Hello again
Close. A method to transform lat/long on one *datum* to lat/lon on another.
Many different datum may exist for the same ellipsoid. The ellipsoid axis
length alone are not suffisient.
ok, so if i understand, a datum might just use the ellipsoid as the datum, but
others may specify a different surface, but possibly using some ellipsoid as a
reference. Is that accurate?
Not exactly... The surface is always the ellipsoid; we don't try to make more
complicated surface (the more complicated surface would be a "geoid", but this
is an other topic). What may change between different datum is the origin of the
coordinate system. For example I found 61 different datum in the EPSG database
using the "GRS 1980" ellipsoid. Below is a few examples. Let emphase that all
those 61 datum use exactly the same "GRS 1980" ellipsoid!
Datum name Origin
-------------------- ------------------------
Taiwan Datum 1997 ITRF94 at epoch 1997.0
Mexican Datum of 1993 ITRF1992 at epoch 1988.00
IRENET95 ETRS89 stations in Ireland
Latvia 1992 Constrained to 4 ETRS89 points in Latvia from
the EUREF Baltic 1992 campaign.
Estonia 1997 Densification of ETRS89 during EUREF-ESTONIA97
campaign through transformation from ITRF96 at epoch 1997.56
... 56 more ...
An ellipsoid is only a mathematical thing. A datum is:
* Choosing a point on the ellipsoid, not necessarily the 0°N,0°E coordinate
- countries will typically choose a (latitude,longitude) on their
territory.
* Specify where on Earth the above point is located, typically through
campaign and marks put in the real world.
Consequently, the coordinate 20°N 30°W (for example) according the "Mexican
Datum of 1993" may be at a slightly different place than the same coordinate
according the "IRENET95" datum; *even if the ellipsoid is exactly the same for
both datum*, because the *origin* of the coordinate system is located at a
slightly different place. The error depends on the particular pair of datum
being considered, but a 1 km error can be considered typical (I not sure if the
same error magnitude apply for datum having the same ellipsoid however, but some
error remain anyway).
Transforming coordinates from one datum to the other is more complicated than
just shifting the origin. Actually the way the ellipsoid is "linked" to the
Earth is determined empirically though "real world" campaigns, and the result
vary between different countries because the campaigns were done in different
landscapes. The most accurate transformations from one datum to an other is to
interpolate in an empirical grid. For example the transformation between NAD27
and NAD83 (two datums used by USA) is nicely illustrated there:
http://www.ngs.noaa.gov/TOOLS/Nadcon/Nadcon.shtml
You can see from the pictures that the shift between those two datum is really
not a simple mathematical function.
An *approximation* of datum shift is often performed by the following methods:
* Convert geographic coordinates to geocentric coordinates
* Apply a scale, translation and rotation of *geocentric* coordinates by
some amount specified empirically (as "Bursa-Wolf parameters") for some
pairs of datum.
* Convert back the resulting geocentric coordinates to geographic
coordinates.
As said above, if those steps are ignored, the error is typically 1 km (sometime
less, sometime more). It may be acceptable or not depending on the
application... A possible approach would be to keep NetCDF referencing
relatively simple, while allowing user to use an other referencing libraries if
they need more precision.
Regards,
Martin
