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###Additional references###

Additional references

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 GR80 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).)

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 Earth as 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.

• 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 Earth as 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.