THEORY OF SENSOR TIME LAGS 41 



Thus the environmental value of 6 can be determined from 



de,k+i = d.,k+i + RX ^ '^' ~ I'-' , (2.10) 



which involves, in a simple fashion, only the indicated or actually meas- 

 sured values of the parameter d. 



One assumes that 6, and Oc are identically the same at /?. = and that 

 successive application of (2.10) will yield a more realistic estimate of the 

 distribution of 6 with height. When one applies a correction procedure 

 of the form of (2.10) to temperature, where the temperature lag constant, 

 \t, is always 3 sec [45], one obtains immediately the corrected temperature 

 profile. The same is true for humidity (provided the temperature is 

 greater than °C), when X/ is assumed to be always 10 sec [40]. Although 

 there is some indication [46] that, for room temperatures, the humidity 

 lag constant may be nearer 5 sec. For temperatures less than °C, how- 

 ever, X/ is a function orf true temperature, true value of relative humidity, 

 fe, and change of the true value of fe (see fig. 2.3). This means that one 

 must use an iterative solution for fe since X/ will change as one's estimate 

 of the true value of /^ and A/^, changes. Since our knowledge of X/ is essen- 

 tially empirical, the correction procedure is limited to the temperatures 

 and values of fe and Afe reported by Wexler [11]. 



In applying the above equations one generally assumes that the time 

 lags are always known and that the environmental and indicated values 

 are identical at the base of each layer [47]. These two conditions are 

 approximately satisfied only for the ground layer since the total lag con- 

 stant of the humidity strip is not known. It is not clear that any correc- 

 tion for sensor lag may be made above the initial layer since, for subse- 

 quent layers, the initial indicated and environmental values are not 

 identical and, further, lag constants have not been determined for this 

 case. 



2.5.3. Radiosonde Profile Analysis 



The utility of the above lag constant corrections is illustrated by 

 analyzing past radiosonde data for the occurrence of ground-based radio 

 ducts. A ground-based radio duct is one in which the gradient of N is 

 sufficient to refract a radio ray to the same curvature as that of the earth. 

 Thus, for ducting, since ray curvature is given by the gradient of the 

 refractive index, 



4t < ~ = -157 A^ units/km (2.11) 



where ro is the earth's radius. The data analyzed were from the months 

 of expected maximum duct occurrence at Fairbanks, Alaska (Feb.), 



