"The geoid is a surface along which the gravity potential is everywhere equal and to which the direction of gravity is always perpendicular. The latter is particularly important because optical instruments containing levelling devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to the geoid. The angle between the plumb line which is perpendicular to the geoid (sometimes called "the vertical") and the perpendicular to the ellipsoid (sometimes called "the ellipsoidal normal") is defined as the deflection of the vertical. It has two components: an east-west and a north-south component."
With GPS becoming more and more relevant in our daily lives, what is the height measurement we get?
Note that with N, that if the geoid is above the ellipsoid, N is positive. If the geoid is below the ellipsoid, N is negative.
How does mass effect the geoid and the ellipsoid?
Where a mass deficiency exists, the geoid will dip below the mean ellipsoid and where a mass surplus exists, the geoid will rise above the mean ellipsoid.
Where are the largest undulations?
Well, the largest undulations known, with the minimum in the Indian Ocean at a value of N = -100 metres and the maximum in the northern part of the Atlantic Ocean with N = +70 metres.
So how do we describe the shape and size of the Earth?
There are three surfaces to be considered:
- The topography - the physical surface of the earth.
- The Geoid - the level surface (also a physical reality).
- The Ellipsoid - the mathematical surface for computations.
Mean Sea Level (MSL) points, an approximation to the geoid, and can be used as reference surfaces for height measurements (i.e. orthometric heights).
Ellipsoidal heights (such as those derived by GPS) have to be adjusted before they can be compared to the orthometric heights given on topographic maps.
The deviation between the geoid and an reference ellipsoid is called Geoid undulation (N). Geoid undulations can be used to adjust the ellipsoidal heights (H = h +/- N).
This is an introduction to the Geoid and the science of Geodesy. It hopefully clears up some questions about this surface.
I'll explain in more detail some of the formulations of the Geoid and how geodesists over time have tried to model it and some of the efforts being conducted presently to come up with a global gravity model to aid in height determination at a later date.
There are some very interesting projects going on in Africa, South America, and Canada.