I am writing a pre-scientific work about the chemtrail conspiracy theory. A part of that is the exact process of contrail formation. There is one more puzzle piece missing. Hopefully the answer to this question doesn't make the puzzle bigger.

But here's the question: According to chemtrail conspiracy theorists, the difference between contrails and chemtrails are their persistence. "Normal" contrails dissolve after a few seconds, but "chemtrails" persist longer, minutes or even hours.

[![Contrail and "Chemtrail"](https://i.stack.imgur.com/hzCzt.jpg)](https://i.stack.imgur.com/hzCzt.jpg)

[Source](http://knowyourmeme.com/memes/chemtrail-conspiracy-theories)

And now to their argument: They say that for a contrail to be persistent, the relative humidity of the ambient air has to be over 100%, hence oversaturated, because then the water vapor resublimates into ice and the contrail grows and stays persistent.

And then they come to their argument: The air in altitudes that planes fly at (~FL340, ~250 hPa pressure altitude (standard atmosphere)) is very rarely oversaturated, but persistent contrails can be seen pretty often.

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Now I need to know, is it true that resublimation is only possible in oversaturated ambient air? If yes, is resublimation even needed for a contrail to stay persistent? Because I found a source that stated that only ~70% relative humidity is needed for a contrail to stay persistent.

Or maybe I've just been unfortunate with all the sounding data I've viewed so far, and the air up there is pretty often oversaturated, although I don't think so.

Please help me understand the last puzzle piece I need in order to finish my pre-scientific work and prove the conspiracy theorists wrong. Thanks a lot!