From an old Science News article:
Curious 'dopers would read the whole article and notice that there was some doubt surrounding the issue- measurements elsewhere showed the ionosphere rising. But the predicted cooling in the middle atmosphere was also detected, supporting the theoretical mechanism.
The article is from 1998. What’s new with this issue? Has the question been settled?
I don’t have an answer to your question, but I found this paper with a lot of background information that might give you some leads on what to search for:
A Study of the True Height Analysis Methods, Liu, Berkey, Wu
I gather from the gist of the paper that we really don’t have any direct method for calculating the actual boundary heights or thickness of the ionosphere. Rather, we infer that from experiments that measure the “virtual height”. The virtual height is essentially the amount of time it takes for a signal of a particular frequency to bounce back to the ground off of the ionosphere, divided by two, and multiplied by the speed of light.
But due to wonkiness in how light propagates through the ionosphere, the virtual height doesn’t correlate very well to the actual height of the reflective layer. And, of course, the virtual height depends on the frequency as well.
To further complicate matters, there are bunch of different mathematical approaches for deriving (well, technically integrating :p) the electron density – which is pretty much the defining factor of the ionosphere – from the virtual height, which is more or less how the actual height is determined.