42 MEASURING THE RADIO REFRACTIVE INDEX 



Washington, D.C. (May), and Swan Island, W.I. (Aug.). All data were 

 for the year 1953. 



As an example of past work, Wagner [40] has assumed that the refrae- 

 tivity lagged its environmental value according to (2.3) with the result 

 that 



A^, - N, = /3.V X^ [1 - exp {-I/Xm)]. (2.12) 



After an analysis of the meteorological conditions of his area of applica- 

 tion, he set \n = Xf = 10 sec; i.e., the time lag of A^ derived from pres- 

 sure, temperature, and humidity was identically that of the humidity 

 sensor for temperature <0 °C. Comparing this method of A'-lag correc- 

 tion with the uncorrected data (first and last columns of table 2.1), one 

 notes an increase in both intensity and incidence of ducts in all climates. 

 This is particularly marked for Fairbanks, where a sixfold incidence in- 

 crease is obtained. However, when one makes individual time-lag correc- 

 tions for both temperature and humidity by means of (2.10) a quite 

 different picture of duct statistics is obtained. For example, the Fair- 

 banks data indicate a twofold increase rather than a sixfold increase. On 

 the other hand, Washington shows an incidence of nine rather than six 

 ducts with a marked increase in N gradient when one corrects for both 

 temperature and humidity. 



The change of ducting statistics at all three locations obtained by the 

 two methods of time-lag correction yields paradoxical results. The near 

 contradiction of the two correction procedures is easily explained and 

 serves as an illustration of the necessity of correcting both the tempera- 

 ture and humidity elements for general application to ducting statistics. 



Consider typical temperature and humidity conditions associated with 

 ground-based ducts within each climate. Such cases are shown in figure 

 2.11. It is sufficient to note that the temperate ducts arise from typical 

 radiation inversion conditions of increasing temperature and decreasing 

 relative humidity with height; the arctic ducts are associated with the 

 intense arctic radiation inversion with ground temperature near —25 °C 

 and nearly constant relative humidity with respect to height; the tropical 

 ducts, however, appear to be due to slight decreases of both temperature 

 and humidity with height at temperatures near +25 °C. The effect of 

 sensor lag upon these different gradients is always to make the indicated 

 gradient appear less than the true or environmental gradient. Thus 

 correcting for sensor lags makes the temperature and humidity gradients 

 more intense. This, in turn, effects the resultant N gradient. One may 

 write 



dN = f~dT + -^ de + jp dP (2.13) 



