An introduction to Coordinate Reference Systems

An introduction to Coordinate Reference Systems
An introduction to Coordinate Reference
Systems
27/11/2009
1. Introduction
A coordinate that defines a position on the Earth is ambiguous unless its coordinate reference system (CRS)
is defined. This ambiguity arises from the fact that the Earth is a complex shape and that, over time, many
different methods of defining position have been developed. Consequently, it is essential that anyone
involved in the management of spatial data has at least a basic grasp of the concepts of CRSs and knows
where to find out further information.
The purpose of this paper is to provide an introduction to CRS concepts and to provide links to further
reference material should the reader wish to read around the subject in more depth.
One of the issues faced by anyone wanting to find out more about the subject of CRSs is that many different
terms are used to describe CRS entities. To make matters worse, some terms mean different things within
different domains. In an attempt to bring a level of clarity to this, the terms used in this paper are taken from
ISO 19111 Spatial Referencing by Coordinates. A useful guide to terminology, including an ISO 19111
reference table, is provided in Iliffe and Lott (2008), Appendix A.
Where appropriate, identifiers are used to specify CRSs and their properties. The identifiers are drawn from
the EPSG Geodetic Parameter Dataset.1
2. The Earth
The Earth is a complex body. Its surface, the ‘topographic surface’, is irregular and encompasses mountains,
valleys and ocean trenches ranging in height between about 9km above, and 11km below, sea level.
Relative to the overall size of the Earth these distances represent only a thin veneer (Smith 1997). However,
for geometric calculations and mapping the topographic surface is too
Geoid… an equipotential
complex.
surface that corresponds
to mean sea level
An alternative surface is represented by the Geoid. This is an
equipotential surface which is defined as the “equipotential surface that
most closely corresponds to mean sea level” (Iliffe and Lott 2008).
When travelling across an equipotential surface no work is done against gravity which suggests that the
Geoid is a level surface with no hills or valleys. The traveller will experience a flat surface but in fact the
Geoid undulates. Whilst the Geoid is a useful reference surface for elevation the undulations mean that it too
is a complex surface for mapping.
To simplify the situation mathematical models of the Earth are derived which provide a smooth surface for
mapping. These models fit the Geoid partially or wholly and are known as ellipsoids.
1 http://www.epsg-registry.org/
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3. Ellipsoid
Geodetic applications that have low demands in terms of accuracy can use a spherical model of the Earth.
However, the geoid is slightly flattened at the poles and bulges slightly at the equator so applications
requiring higher accuracy should use an ellipsoid. An ellipsoid is a simple mathematical model of the geoid.
Illustrations of the ellipsoid are usually greatly exaggerated. In truth, the flattening of the Earth at the poles is
marginal and measures approximately 22km in 6378km (Iliffe and Lott 2008)
Ellipsoid… a simplified
which is just 0.34%. Hence it is not detectable to the naked eye and this is
mathematical model of
borne out by the famous Earthrise photograph taken during the Apollo 11
2
mission in 1969.
the geoid
The defining parameters of an ellipsoid are the semi-major axis length (a)
and the semi-minor axis length (b) (Figure 3.1). In the early days of geodesy, the approximation of the geoid
by an ellipsoid could only be done over relatively small extents and certainly not globally. This has lead to a
proliferation of different ellipsoids each with a different size and shape. While some of these ellipsoids are
now obsolete others are still used in national mapping systems. The national standard topographic mapping
system for Britain, British National Grid, uses an ellipsoid determined in 1830, known as Airy 1830.
Figure 3.1: Ellipsoidal parameters
2 http://nssdc.gsfc.nasa.gov/planetary/lunar/images/as11_44_6552.jpg
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2
19
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An introduction to Coordinate Reference Systems
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Ellipsoid Name (Ordered by Realisation Date)
Figure 3.2: Evolution of estimates of the Length of Semi-major Axis of Ellipsoids
Values are taken from the EPSG Geodetic Parameter Dataset
Figure 3.2 shows how estimates of the length of the semi-major axis of reference ellipsoids have evolved
over time. It can be seen that since 1980 there has been broad agreement on the appropriate value.
4. Geodetic datum
A datum fixes a coordinate system to an object. A geodetic datum fixes an ellipsoid to the Earth and defines
the meridian that is used for zero longitude. Historically, the method by which a geodetic datum was defined
was to first choose an ellipsoid. Typically the chosen ellipsoid was either known to fit the local geoid well or
was acknowledged as the best definition of the shape of the Earth. A grossly exaggerated diagram of this is
shown in Figure 4.1.
Geodetic Datum…
fixes an ellipsoid to the
Earth and defines the
meridian that is used
for zero longitude
Modern techniques for deriving geodetic datums rely on artificial satellites
and the adoption of the International Terrestrial Reference System (ITRS).
In addition, the understanding of the size and shape of the Earth is more
refined (see Figure 3.2) and GRS 19803 is accepted as the best model (Iliffe
and Lott 2008).
3 EPSG Identifier: urn:ogc:def:ellipsoid:EPSG::7019
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However, there is a legacy of different geodetic datum definitions, still in use today, with which we must
contend.
Figure 4.1: Ellipsoids and the Geoid
5. Coordinate system
A coordinate system is expressed by a set of properties that enable the meaning of the coordinates within
the system to be determined. The properties that define a coordinate system are (Iliffe and Lott 2008):
 The dimension – defines the number of axes associated with the system
 For each axis:

The name of the axis (e.g. Easting, Geodetic Latitude)

The sequence of the axis (i.e. the position of the axis in an ordered list)

The direction in which coordinates increase along the axis (e.g. positive up for vertical coordinate
systems)

The units of measure of the axis
It is important to note that the axes of a coordinate system are listed in order and that coordinates within the
coordinate system follow the order. That is to say that if the axis order of a coordinate system is 1) Geodetic
latitude 2) Geodetic longitude and a coordinate is (50, 10) it is known that the value 50 refers to geodetic
latitude while 10 refers to geodetic longitude. This follows the OGC Axis Order Policy Guidance.4 This is
particularly important when encoding data using modern formats such as GML5. In other spatial data formats
the order of coordinates may be part of the data specification and cannot be changed.
4 OGC Axis Order Policy Guidance - http://www.ogcnetwork.net/node/491
5 OGC Geography Markup Language - http://www.opengeospatial.org/standards/gml
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6. Ellipsoidal coordinate system
Pe
rpe
the ndicu
ellip lar
soid to
Ellipsoidal coordinates are measured in terms of geodetic latitude and geodetic longitude and, in the three
dimensional case, ellipsoidal height (Figure 6.1). The coordinates define position relative to an ellipsoid.
Geodetic longitude (λ) is the angle from the prime meridian to the
Coordinates in an
meridian plane of a given point. Geodetic latitude (φ) is the angle from the
ellipsoidal coordinate
equatorial plane to the perpendicular to the ellipsoid through a given
system define the
point. Note that the perpendicular to the ellipsoid does not necessarily
intersect the centre of the ellipsoid, as can be seen in Figure 6.1. If a
position of a point
spherical model is used then the perpendicular will always intersect the
relative to an ellipsoid
centre. The convention is that values of longitude are positive in an
easterly direction and that values of geodetic latitude are positive in a northerly direction.
Figure 6.1: Ellipsoidal coordinates
The fact that different ellipsoids and different geodetic datums have been used over time raises an important
point:
the geodetic latitude and longitude coordinate of a position on the
Earth’s surface is NOT unique
The numeric values of geodetic latitude and longitude for a given position on the Earth’s surface will depend
entirely on the geodetic datum in use. If the geodetic datum is not defined, a coordinate will have an inherent
ambiguity of up to 1500m (OGP Surveying and Positioning Guidance Note 1). In practical terms the geodetic
datum is expressed as part of the CRS definition.
7. Cartesian coordinate system
Hitherto we have considered systems and parameters for mapping
on the curved surface of the Earth. However, when presenting
spatial data on a flat surface, be it a piece of paper or a computer
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Projections always result in
Cartesian coordinate systems
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An introduction to Coordinate Reference Systems
screen6, the coordinates must be projected. Projections always result in a Cartesian coordinate system
which is a coordinate system that has axes that are straight and mutually perpendicular (Figure 7.1).
Projected coordinate systems are derived from ellipsoidal coordinate systems by means of map projections.
A map projection is often explained conceptually in diagrammatic terms such as, in the case of the Mercator
projection, wrapping a piece of paper around the Earth (Figure 7.2 but in practice the process involves the
application of mathematical formulae to ellipsoidal coordinates.
When spatial data are drawn
within a computer mapping
system such as a GIS a
projection is always employed,
regardless of whether the CRS
of the underlying data is
projected or geodetic. If the data are referenced to a geodetic
CRS then typically the Plate Carée projection is used
(Figure 7.3). The data are projected on-the-fly and the
underlying coordinates are not changed. The coordinates
presented to the user as the mouse pointer is moved across the
map display will be those of the geodetic CRS
In a Cartesian
coordinate system
axes are straight and
mutually perpendicular
(e, n)
Northing
Easting
Map projections are also used in some mapping systems to give Figure 7.1: Cartesian coordinate system
(two dimensional case)
a three dimensional appearance to data that are otherwise two
dimensional (Figure 7.4). The same two dimensional data were
used in the
creation of Figure 7.3 and Figure 7.4.
Cartesian coordinate systems are not only associated with
projections. A Cartesian coordinate system can be used at
a global scale, instead of an ellipsoidal coordinate system.
These are termed geocentric coordinate systems. An
example is shown in Figure 7.5. The origin of the
coordinate system is placed to coincide with the Earth’s
Geocentric coordinate systems are
globally applicable Cartesian coordinate
systems where the origin is the Earth’s
centre of mass
Figure 7.2: Diagrammatic representation of
the Mercator projection
centre of mass, or an assumed centre implied by a geodetic
datum (OSNI 1999), the X axis is aligned with the prime
meridian in the equatorial plane, the Y axis is aligned
perpendicular to the X axis in the equatorial plane and the
Z axis is aligned with the minor axis of the ellipsoid.
6 In spite of the fact that a projection has been applied in this case, coordinates may still be expressed as ellipsoidal coordinates as the
user moves the mouse pointer across the map.
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Readers are likely only to come into direct contact with geocentric coordinate systems if they undertake
complex geodetic computations. For most though it will not be obvious when a computer mapping system
makes use of a geocentric coordinate system.7 Some coordinates are published using a geodetic CRS with a
geocentric coordinate system. An example is the International Reference Frame (ITRF)8 and positional
solutions from NAVSTAR GPS are fundamentally computed within the ITRF using geocentric coordinates
(Blewitt 2009).
Figure 7.3: Plate Carée map projection
Figure 7.4: Vertical Perspective projection
7 Some coordinate transformations are computed using geocentric coordinates.
8 ITRF is a realisation of the International Terrestrial Reference System (ITRS). The current (at the time of writing) ITRF realisation is
ITRF2005 – urn:ogc:def:crs:EPSG::4896
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Figure 7.5: Geocentric Cartesian Coordinate System
Strictly, the coordinate system is geocentric only if the origin of the coordinate system coincides with the Earth’s centre of
mass. This is only true in a few cases such as ITRS where the origin is considered to be within 0.1m of the Earth’s centre
of mass (Smith 1997). However, the term geocentric is widely used.
8. Vertical coordinate system
Vertical coordinates are measured along a single axis of a vertical coordinate system. For gravity related
heights the axis is aligned with the Earth’s gravity field. Earlier in this paper it was stated that the geoid was a
complex surface for horizontal computation. However, it provides a
suitable surface to which height, or depth, can be related because it is
Vertical coordinates are
equipotential – the surface is perpendicular to the direction of gravity.
measured along a single
Since mean sea level is a close approximation of the geoid it is a
axis of a vertical coordinate
common starting point for the development of vertical coordinate
system
reference systems. A value of mean sea level is derived by
observation at a certain point (or in some cases more than one point). For the British mainland the value for
mean sea level was observed at Newlyn. This value becomes the vertical datum for the vertical CRS. The
height at the datum is transferred to other positions across the area of interest through surveying techniques.
Nautical charts present safety critical information. Consequently, it is standard practice when compiling
charts and presenting the results from hydrographic surveys to remove the effect of the tide and to present
all depths (and inter-tidal heights) to a datum below which the water level does not normally, or rarely,
falls. This datum is known as Chart Datum.
Chart Datum defines the seabed relative to a tidal surface
which is not an equipotential surface. Consequently it is not
appropriate to use Chart Datum for offshore engineering
without further work.
The vertical datum chosen for
nautical charts is referenced to the
level of water below which the tide
does not normally fall – known as
Chart Datum
Vertical coordinates may be measured in an upwards
direction along the axis, in which case they are termed heights, or downwards along the axis, in which case
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they are termed depths. The convention on nautical charts is that vertical coordinates are presented as
depths. Therefore, depths for areas that dry (i.e. are above the vertical datum) will be negative while those
for areas that are always wet will be positive. The convention for topographic maps is that vertical
coordinates are presented as heights.
9. Coordinate reference system
A CRS associates a coordinate system with an object by means of a datum. Therefore, a CRS definition
must encompass a definition of a coordinate system and a datum. In the context of ISO 19111 a CRS is
defined by its datum. Three types are important in the context of this paper:
 Geodetic CRS – a CRS based on a geodetic datum (e.g. WGS 849 or OSGB 193610 - note that both
these names are also names of geodetic datums)
 Projected CRS – a CRS derived from a geodetic CRS by means of a map projection. The datum is
expressed by the geodetic datum of the base geodetic CRS from which the projected CRS is derived
(e.g. British National Grid11)
 Vertical CRS – a one dimensional CRS based on a vertical datum (e.g. MSL Depth12).
It is the definition of the CRS that must be supplied with a spatial dataset in order that a full understanding of
the meaning of the coordinates in the data can be gained. By extension the CRS should also be expressed
in full on any map products that are produced.
10. Common coordinate reference systems in the UK
10.1.British National Grid
British National Grid (BNG) is the national standard CRS for land mapping in the British Isles. The
components of the CRS are as follows:
 Base Geodetic CRS – OSGB 1936 (urn:ogc:def:crs:EPSG::4277) 13

Geodetic Datum – OSGB 1936 (urn:ogc:def:datum:EPSG::6277)
–
Ellipsoid – Airy 1830 (urn:ogc:def:ellipsoid:EPSG::7001)
–
Prime Meridian – Greenwich (urn:ogc:def:meridian:EPSG::8901)
 Projection Parameters – BNG (urn:ogc:def:coordinateOperation:EPSG::19916)

Projection Method – Transverse Mercator (urn:ogc:def:operationMethod:EPSG:9807)
 Coordinate System – Cartesian (urn:ogc:def:cs:EPSG::4400).
9 EPSG Identifier: urn:ogc:def:crs:EPSG::4326
10 EPSG Identifier: urn:ogc:def:crs:EPSG::4277
11 EPSG Identifier: urn:ogc:def:crs:EPSG::27700
12 EPSG Identifier: urn:ogc:def:crs:EPSG::5715
13 References in brackets refer to the EPSG Registry Database
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BNG was originally created using classical techniques. The geodetic datum was realised by triangulation
using physical monuments (Trig Points). However, the realisation of the datum is now performed through the
use of the OSTN02 coordinate transformation.14
10.2.WGS 1984
The World Geodetic System of 1984 (WGS 1984) is a globally applicable geodetic CRS. It is the CRS that is
employed by NAVSTAR GPS.15 The CRS is defined so that the origin of its coordinate system is
approximately coincident with the Earth’s centre of mass (i.e. it is geocentric).16
The components of the CRS (when it defines ellipsoidal coordinates) are as follows:
 Geodetic Datum – World Geodetic System 1984 (urn:ogc:def:datum:EPSG::6326)

Ellipsoid – WGS 84 (urn:ogc:def:ellipsoid:EPSG::7030)

Prime Meridian – Greenwich (urn:ogc:def:meridian:EPSG::8901)
 Coordinate System – Ellipsoidal (urn:ogc:def:cs:EPSG::6422)
This is the CRS in use in SeaZone’s spatial data products.
10.3.ETRS89
The European Terrestrial Reference System 1989 (ETRS89) was related to ITRF at epoch 1989.0 (i.e. 1st
January 1989) and then fixed to the Eurasian continental plate. Since both WGS 84 and ETRS89 are related
to ITRF they can, for most practical purposes where high levels of accuracy are not required, be considered
equivalent. Since ETRS89 is fixed to the Eurasian plate it has diverged from the ITRF (and hence WGS 84)
as a result of plate tectonic motion at about 2.5cm per year. The total difference (2007) is about 50cm (Iliffe
and Lott 2008).
The components of the CRS (when it defines ellipsoidal coordinates) are as follows:
 Geodetic Datum – European Terrestrial Reference System 1989 (urn:ogc:def:datum:EPSG::6258)

Ellipsoid – GRS 1980 (urn:ogc:def:ellipsoid:EPSG::7019)

Prime Meridian – Greenwich (urn:ogc:def:meridian:EPSG::8901)
 Coordinate System – Ellipsoidal (urn:ogc:def:cs:EPSG::6422).
11. Coordinate operations
Coordinate operations are defined as methods that change coordinates from one CRS to another. A
coordinate conversion is the general case of two specific operations: a coordinate conversion and a
coordinate transformation.
14 http://www.ordnancesurvey.co.uk/oswebsite/gps/docs/geodesy_and_positioning.pdf
15 http://www.gps.gov/
16 Measurement instruments are now so sensitive that it is known that the Earth’s centre of mass is dynamic. It responds to mass
movements, notably atmospheric and hydrological, at or near the Earth’s surface. Movements in the centre of mass are in the order
of 1 to 2cm (Herring 2009).
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A coordinate conversion
changes coordinates from
one CRS to another where
both CRSs are referenced to
the same datum
A coordinate conversion changes coordinates from one CRS to
another where both CRSs are referenced to the same datum. A
map projection is an example of a coordinate conversion.
Coordinate conversion methods are defined and consequently
considered to be exact (Iliffe and Lott 2008). Therefore, coordinate
conversions result in no loss in positional accuracy.
A coordinate transformation changes coordinates from one CRS to
another where the resulting CRS is referenced to a different datum from the source CRS. The realisation of a
datum, through surveying techniques, is inherently error prone although great effort is of course taken to
minimise error. These errors affect coordinate transformations so that a coordinate transformation will always
introduce error. In addition the parameters for a coordinate transformation are empirically derived. Different
sets of observations will result in different parameters
so that any two CRSs may have more than one
A coordinate transformation changes
coordinate transformation defined for transforming
coordinates from one CRS to another
between them. Observations are restricted to certain
where the resulting CRS is referenced to a
extents so that the resulting transformation
different datum from the source CRS
parameters should only be used for datasets within
that extent.
12. Issues
12.1.Terminology
One of the problems faced by anyone new to geodesy is the range of terminology that is in use in the
science. Terminology from ISO 19111 has been used in this paper in order to attempt to achieve clarity.
However, desktop GIS systems use colloquial terms to name geodetic entities in their graphical interfaces
and system documentation. Table 12.1 gives cross reference of terminology in use in ESRI and Cadcorp
desktop GIS. Empty cells indicate that no direct equivalent exists or is evident.
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Table 12.1: Terminology
ISO 19111
ESRI ArcGIS 9.3
Cadcorp SIS 6
Cadcorp SIS 7
Coordinate Reference
System
Coordinate System
Projection
Coordinate Reference
System
Geodetic Coordinate
Reference System
Geographic Coordinate
System
Projected Coordinate
Reference System
Projected Coordinate
System
Geoid Datum17
Geodetic Datum
Semi-major axis (of an
ellipsoid)
Equator
Equator
Semi-minor axis (of an
ellipsoid)
Pole
Pole
Coordinate
transformation
parameters for a 7parameter
transformation method
7 WGS84 conversion
parameters
7 WGS84 conversion
parameters
Geodetic Datum
Coordinate
Transformation
Ellipsoidal Coordinate
System
Transformation
Spherical Coordinate
System
12.2.Coordinate operations in Geographic Information Systems
Most desktop mapping software applications provide mechanisms for implementing coordinate operations.
They give the user powerful tools for manipulating data but users must ensure that the appropriate
operations are applied for their particular application. This section outlines some of the common problems
than can occur in invoking coordinate operations. It highlights the need for care in implementing coordinate
operations.
Software can implement coordinate operations only if it is provided with a definition of the CRS of the source
data, encoded in an appropriate way. This is one reason why it is important to provide a definition of the CRS
in use in a dataset.
17 The approach employed in Cadcorp SIS is that a geoid datum entity is defined in a Library (NOL) file with a set of coordinate
transformation parameters which define the transformation to WGS84. Thus if more than one coordinate transformation exists a
geoid datum will need to be entered more than once in a NOL. This gives the impression that a geodetic datum is defined by its
coordinate transformation to WGS84. This is not the case. A geodetic datum, in fact, exists independently of any coordinate
transformations which may be defined for it. Cadcorp SIS is not the only software which adopts this approach. An additional facet of
Cadcorp’s approach is that there is a one-to-one relationship between a projection and its geoid datum (using Cadcorp SIS 6.2
terminology) which is of course conceptually correct (a CRS can have only one datum). However, since a datum needs to be
defined more than once, in cases where there is more than one coordinate transformation available, the projection must be defined
more than once too. The correct projection must be selected in order to invoke the desired coordinate transformation.
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Software may, in some cases, not apply the full set of steps needed for an accurate coordinate operation.
ESRI ArcGIS, for example, will not apply a coordinate transformation by default when one is required. It will
apply the necessary coordinate conversions so that data are loaded and displayed – to the uninformed user
everything may appear correct. However, it is necessary for the user to select a particular coordinate
transformation in order for it to be applied. Not doing so will lead to errors in position of several hundred
metres but in extreme cases, up to 1500m.18 Figure 12.1 shows the steps that must be implemented when
changing the CRS of a dataset from British National Grid to WGS 84 / UTM Zone 30 using a 7 parameter
coordinate transformation. By default, ArcGIS follows the blue arrows, missing the important coordinate
transformation step. The user must specify the coordinate transformation in order that it is implemented.
It cannot be guaranteed that a software application will include definitions for all possible coordinate
operations. However, most applications provide a user interface to allow the entry of bespoke parameters.
Extreme care must be taken when doing this. Common errors are misinterpreting the units of measure that
are expected by the software application for certain parameters. For example, the Cadcorp SIS 7-WGS84
conversion19 parameters expect X, Y and Z values in metres, rotation values in arc-seconds and the scale
difference (“correction” in Cadcorp terms) in parts per million. Parameters may be published in units different
from these.
To complicate matters further coordinate transformations are directional: they are expressed in terms of
“from CRS A to CRS B”. Users must ensure that parameters are entered such that coordinate
transformations are performed correctly in line with this. Cadcorp SIS expects parameters appropriate for the
“…to WGS84” direction.
If that is not enough, there are two methods for implementing a 7-parameter coordinate transformation:
position vector and coordinate frame. It is not possible to judge from a parameter set alone which method it
is appropriate for (the numeric values will be identical but the signs of the rotation parameters are reversed).
ESRI ArcGIS allows the user to select either method from a drop down list (which is more extensive than
simply 7-parameter coordinate transformations) while Cadcorp SIS implements the coordinate frame method
alone.
18 This is not a fault of the software and no criticism is intended. We have seen that any two CRSs may have more than one coordinate
transformation defined. There is no way of the software knowing which should be applied and it is for the user to decide. From
ArcGIS version 9.2 onwards the user is warned that a coordinate transformation has not been applied.
19 The parameters are for a coordinate transformation, in ISO 19111 terms.
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Figure 12.1: OSGB36 / BNG to WGS 84 / UTM Zone 30N
Users are advised to check the effect of user defined parameters. The best way of checking user defined
parameters for any coordinate operation is to obtain coordinates in source and target CRS by independent
means and to compare these with coordinates generated using the user defined parameters.
13. Further reading
The OGP Surveying and Positioning Committee publish a series of Guidance Notes on geodesy which are
well worth reading. They can be found at:
http://info.ogp.org.uk/geodesy/
Particular attention is drawn to Guidance Note 1 (Geodetic Awareness), which provides an introduction to
geodesy, and Guidance Note 5 (Coordinate Reference System Definition) which describes the parameters
which are necessary to define geodetic entities in full. Advanced readers are directed to Guidance Note 7
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Part 2 (Coordinate Conversions and Transformations including Formulas) which presents mathematical
formulae for projections, coordinate conversions and coordinate transformations.
Attention is also drawn to the UK Offshore Operators Association Guidance Notes on the Use of Coordinate
Systems in Data Management on the UKCS which can be found at:
http://info.ogp.org.uk/geodesy/Exchange/1065.pdf
The Ordnance Survey has published a useful guide to coordinate reference systems in use in Great Britain
which can be found at:
http://www.ordnancesurvey.co.uk/oswebsite/gps/docs/A_Guide_to_Coordinate_Systems_in_Great_Britai
n.pdf
Ordnance Survey Ireland and Ordnance Survey of Northern Ireland also publish useful guides:
http://www.osni.gov.uk/2.2_a_new_coordinate_system_for_ireland.pdf
http://www.osni.gov.uk/5.3_making_maps_compatible_with_gps.pdf
14. References and other literature
Allan, A.L. (2004) Maths for Map Makers, Whittles Publishing, 2nd Edition
Blewitt, G. (2009) GPS and Space-Based Geodetic Methods, in Herring, T.A. and Schubert, G. (eds.)
Geodesy, Treatise on Geophysics, Volume 3, Elsevier
Bugayevskiy, L.M. and Snyder, J (1995) Map Projections: A Reference Manual, Taylor and Francis
Herring, T.A. (2009) Overview, in Herring, T.A. and Schubert, G. (eds.) Geodesy, Treatise on Geophysics,
Volume 3, Elsevier
Iliffe, J. and Lott, R. (2008) Datums and Map Projections for Remote Sensing, GIS and Surveying, Whittles
Publishing, 2nd Edition
OSNI (1999) Making maps compatible with GPS, Director, Ordnance Survey Ireland and Director and Chief
Executive of Northern Ireland20
Smith, J.R. (1997) Introduction to Geodesy: The History and Concepts of Modern Geodesy, John Wiley and
Sons
20 http://www.osni.gov.uk/5.3_making_maps_compatible_with_gps.pdf
27/11/2009
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