# **Geoid**

A geoid is an equipotential surface of Earth's gravity field.

## **Geoid from terrestrial levelling and gravimetry**

A geoid is determined on land by geometric levelling and gravity measurements. Where possible, tide gauge benchmarks are related to a geoid, the reference surface, which we call "geoid from terrestrial levelling and gravimetry."

**Marine geoid**

At sea, the same geoid may be extended using gravity measurements. An important argument for the use of a geoid as a reference for the tide is the fact that the vertical datum of mathematical models used to simulate ocean dynamics is an equipotential surface of the gravity field. At any point the local vertical (plumb line) is always perpendicular to the geoid.

A very common mistake is to confuse it with MSL. Unlike the geoid, MSL is affected by meteorological and oceanic phenomena. These include ocean circulation (at a latitude of 45°, a current of 1 m/s over 10 km wide creates a vertical height variation of 10 cm perpendicular to the current), the average distribution of densities, atmospheric pressure gradients and the non-linear effects of the propagation of waves in shallow areas. For example in the English Channel, non-linear effects alone are responsible for differences of up to ten centimetres. The geoid used as an initial surface in simulation models is also different from the geoid from terrestrial levelling and gravimetry: the geoid at sea is an equipotential of the gravity field which corresponds approximately to the surface of an ocean in equilibrium and at rest, with density equal to the average density of the ocean at the initial time, and with an atmosphere in equilibrium at rest. We call it "marine geoid." The marine geoid is not far in its practical determination from the terrestrial geoid which is usually measured in ancient times and at a distant point. However, they do not coincide exactly (even if only because of secular trends in sea level) and the differences, which cannot be measured accurately today, could be up to several tens of centimetres, which is too much for hydrography and for the study of ocean circulation.

**To find out more:**

**Reference**

- Simon B. (2007). La Marée - La marée océanique et côtière. Edition Institut océanographique, 434pp.

*Last updated: 12/12/2012*