If you heat a column of air, causing it to rise, it will tend to expand upwards, thus creating a core of higher pressure at the upper levels.
Why does it create higher pressure at the higher altitude though. Afterall, the atmosphere is not enclosed so it isn't like heating the gas inside a closed box.
Now, I do remember having read something about this phenomenon about upper and lower levels having different pressures due to heating.
And yes, I did search for the Qs online and in the books. But whenever they attempt to explain how to extrapolate for surface pressure after having measured the station pressure at a higher altitude, they describe it instead of providing math examples. For example, it station pressure at 1,000 ft is 28.92" at 10 degrees, how does one get the sea level pressure?