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Aaron
(and others with similar projection questions)
First,
some basics (in Geosoft-speak - apologies to cartographers out there). I
am elaborating beyond Aaron's question because this theme does come up a
lot.
A
"Datum" defines the earth model used to represent a "Geoid", which is
effectively a surface that would be defined by the sea level throughout an area
being mapped. At this point, we should all understand that the "geoid"
undulates according to the gravitational field, hence it cannot be defined
perfectly by a simple mathematical expression. The business of
cartography is to map features that exist on a local geoid to a flat piece
of paper.
So,
how do we get from a geoid to a map?
The
first step is the "datum". The datum consists of an ellipsoid, a prime
meridian, and a specific part of the earth for which the datum applies.
The datum ellipsoid is a perfect mathematical surface that best approximates the
shape of the earth over the area of a datum. Latitude, longitude locations
on a datum are the closest match of the geoid location to the datum ellipsoid
surface. For example, latitude, longitude coordinates on the NAD27 datum
use the Clarke 1866 ellipsoid with Greenwich as the prime meridian. One
should note that the mapping of the geoid shape to the ellipsoid is not perfect
because of the afore-mentioned imperfections in the geoid.
At
this point it is worth pointing out that many datums share the same
ellipsoid. The difference between them is that a specific datum only
applies to a specific area of the earth, and the geoid of that area is implied
by the datum name. For example, "Luzon 1911", "Mound Dillon" and
"NAD27" are all datums based on the "Clarke 1866" ellipsoid, but are used
to map the geoid from the Philippines, the island of Tobago, and the North (and
central) America respectively.
Once
we have a longitude, latitude on a specific datum, it is the job of a map
projection to convert the latitude, longitude to a Cartesian X,Y coordinate for
a flat piece of paper.
The
next piece of the puzzle is to understand why we need a refinement of the datum
into what Geosoft calls "local datums". The advent of GPS and
satellite mapping required the definition of a single datum that best
approximates the entire earth. After a bit of evolution, we have settled
on WGS 84, which is truly a "perfect" datum that represents an exact
ellipsoid, and the centre of that ellipsoid is at the gravitational centre of
the earth. A fundamental problem in modern cartography is how to convert a
latitude, longitude on the WGS 84 datum to, say, NAD27 so that a location can be
used on NAD27 maps, or vice versa.
Because datums like NAD27 represent a geoid, and WGS
represents a perfect ellipsoid, we need a way to convert the imperfect geoid
shape of NAD27 to the perfect WGS27. The best way to do this is to
measure the difference between known latitude, longitude locations on the NAD27
datum and the WGS84 location that one receives from a GPS measurement.
This has been done throughout Canada to produce the NTv2 model of NAD27, and
throughout the United States to produce the NADCON model. This process is
also being carried out at continental scale in other parts of the world.
Both NTv2 and NADCON are implemented as gridded corrections models,
that given a location, one can look up the correction (both are supported in
Geosoft).
A
second way to make the correction is to force the surface of the WGS 84
ellipsoid to lie as closely as possible to the surface of the datum ellipsoid
(which in turn approximates the geoid), such that a simple mathematical
conversion is within acceptable accuracy. This can be done by adjusting
the location of the centre of the earth of the datum ellipsoid relative to
WGS84, which is the basis of the Molodenski and Bursa Wolf corrections
(parameters are in datumtrf.csv). However, such simple conversions are
only accurate over a relatively small part of the datum, depending , of course,
on the complexity of the geoid of that datum. For datums that cover a
large region, such as NAD27, one needs many different adjustments depending on
which part of the NAD27 datum you are on. For example, the very large area
approximations such as "MEAN Canada" are much less accurate in the Yukon than
"Canada (Yukon)". Both are less accurate than the NTv2 correction
lookup.
With
this background, on to some of Aaron's questions...
> When I but a topographic map of Canada(of say
B.C.)
> it says it uses the NAD27 ellipsoid. It
doesn't say what
>
local transformation it uses?
First,
NAD27 is a datum, not an ellipsoid, and the NAD27 datum uses the Clarke 1866
ellipsoid. You must choose which local datum transform is most appropriate
for for your needs. I would recommend always selecting the local transform
that is most specific to your area, in this case "[NAD27] Canada Alberta;
British Columbia". You could also choose "[NAD27] Canada NTv2 (20 min)" if
the highest accuracy is required, but this is slower and more demanding of
system resources.
In our
"Datum" list we also include the names of all the common earth ellipsoids (with
a "*" prefix). This is because practitioners have commonly confused
ellipsoids with datums, and one often only knows the ellipsoid. By
including the ellipsoid names in the list we make life a bit easier for you when
you receive a map and the information that it is "Clarke 1850, UTM 42S".
However, if you need to do a local datum transform, you must determine (or
guess) at the real datum name, which is also why we list the local transforms by
area of use.
> I found where the ldatum.csv file calls the
datum
>
for say [Nad 27]Canada(Ont.&Man.) but couldn't
>
find the call to the appropriate datum for [Nad27]Canada(BC./AB).
> Did I just not look hard enough? Yes,
these transforms are in the tables. Whenever I am maintaining the tables
(or answering e-mails like this), I load the tables into Excel and use the
Data/Sort function to sort by datum or area of use (or any column) to help me
find things. The ldatum.csv file is used only by the projection wizard to
provide a list of the available projections by datum and by area of use.
This file refers to the actual local datum transform name and parameters in
datumtrf.csv. Note that the tables are only used to construct the
projection information the first time something requires a projection.
Once constructed, the parameters become part of the object in question, and
changing the tables later has no effect.
You
can find more information on how the tables are constructed and related in the
SETIPJ GX help. Another good projection reference site is http://users.netonecom.net/~rburtch/geodesy/datums.html
I hope
this all helps.
Ian
______________
Geosoft Inc. Ian MacLeod [EMAIL PROTECTED] (416) 369 0111 x323 Software and services for effective
earth science decision-making.
|
- [geonet]: Projections Aaron Balasch
- Re: [geonet]: Projections Alan Reid
- Re: [geonet]: Projections Ian MacLeod
- Re: [geonet]: Projections jduval
- [geonet]: projections Beate Leitner
- RE: [geonet]: projections Ian MacLeod
