STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 



217 



to abandon theory entirely in constructing our 

 temperature profiles. A survey of Nicolet's 

 and of the Harris-Priester temperature profiles 

 showed at once that they can all be represented, 

 with a remarkable degree of approximation, 

 by exponential curves of the form 



T=T a ~(T a -T 12 o) exp [-s( 2 -120)], (4) 



where Tn is the temperature at 120 km. and 

 T„ the asymptotic (exospheric) temperature; 



04 



03 



02 



01 

 500° 



1000° 



1500° 



2000° 



T a 



Figure 1. — The coefficient s of equation (4), which determines 

 the vertical temperature distribution, as a function of the 

 exospheric temperature Too. Curve 1 gives the tempera- 

 ture profiles of Nicolet's (1961) models. Curves 2a and 2b 

 are those pertaining to the Harris-Priester models in the 

 COSPAR International Reference Atmosphere 1965 (2a 

 for 4 a.m., 2b for 2 p.m.). Curve 3 gives the temperature 

 profiles of the present tables. 



z is expressed in kilometers and s is a constant 

 different for each profile. If we decide to use 

 equation (4) to represent our temperature 

 profiles, the problem is reduced to finding the 

 value of s appropriate to each value of T„, or, 

 better, an analytical expression for s(T„) which 

 will generate temperature profiles capable of 

 reproducing the observed variations of density 

 with height for any stage of solar activity. 

 For example, Nicolet's (1961) densities are 

 reproduced within a few percent with tem- 

 perature profiles generated by equation (4), 

 with 



s=34.5867 , o ; I -4.414X10- 3 +5.714X10- 7 7 , eo 



(1000°<7' 0O <2000°). 



After a considerable amount of trial-and- 

 error work, we found that the densities derived 

 from satellite drag (Jacchia and Slowey, 1963, 

 plus up-to-date unpublished data) can be 

 satisfactorily represented using temperature 

 profiles generated by the equation 



=0.0291 exp (-tt) 



r.-soo 



= 750+1.722X10- 4 (T <o -800) 2 



(5) 



The present tables were computed by the 

 numerical integration of equation (2) starting 

 from the boundary conditions given in section 2 

 and following the temperature profiles generated 

 by equation (4) with s given by equation (5). 

 In figure 1 these values of s are compared with 

 those which are obtained from the temperature 

 profiles of Nicolet's and the CIRA 1964 models. 

 For the latter, we have selected the curves for 

 4" and 14 h local solar time, i.e., the hours of the 

 minimum and of the maximum of the diurnal 

 temperature variation. Since there is no varia- 

 tion of s with the hour of the day in our static 

 models, our s curve must represent an average 

 over the day with a possible drift toward the 

 morning value at the low-temperature end and 

 toward the afternoon values at the high- 

 temperature end. 



4. Comparison with Nicolet's models 



A revised version (Nicolet II) of Nicolet's 

 original (1961) models, provided to us by the 

 author, has been used by us for the past two 

 years to convert atmospheric densities from 

 satellite drag data into temperatures which are 

 better suited for analysis than the original 

 densities (Jacchia and Slowey, 1963, and various 

 more recent papers). Different temperatures 

 are obtained from the same densities if we use 

 the present models; the corrections to the 

 system of Nicolet II to obtain the temperatures 

 given by our models are plotted in figure 2. 

 As we can see, the correction curves show a 

 systematic negative trend with increasing 

 temperature in the range between 800° and 

 1700° K. This is equivalent to saying that 

 if we consider a certain density variation within 

 these general temperature limits, this variation 

 corresponds to a somewhat smaller temperature 

 range in the present models. For satellites 

 at heights between 350 and 750 km. (i.e., for 



