

 where KH = relative humidity, 



e' = saturation vapor pressure, 

 and since e' is a function of temperature only, it is 

 possible to prepare a table giving i¥„, as a function of 

 EH and t. This is Table 5. 



A table for /, defined by equation (T), is also in- 

 cluded, so that if e is known, !/„ can be obtained by 

 simply taking the product fe as indicated by equation 

 (5). Table 6 gives the values of /. 



Curvature Term. Table 7 gives the values of the 

 linear term h/a X lO", which must be added to obtain 

 the index of refraction modified for use on a "plane 

 earth" diagram. 



Error. The discussion of this first group of tables 

 is concluded with some observations on their order 

 of accuracy. Theoretically any errors which arise are 

 due to the expansions used in calculating M^. At a 

 height as great as 10,000 m, M might be, say, 70°. 

 This would give GaT = 13.3 for t = 0. li the next 

 term had been included the correction would have been 

 only a fraction of this amount. Since at these heights 

 3/—- 1,800, we are safe in saying that the relative error 

 is less than 0.5 per cent, probaltly much less than this 

 amount. At altitudes of 1,000 m or less the approxima- 

 tion introduces errors too small to be reflected in the 

 fourth significant figure. 



Aside from this theoretical error, there are errors 

 in the table due to rounding off in the numerical work. 

 An eft'ort was made to keep this error less than 0.1 

 M units. 



Tables 8 to 11 — Mixing Ratio and 

 Temperature Given 



In terms of atmospheric pressure and water vapor 

 pressure, the mixing ratio w is given by 



. = .^. (13) 



p — e 



Since v; involves the pressure /), the scheme used in 



the first group of tables must be modified. Using 

 equation (13), equation (2) assumes the form 



where 



M = ILf{T,iv) + Ch, 



^^^'-) = ^4 + ^7T623 



\n tJ 



(14) 



(15) 



Table 8 gives F for the range of usable values of 

 temperature and mixing ratio. Since F is sensitive 

 to variations in both T and w, the tabulation is made 

 for all integral values of both T and ir to avoid labori- 

 ous interpolation. 



Following the procedure used in the discussion of 

 dry term in Section 6.5.3, the pressure p is calculated 

 from equation (8). These results are given in Table 

 0. In view of the insensitivity of p to T, the average 

 temperature, it is unnecessary to talDulate p for all 

 values of T; it is sufficient to tabulate p at 5-degree 

 intervals of T. 



The term Cli has been calculated in connection with 

 the first group of tables and is given in Table 7. 



Tables 10 and 11 foe Use at Low Altitudes 



An objectionable feature of the method given in 

 the preceding section is that it involves taking the 

 product, pF, which makes an application of the tables 

 rather slow. The following method circumvents this 

 difficulty for heights less than 500 m. From equations 

 (1), (8), and (15) 



(ft - 1) 10« = Fe -"'''^ . (16) 



For altitudes of less than 500 m it is safe to sui> 

 pose that 



ah ah / t \ 



f 273 \ 273/ ' 



where t is the average centigrade temperature, and 

 that 



-akiT = , -a*/273 , , I a;i7/(273)- _ , -aA/273 



■t + 



Hence 



where 

 and 



alii 

 (273)"= 



-aA/273 



(ft - 1)10" =F-u+^'^, 



u = F{1- e -"''/■"'), 

 aF~t 



An = 



(273)^" 

 Equation (19) is evaluated in Tal)le 10. 



(17) 



(18) 

 (19) 

 (20) 



