Ellipsoids and geoids are methods used by topographers to model the shape of the earth. Although both model types are used to construct the Earth models, crucial differences exist. Ellipsoid models are more general in nature, and fail to take into account mountains and trenches. Ellipsoids and geoids are complemented by a third model type, topographic height.
Ellipsoid comes from the word "ellipse," which is simply a generalization of a circle. Ellipsoids are generalizations of spheres. The Earth is not a true sphere, it is an ellipsoid, as Earth is slightly wider than it is tall. Although other models exist, the ellipsoid is the best fit to Earth's true shape.
Like the ellipsoid, the geoid is a model of the Earth's surface. According to the University of Oklahoma, "the geoid is a representation of the surface of the earth that it would assume, if the sea covered the earth." This representation is also called the "surface of equal gravitational potential," and essentially represents the "mean sea level." The geoid model is not an exact representation of sea level surface. Dynamic effects, such as waves and tides, are excluded in the geoid model.
Topographic elevation (also known as "topographic height") is a more accurate model of the earth than either the geoid or the ellipsoid. Topographers measure the Earth's height using either satellite or aerial photography. This model's elevation values are calculated relative to the average sea level in various places across the planet.
Unlike the geoid, the ellipsoid assumes that Earth's surface is smooth. Additionally, it assumes that the planet is completely homogeneous. If this were true, Earth could have no mountains or trenches. Further, the mean sea level would coincide with the ellipsoid surface. This is not true, however. Vertical distance exists between the geoid and the ellipsoid as a result of the geoid taking into account mountains and trenches as an Earth model. This difference is known as the "geoid height." The differences between the ellipsoid and geoid can be significant, as the ellipsoid is merely a baseline for measuring topographic elevation. It assumes that the Earth's surface is smooth, where the geoid does not.
The geoid and ellipsoid models are used in today's global positioning satellite (GPS) systems. GPS systems use the ellipsoid model as a baseline to measure the elevation of a particular location on Earth. However, some GPS system now use the geoid model to better represent the elevations. Accurate measurements are most useful to topographers, whose job is it to develop as precise measurements of the Earth's surface as possible.