Development of a low-distortion authalic sphere for the oblique azimuthal equal-area map projection of the spheroid

This paper gives a new possible realization of the oblique Lambert Azimuthal Equal-Area map projection for the ellipsoid of revolution. Unlike the realization available in previous literature, the authalic sphere used for the derivation has very low distortion at the neighbourhood of a freely chosen standard parallel. For this reason, the distortions caused by this authalic sphere can be neglected. It is shown that this realization gives a better approximation of the azimuthal equal-area mapping of the sphere in terms of angular distortions. Interesting side results of the study include a numerically stable inverse formulation for the azimuthal equal-area map of the sphere and mathematical connections between the Gaussian conformal sphere and the low-distortion authalic sphere.