The requirement for explicitly defining a Datum for a given
mapping project identifies the coordinate reference system
of the data set(s).
The primary coordinate reference system of interest is the
DATUM. The classical geodetic horizontal datum starts at a
particular point. The North American continent has one
major classical horizontal datum, which is the North
American Datum of 1927. The starting point is defined at
Meades Ranch, Kansas. Most datums have their historical
origins at an astronomical observatory, mainly because when
geodetic reference systems were originated, the best-known
position in a region was at that observatory. That
observatory also had a "mire" or reference point on the
horizon with a known azimuth from true north (North
Celestial Pole). With a known direction reference and a
known position, physically measuring a distance to another
point on the ground allowed the computation of another
known position (latitude and longitude) with reference to
the starting point or datum point. That's how all datums
started. The observatory for NAD 1927 was not in Kansas but
on the East Coast, and was used for earlier datums that
included the New England Datum. Many of these classical
origin points were also Prime Meridians (zero longitude)
because these observatories established an ephemeris of
their own for predicting positions of heavenly bodies with
respect to their own reference meridian. For instance,
classical horizontal datum origins that had their own Prime
Meridians include: Amersfoort, Netherlands; Bogot<,
Colombia; Dehra Dun, India; Tokyo, Japan; Madrid, Spain;
Athens, Greece; Quito, Ecuador; Ferro, Canary Islands;
Singkawang, Borneo; Potsdam, Germany and Greenwich,
England.
When we map an area, we first establish control points that
encompass the entire area. We interpolate - not
extrapolate - when we map, and we use a coordinate
reference system of some sort. The establishment of a
datum from a starting point required many points to be
determined in order to provide control for a national or
regional mapping program. The electronic distance meter
was invented in the late 1940's almost simultaneously in
Sweden and South Africa. Prior to that, steel tapes were
used, commonly made of a quench-annealed nickel alloy
called invar. Geodetic surveyors of the late 18th century
did not have that technology available, and had to use
other types of length-measuring devices. Measuring
distances was extremely difficult and time-consuming.
Triangulation baselines sometimes involved entire seasons
for dozens of surveyors and helpers in the determination of
a single 20-30 kilometer distance. Needless to say, after
a baseline was determined to be reliable by several
separate independent measurements, the last thing those
geodetic surveyors wanted to do was to measure another
baseline anytime soon. Triangulation techniques were
developed to minimize the need for physically measuring
distances on the ground. The basic mathematical formula
they used for this purpose was the Law of Sines:
a b c
------- = --------- =
--------
Sin A Sin B
Sin C
Of course, there are many corrections for systematic error
that need to be made, but the basic principle of classical
triangulation is just this simple. These points were
observed as part of basic figures called quadrilaterals
(four-sided) with all points being visible and all angles
observed from all other points in the quadrilateral.
Within each quadrilateral, there is an over-determination
of lengths, which can be used in a least-squares solution.
Tens of thousands of quadrilaterals observed throughout
the world were run predominantly in North-South directions
to obtain a best-fitting figure of the earth for the region
under observation. Because we had many starting points
(datum origins) with hundreds of crews and thousands of
different instruments and length-measuring devices, we
wound up with many different determinations of the size and
shape of the earth (ellipsoids). Over time, many of the
various ellipsoids never got past a single publication
while a couple dozen became commonly used for actual
mapping in different parts of the world. Ellipsoids were
usually named after the geodesist that computed and
published the values along with the year of the publication
such as Clarke 1866, Everest 1830 and Bessel 1841.
Datums evolve with time and some ellipsoids
have been modified as a result of a re-computation or
re-adjustment of an older datum. In some cases, ellipsoids
have been changed as a result of the adoption of new length
standards such as new "meter bars". Classifying data types
and coordinate systems in terms of specific map projections
and ellipsoids is a common mistake; the most important
classifier is the datum and its adjustment date.
Therefore, once the specific datum is identified, all
other parameters follow by definition. Datums vary in
accuracy and reliability according to how various points
were surveyed. The classical triangulations have evolved
in accuracy as a result of improvements in instrumentation,
field procedures and adjustment techniques. Furthermore,
intersection points were observed as invaluable reference
points for topographic mapping, but at a drastically lower
level of accuracy than the basic quadrilaterals. Many
intersection points could not be realistically occupied
such as church spires, roof finials and water tanks.
Although a datum defines the basic control for a region or
continental area, accuracy varies according to the "order"
of the original survey. Relating two datums to each other
is valid only when we can identify common points that are
part of main triangulation arcs. We cannot develop a
meaningful transformation between datums when we are
indiscriminate in our choice of common points. The chains
of quadrilaterals represent the actual observations made
over decades of datum development. Transformations are
valid only when we relate chains of like accuracy or
"order" for a given region. The larger the region for
which we attempt to develop a relation, the larger the
uncertainty we obtain for our relation. We sometimes use
additional parameters to define a relation so that we can
decrease the uncertainties for a region or given data set.
When we establish control for a mapping project with GPS
receivers, eventually we will have to relate old data to
our new maps. If we undertake this task in the United
States, it's a pretty straightforward and well-documented
procedure thanks to the National Geodetic Survey. However,
the datums and grid systems that exist in the world are
myriad; there are over 1,100 classical horizontal geodetic
datums existing in the world, and over 3,200 known grids.
Therefore, a datum does make a difference in MapInfo
because of the explicit requirement to identify your
dataset. Attempting to "mix" different datums would create
a hiatus or holiday in your coverage such that the two
datasets would not match/dovetail or make sense. It is my
impression that MapInfo is intended to serve as a
cartographic tool within the broad category of "GIS."
Datum identification presumably allows one to identify
cartographic data such that geodetic blunders can be
avoided.
For further reading on this topic, I publish a monthly
column in "Photogrammetric Engineering and Remote Sensing."
My column is on Grids and Datums, and each month I address
the Grids and Datums of a particular country, each month on
a different continent.
Some past columns may be downloaded in "PDF" format from
the society's website:
http://www.asprs.org/resources.html
Just click on Grids and Datums.
I trust this answers your question.
Cliff
Clifford J. Mugnier ([EMAIL PROTECTED])
The Topographic Engineering Laboratory
Department of Civil and Environmental Engineering
UNIVERSITY OF NEW ORLEANS
New Orleans, Louisiana 70148
Voice and Facsimilie: (504) 280-7095
On Friday, 07 May, 1999 12:40 PM, Bill Thoen
[SMTP:[EMAIL PROTECTED]] wrote:
> Here's a really fundamental question for project experts.
> MapInfo's Lat/Long "projection" is really an equi-distant
> cylindrical projection (from pg 419, pp 4 under
> "Projections
> vs.Coordinate Systems"). But from what I read in Snyder's
> book on
> projections used by the USGS, this projection requires 4
> parameters: radius of the earth, central longitude and
> latitude,
> and scale factor along the meridian.
>
> My question is that if this is true, what does it matter
> what
> datum you use? Note that the variable used in the
> projection is
> the radius, not an ellipsoid axis. Why is there any
choice
> of
> Datum then? This appears to be a bit pointless unless
> MapInfo is
> doing something else beyond the basic projection.
>
> And where does MapInfo get its origin of lat and long
from
> for
> this projection? It looks like it might be the map window
> center,
> but I need to know for sure.
>
> Any ideas?
>
> - Bill Thoen
>
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