Calculate longest distance, in KM, between county centroids and their furthest point with PostGIS

Question

Using this shapefile of the US counties at 1:500,000 resolution, I need to know, per county, the length from the centroid of that county to its furthest point away on its polygon. I would like the result in kilometers.

I have uploaded the shapefile to a PostGIS table with:

shp2pgsql -W LATIN1 gz_2010_us_050_00_500k.shp public.county_shapes | psql -h localhost -d counties -U jerickson

I did not know which SRID to use so I did not specify one.

Then, modifying this question/answer, I tried the following query, limiting to name = 'Missoula (a county in Montana that I am familiar with) for now for testing:

SELECT
       t.gid AS county_id,
       max(ST_Distance(dump.geom, ST_Centroid(t.geom))) AS distance
FROM county_shapes t
JOIN ST_DumpPoints(t.geom) dump ON true
where name = 'Missoula'
GROUP BY 1
ORDER BY 1;

While this seems to be correct (logically), I am not sure how to get the resulting value (0.9038766878461234) into kilometers. Using Google Earth to approximate the value, I would expect it to be at least 75 km.

How can I modify my process to get the distance from the centroid to the farthest point on the county polygon for each county in the shapefile?

Answer 1

The value you get there is most likely in decimal degrees...and thus quite useless; a degree doesn't represent the same ground distance in different latitudes and getting from there to metric values is tricky and unnecessary.

First off, you should always define a SRID for your geometries. You can, for example, run ogrinfo on the shapefile, the CRS is usually defined in the metadata.
Now, since ST_Distance returned decimal degrees, it's definetely referenced in a geographical CRS. Possibly the direct and most precise way then is to cast your geometries to geography type, i.e.:

... max(ST_Distance(dump.geom::geography, ST_Centroid(t.geom)::geography)) AS distance ...

This should return values in meter, based on an unknown datum, but calculated on a spheroid and possibly still quite precise, despite the missing CRS. Which is no excuse for not having tried harder to find one!

Update for completeness:
Use ... max(...) / 1000 ... to get results in km.