A GPS receiver reports an ellipsoidal height of 80 meters at a location where the geoid undulation (geoid height above the ellipsoid) is +25 meters. What is the orthometric height — the true elevation above sea level — at that location?
A105 meters — add the geoid undulation to the ellipsoidal height
B55 meters — subtract the geoid undulation from the ellipsoidal height
D25 meters — the geoid undulation is the actual elevation
Orthometric height H = ellipsoidal height h − geoid undulation N. Here: H = 80 − 25 = 55 m. The geoid undulation N is the height of the geoid *above* the ellipsoid; a positive N means the geoid surface is higher than the ellipsoid at that point. GPS measures height above the ellipsoid (a mathematical surface), but sea level and drainage follow the geoid (a physical equipotential surface). Subtracting N converts GPS ellipsoidal height to the meaningful engineering quantity. Adding them (option A) gets the sign wrong.
Question 2 Multiple Choice
A positive geoid undulation — where the geoid surface rises above the reference ellipsoid — occurs over what type of subsurface feature, and why?
AOver a low-density mantle plume, because the lighter material pushes the crust upward, creating a surface bulge
BOver a dense subducting slab, because the extra mass increases gravitational attraction, pulling the equipotential surface upward toward the denser material
COver oceanic trenches, because water is denser than continental crust and raises the gravity field
DOver regions of recent glacial retreat, because removing ice reduces pressure and allows the geoid to rise
A positive geoid undulation (geoid above the ellipsoid) indicates excess mass below. Dense material — like a cold, subducting slab — exerts stronger gravitational attraction, pulling the equipotential surface upward toward it. Conversely, a hot, buoyant, low-density mantle plume creates a mass deficit, and the geoid dips below the ellipsoid (negative undulation). The geoid is a direct map of subsurface mass distribution, not surface topography.
Question 3 True / False
GPS receivers directly measure elevation above sea level, making geoid models unnecessary for surveying and engineering applications.
TTrue
FFalse
Answer: False
GPS receivers measure height above the *reference ellipsoid* — a smooth mathematical surface that approximates Earth's shape. Sea level (and the direction water flows) follows the *geoid*, which is a physical equipotential surface that can deviate from the ellipsoid by up to ±100 meters. Without applying a geoid undulation correction, GPS heights cannot be used for drainage engineering, flood mapping, or any application where gravity-driven flow matters. National geoid models exist precisely to bridge this gap.
Question 4 True / False
The geoid is an equipotential surface of Earth's gravity field, which means water on a perfectly still geoid surface would not flow in any direction.
TTrue
FFalse
Answer: True
An equipotential surface is one where the gravitational potential is constant everywhere — no potential energy gradient exists along the surface, so no gravitational force acts to move an object along it. A ball or water droplet placed on a perfect equipotential would experience no net force parallel to the surface. This is precisely why the geoid is the natural reference for elevation: 'above sea level' means above this surface, and water at rest always lies on it. Any deviation from the geoid creates a slope in the potential, which drives water flow.
Question 5 Short Answer
Why does the geoid deviate from the reference ellipsoid by up to ±100 meters, and what does this tell us about Earth's interior?
Think about your answer, then reveal below.
Model answer: The reference ellipsoid assumes Earth has a smoothly varying, rotationally symmetric internal density. In reality, Earth's interior is heterogeneous: dense subducting slabs, light mantle plumes, thick continental roots, and ocean sediment basins all create lateral density variations. These mass anomalies warp the gravitational potential field, pulling equipotential surfaces toward dense regions and pushing them away from low-density regions. The geoid undulations — where the geoid diverges from the ellipsoid — are therefore a direct map of subsurface mass distribution, revealing structures we cannot directly observe.
This connection between surface gravity measurements and subsurface structure is the foundation of geodesy and satellite gravity missions like GRACE. The GRACE mission exploited this by measuring geoid changes over time, revealing ice sheet loss, groundwater depletion, and post-glacial rebound — all of which represent mass redistribution that shifts the geoid. The geoid is thus not just a static reference surface but a dynamic window into Earth's interior and its ongoing mass transport.