STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 



219 



nighttime temperature on the globe be T and 

 the maximum daytime temperature on the 

 globe be RT . We shall assume that the day- 

 time maxima T D and nighttime minima T N 

 at any point on the globe are given by the 

 equations 



T D =7 , (l + i?cos" ! 7,), (10) 



T N =T (1 + Rsm m d), 

 where 



v=2(<p—&o), 



where <p is the geographic latitude and 5 Q the 

 declination of the sun. 



The temperature T at this given point can 

 be expressed as a function of the hour angle H 

 of the sun (the local solar time). Let us write 



with 



and 



T=T N (l+ A cos" |\ (11) 



lp — -In 



R 



cos" 8 -q— sin m d 

 l+R sin m 



T=H+0+p sin (H+y) (- 7 r<r< 1 r) (12) 



where /3, y, and p are constants, and H=0 

 corresponds to the sun's upper culmination. 



The constant determines the lag of the 

 temperature maximum with respect to the sun's 

 culmination, while p introduces in the tempera- 

 ture curve an asymmetry whose location is 

 determined by y. Replacing T D and T N from 

 equation (10), we can write 



T=T (l+R sin m 0) 



(13) 



cos m rj — sin m 

 +R sin OT 6 



A 

 cos" -J 



Although in these equations the exponents 

 m and n, which determine the mode of the 

 longitudinal and the latitudinal temperature 

 variations respectively, are kept distinct, we 

 find that in practice we can take m = n. There 

 is a distinct possibility that the common value 

 of these coefficients might turn out to be a 

 little smaller than 2.5, the previously assumed 

 value, somewhere between 2.0 and 2.5. We 



shall adopt the following constants: i?=0.28, 

 m =«=2.5, /3= -45°, 2>=12°, 7= +45°. 

 e. Variation with geomagnetic activity. — After 

 the publication of Jacchia (1964), it was found 

 that the relation between the exospheric tem- 

 perature and the 3 hour geomagnetic index a v 

 shows a strong departure from linearity for 

 small values of a v (Jacchia and Slowey, 1964a). 

 The formula given in the last reference can be 

 used without alterations. The increase of 

 temperature with a v is then 



AT=1°.0 a p +125° [1-exp (-0.08 a„)]. (14) 



AT represents the atmospheric heating above 

 the level corresponding to a p =0. During 



1500' 



To, 



(°K) 



IOOO' 



150 



Figure 3. — Daytime maximum and nighttime minimum 

 temperatures above the thermopause as a function of the 

 10.7 cm. solar flux, in units of 10~ 22 watts/m 2 /cycle/sec. 

 bandwidth. Data are averaged over two or three solar 

 rotations. The temperatures in this diagram must be 

 considered as referred to average quiet geomagnetic 

 conditions (K v =2 or a p = 7). (Open circles: individual 

 maxima deduced from satellite drag curves. Circled 

 dots: individual minima deduced from satellite drag 

 curves. Dots: temperatures reduced to the nighttime 

 minimum at times when the curve of the semiannual 

 temperature variation was close to the annual average.) 



