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I will be doing area calculations for 100+ countries using country polygons taken from GADM, a database of global administrative areas. I am using ArcGIS. The GADM data is in WGS84 and is unprojected. I am doing some tests to gauge how area results differ whether I use customized projections vs. continental projections vs. national grids.

There does not appear to be a difference in calculated area whether I use Customized Albers Equal Area Conic Projection (I create country specific parallels and meridian) or Continental Albers Equal Area Conic Projection (built-in projections in ArcGIS). I thought a customized projection would lead to more accurate measurements but apparently the only difference is cosmetic - how the country is oriented on layout. In my limited test sample, all customized vs. continental results are the same except for Ghana. What might explain that? (Column F, Ghana)

I then compared the Albers resuls to results obtained using a country's national grid. There are very very minor differences vs. National Grids, always less than 1% except Brazil, where the difference is 1.12%.

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What explains these minor difference and the Brazil difference in particular? Should the areas be the same?

Given that the observed differences are so small, I am inclined to do all calculations in Continental Albers Equal Area Conic rather than create customized parallels and meridians, or seek out national grids for all countries.

My core question is the whether Continental Albers Equal Area Conic Projections will always produce the same approximate areas as national grids (error <1%, column E)? Is Brazil the exception? Or is this a large country problem more generally? I did a few tests and do not want to test each and every country. I thought I could seek out the wisdom of this StackExchange.

I have scoured the Internet and can't find exact answers to these questions.

  • Welcome to GIS.SE. – Martin F Feb 21 at 3:16
  • Mind "accepting" my answer? (Click the check-mark under the up/down-vote triangles.) – Martin F Mar 8 at 23:24
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In theory, any Equal Area projection will preserve a constant areal scale, all over the map. Customizations, as you have found, allow you to modify the contact point or line, position, orientation, etc, but should not change the fundamental geometric property of consistent areal scale, only the appearance of your map. That is why your column F values are essentially zero (no difference).

It cannot be determined just from the phrase "a country's national grid" for certain which projection is being used. However, the term is commonly used to describe the large-scale topographic mapping system and this is almost always done using a Conformal projection. Now, conformal projections have some useful properties other than equal area. That is why your areal calculations, via national grids, aren't quite right. Because each national grid is chosen to have contact lines (aka, standard lines) in good representative locations within the grid, the areal distortion is kept very small -- except in the case of a very large country (Brasil) where greater areal distortion would be expected.

All your results seem reasonable.

  • I cannot explain Ghana column F. – Martin F Feb 21 at 3:18
  • Thank you for confirming that customized albers projections do not change fundamental geometric properties, only the appearance of the map. I could not find this information after two days of internet searches! Your national grid comments are duly noted. – Alex Feb 21 at 14:31
  • Ghana has a straight northern border. @Alex you might want to see if that line is 2 points or is densified. Try densifying it before projecting it. That may make the area calculations closer. That's something to watch for when reprojecting data, especially big areas. (Canada/US has another one) – mkennedy Feb 21 at 20:38

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