In school, I learned the mechanism of high and low pressure areas, which roughly goes like this:
In the tropics, the sun warms up the air during the day. Water evaporates, so that the air gets warm and moist. Warm air is lighter than cold air, so it rises up, leading to a low-pressure area because the warm air is now "missing", so we need air to horizontally flow in. The rising moist air cools down, so it starts to rain, that's why there are rainforests in the tropics. Some thousand kilometers to the north or south, the air is sinking to compensate for the rising air in the tropics. Sinking air warms up and gets dried, so it is very dry (Azores High), leading to the big deserts in the subtropics, e.g. the Sahara.
I hope this is more or less correct.
There is one thing I do not understand: Why is the air pressure lower in the tropics, and higher in the subtropics (Azores High)?
My intuitive physical reasoning tells me the opposite, for various reasons:
- The reason warm air rises up is not that because "it is light", but that it is lighter than cold air, so the cold air can replace it by flowing under it and lifting it up. So the phrase "warm air rises up, leading to a low-pressure area because the warm air is now missing" is very misleading: it is the inflowing cold air that lifts the warm air up. So there is never a "moment" when we have a lower pressure - the warm air rises because it gets replaced by cold air, and there isn't a reason why the pressure should drop.
- The air pressure is more or less the combined weight of the air above us. The heavier the atmosphere above us, the higher the ambient pressure. Now, when the air warms up and gets lighter, it gets replaced by the cooler air flowing in. So after the warm air has risen up, we should have more air above us: the warm air that has risen up, plus the cold air that has flowed in horizontally. So the atmosphere above us is heavier in total, which again means we should have a high-pressure area.
- Another view could be that since the air in the tropics is warming up, it expands. This large-scale expansion should lead to a high-pressure area. After all, if you expand a large amount of gas, its pressure increases until it has had time to expand properly.
I am very much aware that all these reasons must be wrong in some way. I don't doubt the existence of the Azores High or the rainforest. I just miss an intuitive understanding.
How can the tropics Low and the subtropics High be explained in intuitive physical terms?