The GPS-derived height of a control point is 56.439 meters, while the orthometric elevation of the same point is 8.795 meters. Determine the separation between the ellipsoid and the geoid at the location of the control point.

• A. -47.464
• B. -47.644
• C. + 47.644
• D. +47.464

Answer: (C)

The relation between these heights is that the GPS height gives the ellipsoidal height h (above the reference ellipsoid), while the orthometric height H is measured above the geoid. The separation between the ellipsoid and the geoid at a point, known as the geoid undulation N, is N = h − H. With h = 56.439 m and H = 8.795 m, N = 56.439 − 8.795 = 47.644 m. A positive value means the ellipsoid sits above the geoid by that amount, so the separation is +47.644 meters.