[PROJ] Correcting map projection errors

[Charles Karney]

Sorry, I'm coming rather late into this discussion.

* as Thomas Knudsen says the square of the linear projection scale will
   give you the correction factor for small areas, because your
   projection is conformal.  Use the scale at the center of the cell for
   best accuracy.  (My guess is that for this projection, polar
   stereographic, for Greenland, and for 200m squares, this will give you
   satisfactory accuracy.)

* instead of using GeographicLib's Planimeter program, you might find it
   simpler to use proj's geod_polygonarea function; this implements the
   same algorithm.  It's documented at

 
https://geographiclib.sourceforge.io/1.49/C/geodesic_8h.html#aafa25f138d78c387a107ec0221bbb181

   If you are not tied to proj.4, then use the PolygonArea class in
   GeographicLib

 
https://geographiclib.sourceforge.io/1.49/classGeographicLib_1_1PolygonAreaT.html

* following up on daan's suggestion: transforming to an equal area
   projection is possible, but use the azimuthal equal area projection
   instead of the cylindrical one.  The edges of your squares in the
   polar stereographic projection will be straighter in the azimuthal
   equal area projection and so the distortion involved in the
   reprojection will be less.

* an alternative to using an equal area projection is to project the
   points onto the authalic sphere and then to use the formula for areas
   on a sphere.  This is the route that Oracle takes.  This has the
   advantage of giving small distortion over the whole globe.  If you go
   this route, I recommend compute spherical areas with Eq (64) from my
   paper "Algorithms for geodesics"

     https://doi.org/10.1007/s00190-012-0578-z

-- 
Charles Karney <charles at karney.com>
Princeton, NJ