This is an interesting question, one suggestion I have relates to a method for deriving air density based on the terminal impact velocity of raindrops (density 1), although several process-related assumptions are necessary.  I learned of this method from Dave Pyle (Oxford) in discussion for use with soft pyroclastic ash and possibly impact ejecta, and there are now a few papers applied to the Archaean, see Som et al (Nature 484, 359-362) Air density 2.7 billion years ago limited to less than twice modern levels by fossil raindrop imprints. If splash textures related to terminal velocities of fall-back impact spherules could also be established, it might then be possible to extract more precise estimates based on heavier particles (density >>1), but I am not sure such rock surfaces exist for the Precambrian.  In the ~end Cretaceous Chicxulub global ejecta, potential atmospheric interactions are complex, but may hint at a separate method for future extraction of chemical evidence for oxygen in Precambrian impact ejecta/spherule beds. An on line PhD thesis by Tamara Goldin (university of Arizona, 2008) sets the scene for atmospheric interactions from Chicxulub ejecta, and Precambrian impact spherule beds have been reviewed by Johnson and Melosh (2012, Nature 485, 75-77) and Glass and Simonson (2013) Distal impact ejecta layers (Springer). 

Thanks for interesting answer. I'm asking about the possible troposphere thickness mainly in the context of possibility of hailstone formation [during hailstorms] in the Precambrian atmosphere.

Recently, we have published a paper about hailstone impression in the Neoproterozoic of Western Africa, which at that time was located in high southern latitudes [about 70 degrees], far beyond the recent occurrences of hailstorms.

Remin, Z., Krogulec, T., Drela, T. and Surowski M. 2014. The recognition of hailstone impressions in clay-rich sediment: experimental results and relation to the Neoproterozoic case. Journal of Sedimentary Research, 84, 543–551.

It is well known that the hailstones are produce in thunderstorm cells within the Cumulonimbus clouds combined with strong updrafts, which can reach the height of 10-15 or even 18 km [equatorial areas]. Contrary in the circumpolar areas, where the troposphere is thinnest, the hailstorms are rather extremely rare or absent. It is also because smaller temperature amplitude which can drive the formation of thunderstorm cells.

Therefore, the question is whether the thickness of Neoproterozoic troposphere in circumpolar areas was much thicker then today [interesting climate results…] enabling the formation of Cumulonimbus clouds in which hailstone originate, or what…?

Zbyszek

http://jsedres.geoscienceworld.org/cgi/reprint/84/7/543?ijkey=uBiPvnJGTZWX6&keytype=ref&siteid=gsjsedres

Dear Zybszek

I think the attached paper is useful for your question

Regards

Massih