How does MSLP change with elevation? trying to interpolate MSLP
So the Mean Sea level pressure is defined (simply) as the pressure of the station, corrected to sea level. However, methodological problems occur over terrain, such as assumptions that may not be true.

A common method used to correct the pressure is called the barometric equation. One assumption, for example, is that the mean temperature of the previous 12 hours is used to determine the average temperature of the imaginary atmosphere (where the terrain actually is). Of course this generates problems, such as the idea that the mean temperature used is not representative, the lack of lapse rate information, etc. These problems can yield to extraordinary MSLP gradients that may or may not actually exist in reality.