Define ellipsoidal height and orthometric height, and give their relationship.

• A. Ellipsoidal height h is distance above the geoid; orthometric height H is height above ellipsoid; h = H - N.
• B. Ellipsoidal height h is height above geoid; orthometric height H is height above ellipsoid; h = H + N.
• C. Ellipsoidal height h is distance above the reference ellipsoid; orthometric height H is height above the geoid; h = H + N.
• D. Ellipsoidal height h and orthometric height H are identical.

Answer: (C)

The main idea here is understanding how two different height measures relate through the surface that links gravity and topography—the geoid. Ellipsoidal height is the distance from a point up to the reference ellipsoid along the normal to that ellipsoid. This is the height you typically get from GNSS measurements, because GNSS references the mathematical ellipsoid.

Orthometric height is the height above the geoid, which is the equipotential surface that approximates mean sea level. This is the height used in traditional leveling.

The key link between them is the geoid undulation, N, which tells you how far the geoid is above or below the ellipsoid at a given location. By definition, N = h − H. Rearranging gives h = H + N. So the ellipsoidal height equals the orthometric height plus the geoid height at that point.

In practice, if the geoid sits above the ellipsoid (N positive), the ellipsoidal height is larger than the orthometric height; if the geoid sits below (N negative), the ellipsoidal height is smaller. This explains why GNSS heights (h) and leveling heights (H) differ and how to convert between them.