12
Sep
2016

Seeing as an improvement in our model that transforms height from GPS to one above mean sea level has caused a hill to “grow” into a mountain – we thought it would be a good idea to explain how positions and heights surveyed by our surveyors with GPS make it onto our maps.

OS surveyor

All positioning and surveying, not just that from GPS, has to take place on a mathematically simplified model of the surface of the Earth. The surface that the model attempts to emulate is called the geoid.  The geoid is a complex concept, but can be imagined as a hypothetical surface that would be formed if the water in the oceans, close to mean sea level, continued under the land and was only influenced by Earth’s gravity field. This surface is one we already refer to without perhaps thinking about it – we say oceans have “depth” (below the arbitrary zero height surface) and mountains have “height” (above the surface). The geoid is a complex shape since it is influenced by varying Earth gravity. It is too complex to act as our surface for the calculations involved in positioning and surveying, so we need to fit a simple model shape to it.

The usual practice is for the model surface to be an ellipsoid that best fits the geoid.  An ellipsoid is a sphere that’s squashed down a little bit at the poles – this is a better approximation of the shape of the Earth than a sphere. The chosen ellipsoid can be sized and positioned to just fit the geoid in one particular area, such as for mapping a single country like Great Britain, or to achieve an average fit for the whole Earth.

The model also needs to define a “Datum” or (the more modern term) “Coordinate Reference System”.  This is a theoretical concept that adopts certain parameters required to make the model match the Earth, such as that zero degrees longitude passes close to Greenwich. Often a height datum, related to observations of mean sea level, is also adopted by each country since, as we have said, this is very close to the geoid surface and is a natural way to think about height. The coordinate reference system and mean sea level height need to be turned from theoretical concepts into something “real” available to users – they need to be “realised”. This is done by adopting a set of coordinates and heights for fixed points across the area being mapped so that they form a frame work within which all positioning and mapping can take place. This is the “Coordinate Reference Frame”.

### Britain’s coordinate system

All mapping in Great Britain is in the OSGB36 National Grid coordinate reference system, and heights are above mean sea level defined at Newlyn in Cornwall – Ordnance Datum Newlyn (ODN).  OSGB36 is what might be termed a “traditional” datum.  The “36” refers to 1936 when the coordinate reference system concepts were designed and adopted. It uses an ellipsoid, known as Airy 1830, that’s fitted close to the geoid just across the area of GB. It was realised by the coordinates of the triangulation network (coordinate reference frame) which includes the thousands of very familiar trig pillars. ODN was realised by the heights of thousands of benchmarks across the country.

### Coordinate systems worldwide

A cross section of Earth showing a geoid, plus Britain’s ellipsoid, Airy 1830, and the GPS ellipsoid, GRS80

In contrast to OSGB36, GPS uses a global system called WGS84 and its ellipsoid, known as GRS80, achieves an average fit to the geoid across the whole Earth. There is no mean sea level height datum – heights are measured above the ellipsoid surface. As mentioned in our Is Britain on the move? blog last month, in Europe we have a high accuracy version of WGS84 called ETRS89. In GB ETRS89 is realised through the OS Net permanent GPS stations.

All these different ways of modelling the Earth mean our positions don’t easily fit together, meaning the coordinates of the same physical point on the Earth can be different depending on what system they are in. Sometimes a simple equation can be used to transform coordinates from one system to another system, but more often than not the difference varies from place to place, so the transformation has to be more complex. This is the case in Britain and we have a transformation model between ETRS89 and OSGB36 called OSTN15 and a separate model for ETRS89 height to ODN called OSGM15. When our surveyors are out using OS Net to update our maps their GPS coordinates are transformed to OSGB36 and ODN through OSTN15/OSGM15.

OS Net locations across Britain

### So what’s this got to do with growing hills?

We have recently improved the OS Net coordinates and the transformation models – OSTN15 used to be OSTN02 and OSGM15 used to be OSGM02.  This has resulted in a small average shift in coordinates of less than 1cm, but the height has changed by more than this – about 2.5 cm on average on mainland Britain. So although Calf Top, the hill in the news recently, was accurately surveyed in 2010 as just being short of mountain status, the new models now mean the height sneaks into mountain territory (just)!

### More information

If you’d like technical background to the coordinate and transformation changes read this article on our website (PDF).

The VERY technically minded can also read the 45 pages of A guide to coordinate systems in Great Britain (PDF).

Anything else? Ask on the blog or drop us an email to GeodeticEnquiries@os.uk.

### 19 Responses

1. Paul

Does the geoid also change in response to global warming – as the sea level rises, then the relative height/depth of land/sea must also change accordingly?

1. Hi Paul

The subject of geoids and gravity is highly complex but, seeing as how a definition of the geoid is “… the equipotential surface that would coincide with the mean ocean surface of Earth if the oceans and atmosphere were in equilibrium …” (https://en.wikipedia.org/wiki/Geoid), then if the mean surface has risen due to a sea level rise (however caused) then this could be expected to have an impact on the geoid.

It is well known that sea level has risen and, for example, current mean sea level in Great Britain, according to Admiralty Tide Tables, is approximately 0.2m above the value adopted for Ordnance Datum Newlyn which was observed between 1915 and 1921. What is important however is that there is a well defined and widely accepted datum which all users can reference.

Strictly speaking OSGM15 is not a geoid model but the term is retained for simplicity since it is what the majority of users understand. OSGM15 is a “height corrector surface” since it starts with a “true” geoid model surface based purely on gravity observations which is then fitted to the ODN surface as realised by the levelled heights of the fundamental bench marks.

Thanks, Mark

2. John Lumley

Hi Gemma, how long a GPS observation with Dual Frequency network rover equipment do the Ordnance Survey recommend to establish an accurate benchmark for a site survey at say 10mm level, given open skies and no nearby obstructions etc? Our architects want to put this into a specification and I’m thinking an hour to pick up a whole satellite epoch before the cycle repeats.

1. Hi John

I’ve just checked in with our Geodetics expert Mark and I’m afraid we can’t offer hard and fast advice on GNSS occupation times since locations, equipment and specifications can vary so much. However, for RTK GNSS surveys, using an OS Net derived service, several occupations of the point would be required to ensure a 10mm height accuracy. See the RTK guidelines from TSA (The Survey Association). “Guidance Note – Network RTK GNSS Best Practice 2012” on this page – https://www.tsa-uk.org.uk/downloads/.

Hope that helps.

Many thanks
Gemma

1. Roger Walker

That advice is for RTK, not static observations that the OP was asking about.
An hour of static should be OK in an open sky. The estimated baseline accuracy (sd of the residuals) will be produced by your software.

3. Jim Small

Hi Gemma,

I am currently looking at the RINEX data for the OS Net Station at Chilbolton and am confused. The ETRS89 height: 128.2897m and Orthometic height 81.582m differ from what is neing pushed out by the OS Coordinate transformation tool which produces heights of 130.368m and 83.66m respectively. Why would this be? Surely they should be the same as they are derived form the same models?

1. Jocelyn

Jim, the coordinates for CHIO are in the OS Net coordinate text file and the XYZs are also written into the header of every RINEX data file from CHIO.
ETRS89 XYZ = 4007952.9623, -100634.2663, 4944058.9468
ETRS89 Geo = N 51 08 56.370861, W 001 26 17.941752, 128.2897
OSGB36 (via OSTN15/OSGM15) = 439383.362, 139009.447, 81.582

When any of these are passed through OSTN15/OSGM15 (https://www.ordnancesurvey.co.uk/gps/transformation/) the results match up. If you can offer more information regarding your source, please do so via customerservices@os.uk where (if necessary) attachments can be exchanged. Many thanks, Jocelyn

4. Gershon Steinberg

What is the accuracy of the geoid model? what differences can we have between the GPS derived orthometric heights and the registered heights of the benchmarks? Who prevails?

1. Jocelyn

Gershon, below is an extract from the OSGM15 user guide “Transformations and OSGM15 User Guide” found in the OSTN15 OSGM15 Developers Pack (which can be downloaded from here – https://www.ordnancesurvey.co.uk/business-government/tools-support/os-net/for-developers).

In mainland Great Britain, the datum (origin point) representing mean sea level is Ordnance Datum Newlyn, defined at Newlyn in Cornwall. In the Republic of Ireland, Northern Ireland, and the islands surrounding Great Britain, mean sea level is defined by specific independent vertical datums that are all incorporated in OSGM15 and hence OSGM15 is compatible with the products from each of the Ordnance Surveys and LPS. Other geoid models may give mean sea level heights that are incompatible with the Ordnance Surveys’ and LPS’s products.
The estimated accuracies of OSGM15 for each regional vertical datum are below. The figures quoted assume precise ellipsoidal heights are used; for lower quality GNSS observations additional error budget must be included.
Regional datum Standard error (m)
Great Britain 0.01
Republic of Ireland 0.02
Northern Ireland 0.01
Orkney 0.02
Shetland 0.02
Outer Hebrides 0.01
Isle of Man 0.03
Scilly Isles 0.01

Any discrepancy found between an Ordnance Survey levelled bench mark and a OSGM15 computed orthometric height is likely to be due to bench mark subsidence or uplift and, assuming precise GNSS survey has been carefully carried out, the orthometric height given by OSGM15 should be considered correct in preference to archive bench mark heights.

I hope this helps, Jocelyn.

5. Andy Jones

We are working on an offshore wind farm doing site surveys in OS datum.
In the north of the field we are getting bad positioning. Could we be to far offshore for the OSTN Geoid ?

1. Jocelyn

Andy, thanks for your question. The OSGM15 geoid model is “fully populated” across the whole of the National Grid – 0,0 metres south west corner to 700000,1250000 metres north east corner so if you are within the confines of the NG then you will get transformation parameters. This is different to the previous model OSGM02 which had the parameters “cookie cut” to a 10km offshore boundary and outside of this the parameters were zero.

The offshore geoid parameters in OSGM15 are based on the initial gravimetric geoid fitted to Ordnance Datum Newlyn on mainland GB and then extrapolated outwards so the accuracy will degrade out to the edges of the grid compared to the fitted model on land but will still offer a good realisation of mean sea level. Similarly the positional parameters in the OSTN15 transformation are fitted to OSGB36 / ETRS89 coordinated points on land and degrade offshore to an accuracy of ~3.5m (95%) which is comparable with our published 7 parameter Helmert transformation (see A guide to coordinate systems in Great Britain section 6.6).

The quality of the input positions will be determined by the distance from the OS Net reference stations, assuming you are using GNSS positioning and OS Net as the reference network, and also the quality of the corrections or post processing being applied.

Hope this helps, Jocelyn.

6. Roger Walker

The title of this article is incorrect. The geoid is OSGM15.
OSTN15 is something else.

7. Don’t think this statement on WGS84 geodesy is correct: “In contrast to OSGB36, GPS uses a global system called WGS84 and its ellipsoid, known as GRS80, achieves an average fit to the geoid across the whole Earth. ”

WGS 84 uses WGS 84 datum and WGS 84 Ellipsoid.
https://epsg.io/4326

1. Jocelyn

Marco, thanks for your comment. Yes, WGS84 does use its own WGS84 ellipsoid. However, the differences between WGS84 ellipsoid and GRS80 ellipsoid are very very small. Semi major axis is the same and there is just 0.1mm difference in the semi minor. This small difference is due to slightly different derivations of the inverse flattening values. Both ellipsoids have the same value for angular velocity and used to have the same GM value. WGS84 adopted a slightly refined (0.999999854 of the original) value in 1994 but retained the same a and 1/f values.
EPSG entries for the two ellipsoids are:
GRS80 = https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.epsg-registry.org%2Fexport.htm%3Fgml%3Durn%3Aogc%3Adef%3Aellipsoid%3AEPSG%3A%3A7019&data=02%7C01%7CJoss.Harris%40os.uk%7C271c2ad5e5c5475ff56008d7a599b6d5%7C7988742dc5434b9a87a910a7b354d289%7C0%7C0%7C637159951917862334&sdata=ClO%2BKe1eSlGk0Qdnrqz%2FUQsGo7saXW%2BYdik40d5ugWw%3D&reserved=0
WGS84 = https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.epsg-registry.org%2Fexport.htm%3Fgml%3Durn%3Aogc%3Adef%3Aellipsoid%3AEPSG%3A%3A7030&data=02%7C01%7CJoss.Harris%40os.uk%7C271c2ad5e5c5475ff56008d7a599b6d5%7C7988742dc5434b9a87a910a7b354d289%7C0%7C0%7C637159951917862334&sdata=x%2FCG9oHGDivEpEJ4tYtt%2BtxRn9H8NOFjbATi7D3cCNQ%3D&reserved=0

Hope this helps, Jocelyn

8. Hello
Is it possible to get more information about OSTN transformation development?

Best regards

1. Jocelyn

Dzevad, thanks for your query. You also sent this to us via our geodetic enquiries email address so we will reply to you there. Many thanks, Jocelyn