404
June 2016
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
performed by the British Directorate of Colonial Surveys
(DCS), later renamed to the Directorate of Overseas Surveys
(DOS). The original DCS survey consisted of 51 classical
triangulation stations subsequently densified with DI-10 (IR
EDM) traverse for 357 additional points. The establishment
of elevations was accomplished by a series of both single-
run loops and double-run spurs for a total of 147 stations.
The fundamental benchmark on Grand Cayman Island is
called “Vidal Spot,” established from the observations of
three months. There is some question on the validity of this
benchmark elevation with respect to local mean sea level.
(The full Metonic Cycle of 18.6 years is used at permanent
tide gages for the determination of local mean sea level.)
In 1977, the 512 Specialist Team of the Royal Engineers
“on secondment” to DMA/HTC performed Doppler Satellite
observations but results referenced to the NWL9D Datum
were never sent to the Government of the Cayman Islands
(accuracy was ±1.5 meters). A subsequent survey by the U.S.
National Geodetic Survey determined theWGS 84 coordinates
of a number of existing stations on Grand Cayman Island in
1996-1997.
The current reference system for the islands of Little
Cayman and CaymanBrac, “LC 5 Astro Owen IslandDOS 1961
Datum,” is based on the Origin:
F
o
= 19
o
39´ 46.324˝ North,
L
o
= 80
o
03´ 47.91 West of Greenwich. The defining orientation is
based on two azimuths, which is very unusual, but it is logical
since there is one azimuth per island. The azimuth on Cayman
Brac from CB 2 to CB 1 is 236
o
37´ 36.33˝, and the azimuth
on Little Cayman from LC 5 to LC 6 is 256
o
19´ 02.03˝. This
Datum is referenced to the Clarke 1866 ellipsoid also. The
height Datum was based on the fundamental benchmark for
Little Cayman, which was 3.266 meters. The height datum for
Cayman Brac was based on BM 13, which was 3.720 meters.
The original DOS survey consisted of 27 points, and there was
a closed traverse around each island. A braced connection
between the two islands was performed with angles and
Tellurometer distances. Subsequently, 300 additional points
were added with DI-10 distances.
During the Fall of 1997, with the gracious help of the
Government Office of the Chief Surveyor of the Cayman
Islands, I acquired the “complete” data set of their classical
datums. I provided my graduate class with these data, which
consisted of those points common to the two classical datums
and to the WGS84 Datum. The results of that homework
assignment developed a three-parameter solution for both
datums, and a seven-parameter solution for the Grand
Cayman Datum. The Three-Parameter transformation
from the “GC 1 1959 Datum” to the WGS 84 Datum is:
D
X
= +67.757 meters,
D
Y = +106.114 meters,
D
Z = +138.813
meters. The highest residual of six common points did not
exceed 0.90 meters. On the other hand, if we use a seven-
parameter transformation, the accuracy is improved tenfold.
Those parameters are:
D
X = – 0.75 meters,
D
Y = + 7.93
meters,
D
Z = + 153.87 meters, Scale = –13.63 X 106, Rx =
– 0.52 arc seconds, Ry = –6.49 arc seconds, and R
z
= 1.46
arc seconds. Only two points in common were observed by
the U.S. National Geodetic Survey between WGS 84 and
the local datum for the Little Cayman and Cayman Brac
islands. Therefore, only a three-parameter transformation
is possible:
D
X = +44.423 meters,
D
Y = +108.983 meters,
D
Z
= + 151.666 meters. The highest residual for this two-point
fit was 0.34 meters, and this relation should be considered
quite approximate. The British West Indies (BWI) Grid is not
used in the Cayman Islands. The Cayman Islands use the
standard UTM Grid for both Datums on all three islands, and
all islands are in Zone 17 (Central Meridian = 93
o
West).
U
pdate
The coordinate systems of the Cayman Islands have been
completely updated since the last time a column was
published on the country. The new datum is the Cayman
Islands Geodetic Datum of 2011 (CIDG11). The ellipsoid
by default is the GRS80 because the ITRF05(2011) is the
reference system. With respect to the old datums, the
following transformation from Grand Cayman Geodetic
Datum of 1959 (GCGD59) to CIDG11 is:
D
X = –179.483m.,
D
Y
= –69.379 m.,
D
Z = –27.584 m., R
x
= +7.862², R
y
= –8.163², R
z
= –6.0427²,
d
s = –13.925 ppm; the ESRI/Trimble Coordinate
Frame Rotation convention being utilized. Transformation
accuracy of ±1 foot is claimed by the government. With
respect to Cayman Brac and Little Cayman, the following
transformation from Sister Islands Geodetic Datum of 1961
(SIGD61) to CIDG11 is:
D
X = +8.853 m.,
D
Y = -52.644 m.,
D
Z
= +180.304 m., R
x
= +0.393², R
y
= +2.323², R
z
= -2.96²,
d
s =
–24.081 ppm; the ESRI/Trimble Coordinate Frame Rotation
convention being utilized. Transformation accuracy of ±1 foot
is claimed by the government.
The new plane coordinate system for all of the Cayman
Islands is the Cayman Islands National Grid (CING11)
now using the Lambert Conformal Conic projection where:
Latitude of False Origin is: 19°20´ N, Longitude of False
Origin is: 80°34´ W, Latitude of 1
st
Standard Parallel is 19°20´
N, Latitude of 2
nd
Standard Parallel is 19°42´ N, Easting at
False Origin is 2,950,000 Ft, Northing at False Origin is
1,900,000 Ft, and the International Foot convention is used
where 1 meter = 0.3048 Ft. These parameters are defined by
the National Government as published as EPSG Code 6391.
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).
This column was previously published in
PE&RS
.
