The geoid is the ocean's imaginary calm under gravity alone
The geoid is the shape Earth's oceans would settle into if only gravity and the planet's spin acted on them, with no wind or tides, continued beneath the continents as if through narrow canals. Carl Friedrich Gauss called it the mathematical figure of the Earth. It is lumpy, but only by about 200 metres.
Every point on the geoid has the same geopotential, the combined energy of gravity and rotation. That means gravity pulls straight down onto it everywhere, plumb lines stand perpendicular to it and spirit levels lie parallel with it, and a ball placed on it would not roll. Yet the strength of gravity along the surface is not uniform, and a sailor crossing an ocean feels none of its rises and dips because the local horizon always follows it.
The bumps come from uneven density inside the planet: magma, heavy or light rocks in the crust, mountain ranges, trenches and crust squeezed by old glaciers. Where material is denser and pulls harder, it draws water toward it and the geoid bulges outward. Compared with the smooth reference ellipsoid, the geoid stands about 85 metres higher near Iceland and about 106 metres lower off southern India, tiny next to the ground's range from Everest's 8,800 metres to the Mariana Trench's 11,000-metre depth. The lasting gap between the real mean sea level and the geoid is called ocean surface topography.
This matters every time you read a height. GPS satellites orbit Earth's centre of mass and can only give height above a geometric ellipsoid, so a receiver on a ship may show its altitude drifting during a long voyage even though the vessel never leaves the sea surface. Map heights are measured from mean sea level instead, and many handheld receivers correct the difference by looking up the local geoid height, the undulation, in a stored table, often based on the EGM96 model.
Calculating the geoid is hard. George Gabriel Stokes published a formula in 1849 that derives it from gravity anomalies, but it needs gravity measured everywhere, including oceans, poles and deserts, which ground surveys alone cannot supply. Modern solutions blend land gravimetry with satellite orbit data and dedicated gravity missions such as GOCE and GRACE.
Source: Geoid
