Is the air pressure high or low on cloudy days?

I think it will be lower. I mean near-surface air pressure.

it's like this.

on rainy days, the warm air flow drops, with low density and low pressure

The clear and dry cold air flow rises, with high density and high pressure.

and.

on cloudy days, the atmospheric inverse radiation is relatively strong, that is, the heat preservation effect is significant. Therefore, the ground temperature is relatively high. Then it leads to a low air pressure near the ground.

5th floor, are you all right? Do as I say. It's warm near the ground How can the air pressure be high if the temperature is high?