The general rule of thumb used by meteorologists is that temperature decreases approximately 3.6 degrees F per 1000 feet in the troposphere (the lowest layer of the atmosphere, where we live). This is an average value and varies from season to season. The decrease is slightly less in the summer and slightly greater in the winter.
The atmosphere receives about one-eighth of its heat directly from the Sun in the form of short-wave radiation absorption, but receives almost 70 percent, or 6 times as much heat from the earth, in the form of long-wave radiation.
Earth's surface is primarily from long wave radiation. The very lowest part of the atmosphere, called the boundary layer (up to about 1.5 kilometers on a normal day) warms from the warmer earth surface (mostly by long wave radiation), with the warmer air being mixed upwards by convective air parcels (air warmer than the surrounding air) and mechanical turbulence (from wind). As the air rises (and expands, thereby decreasing in air pressure) it cools, resulting in the adiabatic lapse rate. Since temperature and pressure are roughly proportional for the same volume of air, the temperature decreases with height (during the day).
Long wave radiation is absorbed by the air, primarily water vapor, carbon dioxide, and methane in the air (so-called "greenhouse gases"). Since there is a greater concentration of these gases near the earth's surface, more is absorbed closest to the surface and less with increasing height. Therefore, for this reason also, during the day, the temperature decreases with height in the boundary layer.
So, adiabatic cooling and the distance from the earth's surface are both important. Long wave radiation is most effective in heating the air, with direct contact of the air with the ground being less important.
At night, long wave radiation continues to be lost from the Earth's surface (a lot during cloudless nights) and often causes the temperature at the surface to become less than at greater heights, causing a slight increase in temperature with height (called an inversion) and a decrease in the height of the boundary layer to as little as 300 meters.
Sources:
[1] Dale Bechtold, David Cook, "Heating in the Atmosphere", Online posting. NEWTON BBS Ask a Scientist.
[2] David Cook, "Temperature and Atmosphere", Online posting. NEWTON BBS Ask a Scientist.
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