Geoids, Ellipsoids, and Undulation Height: Understanding the Basics

Introduction to Geoids, Ellipsoids, and Undulation Height

Geoids, ellipsoids, and undulation height are all important concepts in the field of geodesy, which is the study of the Earth’s shape, gravity field, and orientation in space. In this article, we will explore the basics of each of these concepts, including what they are, how they are used, and why they are important.

What is a Geoid?

A geoid is a surface of equal gravitational potential, which closely approximates the shape of the Earth’s sea level. The geoid is an imaginary surface that is used as a reference for measuring the Earth’s gravity field. It is shaped like a slightly squashed sphere and is affected by the distribution of mass within the Earth. The geoid is not a perfect sphere because the Earth’s gravity field is not symmetric.

There are several examples of geoids that have been used or proposed for use in different regions and applications. Some examples include:

• The North American Vertical Datum of 1988 (NAVD 88) geoid: This geoid is used as the reference surface for orthometric heights (heights measured from mean sea level) in North America. It is based on a combination of satellite and terrestrial measurements of the Earth’s gravity field.
• The European Vertical Reference System (EVRS) geoid: This geoid is used as the reference surface for orthometric heights in Europe. It is based on a combination of satellite and terrestrial measurements of the Earth’s gravity field.
• The World Geodetic System 1984 (WGS 84) geoid: This geoid is used as the reference surface for GPS coordinates and as the basis for many geodetic datums. It is based on a global network of satellite measurements of the Earth’s gravity field.
• The Global Geoid Model (GGM) geoids: These geoids are global models of the Earth’s gravity field and are used in a variety of applications, such as mapping and navigation. Examples of GGM geoids include EGM96, EGM2008, and EGM2020.
• The Sea Surface Topography Model (SSTM) geoids: These geoids are used to map the shape of the sea surface and are based on satellite altimeter measurements. Examples of SSTM geoids include the TOPEX/Poseidon and Jason geoids.
• The Theoretical Geoid: A Theoretical Geoid is a mathematical model of the geoid which is based on the Earth’s gravity field and the Earth’s shape. It is often used as a starting point for developing more accurate geoid models.

Please note that these geoids have been developed using different methods, so the axis and flattening may vary depending on the geoid. These are just examples and other geoids may exist and have different axis.

What is an Ellipsoid?

An ellipsoid is a mathematical surface that is used to approximate the shape of the Earth. It is defined as the set of points such that the sum of the distances from the point to two fixed points, called foci, is a constant. The most commonly used ellipsoid is the World Geodetic System 1984 (WGS 84) ellipsoid, which is used as the reference surface for GPS coordinates.

There are several examples of ellipsoids that have been used or proposed for use in different regions and applications. Some examples include:

• The World Geodetic System 1984 (WGS 84) ellipsoid: This ellipsoid is used as the reference surface for GPS coordinates and as the basis for many geodetic datums. It is an oblate spheroid, with semi-major axis of 6,378.137 km and flattening of 1/298.257223563.
• The North American Datum of 1983 (NAD 83) ellipsoid: This ellipsoid is used as the reference surface for the North American Datum of 1983, which is the standard datum for North America. It is an oblate spheroid, with semi-major axis of 6,378.137 km and flattening of 1/298.257222101.
• The European Terrestrial Reference System 1989 (ETRS89) ellipsoid: This ellipsoid is used as the reference surface for the European Terrestrial Reference System 1989, which is the standard datum for Europe. It is an oblate spheroid, with semi-major axis of 6,378,137 m and flattening of 1/298.257222101
• The Geodetic Reference System 1980 (GRS 80) ellipsoid: This ellipsoid is used as the reference surface for the Geodetic Reference System 1980, which is the standard datum for many countries around the world. It is an oblate spheroid, with semi-major axis of 6,378.137 km and flattening of 1/298.257222101.
• The Australian National Spheroid (GDA94) ellipsoid: This ellipsoid is used as the reference surface for the Geocentric Datum of Australia 1994 (GDA94), which is the standard datum for Australia. It is an oblate spheroid, with semi-major axis of 6,378,137 m and flattening of 1/298.257222101
• The International 1924 (Hayford) ellipsoid: This ellipsoid is used as the reference surface for the International 1924, which is the standard datum for many countries around the world. It is an oblate spheroid, with semi-major axis of 6,378,388 m and flattening of 1/297.

What is Undulation Height?

Undulation height, also known as geoid height or geoid-ellipsoid separation, is the difference in elevation between the geoid and an ellipsoid. The geoid is a surface of equal gravitational potential that closely approximates the shape of the Earth’s sea level, while an ellipsoid is a mathematical surface that approximates the shape of the Earth.

Because the Earth’s gravity field is not symmetric, the geoid is not a perfect sphere and deviates from the ellipsoid. The undulation height is a measure of this deviation and is used to convert between ellipsoidal heights (measured from the ellipsoid) and orthometric heights (measured from the geoid).

For example, if you were to measure the elevation of a point on the Earth’s surface using GPS, the measurement would be given in terms of an ellipsoidal height. However, the true elevation of the point may be different from the ellipsoidal height, due to the deviation of the geoid from the ellipsoid. The undulation height can be used to correct for this deviation and to determine the true elevation of the point in terms of an orthometric height.

Undulation height is important in geodetic and surveying applications because it provides accurate height information for mapping and navigation. It is also used for determining gravity field and for many geodetic and geophysical research activities.

How are Geoids, Ellipsoids, and Undulation Height used?

Geoids, ellipsoids, and undulation height are used in a variety of applications, including surveying, mapping, and navigation. Geoid heights are used to convert ellipsoidal heights to orthometric heights, which are used in land surveying and topographic mapping. Ellipsoids are used as a reference surface for GPS coordinates and as a basis for geodetic datums. Undulation height is used to correct for the difference between the ellipsoidal and the geoidal surface and to provide accurate height information in geodetic and surveying applications.

Why are Geoids, Ellipsoids, and Undulation Height Important?

Geoids, ellipsoids, and undulation height are important because they are used as a reference for measuring the Earth’s shape, gravity field, and orientation in space. They provide a consistent and accurate way to measure and map the Earth’s surface, which is essential for a wide range of applications, including land surveying, topographic mapping, navigation, and more.

In conclusion, geoids, ellipsoids, and undulation height are all critical concepts in geodesy that provide a consistent and accurate way to measure and map the Earth’s surface. They are used in a wide range of applications and play a crucial role in our understanding of the Earth’s shape, gravity field, and orientation in space.