Cartographic Projection
every map is wrong, and by exactly how much
Concept

Coordinate metadata — where it appears

The statement of which system a set of coordinates belongs to, carried alongside them. Without it a pair of numbers is not a position, and the exchange formats in general use have a field for the transformation's identifier and none for its uncertainty.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

What changing the datum alone does to a coordinate. The distance on the ground between a point as read on its national datum and the same numbers read on WGS84, computed through the published seven-parameter transformation. The shifts run from 49 to 166 metres. For comparison, the scale error a UTM zone introduces at its edge is under a metre per kilometre — so the datum, which is usually left unstated, dominates the projection, which is usually argued about.

Datum shifts dwarf projection errors

The projection argument is conducted in parts per million and the datum question is answered in hundreds of metres. A coordinate whose datum is unstated is out by more than any projection choice could ever put it, and almost nobody checks.

wrong · Ellipsoid Where the ground is going, six plates. The velocity of the ground under a coordinate, computed as the cross product of each plate's rotation vector with the position, and drawn along the band where that rotation is fastest rather than over an outline this site does not hold. The quickest arrow is 75 millimetres a year on the Pacific plate, which is 1.89 metres in twenty-five years. drawn in Robinson — the arrows' directions are the projection's as much as the plates'.

The epoch is part of the coordinate

A latitude and a longitude with no date on them are incomplete, because the ground they refer to is moving at between ten and seventy millimetres a year. Australia crosses an ordinary survey tolerance in under two years and moved 1.8 metres between two versions of its own datum.

datums · Datum The same coordinate on four datums. One pair of numbers — 2.0° west, 54.5° north — read as a coordinate on OSGB36, ED50, NAD27 and on WGS84, and plotted where each reading puts the mark on the ground. The spread runs to 195 metres, and the height changes by 51, 44, 47 metres, which is the component nobody quotes.

The third coordinate moves too

A datum shift is quoted as a horizontal displacement because horizontal is what people look at. The transformation acts on a three-dimensional point, and its vertical component is between a quarter and a half of the horizontal one — 51 metres, for a British coordinate.

datums · Height

Named alongside it

The objects these essays reach for when they reach for this one.

DatumEpochHelmert transformationOSGB36RealisationToleranceVerificationED50EllipsoidEllipsoidal heightGeodetic latitudeGeoid

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