PostGIS creating an envelope around a buffer returns strange results

Question

For a spatial search I need a 900km buffer around a given point(lon 18 degrees, lat 63 degrees) and search all geometries in a table that intersect with the envelope around the buffer( actually a quadrat or rectangle depends where you look at it). The geometry records in the table have SRID 4326. My problem is the envelope object I get does not seem to be correct. I use the following:

select st_astext(
         st_transform(
           st_envelope(
             st_buffer(
               st_transform(
                 ST_GeomFromText('POINT(18 63)', 4326),
                 3857),
              900000)), 
           4326));

First I convert the center point to srid 3857 which is meter based, create a buffer with 900000m radius(a circle in 3857 srid), than make an envelope around the buffer( a quadrat in 3857), and convert it back to 4326 where I will get a rectangle. The result is the Polygon below:

POLYGON((9.9151 59.0917,
         9.9151 66.4469,
        26.0848 66.4469,
        26.0848 59.0917,
         9.9151 59.0917))

I have removed some of the decimals returned. As seen the polygon has a width of about 17 longitude degrees which seems ok, but the heigth is only about 6,6 latitude degrees that is much too short. What am I doing wrong? Is the accuracy for such large buffers so poor? When the center point has the coordinates POINT(18 33) with a lower latitude value the results seem to be Ok. I use PostgreSQL 9.6 and PostGIS 2.2 on Windows.

Answer 1

In your area at 63°N the degrees in West-East directions are much shorter than at the equator. See for example Calculating longitude length in miles?. The length of latitude is 111461.61 meters while the length of longitude is only 50672.80 meters. Therefore the metric buffer of 900 km must appear flattened when it is shown in the "plate carrée projection" https://en.wikipedia.org/wiki/Equirectangular_projection.

With this SQL you can create the metric buffer from geography and express it as geometry:

SELECT ST_AsText(
ST_Envelope(
ST_Buffer(
ST_GeogFromText('POINT(18 63)'),900000)::geometry));

And this is the result as an image showing the centre point, the 900 km buffer and the envelope of the buffer.

The envelope as WKT is

POLYGON ((
        0.0427499612517697 54.92603943866185, 
        0.0427499612517697 71.05803605306652, 
        35.880482526992445 71.05803605306652, 
        35.880482526992445 54.92603943866185, 
        0.0427499612517697 54.92603943866185
    ))

It is 35.8377325657406753 degrees wide and 16.13199661440467 degrees high. With the lengths of longitude and latitude given above the size of the envelope in kilometers is 1815.998 (W) 1798.098 (H). Not exacty 1800 but not much different either.

If you place a round sticker to a football and look at it from different angles you will notice that it is not odd at all that at the sticker seems to be wider than high when looked at flat angle.