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February 2014
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
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 in-
stance, classical horizontal datum origins that had their own
Prime Meridians include: Amersfoort Netherlands, Bogotá
Colombia; Dehra Dun India; Tokyo Japan, Madrid Spain;
Athens Greece, Quito Ecuador, Ferro Canary Islands, Sing-
kawang Borneo, Potsdam Germany and Greenwich England.
When we map an area, we first establish control points
that encompass the entire area. We interpolate – not extrap-
olate – when we map, and we use a coordinate reference sys-
tem of some sort. The establishment of a datum from a start-
ing 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-an-
nealed nickel alloy called invar. Geodetic surveyors of the late
18
th
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. Trian-
gulation baselines sometimes involved entire seasons for doz-
ens 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 indepen-
dent 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
A
b
B
c
C
sin sin sin
= =
Of course, there are many corrections for systematic error
that need to be made, but the basic principle of classical tri-
angulation 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 map-
ping 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 tech-
niques. Furthermore, intersection points were observed as
invaluable reference points for topographic mapping, but at
a drastically lower level of accuracy than the basic quadri-
laterals. 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. Last summer, I keyed in the classical
geodetic coordinates of several dozen Datum origins into
Google Earth™. Of course, when the software scrolled over
to those parts of the world, the old origin points were not
immediately apparent since Google Earth™ is referenced
to the WGS84 Datum and ellipsoid. However, many, if not
most are easily located based on their descriptions especially
when the origin points are observatories. Most can be found
within a kilometer or so, primarily in an East-West offset.
The contents of this column reflect the views of the author, who is
responsible for the facts and accuracy of the data presented herein.
The contents do not necessarily reflect the official views or policies of
the American Society for Photogrammetry and Remote Sensing and/
or the Louisiana State University Center for GeoInformatics (C
4
G).
