Three different "heights" — and only one is the one you want
Hand a GNSS receiver to someone new and the first surprise is the height. They set up over a benchmark stamped, say, 42.10, and the controller reads 56-something. Nobody calibrated anything wrong. The receiver is telling the truth — it is just telling a different truth. A GNSS height is measured up from a smooth mathematical ellipsoid, a tidy surface chosen to approximate the whole Earth. The benchmark height is measured up from the geoid — the lumpy, gravity-defined level surface that mean sea level traces around the planet. Water, drainage, and every engineer's intuition about "uphill" live on the geoid. The ellipsoid knows none of that.
So on every job we deal with three numbers, and we are careful never to mix them: the ellipsoidal height (h) the satellites give us, the orthometric height (H) the client actually wants, and the geoid undulation (N) that separates them. Get the relationship between these wrong and you can deliver a survey that is geometrically beautiful and hydraulically useless.
Where these heights show up in our work
- 800,000+
- Feddans levelled
- Every one tied to a real vertical datum, not a raw GNSS height.
- 3000+ km
- Roads surveyed
- Gradients that only make sense in orthometric heights.
- 600+ km
- Railways
- Where a few centimetres of height error is a real problem.
The one equation that ties it together: H = h − N
The whole subject collapses to a single, honest little equation: H = h − N. Your orthometric height equals your ellipsoidal height minus the geoid undulation. The receiver measures h geometrically. A geoid model — a gridded surface that says how far the geoid sits below (or above) the ellipsoid at every point — supplies N. Subtract, and out comes H, the height that respects water.
Two things trip people up here. First, N is not a constant you can carry in your head; it tilts and ripples across a region, which is exactly why a relative survey on a big site still drifts if you ignore it. Second, the geoid model fixes the shape of the separation, but not necessarily your country's exact datum origin. That is what the benchmark tie is for. Below is the field routine we run so that a GNSS height becomes a height we will sign off on.
How we turn a GNSS height into a trustworthy orthometric height
- 1
Capture the ellipsoidal height (h) over your point with a properly initialised GNSS observation — fixed solution, good geometry, long enough occupation for the accuracy you need.
- 2
Apply the correct geoid model for the region to read the geoid undulation (N) at that location, so you can compute H = h − N.
- 3
Occupy a known, published benchmark the same way and compare the geoid-derived H against its certified orthometric value — this exposes any datum offset the model alone cannot see.
- 4
Apply the resulting tie/offset (and, where it matters, run a short digital-level loop between benchmarks) to bring your GNSS heights onto the official vertical datum.
- 5
Document the geoid model used, the benchmark IDs, and the residuals in the survey report so the height is reproducible and auditable, not a black box.
Ellipsoidal vs orthometric height at a glance
| Property | Ellipsoidal height (h) | Orthometric height (H) |
|---|---|---|
| Reference surface | Mathematical ellipsoid (e.g. WGS84/ITRF) | Geoid (mean-sea-level equipotential) |
| What measures it | GNSS receiver, directly | Levelling, or GNSS + geoid model |
| Respects water flow / gravity | No | Yes |
| Best for | Geometry, 3D coordinates, datum transforms | Drainage, gradients, design levels |
| Bridge between them | N (geoid undulation) — region-specific, varies spatially | N (geoid undulation) — region-specific, varies spatially |
The two heights answer different questions — and the geoid undulation N is the bridge that converts one into the other. · Conceptual summary; see EPSG coordinate-system registry and NGS RTK/height guidance for the formal definitions.
Typical height precision by method (illustrative)
Standard practice: never trust a GNSS height it cannot prove
Following NGS RTK guidance and FIG good practice, we treat GNSS-derived heights as provisional until they are tied to the published vertical datum. That means a current geoid model, an occupation on at least one known benchmark, and — on gradient-critical work — a levelling check between benchmarks. The geoid model handles the shape of the ellipsoid-to-geoid separation; the benchmark fixes the absolute datum. Both, every time.
Heights only mean something on a referenced map
Keep reading
References
- Guidelines for Real-Time Kinematic (RTK) GNSS surveying and geodetic control — US National Geodetic Survey (NGS/NOAA)
- EPSG registry of coordinate reference systems and map projections — EPSG Geodetic Parameter Dataset
- International Federation of Surveyors publications on professional and cadastral standards — International Federation of Surveyors (FIG)
