How atmosphere gases affect Earth’s temperature?

Recently, several researchers argued that the main mechanism affecting heat transfer near the surface of Earth is not radiation, but convection. For detailed analysis, please refer to the link provided at the end. We can use a simple and familiar example to illustrate this point.

Suppose we park a car under the direct sunshine in a hot day. If we leave all car windows closed, the temperature inside the car will rise very sharply in a short time. If we keep car windows open, the temperature will be much lower. This means convection, not radiation, is the main channel to reduce heat.

The main pillar of the dominant climate theory is infrared radiation by carbon dioxide and other greenhouse gases. If the above argument is valid, the dominant climate theory will collapse. Does it mean different gases have no differences in affecting Earth’s temperature. Yes, they do, but mainly through a different mechanism, I think.

Carbon dioxide, with a molecule weight of 44, is heavier than nitrogen, 28, or oxygen, 32. With the same temperature, carbon dioxide molecules move slower than nitrogen or oxygen. Hence, heat loss is slower with carbon dioxide than with nitrogen or oxygen.

Furthermore, carbon dioxide, being heavier, produce higher atmosphere pressure than nitrogen or oxygen. Higher pressure means higher density. Carbon dioxide molecules bump into each other more frequently. This further slows down heat transfer. As a result, heat transfer is slower in convection when gases are mainly carbon dioxide instead of nitrogen or oxygen.

I try to find an analytic formula for the relation between molecule weight and atmosphere pressure. It is a large-scale problem. Gravitational force, temperature, and gas density are changing with altitude. I haven’t been able to put them together.  

I consulted ChatGPT. It noted that obtaining an analytical formula is “challenging”. As ChatGPT couldn’t offer an analytical formula, it is likely that such an analytical formula doesn’t exist in academic literature. I will be very grateful if someone can show me the answer.

References

Tom Shula: A Novel Perspective on the Greenhouse Effect | Tom Nelson Pod #98

https://youtu.be/NS55lXf4LZk