What is geoid undulation N, and how is it used in height conversion?

• A. N(x,y) is the geoid height above the ellipsoid; height conversion uses h = H + N.
• B. N(x,y) is the ellipsoid height; height conversion uses h = H - N.
• C. N(x,y) is the difference between ellipsoid and datum origin; height uses h = H * N.
• D. N(x,y) is the gravity potential; height uses h = H / N.

Answer: (A)

Geoid undulation is the offset between the geoid (mean sea level surface) and the reference ellipsoid at a given location. It tells you how far the geoid sits above or below the ellipsoid, with positive values meaning the geoid is above the ellipsoid and negative values meaning it is below.

In height conversion, this offset links ellipsoidal height to height above sea level. The relationship is h = H + N, where h is the ellipsoidal height, H is the orthometric height (height above the geoid/mean sea level), and N is the geoid undulation. So if you know the orthometric height and N, you add N to get the ellipsoidal height. Conversely, H = h − N when you have h and N. This additive connection is why geoid undulation is central to converting GNSS heights to heights referenced to mean sea level.