The orthometric height is the distance H along a line of force from a given point P at the physical surface of an object to the geoid.
Orthometric heights are what are usually used in the US for ordinary engineering work. Values for measured points can be obtained from the National Geodetic Survey data sheets. This data was gathered over many years by massive projects of precise optical leveling.
Orthometric heights relate approximately to the "height above sea level" but the current NAVD88 datum is tied to a specific elevation at a chosen point rather than to any location's exact mean sea level.
GPS measurements give earth-centered coordinates, usually displayed as height above the reference ellipsoid, which cannot be related accurately to orthometric height above the geoid unless accurate gravity data is available for that location. NGS is undertaking the GRAV-D program to obtain such data.
Alternatives to orthometric height include dynamic height and normal height.
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“How frightening it is to have reached the height of human accomplishment in art that must forever borrow from life’s abundance.”
—Franz Grillparzer (1791–1872)