The air moving away from the High pressure system leaves a “hole” to be filled, so air from above sinks into that “hole”.
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You may have seen a weather map with a blue H on it. This blue H means there is a high pressure system over that area of the map. Just what does that mean?
There are no exact measurements that would make a system a High. It’s all relative! If a certain system is a High pressure system, that means it has higher pressure then the areas around it.
The differences in pressure from one place to another on Earth are what cause wind. You see, air wants to move from areas of high pressure to areas of low pressure. Away from areas of high pressure and into areas of low pressure.
The Coriolis Force also adds rotation to the movement of air. In the Northern Hemisphere, air moves clockwise around a High and counter-clockwise around a Low.
Now the air moving away from the High pressure system leaves a “hole” to be filled, so air from above sinks into that “hole”. As the air sinks, water that was in the condensed form (like clouds) tends to evaporate into water vapor. This means the water is not in the condensed form needed to make clouds and precipitation. That’s why many people see a blue H on a weather chart and know good weather and clear skies are coming!