Shortwave radiation passes largely unimpeded through the atmosphere. It strikes the ground and warms it. The warmed ground emits longwave radiation, some of which is absorbed by greenhouse gases, causing the atmosphere to warm.
If there were no greenhouse gases, almost all of the surface heat would radiate back into space without warming the atmosphere. A small amount of heat would transfer kinetically directly at the ground surface, but the atmosphere would be very cold. This is basically what happens in Antarctica, where there are very few greenhouse gases.
How could a weather model possibly work without a radiative transfer model which models the greenhouse effect?