[Qgis-user] Confusion with ellipsoidal method of $area
Rahkonen Jukka (MML)
jukka.rahkonen at maanmittauslaitos.fi
Wed Jan 6 04:17:59 PST 2021
Hi,
I did my homework and learned that all spheroids are ellipsoids but not all ellipsoids are spheroids. This source puts it into a compact sentence elearning.algonquincollege.com/coursemat/viljoed/gis8746/concepts/geodesy/spheroid.htm
"Ellipsoid is a solid for which all plane sections through one axis are ellipses and through the other are ellipses or circles. If any two of the three axes of that ellipsoid are equal, the figure becomes a spheroid (ellipsoid of revolution). If all three are equal, it becomes a sphere."
The geodetic ellipsoids have two axis with equal length and the third axes is shorter. Therefore in this context terms ellipsoid and spheroid can be used interchangeably https://support.esri.com/en/technical-article/000006398. A tri-axial ellipsoid (https://en.wikipedia.org/wiki/Ellipsoid) is the only sort of ellipsoids that is not spheroid by the same but we do not use such as Earth surface models.
So back to the test. I have the QGIS project in EPSG:4326, the layer in EPSG:4326, and the Project-Properties-General-Measurement-Ellipsoid is set to WGS 84 (EPSG:7030). The $area function returns
249566957499.7546
The ST_Area function of PostGIS https://postgis.net/docs/ST_Area.html with option "use_spheroid=true" returns
251199344354.4308
I modified my SQL to ensure that the geography type is using the WGS 84 spheroid/ellipsoid by adding a cast from EPSG:4326 geometry into geography (reference https://postgis.net/docs/postgis_usage.html#PostGIS_Geography). That did not change the result so obviously WGS 84 spheroid/ellipsoid is the default for PostGIS geography type.
My SQL is now
select ST_Area(ST_GeomFromText('POLYGON ((
20.13293641 59.95688345,
26.94617837 60.47397663,
29.74782155 62.56499443,
27.45254202 68.70650340,
23.75771765 68.24937206,
25.42698984 65.27444593,
21.51545237 63.10353609,
21.40562760 61.12318104,
19.41123592 60.40477513,
20.13293641 59.95688345))',4326)::geography , true)
I have done my best to force both software to make an ellipsoidal/spheroidal area measurement (not spherical) on WGS 84 ellipsoid/spheroid. This is my informed choice, please point where is the mistake if I have done such.
If I have used the right methods with both QGIS and PostGIS then there is still this 0.654% difference in the measured areas. It feels a bit too large to be caused only by minor differences in implementations if the mathematics is the same. Could it possibly mean that either PostGIS or QGIS computes the area wrong?
-Jukka Rahkonen-
-----Alkuperäinen viesti-----
Lähettäjä: Nyall Dawson <nyall.dawson at gmail.com>
Lähetetty: tiistai 5. tammikuuta 2021 23.46
Vastaanottaja: Rahkonen Jukka (MML) <jukka.rahkonen at maanmittauslaitos.fi>
Kopio: Nicolas Cadieux <njacadieux.gitlab at gmail.com>; qgis-user at lists.osgeo.org
Aihe: Re: [Qgis-user] Confusion with ellipsoidal method of $area
On Wed, 6 Jan 2021 at 07:40, Rahkonen Jukka (MML) <jukka.rahkonen at maanmittauslaitos.fi> wrote:
>
> Hi,
>
>
>
> Sorry, I am amateur on this area and I do not know what is the difference between spheroids and ellipsoids. Do you mean that QGIS is using more accurate method than PostGIS for calculating the lengths and areas over the WGS 84 ellipsoid?
You're definitely not alone in this, but I'd strongly recommend doing a bit of research into the differences and how they affect measurements. There's no single "right" answer to how things should be accurately measured, so the decisions regarding this are the user's responsibility, and it's up to you to make an informed choice here.
Suffice to say that both QGIS and geographiclib can do either spherical or ellipsoidal calculations -- to compare them you need to ensure that the exact same sphere/ellipsoid parameters are used.
Nyall
>
>
>
> The article that is used as a reference on the GeographicLib page
> (Charles F. F. Karney, Algorithms for geodesics,
>
> J. Geodesy 87(1), 43–55 (Jan. 2013) does not use word spheroid in the text at all but ellipsoid appears there 29 times. So perhaps the library deals actually with ellipsoid but PostGIS and Spatialite documentation talks about spheroid?
>
>
>
> Could you give one linestring and one polygon as reference geometries and the most accurate lengths and areas that you know for some of your favorite ellipsoids to be used as true values?
>
>
>
> -Jukka Rahkonen-
>
>
>
>
>
>
>
> Lähettäjä: Nicolas Cadieux <njacadieux.gitlab at gmail.com>
> Lähetetty: tiistai 5. tammikuuta 2021 22.52
> Vastaanottaja: Rahkonen Jukka (MML)
> <jukka.rahkonen at maanmittauslaitos.fi>; qgis-user at lists.osgeo.org
> Aihe: Re: [Qgis-user] Confusion with ellipsoidal method of $area
>
>
>
> Hi,
>
> QGIS is currently built on Proj version 6.3.2-1. If the other libraries are using a spheroid by default, then they use a sphere for speed and not an ellipsoid for precision. You can probably force this measurement in QGIS by creating a custom CRS with a spheroid rather than an ellipsoid. The other option is to use the python in QGIS and to force a geoid.
>
> Nicolas
>
> On 2021-01-05 1:33 p.m., Rahkonen Jukka (MML) wrote:
>
> Hi,
>
>
>
> I suppose that PostGIS is using the WGS 84 ellipsoid but I am not sure where from the documentation I could find that information. The ST_Area document https://postgis.net/docs/ST_Area.html says only “For geography types by default area is determined on a spheroid with units in square meters”. Same thing with Spatialite, documentation suggests just that it is “the” spheroid http://www.gaia-gis.it/gaia-sins/spatialite-sql-latest.html.
>
>
>
> I did not notice this paragraph in the ST_Area document earlier “Enhanced: 2.2.0 - measurement on spheroid performed with GeographicLib for improved accuracy and robustness. Requires Proj >= 4.9.0 to take advantage of the new feature.” So no wonder that the web app and PostGIS give the same results because they both use GeographicLib. And SpatiaLite 5.0 is using RTTopo that is a library that is based on LWGeom so close connection in there too.
>
>
>
> So perhaps the way to get identical areas from QGIS would be to make it to use GeographicLib as well. I have no idea if it is a realistic approach and worth making a feature request.
>
>
>
> -Jukka Rahkonen-
>
>
>
> Lähettäjä: Nicolas Cadieux <njacadieux.gitlab at gmail.com>
> Lähetetty: tiistai 5. tammikuuta 2021 20.04
> Vastaanottaja: Rahkonen Jukka (MML)
> <jukka.rahkonen at maanmittauslaitos.fi>; qgis-user at lists.osgeo.org
> Aihe: Re: [Qgis-user] Confusion with ellipsoidal method of $area
>
>
>
> Hi,
>
> Your method in QGIS is sound. Area is calculated using the wgs84 ellipsoid EPSG 7030. If you reproject to wgs84 zone 35N (I think this is close), area goes from 249566957499.7546m2 to 249566957499.721m2 or a difference of 0.0336 m2. I don't think densification would change things much.
>
> My question is the following: You know that QGIS uses the WGS84 Ellipsoid. What Ellipsoid are using used in the other software??? If you don't know, I would proceed until you figure that out.
>
> This is the currently used ellipsoid in the proj database in QGIS 3.16. You can get this by typing proj -le in the OSFeo4W Shell.
>
>
> MERIT a=6378137.0 rf=298.257 MERIT 1983
> SGS85 a=6378136.0 rf=298.257 Soviet Geodetic System 85
> GRS80 a=6378137.0 rf=298.257222101 GRS 1980(IUGG, 1980)
> IAU76 a=6378140.0 rf=298.257 IAU 1976
> airy a=6377563.396 rf=299.3249646 Airy 1830
> APL4.9 a=6378137.0 rf=298.25 Appl. Physics. 1965
> NWL9D a=6378145.0 rf=298.25 Naval Weapons Lab., 1965
> mod_airy a=6377340.189 b=6356034.446 Modified Airy
> andrae a=6377104.43 rf=300.0 Andrae 1876 (Den., Iclnd.)
> danish a=6377019.2563 rf=300.0 Andrae 1876 (Denmark, Iceland)
> aust_SA a=6378160.0 rf=298.25 Australian Natl & S. Amer. 1969
> GRS67 a=6378160.0 rf=298.2471674270 GRS 67(IUGG 1967)
> GSK2011 a=6378136.5 rf=298.2564151 GSK-2011
> bessel a=6377397.155 rf=299.1528128 Bessel 1841
> bess_nam a=6377483.865 rf=299.1528128 Bessel 1841 (Namibia)
> clrk66 a=6378206.4 b=6356583.8 Clarke 1866
> clrk80 a=6378249.145 rf=293.4663 Clarke 1880 mod.
> clrk80ign a=6378249.2 rf=293.4660212936269 Clarke 1880 (IGN).
> CPM a=6375738.7 rf=334.29 Comm. des Poids et Mesures 1799
> delmbr a=6376428. rf=311.5 Delambre 1810 (Belgium)
> engelis a=6378136.05 rf=298.2566 Engelis 1985
> evrst30 a=6377276.345 rf=300.8017 Everest 1830
> evrst48 a=6377304.063 rf=300.8017 Everest 1948
> evrst56 a=6377301.243 rf=300.8017 Everest 1956
> evrst69 a=6377295.664 rf=300.8017 Everest 1969
> evrstSS a=6377298.556 rf=300.8017 Everest (Sabah & Sarawak)
> fschr60 a=6378166. rf=298.3 Fischer (Mercury Datum) 1960
> fschr60m a=6378155. rf=298.3 Modified Fischer 1960
> fschr68 a=6378150. rf=298.3 Fischer 1968
> helmert a=6378200. rf=298.3 Helmert 1906
> hough a=6378270.0 rf=297. Hough
> intl a=6378388.0 rf=297. International 1909 (Hayford)
> krass a=6378245.0 rf=298.3 Krassovsky, 1942
> kaula a=6378163. rf=298.24 Kaula 1961
> lerch a=6378139. rf=298.257 Lerch 1979
> mprts a=6397300. rf=191. Maupertius 1738
> new_intl a=6378157.5 b=6356772.2 New International 1967
> plessis a=6376523. b=6355863. Plessis 1817 (France)
> PZ90 a=6378136.0 rf=298.25784 PZ-90
> SEasia a=6378155.0 b=6356773.3205 Southeast Asia
> walbeck a=6376896.0 b=6355834.8467 Walbeck
> WGS60 a=6378165.0 rf=298.3 WGS 60
> WGS66 a=6378145.0 rf=298.25 WGS 66
> WGS72 a=6378135.0 rf=298.26 WGS 72
> WGS84 a=6378137.0 rf=298.257223563 WGS 84
> sphere a=6370997.0 b=6370997.0 Normal Sphere (r=6370997)
>
> Nicolas
>
>
>
> On 2021-01-05 11:43 a.m., Rahkonen Jukka (MML) wrote:
>
> Hi,
>
>
>
> I wonder what method QGIS is using when it computes ellipsoidal area with $area function. I made a test with this EPSG:4326 polygon:
>
> POLYGON (( 20.13293641 59.95688345, 26.94617837 60.47397663,
> 29.74782155 62.56499443, 27.45254202 68.7065034, 23.75771765
> 68.24937206, 25.42698984 65.27444593, 21.51545237 63.10353609,
> 21.4056276 61.12318104, 19.41123592 60.40477513, 20.13293641
> 59.95688345 ))
>
>
>
> I checked that the CRS of the project and layer were both EPSG:4326.
> The ellipsoid in the Project-Settings was WGS 84 (EPSG:7030). The area
> that $area returns is
>
> 249566957499.7546
>
>
>
> As a references I used PostGIS and web site https://geographiclib.sourceforge.io/scripts/geod-calc.html#area. With my test polygon they both give this result:
>
> 251199344354.4308
>
>
>
> PostGIS returns bigger area. The difference is 0.654% so not huge but not negligible either.
>
>
>
> A third test with SpatiaLite 5.0 gives a result that is very close to PostGIS (difference 0.001%).
>
> 251195856999.549927
>
>
>
> As a conclusion I have decided to trust in PostGIS because it gives the same results than the web site https://geographiclib.sourceforge.io/scripts/geod-calc.html that feels scientifically sound. However, I wonder if I have used QGIS in a correct way or if there is anything I could do for getting areas to match better with PostGIS for example by densifying the long segments in my test polygon.
>
>
>
> For getting testing easy I attach directly runnable SQL for PostGIS and Spatialite (version 5.0 with RTTopo is needed) as well as a coordinate list for the web app.
>
>
>
> PostGIS
>
> select st_area(st_geogfromtext('POLYGON ((
>
> 20.13293641 59.95688345,
>
> 26.94617837 60.47397663,
>
> 29.74782155 62.56499443,
>
> 27.45254202 68.70650340,
>
> 23.75771765 68.24937206,
>
> 25.42698984 65.27444593,
>
> 21.51545237 63.10353609,
>
> 21.40562760 61.12318104,
>
> 19.41123592 60.40477513,
>
> 20.13293641 59.95688345))') , true);
>
>
>
> Spatialite
>
> select st_area(st_geomfromtext('POLYGON ((
>
> 20.13293641 59.95688345,
>
> 26.94617837 60.47397663,
>
> 29.74782155 62.56499443,
>
> 27.45254202 68.70650340,
>
> 23.75771765 68.24937206,
>
> 25.42698984 65.27444593,
>
> 21.51545237 63.10353609,
>
> 21.40562760 61.12318104,
>
> 19.41123592 60.40477513,
>
> 20.13293641 59.95688345))') ,true);
>
>
>
> Web site (notice lat-lon order)
>
> 59.95688345 20.13293641
>
> 60.47397663 26.94617837
>
> 62.56499443 29.74782155
>
> 68.70650340 27.45254202
>
> 68.24937206 23.75771765
>
> 65.27444593 25.42698984
>
> 63.10353609 21.51545237
>
> 61.12318104 21.40562760
>
> 60.40477513 19.41123592
>
> 59.95688345 20.13293641
>
>
>
> -Jukka Rahkonen-
>
>
>
>
> _______________________________________________
>
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> --
>
> Nicolas Cadieux
>
> https://gitlab.com/njacadieux
>
> --
>
> Nicolas Cadieux
>
> https://gitlab.com/njacadieux
>
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