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From Hurth's book, The Lost Art of Finding Our Way , there is a section on Air Mass and Fronts (page 267)

On average, since cold air is denser than warm air, the northern stretches of continental landmasses create high-pressure systems, and the warmer maritime air creates low-pressure systems.

How does density come into play here to create a high-pressure system?

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I ended up asking him directly:

It's a bit of a simplification of what happens.

You can picture a large column of air stretching into the sky. To a first approximation, we live an equal pressure environment, which is why the air pressure is about 1013 millibars both in summer and in winter , as the surface temperature changes. This column of air that stretches into the sky expands and contracts, depending on the temperature. It expands in warmer temperatures and contracts in smaller temperatures.

The second order effect is associated with what you might expect from buoyancy. A hot air balloon rises because the warm air is less dense than the surrounding air, and by Archimedes' principle. So, hot air tends to be less dense than cool air.

The way I understand is you can imagine that warm air would cause the column of air to expand, and thus create a lower pressure than where it's colder. Since air goes from high pressure to low pressure, there would be a vacuum.

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