Tag Archives: utm

Accurate distance buffers over very large distances

Today, I’m going to describe how I get fairly accurate buffer distances over a really large area.

But first, I’m going to send a huge look of disapproval (great big red look of disapproval, if your browser doesn't support inline data) to Norway. It’s not for getting all of the oil and finding a really mature way of dealing with it, and it’s not for the anti-personnel foods (rancid fish in a can, salt liquorice, sticky brown cheese …) either. It’s for this:

norway I disapprove of what you did there

The rest of the world is perfectly fine with having their countries split across Universal Transverse Mercator zones, but not Norway. “Och, my wee fjords…” they whined, and we gave them a whole special wiggle in their UTM zone. Had it not been for Norway’s preciousness, GIS folks the work over could’ve just worked out their UTM zone from a simple calculation, as every other zone is just 6° of longitude wide.

Canada has no such qualms. In a big country (dreams stay with you …), we have a lot of UTM zones:

canada's UTM zones; *EAT* it, Norway…We’re in zones 8–22, which is great if you’re working in geographic coordinates. If you’re unlucky enough to have to apply distance buffers over a long distance, the Earth is inconveniently un-flat, and accuracy falls apart.

What we can do, though, is transform a geographic coordinate into a projected one, apply a buffer distance, then transform back to geographic again. UTM zones are quite good for this, and if it weren’t for bloody Norway, it would be a trivial process. So first, we need a source of UTM grid data.

A Source of UTM Grid Data

Well, the Global UTM Zones Grid from EPDI looks right, and it’s CC BY-NC-SA licensed. But it’s a bit busy with all the grid squares:

canada-gridWhat’s more, there’s no explicit way of getting the numeric zone out of the CODE field (used as labels above). We need to munge this a bit. In a piece of gross data-mangling, I’m using an awk (think: full beard and pork chops) script to process a GeoJSON (all ironic facial hair and artisanal charcuterie) dump of the shape file. I’m not content to just return the zone number; I’m turning it into the EPSG WGS84 SRID of the zone, a 5-digit number understood by proj.4:

32hzz

where:

  • h is the hemisphere: 6 for north, 7 for south.
  • zz is the zone number.

I live in Zone 17 North, so my SRID is 32617.

Here’s the code to do it: zones_add_epsg-awk (which you’ll likely have to rename/fix permissions on). To use it:

  1. Unzip the Global UTM zones grid.
  2. Convert the shape file to GeoJSON, using ogr2ogr:
    ogr2ogr -f GeoJSON utm_zones_final.geojson utm_zones_final.shp
  3. Process it:
    ./zones_add_epsg.awk utm_zones_final.geojson >  utm_zones_final-srid.geojson
  4. Convert the modified GeoJSON back to a shapefile:
    ogr2ogr utm_zones_final-srid.shp utm_zones_final-srid.geojson
  5. Now some magic: create a simplified shapefile with entire UTM zones keyed against the (integer) SRID:
    ogr2ogr wgs84utm.shp utm_zones_final-srid.shp -dialect SQLITE -sql 'SELECT epsgsrid,ST_Union(Geometry) FROM "utm_zones_final-srid" GROUP BY epsgsrid;'

And, lo!

canada-sridSo we can now load this wgs84utm shapefile as a table in SpatiaLite. If you wanted to find the zone for the CN Tower (hint: it’s the same as me), you could run:

select EPSGSRID from wgs84utm where within(GeomFromText('POINT(-79.3869585 43.6425361)',4326), geom);

which returns ‘32617’, as expected.

Making the Transform

(I have to admit, I was amazed when this next bit worked.)

Let’s say we have to identify all the VOR stations in Canada, and draw a 25 km exclusion buffer around them (hey, someone might want to …). VOR stations can be queried from TAFL using the following criteria:

  • the licensee is Nav Canada, or similar,
  • the TX frequency is between 108–117.96 MHz,
  • the location  contains ‘VOR’.

This can be coded as:

SELECT *
FROM tafl
WHERE licensee LIKE 'NAV CANADA%' AND tx >= 108
AND tx <= 117.96 AND location LIKE '%VOR%';

which returns a list of 67 stations, from VYT80 on Mount Macintyre, YT to YYT St Johns, NL. We can use this, along with the UTM zone query above, to make beautiful, beautiful circles:


SELECT tafl.PK_ROWID, tafl.tx, tafl.location, tafl.callsign,
Transform (Buffer ( Transform ( tafl.geom, wgs84utm.epsgsrid ), 25000 )
, 4326 ) AS bgeom
FROM tafl, wgs84utm
WHERE
tafl.licensee LIKE 'NAV CANADA%'
AND tafl.tx >= 108
AND tafl.tx < 117.96
AND tafl.location LIKE '%VOR%'
AND Within( tafl.geom, wgs84utm.geom );

Ta-da!

ont-vor-buffer-geoYes, they look oval; don’t forget that geographic coordinates don’t maintain rectilinearity. Transformed to UTM, they look much more circular:

ont-vor-buffer-utm

tale of two cities: coordinate reference systems, and what on earth is the maywood tot lot?

For reasons that are not particularly clear, the Toronto.ca|Open data is in two different coordinate reference systems (CRS), MTM 3 Degree Zone 10, NAD27 (EPSG 2019) and UTM 6 Degree Zone 17N NAD27 (EPSG 26717). This confuses QGIS even if you’ve input the proper SRIDs into SpatiaLite. The image above shows two apparent Torontos, one in each of the CRSs.

What you have to do is go to to the Project Properties, select the Coordinate Reference System (CRS) tab, and “Enable ‘on the fly’ CRS transformation”. This will line those city layers right back up.

Once we do that, things align as they should. Here’s my neighbourhood, with its parks

But things are still off if you’re querying the SQL directly:


select Distance(Parks.geometry, Neighbourhoods.geometry)/1000
 as Distance_km
 from Parks, Neighbourhoods
 where Parks.name='CORVETTE PARK'
 and Neighbourhoods.hood='Kennedy Park'

which returns a distance of over 314 km. That’s not right.

So we need to transform the geometries to the same CRS.

!!! NB: I might be doing the next bit wrong. CRS transformation is subtle. I’m not, particularly.

The OGR Simple Feature Library is your friend. It can convert pretty much any geo format to another, and can transform coordinates between systems. In exchange for this power, it wants your soul is rather complex.

I’ve chosen to use NAD83(CSRS) / UTM zone 17N (EPSG 2958) for my Toronto maps. It’s fairly accurate over the whole city area. To convert the Parks and Neighbourhoods shape files:

ogr2ogr -s_srs EPSG:2019 -t_srs EPSG:2958 dest/2958/parks/TCL3_UPARK.shp src/2019/parks/TCL3_UPARK.shp
ogr2ogr -s_srs EPSG:26717 -t_srs EPSG:2958 dest/2958/neighbourhoods/Neighbourhoods.shp src/26717/neighbourhoods/Neighbourhoods.shp

Note that it wants the destination file first, then the source. Haven’t seen that order since PIP under CPM/2.2. I was also a bit nerdly, and arranged the files in directories by SRID:

src/2019/address-points
src/2019/business-improvement-areas
src/2019/city-wards
src/2019/parks
src/2019/solid-waste-management-districts
src/2019/toronto-centreline
src/26717/food-banks
src/26717/neighbourhoods
src/26717/places-of-worship
src/26717/priority-invest-neighbourhoods
src/26717/rent-bank-zones
src/26717/rent-banks
src/26717/transit-city
dest/2958/address-points
dest/2958/business-improvement-areas
dest/2958/city-wards
dest/2958/food-banks
dest/2958/neighbourhoods
dest/2958/parks
dest/2958/places-of-worship
dest/2958/priority-invest-neighbourhoods
dest/2958/rent-bank-zones
dest/2958/rent-banks
dest/2958/solid-waste-management-districts
dest/2958/toronto-centreline
dest/2958/transit-city

If we load the transformed shapefiles into Spatialite, and run that query again, it comes out with the correct distance: 0.0 km, as Corvette Park is in the Kennedy Park Neighbourhood.

Now we can run a proper query: what parks are in Kennedy Park, and what are their areas?

select tp.name, round(Area(tp.geometry)/10000,1) as Area_ha
 from Parks as tp, Neighbourhoods as tn
where tn.hood='Kennedy Park'
 and within(tp.geometry, tn.geometry)
order by Area_ha
NAME Area_ha
MAYWOOD TOT LOT 0.7
KITCHENER PARK 0.8
GLEN SHEPPARD PARK 1.0
GREYSTONE PARK 1.1
CORVETTE PARK 2.5
MID-SCARBOROUGH C.C. & ARENA 2.9
FARLINGER RAVINE 2.9

(note how I sneakily used the round() function to avoid too many decimal places?)