[PROJ] Correcting map projection errors

[Ken Mankoff]

Dear Proj list,

Please excuse duplicates - Even sent this with a different subject "Fwd: proj list issue" and I have not gotten any replies. I'm resending with an improved subject in case people skipped the email with that subject.

I'm following up on a helpful thread from this list from 2017: https://lists.osgeo.org/pipermail/proj/2017-November/007496.html

I'm calculating map projection errors, and want to check my interpretation of the results with someone who knows proj better. I'm using EPSG:3413 projection and the following proj string:

+proj=stere +lat_0=90 +lat_ts=70 +lon_0=-45 +k=1 +x_0=0 +y_0=0 +no_defs +a=6378137 +rf=298.257223563 +towgs84=0.000,0.000,0.000 +to_meter=1

To estimate the error in Southern Greenland, I do:

echo -40 60 | proj -VS ${PROJSTR}

and see

#Stereographic
#       Azi, Sph&Ell
#       lat_ts=
# +proj=stere +lat_0=90 +lat_ts=70 +lon_0=-45 +k=1 +x_0=0 +y_0=0 +no_defs
# +a=6378137 +rf=298.257223563 +towgs84=0.000,0.000,0.000 +to_meter=1
#Final Earth figure: ellipsoid
#  Major axis (a): 6378137.000
#  1/flattening: 298.257224
#  squared eccentricity: 0.006694379990
Longitude: 40dW [ -40 ]
Latitude:  60dN [ 60 ]
Easting (x):   289632.50
Northing (y):  -3310514.64
Meridian scale (h) : 1.03942808  ( 3.943 % error )
Parallel scale (k) : 1.03942808  ( 3.943 % error )
Areal scale (s):     1.08041073  ( 8.041 % error )
Angular distortion (w): 0.000
Meridian/Parallel angle: 90.00000
Convergence : 5d [ 5.00000000 ]
Max-min (Tissot axis a-b) scale error: 1.03943 1.03943

The key values for Northern Greenland are:

echo -40 82 | proj -VS ${PROJSTR}
...
...
Meridian scale (h) : 0.97460025  ( -2.54 % error )
Parallel scale (k) : 0.97460025  ( -2.54 % error )
Areal scale (s):     0.94984565  ( -5.015 % error )

My question is how to interpret the Areal scale error

I think that in this projection N. Greenland is over-represented by 8% area and any areal feature there should be divided by 1.0804 or linear features divided by 1.0394 to bring them to true scale. Similarly, in S. Greenland I should adjust a areal feature by dividing by 0.94984565. Is this correct?

Essentially, does "-2.54 % error" mean that the EPSG:3413 projection is smaller than it should be, or that the "true" spheroid is smaller than EPSG:3413 here?

Thanks,

  -k.