10 RADIO REFRACTIVE INDEX OF AIR 



It was mentioned earlier that the differences in refractive index ob- 

 tained by the two most commonly used formulas, those of Essen and 

 Froome and of Smith and Weintraub, are small compared to the error 

 made in observing P, T, and e. For example, by assuming errors of ±2 

 mbar in P, ±1 °C in T, and ±5 percent in relative humidity (RH) com- 

 mon in radiosonde measurements with sea-level values of P = 1013 

 mbar, T = 15 °C and 60 percent RH, a standard error of 4.1 A^ units may 

 be obtained compared to the difference of about 0.5 A'^ units between the 

 values obtained from the two formulas. It is seen from table 1.6 that 

 (over the normal range of sea-level temperatures, —50 °C to +40 °C) 

 the differences in the formulas are comparable to those associated with 

 surface meteorological measurements but are significantly less than the 

 errors that may arise in radiosonde observations. 



In addition to these errors, there is an additional source of error in the 

 uncertainty of the constants in the equation for N. Equation (1.22) 

 may be written to include this additional source of error as 



AA^' = a^T + 6Ae -f cAP + dAA^ + /AK2 + g^Kz, 



and, again assuming that the errors are uncorrected, the rms error may 

 be evaluated as before. Table 1.7 lists the percentage error arising from 

 errors in the various surface meteorological observations as well as those 

 of the constants. It is seen that the errors in constants constitute no 

 more than 30 percent of the total error. All sources of error combined 

 will yield errors no larger than 1.5 percent in N. Thus, although the 

 Smith and Weintraub equation has a stated accuracy of 0.5 percent due to 

 the constants alone, total errors of nearly twice that figure may occur 

 under conditions of extremely high humidity. 



Currently one must use radiosonde data for estimation of A'^ gradients, 

 with the result that the overall accuracy is determined much more by the 

 errors in the meteorological sensors than by errors between constants in 

 the equation for A''. Until such time as better measurement methods for 

 T and e are developed, there appears to be little or no need for more 

 accurate determinations of the constants in (1.10). The different deter- 

 minations of the constants now available are in essential agreement. For 

 example, the use of the Essen and Froome expression will give values of 

 A^ that generally lie within the standard error of ±0.5 percent of the 

 Smith-Weintraub expression. It a])pears desirable for our pur})oses to use 

 the Smith-Weintraub constants since they represent the weighted mean 

 of several independent determinations, noting also that the value of K2 

 given by Essen and Froome was obtained by extrapolation from optical 

 measurements rather than direct measurements at radio frequencies. 



