In Absorption, Not Reflection we showed that heat leaves the atmosphere almost entirely by radiation. Conduction of heat through columns of air is insignificant compared to radiation absorbed by carbon dioxide and water in the atmosphere.
Heat cannot leave the atmosphere by convection, but it does enter by convection. The ground warms up in the light of the sun. Air in contact with the ground warms up. It becomes less dense, and rises. It is replaced by cool air from above, which soon warms up and rises itself.
Lack of convection is responsible for the warming of greenhouses. Heat from the sun enters the greenhouse and warms the floor. The floor warms the air. But the air cannot rise out of the greenhouse, and so the same body of air continues to warm up.
We demonstrated the greenhouse effect in our laboratory. We used a rock salt crystal as a roof for a black-walled space. We heated the space with a 60-W incandescent bulb. At first, we removed two walls and raised the roof to allow air to flow freely, as shown here. The black-walled space warmed up from 19°C to 26°C (with a few hiccups along the way because we had to replace the bulb). We lowered the rock salt crystal onto the space and added the two remaining walls, as shown here. The air inside the space was trapped. The temperature rose from 26°C to 30.5°C.
We used rock salt because it is transparent to both visible and infrared light. Our 60-W bulb filament is a around 3000 K, with peak emission wavelength of 1 μm. Our black-walled space is at around 300 K, with peak emission wavelength of around 10 μm. Rock salt is transparent to both frequencies. For a more detailed description of our apparatus and methods, see here.
The warmth in a greenhouse is due to the heating of trapped air by the sun. Outside greenhouses, heat enters the atmosphere by convection. Conduction plays a role only at the surface, where air in contact with the ground gains heat by conduction, thus initiating convection.