6. Why the Geoid Exists
A receiver visits a benchmark whose published elevation is 30.2 meters. RTK reaches FIX, and the display reports something near 61 meters instead.
The horizontal position is excellent. Repeated measurements agree within a few centimeters. The antenna height was entered correctly. So why is the elevation off by roughly 31 meters?
The receiver may not be wrong at all. It may simply be reporting height above a different surface entirely.
There is no single, universal surface called zero elevation. GNSS naturally measures height above an ellipsoid. Most maps, benchmarks, and engineering projects instead use elevation above a gravity-shaped vertical datum, and those two surfaces are not the same thing.
A Smooth Shape for the Mathematics
Earth is lumpy, mountainous, slightly flattened at the poles, and constantly shifting. That real, irregular surface is far too complicated to use directly inside satellite-positioning equations.
GNSS instead relies on a simple mathematical shape called an ellipsoid, essentially a smooth, gently squashed sphere fitted to the planet as a whole. The ellipsoid ignores mountains, valleys, and sea level entirely. Its entire job is providing a stable, well-defined geometric surface that latitude, longitude, and height can actually be calculated against.
That mathematical surface is exactly what satellite positioning needs. It is not the surface most people picture when they hear the word elevation. A GNSS receiver reports height relative to this ellipsoid, called ellipsoid height, written h.
Why Sea Level Was Never as Simple as It Sounds
"Height above sea level" sounds straightforward: pick the ocean's surface and measure upward from there. The ocean is shaped by tides, wind, currents, temperature, salinity, and atmospheric pressure, and even stripping all of that away, gravity itself is not equally strong everywhere on Earth.
Mass inside the planet is distributed unevenly. Mountains, ocean trenches, density variations in the rock, and structures buried deep inside the Earth all subtly bend the direction and strength of gravity. If the oceans could somehow settle without tides, currents, or weather at all, their surface would follow gravity exactly, and that gravity-shaped surface, extended conceptually beneath the continents too, is the geoid.
The geoid is an equipotential surface of Earth's gravity field, closely tracking global mean sea level without actually being a simple ellipsoid. It rises and falls, gently, because the gravity field producing it is genuinely uneven, not because anyone designed it to.
Three Heights, Three Different Questions
Once the ellipsoid and the geoid are treated as two separate things, the vocabulary becomes much easier to hold onto.
| Symbol | Name | Measured from | What it answers |
|---|---|---|---|
| h | Ellipsoid height | Reference ellipsoid | How high is the point above the mathematical GNSS surface? |
| N | Geoid height, or geoid undulation | Ellipsoid to geoid | How far apart are the geoid and ellipsoid at this location? |
| H | Orthometric height | Geoid to the point | What is the practical elevation above the gravity-based zero surface? |
The relationship between them is simply H = h − N, or equivalently h = H + N. The geoid never changes what GNSS actually measured. It supplies the one missing piece, N, needed to convert a measured ellipsoid height into the orthometric height people actually mean by "elevation."
Run the numbers from the opening scene: an ellipsoid height of 61.3 meters, at a location where the selected geoid model puts the geoid 31.1 meters above the ellipsoid, gives H = 61.3 − 31.1 = 30.2 meters. The receiver and the benchmark agree completely. Nothing was ever wrong with the satellite solution. The two values were simply referenced to two different vertical surfaces.
The Geoid Itself Is a Model
The real gravity field is extraordinarily complex, and no receiver or phone carries a perfect physical copy of it. Software instead relies on a geoid model, a grid or mathematical representation estimating N at any given location.
Different geoid models produce different values. A global model works reasonably everywhere on Earth. A national or regional model can fit a specific country's official vertical datum far more closely. Choosing a geoid model isn't picking whichever elevation looks nicer. It has to actually match the coordinate frame, the vertical datum, the location, and the accuracy a project genuinely needs.
The same receiver, connected to several different applications at once, reports several slightly different elevations for the identical position. Is the GNSS measurement wrong? Almost certainly not. One app may be showing raw ellipsoid height, another may be subtracting its own built-in geoid model, and a third may be applying an entirely different regional geoid grid. All three can be behaving exactly as configured.
Many receivers store a reduced, compressed geoid model internally, since onboard memory is limited, and for ordinary navigation that's more than adequate. Surveying and other high-accuracy work often turns to a higher-resolution national or regional model instead, running on a computer or a mobile device rather than the receiver itself. Two applications connected to the exact same receiver, using the exact same observations, can genuinely report different elevations, not because the GNSS measurement changed, but because the geoid model doing the converting did.
A Map of Hidden Mass
Mountains are only part of the story. The geoid responds to the Earth's entire mass distribution, not merely the height of visible terrain, and differences in rock density, crustal thickness, mantle structure, ancient tectonic boundaries, and even the lingering effects of long-vanished ice sheets can all leave a real signature in the gravity field.
The US National Geodetic Survey's own account of North America's geoid highlights the Yellowstone hot spot specifically as the most dramatic feature in it, a rising mantle plume that stands as the main contributor to a broad geoid high over Montana. A geoid map isn't only a conversion surface for GNSS heights. It's a faint picture of structures sitting well below the ground anyone can actually see.
Displayed Value Is Not the Same as Reliable Metadata
Connect the same RTK receiver to two applications, and the horizontal coordinates can match perfectly while the elevations disagree.
| Displayed value | Likely processing | Question worth asking |
|---|---|---|
| Ellipsoid height | Direct GNSS geometric height | Which ellipsoid and reference frame? |
| MSL height from the receiver | Receiver subtracts its own internal geoid model | Which built-in model and version? |
| Orthometric height from an app | App subtracts a selected geoid grid | Which grid and vertical datum? |
Labels like "altitude," "height," and "elevation" don't get used consistently across software. The metadata behind a number matters considerably more than whatever word happens to be printed next to it on screen.
Related Terms That Are Still Not the Same Thing
A geoid model and a vertical datum sound interchangeable and aren't. A geoid model estimates the separation between the ellipsoid and a gravity-based surface. A vertical datum defines the actual official zero surface a region publishes its elevations against.
In the United States, GEOID18 commonly connects NAD83(2011) ellipsoid heights to NAVD88 orthometric heights, and that relationship is specific: changing the horizontal reference frame, the geoid model, or the vertical datum can each independently change the resulting elevation. The modernized National Spatial Reference System will eventually carry its own new terrestrial and geopotential reference frames, with new models built specifically for them.
GNSS naturally measures ellipsoid height. Practical, usable elevation almost always requires a geoid model to convert that geometric height into orthometric height above an actual, gravity-based vertical datum, and confirming which conversion actually happened is what turns a number labeled "altitude" into an elevation that can be trusted, reproduced, and compared.
The major pieces are all on the table now: a reference frame, an epoch, a precise GNSS solution, and a way to convert ellipsoid height into elevation. Chapter 7 connects all of them into one complete workflow, following a coordinate from raw satellite observations all the way to a usable position on a map or an engineering plan.