The hook
Geodesy is what happens when surveying gets honest about the earth being round (and lumpy). Three surfaces matter: the ellipsoid (math), the geoid (gravity-equipotential sea level), and the topographic surface (the dirt). Every elevation you publish is a height above ONE of these — get the wrong one and you're off by 25 meters somewhere.
Memorize these
Concepts that show up on the exam
Ellipsoid
A mathematically perfect oblate spheroid that approximates earth's shape. Defined by semi-major axis (a) and flattening (f). GRS80 and WGS84 are the modern ones.
Geoid
The surface of equal gravitational potential corresponding to mean sea level extended through continents. NOT smooth — bulges where crust is dense, dips where light.
Geoid undulation (N)
Vertical separation between geoid and ellipsoid: N = h − H. Negative across most of the U.S. (geoid is BELOW the ellipsoid).
Orthometric height (H)
Height above the geoid. What you get from leveling. The "elevation" on USGS quads.
Ellipsoid height (h)
Height above the ellipsoid. What raw GPS gives you. NOT what shows up on signs at mountain summits.
Geoid model
A grid of N values across the country. NGS publishes GEOID18 (current); GEOID12B (older). Software uses it to convert h ↔ H.
Convergence of meridians
Meridians converge toward the poles. The angular convergence between two stations affects azimuths read in different reference frames.
Deflection of the vertical
Angle between a plumb line (perpendicular to geoid) and the ellipsoid normal at the same point. Small (typically <30") but matters for high-order work.
Keep these in muscle memory
Formulas to know cold
Orthometric / ellipsoid height relation
h = H + Nh = GPS-derived ellipsoid heightH = leveled elevationN = geoid undulation (from model)
Flattening
f = (a − b) / aa = semi-major axis (equator)b = semi-minor axis (pole)
Eccentricity (squared)
e² = 2f − f²Used in coordinate transformations between geodetic and geocentric.
Try it before you peek
Worked example
The problem
A GPS receiver reports the ellipsoid height of a benchmark as h = 432.18 m. The geoid model gives N = −28.45 m at that location. What is the orthometric (sea-level) elevation?
Don't fall for these
What trips people up
Sign of N
In CONUS, N is negative everywhere except a small region in the West. A positive answer for N usually means you misread the model.
GPS accuracy ≠ elevation accuracy
RTK-GPS gives 1–2 cm horizontal but the ellipsoid height has the GPS error PLUS the geoid model error (typically 2–5 cm). Don't blame GPS for elevation discrepancies caused by an old geoid model.
WGS84 vs. NAD83 ellipsoids
WGS84 (the GPS native frame) and NAD83 (U.S. ground frame) use ALMOST the same ellipsoid (GRS80) but their realizations differ by ~1–2 m. They are NOT equal in general.
Test yourself
How well did it stick?
A quick 5-question check on Geodesy. See where you stand and what to review.