Static Diffusion Models of the Upper Atmosphere with 

 Empirical Temperature Profiles' 



Luigi G. Jacchia 2 



1. Static and time-dependent models 



The first multitemperature models of the atmos- 

 phere above 120 km. based on diffusion equilib- 

 rium were produced by Nicolet (1961, 1963). 

 These models proceed from a fixed set of bound- 

 ary conditions, temperature and partial den- 

 sities, at 120 km. Above this height the partial 

 densities vary according to diffusion theory, 

 except for hydrogen for which diffusion equi- 

 librium is reached only at greater heights 

 (Kockarts and Nicolet, 1962, 1963); thermal 

 diffusion is taken into account for helium. The 

 vertical temperature distribution is computed 

 for the "hottest" model, i.e., the one with the 

 highest exospheric temperature, assuming 

 thermal equilibrium; the other models are 

 obtained from this model by conduction cooling 

 of the atmosphere in the absence of external 

 energy sources. The temperatures which are 

 obtained in this manner at the height of 150 

 km. (a nearly isopycnic layer) are linearly con- 

 nected with the constant temperature at 120 

 km. Models can be computed by this pro- 

 cedure for conveniently spaced values of the 

 exospheric temperature. These quasistatic 

 models have proved very practical as a back- 

 ground for deriving and analyzing atmospheric 



1 This work was supported in part by grant NsG 

 87-60 of the National Aeronautics and Space Admin- 

 istration. A preprint of this paper has appeared as 

 Smithsonian Astrophysical Observatory Special Report 

 No. 170. Owing to an imperfection in the numerical- 

 integration program, table 1 in that publication is 

 affected by a small systematic error, whose maximum 

 value, 0.011 in log p, occurs at a height around 200 km. 

 when T„ is large. For normal satellite heights and 

 temperatures the error amounts to only 0.006 in log p, 

 so its practical effect can be considered to be negligible. 



2 Physicist, Smithsonian Astrophysical Observatory. 



densities from satellite drag (Jacchia and 

 Slowey, 1963). 



Atmospheric models can be constructed only 

 at the expense of oversimplifications. Such 

 are, for example, the invariance of the boundary 

 conditions at 120 km. and the constant tempera- 

 ture gradient between 120 and 150 km. found 

 in Nicolet's models. Another serious limitation 

 is the assumption of static equilibrium in an 

 atmosphere which is subject to large day-to- 

 night temperature variations, with a period 

 which is not much longer than conduction time 

 in the lower thermosphere. 



Atmospheric models which attempt to take 

 into account the diurnal variation at low lati- 

 tudes have been computed by Harris and 

 Priester (1962a, 1962b). They also assumed 

 fixed boundary conditions at 120 km. and dif- 

 fusion above this height, but the hydrostatic 

 equation and the heat-conduction equation 

 were integrated simultaneously and the heat 

 input varied with a 24 hour cycle. Since the 

 amount of solar EUV necessary to maintain 

 the heat balance gave diurnal density oscilla- 

 tions much in excess of those observed, Harris 

 and Priester (1962 a, b) were obliged to intro- 

 duce a second source of heat with a maximum at 

 a different hour. This device may perhaps have a 

 counterpart in the actual heating process, but 

 doubts have been voiced that it may mostly re 

 fleet the inadequacy of an oversimplified theory. 

 By suitably varying the "second heat source," 

 the Harris-Priester models can be made to fit 

 the densities from satellite drag with almost any 

 degree of accuracy, and their new version, pre- 

 pared for the new C'OSPAR International 

 Reference Atmosphere (CTRA 1965) to be 

 published shortly, is remarkably successful 

 in thii: respect. 



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