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I am looking for a projection (or a set of projections) that decently preserve distances so that I can buffer every country in the world and have a similar level of minimal distortion for each.

I then need a projection (or set of projections) to compute the areas of these buffers so that each country in the world's buffer area can be compared with any other country's buffer area.

Eventually I will need to do a bunch of overlays onto these areas to chop up and assign other statistics based on proportion of overlap and such. All of these resulting stats need to be comparable with every other country in the world. At this stage in the game, I am thinking that must be done in an equal-area projection(s) as well.

It is the first time I am operating at a scale smaller than local or regional, and the results will have to be defensible and open to peer-review. I am assuming it is improper to do all of these things in lat/lng, but then when I think about the logic of why, I confuse myself!

I appreciate any info, opinions, reflections on similar experiences, etc anyone has about this!

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2 Answers 2

up vote 1 down vote accepted

Map projection selection tool suggests Eckert IV and Mollweide http://people.oregonstate.edu/~savricb/selectiontool/

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I took a quick look at the Mollweide: although it's equal-area, which is good, it introduces a lot of distortion away from the Equator. The additional area of the buffer for certain countries--most notably Russia--will be almost 100% too great whereas that of other countries, such as New Zealand, will be almost 50% too small. Those errors might or might not be of concern in this application, but they suggest that for accurate peer-reviewed work another solution should be sought, such as working in spherical coordinates directly or using multiple projections suited for individual countries. –  whuber Sep 9 '13 at 21:58
    
That is good to know! Where did you find this info? I would love to see a one-stop shop that listed the appropriate uses for all of the major projections. –  MelissaN Sep 10 '13 at 0:03
    
I derived it from Tissot indicatrices. We have a thread on this general topic, too. The closest there is to a "one-stop-shop" is John Snyder's manual. –  whuber Sep 10 '13 at 1:04
    
Great tool - thanks for sharing –  jbaums Jun 4 at 6:33

The latest PostGIS has a "Geography" data type which does calculations on Lat/Lon WGS84 spatial reference system data, and returns the distance or area results in meters/sq. meters based on the WGS84 ellipsoid. So you could bring your country data into PostGIS in WGS84 Lat/Lon, using Geography instead of Geometry and then create the buffers, and do the area calculations with the built in functions.

See: ST_Buffers ST_Area and PostGIS Geography

-- Micha

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This looks promising. I was thinking of writing a script that shifts Mercator or Transverse Mercator so that the area of low distortion overlays a country (if possible), but there are faults in that. Looks like ST_Buffer does something similar "favoring UTM, Lambert Azimuthal Equal Area (LAEA) north/south pole, and falling back on mercator in worst case scenario" There doesnt happen to be something similar to ST_buffer that ArcGIS or FME does? –  MelissaN Jun 22 '12 at 21:53
    
I wouldn't know about FME. Writing your own script to project each county on the fly, then do the buffer, would be tricky since many countries stretch across several CRS's. Using the PostGIS Geography data type avoids the issue. –  Micha Jun 24 '12 at 7:56

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