Why do we get frosts above zero degrees?

The ground is loses heat by radation. It can see the clear cold sky above it on a clear night and the ground radiates away its energy, getting down to zero or below zero very effectively, because the ground is good at giving up energy. But the air, and the atmosphere sitting above the ground, is effectively transparent to the radiation, it doesn't absorb or emit radiation well and so it doesn't cool down nearly as fast or insulate the ground very much. So the air loses its energy much more slowly than the ground does. This means that the air can be several degrees above zero but the ground is now lower that, say zero or even minus three degrees. And when the warmer, damp air meets the freezing ground, it cools down, the moisture condenses out and forms frost on the ground, even though the air temperature is still not quite freezing...