Consider a clear night. The infrared loss from the surface will result in the surface cooling faster than the air above. This is a critical point. Although we earlier noted that radiation emission is a function only of temperature, that is not quite true. It turns out that at a given temperature, some materials are more efficient at emitting radiation than others.
Air is much less efficient at emitting radiation than the surface.
So on a clear night, the surface will cool more rapidly than the air above . As the surface cools due to infrared loss, the air in direct contact with the surface will also cool, as heat flows down to the surface. Note that in this situation, the temperature near the surface is increasing with height. This is called an inversion. Eventually, if the surface cools enough, then the dewpoint temperature of the air in contact with the surface can be reached.