orthometric

An orthometric height is a vertical distance measured along a plumb line from a reference surface, accounting for the actual pull of gravity rather than treating elevation as a simple geometric distance. In practice, this means the height of a point above the geoid, which is the imaginary equipotential surface that best fits global mean sea level. Because gravity varies with latitude and local geology, a plumb line does not point toward the geometric center of the Earth; orthometric correction accounts for this.

The distinction matters in precision surveying and engineering. If you measure elevation with a level staff and telescope, your instrument naturally follows gravity: the bubble in a level tube aligns with an equipotential surface. Over short distances (say, a few kilometers), the error from treating this as geometric height is negligible. Over distances of tens of kilometers, or in projects requiring accuracy better than 5 centimeters, ignoring gravity effects introduces systematic error that compounds with distance. Major infrastructure projects, national geodetic datums, and hydrological surveys depend on orthometric heights.

Computing orthometric height

Raw leveling data must be reduced using gravity measurements at observation points. The formula involves the observed elevation difference, mean gravity along the path, and latitude-dependent terms. Dynamic height and normal height are alternative reference systems: dynamic height removes all gravity variation, while normal height uses an ellipsoidal reference and standard gravity. Most national datums now publish orthometric heights because they align with what leveling instruments actually measure.

The geoid itself is not constant; it undulates by up to 100 meters across the Earth's surface due to density anomalies in the crust and mantle. Ellipsoidal heights (the output of GPS) can differ from orthometric heights by this amount. This is why surveyors converting GPS coordinates to project datums must apply geoid models, typically provided as gridded files by national agencies.