In the equation h = H + N, what does N stand for?

• A. ellipsoidal height
• B. hourly height
• C. ellipsoid-geoid separation
• D. geoidal height

Answer: (C)

The key idea is how heights referenced to different surfaces relate. Ellipsoidal height h measures distance above the reference ellipsoid, while orthometric height H measures distance above the geoid (mean sea level). The difference between those two surfaces at a point is the geoid’s separation from the ellipsoid, called the geoid height or geoid undulation, and in this equation that quantity is N. Because h = H + N, you’re essentially adding how far the geoid is from the ellipsoid to the height above the geoid to get the height above the ellipsoid. So N stands for the ellipsoid-geoid separation. This quantity can be positive or negative depending on where you are. The other terms don’t fit the role in the equation: ellipsoidal height is h itself, hourly height isn’t applicable, and while geoidal height is related, the standard name used here is ellipsoid-geoid separation (geoid undulation).