Below 86 kilometers altitude, the standard atmosphere assumes that there is perfect mixing of the air and that a sample taken at any altitude will have the same proportions of gases. This implies that the molecular weight of the air is the same at all altitudes and allows us to use the simple hydrostatic equation to compute pressure and density.
Above 86 km, this approximation is no longer valid. There are two principal reasons for this breakdown. The first reason is dissociation. The diatomic gases oxygen and nitrogen are constantly breaking apart into separate atoms and constantly combining back into molecules. These competing processes have an equilibrium; at the higher pressures of the lower atmosphere the equilibrium is almost 100 percent in the molecular form. As you go above 86km, you find that much of the oxygen is in the atomic form. Nitrogen molecules seem to be more tightly bound than those of oxygen, and dissociation is not a significant factor.
The second reason for non-uniformity of the composition of the atmosphere is diffusion. Without the turbulence and mixing found at lower altitudes, the lighter gases tend to rise and the heavier gases fall. Oxygen becomes more plentiful than nitrogen because it is lighter. This seems contrary to intuition, but the oxygen is mostly in the atomic form with a molecular weight of 16, while the nitrogen is diatomic, with a molecular weight of 28. At altitudes in excess of 500km, helium and hydrogen become the prevalent gases and all of the hydrogen is in atomic form.
The reference publication, The U.S. Standard Atmosphere, 1976 outlines the development of the theoretical equations used for the calculation of the composition of the upper atmosphere. [see Ch xx, pp.xx-xx]. The essential idea is that one calculates the number density of each species from the equations describing dissociation and diffusion. From the number density of each species and properties of the species, one computes the partial pressure and partial density of each component. These are summed, or integrated, to form the overall density, pressure, and temperature.
Back in 1996, I put on my 'TO-DO' list that I would develop a subroutine that would enable everyone to calculate the properties of the upper atmosphere. I got bogged down with all of the coupled differential equations and other aspects of the calculation. At this point, I encountered the work of Steve Pietrobon of Small World in Australia. Steve had coded the entire process and he graciously allowed me to distribute his computing procedure as part of the atmosphere package from PDAS. I had concluded before this that the computing process was too complex for ordinary enginners to use on everyday projects. I was amazed that Steve had come to the same conclusion and agreed with my concept of taking selected values from the complex calculation and finding values at intermediate altitudes by interpolation. This became the basis of the upper atmosphere routine in the PDAS package.
Go to the Upper Atmosphere Computing Page.
Go to Steve Pietrobon's home page. He is into error control for FPGAs and ASICs these days.