Hmmmmmm . . . seems rather complex and more relevant to the tropics and subtropics . . . we still seem to be talking about cirrus clouds . . . seems -41C is the upper temperature limit for persistent aerodynamic contrails which is also the highest temperature at which exhaust mediated persistent contrails propagate and both seem to form at or near cruising altitudes. . . simply stated the higher and colder . . . the persistent contrails are primarily exhaust mediated and the lower but still high altitudes are where temperatures are higher (above -41C) the persistent contrails are mediated by aerodynamic processes. . . My question is: what is the lowest altitude at which persistent contrails of any species may form?
Holy Moley, you are over thinking it, man.
Guestimating, 90% of the time...
Persistent
exhaust condensation trails: above about 28,000 feet (provided temperature and RH conditions are met), below tropopause 45,000 feet (varies a lot).
Persistent
aerodynamic condensation trails: above 10,000 to 15,000 feet (provided temperature and RH conditions are met), below tropopause 45,000 feet (varies a lot).
Persistence depends of the moisture content of the air, usually quantified by the Relative Humidity with respect to water, which needs to be above about 63% at temperatures around -48°C.
I made this handy table...
Altitude Press Temp RHw
25000 376.0 -34.5 71%
26000 359.9 -36.5 70%
27000 344.3 -38.5 69%
28000 329.3 -40.5 68%
29000 314.9 -42.5 66%
30000 300.9 -44.4 65%
31000 287.4 -46.4 64%
32000 274.5 -48.4 63%
33000 262.0 -50.4 62%
34000 250.0 -52.4 61%
35000 238.4 -54.3 60%
36000 227.3 -56.3 59%
37000 216.6 -56.5 59%
38000 206.5 -56.5 59%
39000 196.8 -56.5 59%
40000 187.5 -56.5 59%
This relates the altitude, pressure and temperature in the
International Standard Atmosphere with the RH (with respect to water) at the ice-saturation point. (Also at this RH the Frost Temperature is the same as the ambient Temperature - in case you want to conceptualise it that way.)
At higher RH than these listed at those temperatures, the air is ice-supersaturated, and this is the condition for persistence of contrails - ice cannot evaporate with this much water vapor already in the air at this temperature.
(The table doesn't extend down into the aerodynamic contrail zone - it was constructed for the exhaust contrails case.)
These amounts of water vapor in the air are tiny. For the level
bolded there, the water content at ice-saturation is 0.1155 grams per kilogram of dry air, which (at that pressure and temperature) occupies 2.4 cubic metres. That's a cube 1.33 metres on an edge (4 feet 4 inches). One teaspoon of water is 5 grams, so it's a couple of drops in a 4 foot 4 inch on-a-side cube.
It's no wonder cheap disposable automatic (radiosonde) instruments have difficulty measuring it accurately.