There's no simple answer I'm afraid Prof. Chen (University of Wisconsin) outlines the problem:
This problem involves several components. First, (s)he must estimate the temperatures of jet exhaust. A good model developed from another PCOL project, 'How Hot is The Flame' [Zielinski, 2001] would be a starting point. Second, the temperatures and humidity of the atmosphere must be known. These data can be either estimated (by barometric formula [Atkins and de Paula, 2002a], and adiabatic air expansion formula [Atkins and de Paula, 2002b]) or found from satellite data bank [Thompson,2000]. Third, (s)he must construct vapor-pressure diagrams of ice and water[Atkins and de Paula, 2002c]. These diagrams can be found in many references. Lastly, (s)he must articulate the cooling mechanisms of jet exhaust and predict the frost/fog formation behind the jet in the sky.
Yeah, right!
Here's a link- but it's not a great deal of help in waking up, looking at the sky, saying "today's perfect" & phoning the cameraman, focus-puller, clapper-loader and soundman, I'm afraid!
www.tpub.com/weather3/6a-26.htm
Good luck