40 MEASURING THE RADIO REFRACTIVE INDEX 



constant, and the subscripts i and e stand for the indicated and environ- 

 mental values, respectively. The solution to (2.1) depends upon the 

 manner in which the environmental value of 6 varies. For example, if it 

 is assumed that de varies linearly with time, 



Be -^ e, + ^t, (2.2) 



one obtains for the solution to (2.2) 



Be - 9, = +^X [1 - exp (-t/\)], (2.3) 



as compared to 



^ [(/3X - Dexp (t/X)]d, 

 ^ /3X exp m - exp {t/\) ' ^ ^ 



under the assumption that de varies exponentially with time, 



de = 00 exp i-^t). (2.5) 



For a column of air, one normally knows the initial reading of the 

 sensing strij), 0o, and for an assumed linear decrease of 6 with height the 

 coefficient (8 becomes 



rj _ Bj Pq /„ n\ 



^ ~ t-\[\ - exp (-«/X)]' ^ ^ 



with the result that (2.2) is written 



6e — Qo -{- ', 7T\ 1 . /x M ■ (2-7) 



i — X[l — exp ( — V^)J 



Once the value of X is determined, estimates of the true properties of the 

 air can be found at all heights up to the point where the gradient changes. 

 One may proceed by a different course by noting in (2.1) that 



dt ~ dh ' dt ~ ^ dh' ^ ^ 



where R is ascension rate of the radiosonde (assumed a constant 300 

 m/min). 



If it is further assumed that di varies linearly between reported values 

 {an assumption compatible with radiosonde reporting procedure), then 



R^ = R ^-'"-' ~['\ (2.9) 



dh hk+i — hk 



where the /cth and the (A- + l)st layers are the boundaries considered. 



