Geodetic Coordinates And Latitude, Longitude

Question

Would it right to say that geodetic coordinates (phi & lambda) are the same as latitude & longitude?

Answer 1

This is a great question because it uncovers important sources of common misunderstandings. The brief answer is that although of course geodetic latitude and longitude are a form of latitude and longitude, they are not the only ones and the differences are not trivial, so we should be cautious not to confuse them.

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In all cases, latitude and longitude are numbers used to designate points on the earth's surface. Usually, the definition of longitude is straightforward because all but the most detailed models of the earth's surface assume it is rotationally symmetric. (Geoids, which account for gravitational anomalies, are a possible exception, but this level of detail is normally used only to develop precise elevation coordinates without modifying the underlying latitude and longitude.) Lines of longitude are meridians and can be designated by the angle they make with a designated meridian of origin, a "prime meridian."

There are many different kinds of latitude. They are best discussed in a context where an ellipsoidal model of the earth is given, such as the WGS84 or GRS80 ellipsoids. The latitude depends on the reference ellipsoid. (This is important when using data referenced to historical ellipsoids, such as the Clarke 1866 ellipsoid. With more recent ellipsoids, established through satellite measurements, the differences are so small as to be of interest only when accuracy and precision needs are extremely high (sub meter).)

• Geodetic latitude is the (signed) angle between the local normal ("straight up" direction) and the plane of the equator. This should be a professional's default understanding of what a "latitude" means, even though it differs from the definition taught to children--and therefore is the common understanding among laymen--which corresponds to the geocentric latitude (for a spherical model). The two can differ by tens of kilometers, a sizable fraction of one degree.

• Geocentric latitude, on the other hand, is the (signed) angle determined by the direction from the center of the earth to the point. The distinction between geocentric and geodetic latitudes is illustrated in the links and also in my reply at How do you compute the earth's radius at a given geodetic latitude?.

• Additional latitudes have been defined to help create accurate maps that have particular properties, such as being conformal, equal-area ("authalic"), or isometric. (By changing the latitude slightly we "project" the ellipsoid onto the sphere and then we apply a projection from the sphere to the plane to make a map. This last step is relatively simple, because it does not need to handle the complicated ellipsoidal formulas, while the initial change of latitude increases the overall accuracy of the map.)

• An "isometric latitude" isn't even in degrees; it's essentially the northing coordinate for a Mercator projection.

When we change the model of the earth (the reference ellipsoid), we obtain a different set of latitudes altogether. Frequently this happens when a latitude based on an ellipsoid is considered to be a latitude based on a spherical model. I recently analyzed the resulting error at How accurate is approximating the Earth as a sphere?, finding the displacements (between the correct location designated by a latitude and the apparent location) can be as great as 20 km. Differences among the various latitudes in use (see "additional latitudes" above) can be of the same order of magnitude, so even for very rough mapping purposes one should pay attention to what is going on.

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Additional references

A good, but highly technical, source of information on many forms of latitude is

Bugayevskiy, Lev M. & John P. Snyder, Map Projections, A Reference Manual. Taylor & Francis, London (1995).

See pp. 33-37 for formulae and Appendix 5 for a table of isometric latitudes.

Answer 2

Yes, to quote Wikipedia:

In geodetic coordinates the Earth's surface is approximated by an ellipsoid and locations near the surface are described in terms of latitude (phi), longitude (lambda) and height (h)

But, as Alex Markov commented, to keep in mind datums

Answer 3

I think this would be an adequate explanation for you (read all of them.).

Geodetic Coordinates

The geographical latitude and longitude of a point on the earth’s surface, determined by means of geodetic measurement of the distance (mainly by the method of triangulation) and the bearing (azimuth) from several other points whose geographic coordinates are known. Geodetic coordinates are calculated on the surface of a reference ellipsoid, which is a characterization of the shape and dimensions of the earth. They differ to a small degree from latitude and longitude as measured by astronomical methods, because of inaccuracies in the measurements of the adopted ellipsoid and deviations from the perpendicular. Along with the geodetic coordinates of a point, its altitude is also considered. It is calculated from the surface of the adopted reference ellipsoid and differs from its altitude above sea level by the size of its geoidal deviation from this ellipsoid.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979).