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Caribbean Datums and the Integration of Geographical Data

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Caribbean Datums and the Integration of Geographical Data Caribbean Journal of Earth Science, 37 (2003), 1-10. © Geological Society of Jamaica. Caribbean datums and the integration of geographical data KEITH M. MILLER Department of Surveying and Land Information, Faculty of Engineering, University of the West Indies ABSTRACT. Modern electronic positioning systems are capable of locating a point in the vicinity of the Earth’s surface to very high precision. Depending on the sophistication of equipment in use, whether the requirement is relative or absolute and the data processing time available, accuracy from 10 m down to a few millimetres can be achieved in three dimensions. While it is not difficult to measure the position of a point using today’s technology, it can be problematic to relate measurements made today to those made in the past. Advances in applications such as Geographical Information Systems (GIS) for example, that integrate geographic data from a wide range of sources may give misleading results if one position on the surface of the Earth can have a number of different coordinate values. This paper is aimed at explaining the reasons behind such dilemma while giving particular examples that relate to the Caribbean region. It defines and explains the different conventions that are adopted while providing local parameters that enable conversion between modern and some of the traditional datums. The reliability of this information is shown to be variable and there is a need for improvement in the quality of parameters that are made publicly available. 1. INTRODUCTION pole Perpendicular to spheroid The study of geodesy has advanced significantly P in recent times, particularly as the analysis of Greenwich b me rid ian Tangent satellite data has provided a global to spheroid approximation of the geoid. Variations in density ϕ through the Earth mean that this figure is a a λ smooth undulating surface similar to that of a flattened pear. The problem of mapping such a equator surface is impractical, so for this purpose a spheroid or ellipsoid is used to approximate the geoid. Positions are then provided as geodetic coordinates that are in polar form as shown in Figure 1. Geodetic latitude (ϕ) and longitude (λ) Figure 1. Difficulties arise with the way that data has been acquired and stored at national levels, 2. SPHEROIDS with the compatibility between national conventions, and in integrating further Historically, a horizontal datum for a country was information that is acquired using modern established by coordinating a single point in technology. Problems that arise are particularly geographical coordinates on a selected spheroid. pronounced when the region is made up of small Astronomical observations would be used to locate island states. The Caribbean for example has the datum point and to provide orientation from numerous traditional mapping datums, one or there to other points. Triangulation techniques from more for each island, and the current trend in this origin established other geodetic control points regional research and monitoring necessitates for the country and coordinates for all such points integration of data from the different states as would be computed in geodetic coordinates on a well as the superposition of new information. spheroid. Spheroids of different dimensions have The purpose here is to examine the existing been used to represent the Earth, the size and shape situation with regard to availability and precision of these were observed on the Earth’s surface using of datum conversion parameters. In order to triangulation techniques and by making achieve this, the different mapping conventions astronomical observations. Until recent times, the and processes that are implemented are precise measurements required could only be made explained. This commences with a description of on land, so for each landmass different spheroids the figures that are used to represent the Earth were adopted. There are in excess of 150 different and the adoption of a datum point. spheroids that have been used since 1800. Some 1 KEITH MILLER - CARIBBEAN DATUMS AND GEOGRAPHICAL DATA Table 1. Parameters of Some Spheroids Spheroid Name Semi-major Semi-minor Flattening, f Eccentricity Axis, a (m) Axis, b (m) squared, e2 Clarke 1858 6378293.645 6356617.938 1/294.26 0.006785 Clarke 1866 6378206.400 6356583.800 1/294.9787 0.006769 Clarke 1880 6378249.145 6356514.870 1/293.465 0.006804 Clarke 1880 modified 6378249.145 6356514.966 1/293.4663 0.006803 South American 1969 6378160.000 6356774.719 1/298.25 0.006695 International 1924 6378388.000 6356911.946 1/297 0.006723 were designed to best fit the geoid over some models. Unfortunately there is still disagreement region; others used all of the world data that was when it comes to applications for positioning on the available at the time. Dimensions of some that have Earth using satellite data. The Global Positioning been used in the mapping and charting of the System (GPS) that is operated by the United States Caribbean are given in Table 1 where numerical Department of Defense uses the World Geodetic values are from DMA Technical Manual (1990) System of 1984 (WGS84) spheroid with dimensions and definitions for datums that use these particular a = 6378137 m, b = 6356752.314 m as its reference. spheroids. Another satellite system, GLONASS, that was For each spheroid a semi-minor and a semi- developed by the former Soviet Union adopts PZ90, major axis are defined such that the surface best fits which has a = 6378136 m and b = 6356751.362 m. the curvature of the Earth. Therefore, the centres of There is a small difference between these the different spheroids that have been adopted are dimensions, however the spheroids are further not necessarily coincident and neither are their axes separated by the displacement of their origins in necessarily parallel to each other. So, when a datum space. point and geodetic control network for a country are specified, the spheroid and datum on which the 3. PROJECTIONS geodetic coordinates are provided must be identified. In situations where different spheroids Neither the sphere nor the spheroid can be have been adopted it is apparent that a single point developed to produce a flat sheet, so in producing a will have more than one defined position, map the accepted spheroidal figure of the Earth depending on the particular spheroid in use. must be stretched in some way, which gives rise to Furthermore, even on the same spheroid a single distortion. The way in which the spheroidal surface point can have different sets of coordinates is manipulated to produce a map is known as the depending on the datum that is in use. For example, projection. A grid is placed over the projection to the Provisional South American Datum of 1956 provide a rectangular horizontal coordinate frame to uses the International 1924 spheroid and has La identify points in terms of their distance east and Canoa in Venezuela as its datum point, north of some origin. The way that the origin is observations made on this datum give coordinates selected is critical to computations, and the size of for Naparima Hill, Trinidad as 10º17’02.416” the grid will change across the map due to variation North, 61º27’22.606” West. This location provides in scale with the projection. The concept of scale is the datum point for the Naparima datum of straightforward in that the map scale (s0) is a factor Trinidad and Tobago which also adopts the that is multiplied by a distance on the map to give International 1924 spheroid, on this datum the equivalent distance on the ground. Due to Naparima Hill has coordinates 10º16’44.860” distortion within the projection however, this will North, 61º34’22.620” West. So, it is shown that the not be uniform across the map, but will vary, so a same point using the same spheroid can have scale factor (sf) is introduced such that at some point different coordinates using different datums. In this on the map the scale is given by: case a few hundred miles separate the datum points and yet the horizontal displacement between the s = s0 × s f two coordinates for the single point provided is There are a number of types of projection that around 650 metres in space. are in use, a full review is given by Maling (1992). With the advent of modern satellite aids to Two that are commonly used for mapping purposes positioning that operate on a global basis, a best are the Transverse Mercator (TM), and the Lambert fitting global spheroid is essential. It is the motion Conical Orthomorphic. These projections are both of the satellites themselves that has been observed orthomorphic, which means that for any point on and used to improve geoidal and hence spheroidal the map the scale in the east-west direction is the 2 KEITH MILLER - CARIBBEAN DATUMS AND GEOGRAPHICAL DATA same as that in the North South direction. This is It must also be appreciated that the ECEF not true for all projections; for example the early coordinates X, Y and Z are spheroid dependent. The mapping of Trinidad, prior to 1963, used a Cassini centres of two different spheroids are not Soldner Projection that is not orthomorphic. necessarily coincident and their axis need not be To avoid large variations in scale factor parallel, so ECEF coordinates for a point will nationally, countries that cover a large variation in change with a change of spheroid. longitude tend to be mapped using Lambert while those that cover a large amount of latitude use a TM projection. Projections that are used in 4.1 . International Terrestrial Reference Frame countries of the Caribbean are identified in Table 2. (ITRF) In some cases, countries are mapped on more than one projection, which leads to a point on the Earth Boucher and Altamimi (1996) document ITRF being defined by multiple pairs of grid coordinates, and early variations, more recent information however these are usually significantly different can be found on the International Earth Rotation and any confusion becomes obvious.
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