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I have a DEM dataset which describes the vertical reference used as "height above the WGS84 ellipsoid".

As I understand it this assumes vertical values to have MSL as a reference and NOT something like EGM2008, correct?

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3 Answers 3

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In short

I have a DEM dataset which describes the vertical reference used as "height above the WGS84 ellipsoid".

As I understand it this assumes vertical values to have MSL as a reference and NOT something like EGM2008, correct?

No this is not correct. The reference is the reference ellipsoid used for the datum, not MSL. The values are ellipsoidal heights, not altitudes.

EGM2008, which is also part of WGS 84 system, is not concerned here. It's a model of geoid, i.e. a model of the mean sea level. However, if you wanted to compute altitudes, you'd need to subtract geoid heights in EGM2008 from ellipsoidal heights in your file. These heights are measured along the normal to the ellipsoid, a straight line generally not matching with the curvilinear vertical, thus there is a tiny error in altitudes determined this way, not significant for usual calculations.

See below for details.


GPS basic constraints

It's good to know about some GPS basic principles, in order to understand why such notions as ellipsoidal height are used.

  • A satellite orbit is more easily described and manipulated in ECEF coordinates. WGS 84 and Navstar satellites are closely entangled, the primary coordinates in WGS 84 are ECEF-based. Thus the user must be provided with a way to convert a position from ECEF to geodetic (latitude/longitude/height). Latitude and longitude can be computed using an ellipsoidal model of Earth. Height is more tricky, and requires a reference, the sea level which can be modeled from gravimetric campaigns.

  • The WGS 84 World geodetic system is a theoretical representation of points on Earth and in space, it's a mathematical view. However neither the GPS satellites nor the GPS final users can work with a system defined by, e.g. "the Z axis of WGS 84 is aligned with Earth mean axis of rotation". They would need to determine the physical axis of rotation in order to use the mathematical model.

  • Instead they need a physical realization (reference frame) of this system, the realization determines what is the Earth mean axis of rotation at the current time, and use this information to provide users with an alternate way to determine points without relying on the actual Earth axis.

WGS 84 current physical realization: G2139

A realization (frame) is a network of permanent reference frame stations (GPS receivers) which positions in WGS 84 are assumed, and updated by actual measurements. The G in G2139 indicates this frame used GPS measurements exclusively, and 2139 indicates it was frozen on GPS week 2139 (January 2021).

Such realization is comparable to a network of geodetic marks in traditional surveying. Users are able to determine the position of any other point from these geodetic marks without determining the direction of the north or the mean level of the sea.

The GPS control stations measure the orbital parameters of the Navstar satellites using this frame. These parameters are uploaded to the satellites, which broadcast them to final users. GPS users (receivers) use orbital parameters to determine satellite positions, and transit times to determine their own position which is, per construction of the orbital parameters, within the same physical frame. Neither the satellites, nor the users have to deal with data such as Earth rotation axis. This is one of the key points of a WGS 84 frame.

Now back to practical elements.

Ellipsoid and geoid

To allow WGS 84 frames and the subsequent determination of horizontal (latitude, longitude) and vertical (altitude) coordinates, the WGS 84 system defines two key surfaces:

  • The oriented WGS 84 ellipsoid, a perfect oblate spheroid which origin is Earth center of mass, X axis points to the reference meridian and Z axis to Earth north pole. The distance h from the ellipsoid is usually referred to as ellipsoidal/geodetic height (sometimes ellipsoidal/geodetic altitude but this is not correct). The ellipsoid height does not take into account gravity, thus the direction water flows cannot be determined from ellipsoidal heights.

    The US GPS, but also other GNSS (EU Galileo, Russian Glonass since 2007, etc), use WGS 84. The receiver always determines Cartesian coordinates XYZ, and convert them to longitude, latitude and ellipsoidal height using the ellipsoid parameters.

  • An equipotential of gravity is a surface where the gravity field has a constant value. The geoid is the equipotential corresponding more or less to the mean of the old mean sea levels (each region had/has its own mean sea level, defined by its own tide gauge, not using the same protocols). The geoid is the reference for altitude, as defined by ISO: "height where the chosen reference surface is mean sea level". The geoid surface is based on EGM2008, the Global Gravitational Model (GGM) part of WGS 84.

    Altitude is usually measured by the orthometric height (aka normal height), the distance between the point and the geoid, measured along the vertical.

    The vertical itself is the direction of gravity, therefore a curvilinear line crossing equipotentials at right angle. Orthometric heights indicate the direction water flows.

No equipotential can match the mean level of all oceans, but there is one which best fits this role.

enter image description here

Source.

This equipotential has been selected using the Earth Gravitational Model, EGM2008 and a model of mean sea levels (MSS), CLS01. The geoid is the surface W0 with a gravity potential of 62,636,854.25 m²s-².

The geoid undulates above and below the ellipsoid, following the local level of the sea, depending on local Earth density, salinity, and other factors. The distance between the ellipsoid and the geoid is the geoid undulation (or geoid height), N.

In practice on Earth, sea levels differ by up to 200 m, not a good example of communicating vessels. Like the ellipsoidal height, the geoid height is measured perpendicularly to the ellipsoid. The geoid height, can be visualized:

enter image description here

Source.

Subtracting the height of the geoid from the ellipsoidal height results in a sufficient approximation of the altitude MSL.

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  • Might be worth editing in a summary answer to the question in OP's title as well, as your first line is slightly confusing given OP's asking two almost inverted questions.
    – naught101
    Jan 23 at 1:39
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Mean sea level is a geoid surface of the ocean in rest, EGM2008 is a model approximation of the geoid.

https://en.wikipedia.org/wiki/Geoid

An ellipsoid is the first order approximation of the shape of the Earth.

https://en.wikipedia.org/wiki/Ellipsoid

Elevations are usually expresssed relative to the geoid as spirit levels are used for measurements. Every country used to have a national vertical reference datum.

So usually a national vertical datum is used and not ellipsoid height.

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Here's the information I was looking for: https://en.wikipedia.org/wiki/World_Geodetic_System

Quote: "WGS 84 uses the Earth Gravitational Model 2008."

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