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My answer is that conduction affects the least amount of air directly. However, it is still absolutely essential for heating and cooling the atmosphere. Somehow, the heat energy must travel from the solid ground to the air, and the main way that happens is by air molecules randomly coming into contact with the ground and picking up the heat energy directly. But it's only a very thin layer of the atmosphere that gets heated like that. Air is about twenty-five times worse at conducting heat energy than water. (But you knew that already. How?)
Once the lowest layer (a few centimeters) of air gets heated, it takes some form of mixing to distribute that heated air into a deeper layer of the atmosphere and replace it with cooler air that can in turn be heated. And by the same token, if the ground is cooling the air, it takes some form of mixing to distribute that cooled air into a deeper layer of the atmosphere and replace it with warmer air that can in turn be cooled.
Convective mixing is more important for heating, and mechanical mixing is more important for cooling, and here's why: to get convective mixing, you need to have what we call "unstable stratification": light fluid underneath heavy fluid. The light fluid tries to rise, and the heavy fluid tries to sink. Voila - convective mixing. But if the heavy fluid is on the bottom and the light fluid is on the top, that's stable. The heavy fluid wants to stay on the bottom and the light fluid wants to stay on the top, and there's no convective mixing. The only way you get mixing under those circumstances is by stirring up the air through wind or flow over and around obstacles: mechanical mixing.
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