What is the term for the height above the geoid?

The term that defines the height above the geoid is orthometric height. Orthometric height is the vertical distance between a point on the Earth's surface and the geoid, which represents mean sea level. This measurement reflects the gravitational potential and is commonly used in surveying to represent elevations in a way that is relevant to the physical reality of land measurements.

In surveying and geodesy, orthometric height is crucial because it accounts for variations in gravitational forces due to Earth's topography and density variations. This gives a more precise reading for elevation purposes as compared to other height measurements that do not take gravity into account.

In contrast, geodetic height refers to the vertical distance above a reference ellipsoid, which is a mathematical model of the Earth's shape. Ellipsoidal height also signifies the same concept as geodetic height and is critical for applications like GPS where positions are typically referenced to the ellipsoid. Meanwhile, geoid height is the height of the geoid above or below the reference ellipsoid, which is not the same as the height of a point on the Earth above the geoid itself.