Latitude and longitude pin a point to a smooth mathematical surface, and that surface is not the one water finds. The ellipsoid is a tidy approximation of the Earth's shape; the geoid is the lumpy surface of equal gravitational potential that approximates mean sea level. They differ by tens of metres, and that difference is the reason an elevation from a GNSS receiver is not the elevation on a topographical map.
| Ellipsoid | Geoid | |
|---|---|---|
| What it is | A smooth mathematical surface: a sphere flattened at the poles | The equipotential surface of the Earth's gravity field closest to mean sea level |
| Defined by | Two numbers — semi-major axis and flattening | Gravity measurements, satellite altimetry and a global gravity model |
| Shape | Perfectly regular | Irregular, undulating by up to about 100 m worldwide |
| Height measured from it | Ellipsoidal height, h | Orthometric height, H — elevation above sea level |
| Used for | Latitude, longitude, GNSS positioning | Surveying, drainage, engineering, anything that involves water flowing |
The ellipsoid exists because positioning needs a surface simple enough to do mathematics on. Every latitude and longitude you have ever seen is an angle measured from the ellipsoid, and the ellipsoidal height that comes with it is the distance above that surface along the normal. The geoid exists because gravity is what water, surveying instruments and drainage systems actually respond to, and the geoid is the surface that gravity defines.
Every practical problem in height comes from this one equation and from forgetting which term a particular number represents. Elevation on a map, on a bench mark, on a flood study — those are H, orthometric height, because they are derived from spirit levelling or from a geoid model. The position solution from a GNSS receiver gives h, ellipsoidal height, because that is what the geometry produces. They differ by N, which is tens of metres and which varies from place to place.
Worldwide, geoid undulations range over roughly 100 m, with the deepest low near the Indian Ocean. Over a single country the range is smaller but still far larger than any elevation precision anyone cares about in construction: across the continental United States the separation between the geoid and the ellipsoid is of the order of 10 to 35 m, changing gradually across the country.
That is why a receiver reporting an altitude of, say, 1,600 m is not necessarily telling you the site is at 1,600 m above sea level. It is telling you the height above the ellipsoid. Converting it needs N at that point, which comes from a geoid model — GEOID18 and its successors in the United States, EGM2008 or a national model elsewhere.
A test that catches the error immediately. Take a point with a published elevation and compare it with the raw ellipsoidal height from a GNSS receiver. A difference of tens of metres is normal and expected; a difference of a few metres is not, and a difference of nearly zero suggests the receiver has already applied a geoid model internally. That matters, because if the receiver applies one and your software applies another, you have subtracted the separation twice.
It is worth separating two questions that sound alike. A horizontal datum decides what latitude and longitude mean — which ellipsoid and which realisation of it. A vertical datum decides what zero elevation means, and is usually tied to a reference tide gauge plus a levelling network, with a geoid model used to extend it. In the United States, NAVD88 is the commonly used vertical datum, with a successor being rolled out from the mid-2020s onwards.
The two are independent. Changing the horizontal datum moves a point around on the map; changing the vertical datum changes the number attached to its height. A dataset can be correct in one and wrong in the other, and the error will only show up when it is merged with data that made the opposite choice.
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