How is ellipsoidal height defined?

Ellipsoidal height is defined as the vertical distance of a point above the mathematically defined surface of a reference ellipsoid. This ellipsoid is an idealized mathematical model of the Earth's shape, used in geodesy, and is essential for accurate positioning and navigation. Because the reference ellipsoid is a smooth, continuous surface, ellipsoidal height provides a way to describe elevations that is independent of variations in local topography, such as hills or valleys.

When considering the other definitions, height above the geoid refers specifically to the geoid, which is the equipotential surface of the Earth's gravity field and represents mean sea level in a gravitational context. Height relative to mean sea level is a more practical measurement that includes the effects of water levels, atmospheric conditions, and other local variations. Orthometric height describes the height above the geoid, incorporating the variation in gravitational potential, and thus is fundamentally different from ellipsoidal height which is strictly measured from the reference ellipsoid. Therefore, the definition that aligns precisely with ellipsoidal height is the one indicating it is the height above the reference ellipsoid.