# Geoid ellipsoid and datum relationship

### 1-Mean Sea Level, GPS, and the Geoid

A comprehensive introduction to datums, geoid and ellipsoid, geodetic Flattening (f) is the ratio of the difference between the semi-major axis (a) and. Ellipsoid and Datum, Projection,. Coordinate system, and Earth Surface: Ellipsoid, Geoid, Topo latitude and longitude (Φ, λ) and geoid / ellipsoid separation . Scale refers to the relationship or ratio between a distance on. Relationship between orthometric height, ellipsoid height, and geoid height This is still the geodetic datum currently adopted by Canada and the United States.

Also, in the modern digital era, techniques have vastly improved and many modern datum are very similar to each other. However, also in this modern digital era, people like to know locations precisely so even a small difference may be significant. Naming Datums and Projections There are many different datums and projections in existence.

To ensure that these can be easily identified each version of a datum or projection is given a unique name: About the Geometry of Datums In order to calculate where latitudes and longitudes occur on the surface of the Earth a number of fundamental geometric concepts and practices need to be applied.

In simple terms these include: This is called a Sphere. From an imaginary centre of the Earth, calculations are made from the centre of the Earth to the surface of the Earth.

### Datums | Intergovernmental Committee on Surveying and Mapping

This is called an Ellipsoid or a Spheroid. Be warned, the use of the terms Ellipsoid and Spheroid can be confusing as they are used interchangeably within the geodetic community.

A Spheroid is simply a type of Ellipsoid which is as wide as it is long i. All other Ellipsoids are longer than they are wide i.

## FAQ: What do the terms geoid, ellipsoid, spheroid and datum mean, and how are they related?

In Australia, most datums refer to the Australian National Spheroid. Dynamic effects, such as waves and tides, are excluded in the geoid model.

**A Simple Explanation of Datum**

Sciencing Video Vault Topographic Elevation 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.

Key Differences 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. Conceptually, this precisely calculated ellipsoid, called an oblate ellipsoid of revolution, was intended to replicate the MSL as the main geodetic reference or vertical datum.

If this ellipsoid vertical datum is used, height above the ellipsoid will not be the same as MSL and direct elevation readings for most locations will be embarrassingly off.

This is caused, in part, because the GPS definition of altitude does not refer to MSL, but rather to a gravitational surface called the reference ellipsoid. Because the reference ellipsoid was intended to closely approximate the MSL, it was surprising when the two figures differed greatly.

These measurements have demonstrated that neither human error nor GPS inaccuracies are responsible for the sometimes substantial discrepancies between ellipsoid and MSL measurements. In fact, the three-dimensional surface created by the earth's sea level is not geometrically correct, and its significant irregularities could not be mathematically calculated; this explains the difference between the ellipsoid-based GPS elevation readings and elevations shown on accurate topographic maps.

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A brief examination of elevation readings for Esri headquarters in Redlands, California, demonstrates these differences. The campus elevation is shown on topographic quadrangle maps and high-resolution digital elevation models DEMs for the area as approximately meters above MSL. However, a precise, nonadjusted GPS reading for the same location typically shows the elevation as meters.

The map shows the areas of the globe that would have a sea level below the theoretical surface of the WGS84 ellipsoid, or the theoretical and geometrically correct sea level shown in blue.

### Datums Explained in More Detail | Intergovernmental Committee on Surveying and Mapping

The sharp contrast between the blue and green indicates where the ellipsoid and geoid intersect. With the continents displayed as opaque, the remaining area covered by water reveals where sea level is actually at zero elevation relative to the WGS84 ellipsoid. Why is there a meter difference? The MSL, approximated by an ellipsoid, is related to gravity or the center of mass of the earth. Discrepancies between a WGS84 ellipsoid, and the geoid vary with location.

To continue with this example, elevation readings for Yucaipa, a city located less than 10 miles east of Redlands, differ by