Geodesy and Reference Systems
The exam tests whether you can keep the three surfaces - the physical Earth (geoid), the reference ellipsoid, and the grid you finally plot on - strictly separate, and whether you can move coordinates between systems, frames, epochs and height types without sign errors.
The three surfaces and their heights
- Ellipsoidal height h is measured from the reference ellipsoid and is what GNSS delivers natively.
- Orthometric height H is measured from the geoid (approximated by mean sea level) and is what levelling and most national height datums use.
- The geoid undulation N links them: h = H + N, so H = h − N. N is typically ±10–50 m over continental areas.
Systems versus frames
A reference system is an ideal definition; a reference frame is its realisation by stations with coordinates and velocities. ITRF is global and kinematic. ETRS89 is the European realisation, aligned to ITRF at epoch 1989.0 and then held fixed to stable Eurasia, so ETRS89 coordinates carry no plate-motion velocity. WGS84 is the GPS broadcast frame - close to ITRF, not identical, and not automatically acceptable as a legal or engineering datum without a documented transformation.
Worked example: a GNSS receiver reports h = 512.34 m in ETRS89. Your national geoid model gives N = 47.12 m at that point. Orthometric height H = 512.34 − 47.12 = 465.22 m. If the model's stated accuracy is 3 cm (1σ), report 465.22 m ± 0.03 m and name the vertical datum. Stating the uncertainty earns marks; a bare number does not.
Traps
- Reversing the sign in h = H + N. Sanity check: the geoid lies above the ellipsoid in the North Atlantic and below it over much of the Indian Ocean.
- Using WGS84 ellipsoidal heights as if they were orthometric heights.
- Mixing ITRF/CORS coordinates from different epochs; plate motion in Europe is roughly 2–3 cm per year.