WGS84 and the Greenwich Meridian

When visitors to the Royal Observatory, Greenwich stand astride the Meridian, they are often perplexed to discover that their GPS does not give their longitude as zero. Likewise, users of Google Earth are sometimes surprised to see that the Meridian as marked, appears to pass around 100 m to the east of where they expected.

The explanation for these apparent anomalies is rooted in the history of longitude determinations, the assumed shape of the Earth and the way in which maps have been historically constructed.

When the Royal Observatory was founded back in 1675, it was widely believed that the Earth was spherical. This notion was challenged by Newton with the publication of the third volume of his Principia in 1687 in which he hypothesized that the Earth was an oblate spheroid, also known as an ellipsoid, the shape generated by spinning an ellipse on its minor axis. He estimated the equatorial diameter would differ from the polar by about 1 part in 230. The parameters of the ellipsoid have since been refined, but the ellipsoid is not a perfect fit either.

From the earliest of times, it was a priority for astronomers to get an accurate determination of the difference in longitude between the observatory at Greenwich and ones elsewhere. In the case of the Paris Observatory, there had been at least 18 different determinations by the 1920s. The first attempt to accurately fix the relative longitude of an American observatory, that of Harvard Observatory in Cambridge, Massachusetts, took place in the 1840s when nearly four hundred chronometers were transported back and forth across the Atlantic. From the 1860s onwards, following the laying of the first transatlantic cable, the time difference, and hence longitude difference between the two observatories, was determined with even greater precision by telegraphic means. It was through this single connection that the longitude (relative to Greenwich) of all other places in the United States was originally determined.

Most accurate maps show only a small part of the Earth’s surface. Before the space age, when choosing an ellipsoid to represent the shape of the Earth, it was the practice to pick one whose surface had a good alignment with reality over the area of the map. In the UK for example, the maps produced by the Ordnance Survey were (and still are) based on the ‘Airy Ellipsoid’ – an ellipsoid defined by the seventh Astronomer Royal George Airy in 1830. The chosen ellipsoids differed slightly in centre position and orientation as well as in size and shape. The advent of satellite technology enabled ellipsoids to be defined for the first time with their centre coincident with the Earth’s centre of mass.

Some relevant ellipsoids and their dates of adoption (from Wikipedia)
Reference ellipsoid name Equatorial radius (m) Polar radius (m) Inverse flattening Where used
Airy (1830) 6,377,563.396 6,356,256.909 299.3249646 Britain (OSGB36)
Clarke (1866) 6,378,206.4 6,356,583.8 294.9786982 North America
Clarke (1878) 6,378,190 6,356,456 293.4659980 North America
NAD 27 (1927) 6,378,206.4 6,356,583.800 294.978698208 North America
NAD83 (1983) 6,378,137 6,356,752.3 298.257024899 North America
WGS84 (1984) 6,378,137 6,356,752.3142 298.257223563 Globally

In the late 1950s (under the auspices of the US Navy), the Applied Physics Laboratory (APL) of the Johns Hopkins University began the development of what was to become the world's first operational satellite navigation system. Known as Transit, it worked by making use of the Doppler effect, the same effect that makes a siren carried by a moving vehicle change in pitch as it passes. The surveyed longitude of the Laboratory's site in Maryland, as measured in the North American Datum (NAD27), became its assumed longitude in the first World Datum, the APL datum. It was this pragmatic adoption of the longitude coordinate on one ellipsoid as the assumed value on another that has caused the apparent shift not only in the position of the Meridian, but also of all other locations.

The size of the shift remained unknown until the summer of 1969, when an opportunity arose to measure it. A satellite receiver was set up on a platform above the roof over the Airy Transit Circle at Greenwich. The results showed that fixes resulting from the use of the satellite navigation system should have their longitude values shifted by 5.64" if the Greenwich (Geodetic) Meridian was to have its longitude as zero in this system. Although an academic paper on this subject was published in 1971, it appears to have been largely forgotten about until the mid noughties. The offset (since refined) also applies to the WGS84 datum used by current GPS systems. WGS84 was adopted as the global standard for air navigation on 1 January 1998 and soon afterwards by hydrographers for use on electronic and nautical charts.

Until the advent of GPS, local datums were only ever used in a local context. Although usually inappropriate to do so, it is possible with GPS to set a receiver to get a latitude and longitude fix anywhere in the world in any of the different datums. The precise latitude and longitude of a place will vary with the particular coordinate system or datum that is used. Paradoxically, as we have already seen, this also applies to the Airy Transit Circle, whose longitude by definition one might reasonably expect to be zero. The difference between the co-ordinates on different datums also varies from place to place. Most datums agree with each other to within half a kilometre or so. The most commonly used in the UK are OSGB36 & WGS84.

At the time of the International Meridian Conference in 1884, the concepts of continental drift and plate tectonics did not exit. The first evidence of plate movement came in the mid 1950’s as the space age was about to begin. The Earth’s tectonic plates move relative to one another at about the same rate at which human finger nails grow – not much on a day to day basis, but a substantial amount over a period of decades and centuries. With the introduction of satellite technology, came the ability to create a more accurate global datum, and with it the necessity to define a reference meridian that, whilst being derived from the Airy Transit Circle, would also take into account the effects of plate movement and variations in the way that the Earth was spinning. The International Terrestrial Reference Frame (ITRF), which defines the International Meridian and poles, is based on the combination of sets of station coordinates and velocities derived from a variety of different types of observations: Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), and Lunar Laser Ranging (LLR). Data from Global Positioning System (GPS) was introduced in 1991 and from Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) in 1994. The International Reference Meridian and Poles and, hence the WGS84 datum, are stationary with respect to the average motion of the Earth’s crustal plates. As a consequence, all individual locations are in motion relative to them. In the UK WGS84 latitudes and longitudes are changing at about 2.5 cm per year in a north-easterly direction. In 1989, the International Reference Meridian passed an estimated 102.478 m to the east of the Airy Transit Circle at Greenwich.

Links:
Transit navigation system
Ordnance Survey – A guide to coordinate systems in Great Britain
Further reading

G. Gebel and B. Matthews, Navigation at the Prime Meridian, Navigation: Journal of the Institute of Navigation (Washington, DC) 18/2 (Summer 1971) 141-146.

Rear Admiral Robert W. Knox, Precise determination of Longitude in the United States, Geographical Review, Vol 47, No. 4 (Oct 1957), pp555-563 American Geographical Society.