These odd-looking streaks appeared in the cirrostratus-cirrocumulus cloud layer over my house a few weeks back. They look like reverse contrails formed by two planes taking off from Portland, Oregon, minutes after each other. In fact, they are called "distrails"--short for dissipation trails. They form when the plane's exhaust is warm enough to evaporate some of the water particles in the cloud layer, or when drier air surrounding the cloud is mixed in by the plane's turbulence, or when the particles in the exhaust of the plane serve as condensation nuclei. The cloud droplets grow large and heavy enough to fall out of the cloud layer. They evaporate (dissipate) as they fall into the warmer air below and leaving these clear streaks behind.
This type of cloud phenomenon is apparently rare. I'd say capturing two parallel trails might be a once-in-a-lifetime photo op even though planes take off from Portland all day long.