5: Ordnance Survey coordinate systems

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Let's now take a look at the coordinate systems used by Ordnance Survey for mapping Great Britain. There are three coordinate systems to consider:

• OS Net, a modern 3-D TRF using the ETRS89 datum (as just described in section 4.2). This coordinate system is the basis of modern Ordnance Survey 'control survey' (the surveyor's jargon for adding local points to a TRF for mapping purposes), and is the basis of definition of all Ordnance Survey coordinates.  A subset of OS Net (see section 5.1) has been ratified as the official densification of ETRF89 in Great Britain.
  
  
• The National Grid, a traditional horizontal coordinate system, which consists of: a traditional geodetic datum (see section 3.2) using the Airy ellipsoid; a TRF called OSGB36^® (Ordnance Survey Great Britain 1936) which was observed by theodolite triangulation of trig pillars; and a Transverse Mercator map projection (see section 7 below), allowing the use of easting and northing coordinates. This coordinate system is important because it is used to describe the horizontal positions of features on British maps. However, its historical origins and observation methods are not of interest to most users and will be skipped over in this booklet. National Grid coordinates are nowadays determined by GPS plus a transformation rather than theodolite triangulation.
  
  
• Ordnance Datum Newlyn (ODN), a 'traditional' vertical coordinate system, consisting of a tide gauge datum with initial point at Newlyn (Cornwall) and a TRF observed by spirit levelling between 200 fundamental bench marks (FBMs) across Britain. The TRF is densified by more than half a million lower-accuracy bench marks. Each bench mark has an orthometric height only (not ellipsoid height or accurate horizontal position). This coordinate system is important because it is used to describe vertical positions of features on British maps (for example, spot heights and contours) in terms of height above mean sea level. Again, its historical origins and observation methods are not of interest to most users. The word Datum in the title refers, strictly speaking, to the tide gauge initial point only, not to the national TRF of levelled bench marks.

Because triangulation networks need hilltop stations whereas levelling networks need low-lying, easily accessible routes, there are hardly any common points between the height bench mark network and the OSGB36 horizontal network. OS Net provides a single 3-D TRF which unifies ODN and OSGB36 via transformation software (see section 6 below). Using transformation techniques, precise positions can be determined by GPS in ETRS89 using OS Net and then converted to National Grid and ODN coordinates. This is the approach used today by Ordnance Survey.

5.1 OS Net

GPS is the standard tool for precise surveying and mapping, used for all Ordnance Survey precise surveying work. Some characteristics of GPS as a surveying tool are:

• GPS is a three-dimensional positioning system: a precise GPS fix yields latitude, longitude and ellipsoid height.
  
  
• The highest precision of GPS positions is at the 2 mm level horizontally relative to a global datum. To achieve this requires networks of permanently installed GPS receivers. Typical field GPS survey gives accuracies of a few centimetres relative to a global datum. Vertical position quality is generally about 2.5 times worse than horizontal.
  
  
• GPS is a purely geometric positioning tool; that is, GPS coordinates do not give you any information in relation to level surfaces, only in relation to the geometric elements of coordinate system axes and ellipsoid. For this reason GPS does not give orthometric height information.
  
  
• GPS does not require intervisibility between ground reference points; neither is the geometric arrangement of the ground network crucial to the results as it is in theodolite triangulation survey.
  
  
• With care, GPS can be used very accurately for terrestrial survey over any distance - even between points on opposite sides of the world. For this reason, global datums are used for GPS positioning. This feature makes GPS vastly more powerful than traditional survey techniques.

The datum of OS Net is the European Terrestrial Reference System 1989 (ETRS89) which we looked at in section 4.2. Since this datum is realised by many European precise GPS reference points, OS Net is actually just a TRF enabling easier access to this datum in Great Britain.

OS Net comprises of a network of over 100 continuously operating permanent GNSS receivers (COGRs). Because precise GPS positioning is always carried out in relative mode (that is, observing the vector difference in coordinates between two simultaneously recording GPS stations), a network of COGRs with precisely known coordinates is a very useful infrastructure.  Precise positioning can then be carried out by one person with a single geodetic-quality GPS receiver, using data downloaded from the COGRs.

All OS Net stations are coordinated in three dimensions by GNSS in the ETRS89 terrestrial reference system. Hence, the user obtains ETRS89 coordinates for their unknown points, which are suitable for use with the Ordnance Survey transformations to the mapping coordinate systems OSGB36 and ODN (see section 6 below). ETRS89 coordinates can also very easily be converted to the international ITRS datum (using the transformation given in section 6.5 below); this is usually only required for international scientific applications.

5.2 National Grid and the OSGB36 TRF

The latitudes and longitudes of all features shown on Ordnance Survey maps are determined with respect to a TRF called OSGB36. This is what land surveyors would call a 'traditional triangulation datum' (as we saw before, this is strictly a misuse of the term datum - OSGB36 consists of a datum and a TRF). OSGB36 is usually used with the latitude and longitude coordinate types, but we can also work with OSGB36 ellipsoid heights and OSGB36 Cartesian coordinates if required. OSGB36 latitudes and longitudes can be directly converted into National Grid easting and northing coordinates (see section 7 below) using the formulae given in annexe C.

The OSGB36 datum

OSGB36 was not created in quite the logical way specified in traditional surveying textbooks for the establishment of a geodetic coordinate system. Those textbooks say one should first choose an astronomical observatory as the initial point at which the datum will be defined. Here one measures the latitude and the direction of north by astronomy, and defines the direction towards the centre of the mapping ellipsoid. By defining an ellipsoidal latitude, longitude and ellipsoid height for the initial point, the mapping ellipsoid and Cartesian axes of the coordinate system is fixed in space relative to that point - that is, the datum is defined. This is the traditional procedure we outlined in section 3.2.

The original triangulation of Britain was carried out between 1783 and 1853 and is known as the Principal Triangulation. However, when the country was entirely retriangulated between 1936 and 1953 to create OSGB36, the datum definition (the arbitrary position and orientation of the ellipsoid relative to the primary control stations) was adopted from the original triangulation using the average of 11 old primary control station coordinates . Therefore OSGB36 does not have an initial point - the datum is defined implicitly by the primary control station coordinates. This is an equally acceptable way of defining a datum: the datum being a matter of convenience, it does not matter much how you define it.

The ellipsoid used in the OSGB36 datum is that defined by Sir George Airy in 1830 (later Astronomer Royal). Its defining constants are given in annexe A of this document. The Airy 1830 ellipsoid is a bit smaller than Geodetic Reference System 1980 (GRS80) and a slightly different shape. Also, it is not geocentric as GRS80 is: it is designed to lie close to the Geoid beneath the British Isles. Hence, only a tiny fraction of the surface of the ellipsoid has ever been used - the part lying beneath Great Britain. The rest is not useful. So the Airy ellipsoid differs from GRS80 in size, shape, position and orientation, and this is generally true of any pair of geodetic ellipsoids.

The OSGB36 TRF

Before the 1950s coordinate system TRFs contained many angle measurements but very few distance measurements. This is because angles could be measured relatively easily between hilltop primary control stations with a theodolite, but distance measurement was very difficult. A consequence of this was that the shape of the TRF was well known, but its size was poorly known. The distance between primary control stations was established by measuring just one or two such distances, then propagating these through the network of angles by trigonometry (hence the name 'trig pillars').

When the OSGB36 triangulation TRF was established, no new distance measurements were used. Instead, the overall size of the network was made to agree with that of the old 18th-19th century Principal Triangulation using the old coordinates of the 11 control stations mentioned in the previous section. Hence, the overall size of the TRF still used for British mapping came to be derived from the measurement of a single distance between two stations on Hounslow Heath in 1784 - using eighteen-foot glass rods! The error thus incurred in OSGB36 is surprisingly low - only about 20 metres in the length of the country.

The 326 primary control stations of the OSGB36 TRF cover the whole of Great Britain, including Orkney and Shetland but not the Scilly Isles, Rockall or the Channel Islands. It is also connected to Northern Ireland, the Irish Republic, and France. This primary control network was densified by the addition of 2 695 secondary control stations, 12 236 tertiary control stations and 7 032 fourth order control stations. Hence, until recently the official OSGB36 included more than 22 000 reference points. In continuous survey work over the decades, Ordnance Survey surveyors have added many tens of thousands more minor control points which are used in map revision.

OSGB36 coordinates are latitudes and longitudes on the Airy ellipsoid. Ideally, ellipsoid heights relative to the Airy ellipsoid would be added to give complete three-dimensional information. Unfortunately, no easy method of measuring ellipsoid height was available before the late 1980s, so we only have horizontal information in OSGB36. The coordinates of all OSGB36 control points are available from Ordnance Survey.

In 2002 the definition of OSGB36 underwent a fundamental change with the release of the Definitive Transformation OSTN02^TM. OSTN02 in combination with the ETRS89 coordinates of the OS Net stations, rather than the fixed triangulation network, now define the National Grid. This is a subtle change in definition only and does not mean that existing OSGB36 coordinates need to be changed in any way.

Relative accuracy of OSGB36 control points

The following table is a statistical statement of the accuracy of OSGB36 control points relative to surrounding control stations of the same type. The primary layer of the OSGB36 TRF consists of the primary triangulation stations that are considered error free within the OSGB36 coordinate system. The Ordnance Survey ETRS89-OSGB36 transformation (see section 6.3 below) describes the real distortions in OSGB36 which are not considered here. Table 2 shows the expected accuracy of control station positions in relation to other control stations of the same type within a circular area of the given diameter.

Table 2: Relative accuracy of control stations within the OSGB36 coordinate system

5.3 Ordnance Datum Newlyn

Before satellite surveying methods became available in the 1970s, ellipsoid height was a rare and specialised coordinate type. The everyday vertical coordinate type was orthometric height or, more exactly, mean sea level height relative to the national tide gauge datum, as realised in Great Britain by the ODN heights of Ordnance Survey bench marks. Even though anybody with a GPS receiver can now measure ellipsoid heights quite easily, Geoid-related height coordinates such as ODN heights are much more useful for most applications because they are heights relative to a level surface.

The ODN datum

Like horizontal datums, vertical datums were traditionally defined at a single initial point. In the case of horizontal datums this is an astronomical observatory. In the case of vertical datums it is a coastal tide gauge. Tide gauge based vertical datums are still used in most countries.

The tide gauge has a height reference bench mark, the height of which on the gauge scale is known. A long series of sea level records from the tide gauge is averaged to give the vertical offset of MSL from the bench mark. This is the MSL height of the bench mark.

In Great Britain the MSL of the tide-gauge bench mark at Newlyn, near Penzance in Cornwall, is used - hence, the name Ordnance Datum Newlyn. Its MSL height was established from continuous tide readings between 1915 and 1921. That adopted value has remained unchanged in the ODN system, even though MSL at the Newlyn gauge has slowly changed. Hence, the height of a point above MSL given by Ordnance Survey is not affected by variations in MSL and the proper description of an Ordnance Survey height is 'orthometric height relative to Ordnance Datum Newlyn'.

The ODN TRF

A network of about 200 fundamental bench marks for height measurement was constructed across Great Britain in the first half of the twentieth century. These are underground chambers containing a height reference object, topped by a small pillar on which is another reference point. The idea is that the point on the top is easy to access for normal use, whereas the hidden underground mark is less susceptible to damage.

The orthometric height of each fundamental bench mark relative to Newlyn was determined by a network of precise levelling lines across Britain. You can find descriptions of the precise levelling technique in land surveying textbooks. This technique is capable of transferring orthometric height from one point to another with an error of less than 2 x d^1/2 millimetres, where d is the distance levelled in kilometres. Today the accuracy of the precise levelling technique is rivalled by the combination of GPS ellipsoid heighting with a precise gravimetric Geoid model, which allows the ellipsoid height difference between two points to be easily converted to an orthometric height difference.

The ODN TRF was subsequently densified by less precise levelling to obtain the heights of about three-quarters of a million Ordnance Survey bench marks all over Britain. These lower order bench marks are often seen cut into stone at the base of a building, church or bridge. About half a million of them are in existence and usable today. An important error source to bear in mind is possible subsidence of Ordnance Survey bench marks, especially in areas where mining has caused collapse of the ground. In these areas cases of bench mark subsidence of several metres have been reported. Ordnance Survey from time to time installs new bench marks which are needed for surveying projects requiring accurate height control over a large area - precise GPS survey and the National Geoid Model OSGM02^® (see section 6.4) are used for this task.

Relative accuracy of ODN bench marks

The following table is a statistical statement of ODN bench mark accuracy relative to other bench marks in the same area. The primary layer of the ODN TRF consists of the fundamental bench marks, which are considered error free within the ODN coordinate system. The Ordnance Survey National Geoid Model (see section 6.4 below) relates ODN orthometric heights to the GPS ellipsoid GRS80. Table 3 shows the expected maximum levelling error between bench marks on the same levelling line. This only describes the original measurement error. The Ordnance Survey bench mark network has not been maintained since the 1970s, so beware of possible bench mark subsidence.

Table 3: Accuracy of Ordnance Survey bench mark levelling where d is the distance levelled in kilometers.

5.4 Other height datums in use across Great Britain

As discussed in section 5.3, ODN is the national height datum used across mainland Great Britain. There are however a number of other British height datums that are used on the surrounding islands. The main ones being; Lerwick on the Shetland Islands, Stornoway on the Outer Hebrides, St. Kilda, Douglas on the Isle of Man and St. Marys on the Scilly Isles. All of these height datums are incorporated within the National Geoid Model OSGM02.

5.5 The future of British mapping coordinate systems

OSGB36 and ODN will be retained as the basis of Ordnance Survey mapping, but OS Net will be used to access both these coordinate systems by GPS, using coordinate transformations from ETRS89 to OSGB36 and ODN provided by Ordnance Survey. These transformations are currently the National Grid Transformation OSTN02 and the National Geoid Model OSGM02. In this way, Ordnance Survey surveyors and GPS-equipped customers will have access to the national horizontal and vertical datums at any point without visiting traditional control points. In this way, the traditional TRFs of OSGB36 and ODN (the trig points and bench marks) are now being replaced by OS Net as the definitive realisation of the Ordnance Survey mapping coordinate systems. Using OSTN02 and OSGM02, OSGB36 and ODN coordinates are obtained by 3-D transformation software which converts ETRS89 GPS coordinates obtained from OS Net into the equivalent OSGB36/height datum position.

Using this method of access, OSGB36 and the appropriate datum heights will be continuously accessible, rather than being available only at Ordnance Survey monuments. With the release of OSTN02, the National Grid has become by definition a transformation of the ETRS89 GPS coordinate system. Because both horizontal and vertical national mapping coordinate systems will be defined in terms of ETRS89, which is easily related to ITRS (see section 6.5 below), the geodetic basis of British mapping will be implicitly related to all other national datums which have a known relationship to ITRS.

The coordinates and other information of the traditional networks are no longer actively maintained by Ordnance Survey. Access to these traditional control archives is made available through online serives on the Ordnance Survey website.

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