Latitude - Auxiliary Latitudes

There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and the theory of map projections:

• geocentric latitude,
• reduced (or parametric) latitude,
• rectifying latitude,
• authalic latitude,
• conformal latitude,
• isometric latitude.

The definitions given in this section all relate to locations on the reference ellipsoid but the first two auxiliary latitudes, like the geodetic latitude, can be extended to define a three dimensional geographic coordinate system as discussed below. The remaining latitudes are not used in this way; they are used only as intermediate constructs in map projections of the reference ellipsoid to the plane: their numerical values are not of interest. For example no one would need to calculate the authalic latitude of the Eiffel Tower.

The expressions below give the auxiliary latitudes in terms of the geodetic latitude, the semi-major axis, a, and the eccentricity, e. The forms given are, apart from notational variants, those in the standard reference for map projections, namely "Map projections — a working manual" by J.P.Snyder. Derivations of these expressions may be found in Adams and web publications by Rapp and Osborne