What claim?
Where did I say temp and humidity will be the same at various altitudes?
You claimed a change in altitude wouldn't affect the appearance of contrails, but they are directly affected by temperature and humidity, the implication of your statement is that those factors would be constant at various altitudes. If I misunderstood, please clarify.
Is it also your claim that cirrus clouds should dissipate just as rapidly as "real" contrails? A contrail is just a cloud. Why are some naturally formed clouds persistent and others dissipate quickly?
When jet fuel combusts, it forms water as a byproduct. Tiny droplets shoot out in a blast of hot air as the plane soars along. So do minute particles of oxidized sulfur and nitrogen. What else? Impurities or additives, in minute quantities. Metal particles, soot, that sort of thing. These minims give the water vapor already in the air something to cling to. Just as important, though, is the condition of the air through which the jet fliesnamely, its temperature and humidity. Contrails dont always appear behind the jets. In fact, they usually dont. They form about a third of the time, on average.
Humidity and temperature: The forces that create a contrail are quite similar to the forces that make your breath visible on a cold, damp day.
Shoot a plume of hot air laden with tiny particles into the upper atmosphere, where the temperature is, say, sixty below zero and the humidity is somewhat high. The air is suddenly unable to hold its water. Vapor condenses and clings to the matter in the jets plume. The air soon mixes and cools and the particles of water freeze. A contrail is born.
What happens next also depends on atmospheric conditions. If the air is just barely humid enough and cold enough to allow water vapor to condense, a contrail appears but doesnt stick around. Those are the ones you call 'real' contrails, disappearing almost as quickly as it appears.
If the air is sufficiently frigid and humid, a contrail forms easily, stretching out over the sky, coaxing tiny ice crystals out of the atmosphere. Chances are on days like these (especially if you live under a busy flight path) the sky will be marred with the lines of contrails, roughly parallel, varying in density and width. On days like these, a contrail can persist long after the jet has passed. The contrail splays out and takes the appearance of a naturally formed cirrus (or cirrocumulus) cloud.
Broken contrails are explained in exactly the same way. The amount of water in the exhaust is pretty constant, but the amount of moisture in the air is not. As I mentioned, the humidity varies with altitude, and a layer of low humidity can be sandwiched between two layers of high humidity. As a plane climbs or descends through this layer, then the trail will only form in the areas of high humidity, and so look like it was switched off in the area of low humidity.
You can get the same effect with temperature. A warm layer of air can actually lay on top of a colder layer in what is called an
inversion (youll hear this on the weather sometimes, referred to as an inversion layer). When a plane flies through this inversion layer, the trail can be broken.