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<p>Hi,</p>
<p>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.<br>
</p>
<p>Nicolas <br>
</p>
<div class="moz-cite-prefix">On 2021-01-05 1:33 p.m., Rahkonen Jukka
(MML) wrote:<br>
</div>
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<p class="MsoNormal">Hi,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US">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
<a href="https://postgis.net/docs/ST_Area.html"
moz-do-not-send="true">https://postgis.net/docs/ST_Area.html</a>
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
<a class="moz-txt-link-freetext" href="http://www.gaia-gis.it/gaia-sins/spatialite-sql-latest.html">http://www.gaia-gis.it/gaia-sins/spatialite-sql-latest.html</a>.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">-Jukka Rahkonen-<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<div>
<div style="border:none;border-top:solid #E1E1E1
1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span
style="mso-fareast-language:FI">Lähettäjä:</span></b><span
style="mso-fareast-language:FI"> Nicolas Cadieux
<a class="moz-txt-link-rfc2396E" href="mailto:njacadieux.gitlab@gmail.com"><njacadieux.gitlab@gmail.com></a>
<br>
<b>Lähetetty:</b> tiistai 5. tammikuuta 2021 20.04<br>
<b>Vastaanottaja:</b> Rahkonen Jukka (MML)
<a class="moz-txt-link-rfc2396E" href="mailto:jukka.rahkonen@maanmittauslaitos.fi"><jukka.rahkonen@maanmittauslaitos.fi></a>;
<a class="moz-txt-link-abbreviated" href="mailto:qgis-user@lists.osgeo.org">qgis-user@lists.osgeo.org</a><br>
<b>Aihe:</b> Re: [Qgis-user] Confusion with ellipsoidal
method of $area<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p>Hi,<span style="mso-fareast-language:FI"><o:p></o:p></span></p>
<p>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.<o:p></o:p></p>
<p>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.<o:p></o:p></p>
<p>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.<o:p></o:p></p>
<p><br>
MERIT a=6378137.0 rf=298.257 MERIT 1983<br>
SGS85 a=6378136.0 rf=298.257 Soviet Geodetic
System 85<br>
GRS80 a=6378137.0 rf=298.257222101 GRS 1980(IUGG,
1980)<br>
IAU76 a=6378140.0 rf=298.257 IAU 1976<br>
airy a=6377563.396 rf=299.3249646 Airy 1830<br>
APL4.9 a=6378137.0 rf=298.25 Appl. Physics.
1965<br>
NWL9D a=6378145.0 rf=298.25 Naval Weapons
Lab., 1965<br>
mod_airy a=6377340.189 b=6356034.446 Modified Airy<br>
andrae a=6377104.43 rf=300.0 Andrae 1876 (Den.,
Iclnd.)<br>
danish a=6377019.2563 rf=300.0 Andrae 1876
(Denmark, Iceland)<br>
aust_SA a=6378160.0 rf=298.25 Australian Natl
& S. Amer. 1969<br>
GRS67 a=6378160.0 rf=298.2471674270 GRS 67(IUGG 1967)<br>
GSK2011 a=6378136.5 rf=298.2564151 GSK-2011<br>
bessel a=6377397.155 rf=299.1528128 Bessel 1841<br>
bess_nam a=6377483.865 rf=299.1528128 Bessel 1841
(Namibia)<br>
clrk66 a=6378206.4 b=6356583.8 Clarke 1866<br>
clrk80 a=6378249.145 rf=293.4663 Clarke 1880 mod.<br>
clrk80ign a=6378249.2 rf=293.4660212936269 Clarke 1880
(IGN).<br>
CPM a=6375738.7 rf=334.29 Comm. des Poids et
Mesures 1799<br>
delmbr a=6376428. rf=311.5 Delambre 1810
(Belgium)<br>
engelis a=6378136.05 rf=298.2566 Engelis 1985<br>
evrst30 a=6377276.345 rf=300.8017 Everest 1830<br>
evrst48 a=6377304.063 rf=300.8017 Everest 1948<br>
evrst56 a=6377301.243 rf=300.8017 Everest 1956<br>
evrst69 a=6377295.664 rf=300.8017 Everest 1969<br>
evrstSS a=6377298.556 rf=300.8017 Everest (Sabah
& Sarawak)<br>
fschr60 a=6378166. rf=298.3 Fischer (Mercury
Datum) 1960<br>
fschr60m a=6378155. rf=298.3 Modified Fischer
1960<br>
fschr68 a=6378150. rf=298.3 Fischer 1968<br>
helmert a=6378200. rf=298.3 Helmert 1906<br>
hough a=6378270.0 rf=297. Hough<br>
intl a=6378388.0 rf=297. International 1909
(Hayford)<br>
krass a=6378245.0 rf=298.3 Krassovsky, 1942<br>
kaula a=6378163. rf=298.24 Kaula 1961<br>
lerch a=6378139. rf=298.257 Lerch 1979<br>
mprts a=6397300. rf=191. Maupertius 1738<br>
new_intl a=6378157.5 b=6356772.2 New International
1967<br>
plessis a=6376523. b=6355863. Plessis 1817
(France)<br>
PZ90 a=6378136.0 rf=298.25784 PZ-90<br>
SEasia a=6378155.0 b=6356773.3205 Southeast Asia<br>
walbeck a=6376896.0 b=6355834.8467 Walbeck<br>
WGS60 a=6378165.0 rf=298.3 WGS 60<br>
WGS66 a=6378145.0 rf=298.25 WGS 66<br>
WGS72 a=6378135.0 rf=298.26 WGS 72<br>
WGS84 a=6378137.0 rf=298.257223563 WGS 84<br>
sphere a=6370997.0 b=6370997.0 Normal Sphere
(r=6370997)<o:p></o:p></p>
<p>Nicolas<o:p></o:p></p>
<p><o:p> </o:p></p>
<div>
<p class="MsoNormal">On 2021-01-05 11:43 a.m., Rahkonen Jukka
(MML) wrote:<o:p></o:p></p>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<p class="MsoNormal">Hi,<o:p></o:p></p>
<p class="MsoNormal"> <o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">I wonder what method
QGIS is using when it computes ellipsoidal area with $area
function. I made a test with this EPSG:4326 polygon:</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">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 ))</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">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</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">249566957499.7546</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">As a references I used
PostGIS and web site
<a
href="https://geographiclib.sourceforge.io/scripts/geod-calc.html#area"
moz-do-not-send="true">https://geographiclib.sourceforge.io/scripts/geod-calc.html#area</a>.
With my test polygon they both give this result:</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">251199344354.4308</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">PostGIS returns bigger
area. The difference is 0.654% so not huge but not
negligible either.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">A third test with
SpatiaLite 5.0 gives a result that is very close to
PostGIS (difference 0.001%).</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">251195856999.549927</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">As a conclusion I have
decided to trust in PostGIS because it gives the same
results than the web site
<a
href="https://geographiclib.sourceforge.io/scripts/geod-calc.html"
moz-do-not-send="true">https://geographiclib.sourceforge.io/scripts/geod-calc.html</a>
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.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">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.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">PostGIS</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">select
st_area(st_geogfromtext('POLYGON ((</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">20.13293641
59.95688345,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">26.94617837
60.47397663,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">29.74782155
62.56499443,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">27.45254202
68.70650340,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">23.75771765
68.24937206,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">25.42698984
65.27444593,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">21.51545237
63.10353609,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">21.40562760
61.12318104,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">19.41123592
60.40477513,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">20.13293641
59.95688345))') , true);</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">Spatialite</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">select
st_area(st_geomfromtext('POLYGON ((</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">20.13293641
59.95688345,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">26.94617837
60.47397663,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">29.74782155
62.56499443,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">27.45254202
68.70650340,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">23.75771765
68.24937206,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">25.42698984
65.27444593,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">21.51545237
63.10353609,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">21.40562760
61.12318104,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">19.41123592
60.40477513,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">20.13293641
59.95688345))') ,true);</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">Web site (notice
lat-lon order)</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">59.95688345
20.13293641 </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">60.47397663
26.94617837 </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">62.56499443
29.74782155 </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">68.70650340
27.45254202 </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">68.24937206
23.75771765 </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">65.27444593
25.42698984 </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">63.10353609
21.51545237 </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">61.12318104
21.40562760 </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">60.40477513
19.41123592 </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">59.95688345
20.13293641</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">-Jukka Rahkonen- </span><o:p></o:p></p>
<p class="MsoNormal"><span style="mso-fareast-language:FI"><br>
<br>
<o:p></o:p></span></p>
<pre>_______________________________________________<o:p></o:p></pre>
<pre>Qgis-user mailing list<o:p></o:p></pre>
<pre><a href="mailto:Qgis-user@lists.osgeo.org" moz-do-not-send="true">Qgis-user@lists.osgeo.org</a><o:p></o:p></pre>
<pre>List info: <a href="https://lists.osgeo.org/mailman/listinfo/qgis-user" moz-do-not-send="true">https://lists.osgeo.org/mailman/listinfo/qgis-user</a><o:p></o:p></pre>
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</blockquote>
<pre>-- <o:p></o:p></pre>
<pre>Nicolas Cadieux<o:p></o:p></pre>
<pre><a href="https://gitlab.com/njacadieux" moz-do-not-send="true">https://gitlab.com/njacadieux</a><o:p></o:p></pre>
</div>
</blockquote>
<pre class="moz-signature" cols="72">--
Nicolas Cadieux
<a class="moz-txt-link-freetext" href="https://gitlab.com/njacadieux">https://gitlab.com/njacadieux</a></pre>
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