Transformations and OSGM02 user guide
Contents
1. m 40 Chapter 1 Introduction Coordinate transformations and the Geoid model All Ordnance Survey mapping relates to a coordinate reference system In Great Britain Ordnance Survey coordinates relate to OSGB36 the National Grid within Northern Ireland and the Republic of Ireland the coordinate reference System is the Irish Grid These reference systems are traditionally realised on the earth s surface by monumented triangulation stations The users of mapping products in both the public and private sectors have invested in geographical information systems GIS and asset management systems based on these grid systems which have been accepted as de facto national standards The National Grid and the Irish Grid are capable of supporting surveying and mapping in UK and Ireland to meet all the requirements of users both now and in the future however an increasing number of spatial datasets are available in GPS Global Positioning System coordinate systems When two or more coordinate datasets are to be integrated it is essential that each relates to the same coordinate reference system irrespective of accuracy issues In order to relate GPS derived positions to Ordnance Survey s mapping GPS coordinates need to be converted to Irish Grid or to National Grid which requires a specialised datum transformation For this reason the Ordnance Survey of Northern Ireland and Ordnance Survey Ireland have developed a polynom2. 22 The OSi OSNI polynomial transformation 23 Table of coefficients for OSI OSNI polynomial transformation 24 Thie Ordnance Survey Geoid model OSGMU 2 ictor rare dett dne ku Ead E EAS ERE ELA BA ELE 25 27 Se n n T 27 Accuracy of Ordnance Survey transformations eiie 27 OS GMOD rear EE 28 Appendix A Appendix B Appendix C Appendix D Transforming ETRS89 GPS coordinates to OSGB36 and orthometric height 29 vehi casted S 29 Inverse transformation OSGB36 to ETD RSS9 isuu sia 32 ier cel 32 Converting latitude and longitude to easting northing 33 Worked example using the Airy 1830 ellipsoid and National Grid 36 Converting easting and northing to latitude and longitude 37 Worked example using Airy 1830 ellipsoid and National Grid 39 Gos S
3. N 1 IK A Ay HI A A A B7 E E IV A A V A Ay VA Ay B8 Worked example using the Airy 1830 ellipsoid and National Grid Intermediate values are shown here to 10 decimal places Compute all values using double precision arithmetic 52 39 27 2531 N 1 43 4 5177 E os v 6 3885023333e 06 6 3727564399e 06 D 2 4708136169e 03 M 4 0668829596e 05 3 0668829596e 05 1 54040790926 06 1 5606875424e 05 2 0671123011e 04 IV 3 8751205749 06 V 1 7000078208 05 1 0134470432e 05 E 651 409 903 m N 313 177 270 m Appendix C Converting easting and northing to latitude and longitude Obtaining 4 from E is an iterative procedure You need values for the ellipsoid and projection constants a b e Ey Fy and A given in appendix B Remember to express all angles in radians First compute C1 ES 0 ct and M from equation 86 in appendix B substituting for If the absolute value 0 01 mm obtain a new value for using I C2 recompute M substituting for Iterate until the absolute value of lt 0 01 mm then compute p v and 7f using equations B3 B4 and B5 in appendix B and compute tang VII n 9 tan on 24pv 3 tan 720 pv IX 614 90 tan 45 tan g se
4. 108 05 44 244 63 806 Lois So Caister Water Tower has National OSGB36 coordinates 651 409 792 313 177 448 and height 63 806 m relative to the vertical datum as indicated by the datum flag field which this case 1 indicating Ordnance Survey Datum Newlyn Using the procedure in appendix C these coordinates can be converted to latitude and longitude A worked example of this step is given in appendix C Inverse transformation OSGB36 to ETRS89 Worked example Taking the OSGB36 coordinates from the example above that is 651 409 792 313 177 448 the procedure for the inverse transformation OSGB36 to ETRS89 gives the following iterative solution First values OSGB36 to ETRS89 shifts 102 792064 east 78 240505 north First values of ETRS89 easting and northing 651 306 999936 east 313 255 688505 north Second values of OSGB36 to ETRS89 shifts 102 788790 east 78 238161 north Second values of ETRS89 easting and northing 651 307 003210 east 313 255 686161 north Third values of OSGB36 to ETRS89 shifts 102 788790 east 78 238161 north Third values of ETRS89 easting and northing 651 307 003210 east 313 255 686161 north Since the second and third iterations show convergence at the required level the calculation is stopped Feeding the ETRS89 coordinates 651 307 003210 313 255 686161 back into the procedure for transforming coordinates gives the OSGB36 coordinates 651 409 79
5. 2 and OSGM02 are released as a combined data file using the same 1 km grid This grid covers an area 700 km east west and 1 250 km north south the origin being the origin of the projected ETRS89 coordinates see appendix B However the area to which the models are valid has been cookie cut to a 10 km polygon beyond the coastline This means that any position more than 10 km offshore will have fields 4 5 6 and 7 see below all set to zero It is strongly recommended that the transformation software be written to return an outside transformation boundary type error when a point outside this area is encountered Each record occupies a separate line with the south west corner of the grid being the first record in the file The format of each record is indicated by the following table Record no ETRS89 ETRS89 OSTNO2 east OSTNO2 north OSGMO02 Geoid easting m northing m shift m Geoid datum flag 1 0 0 2 1 000 0 3 2 000 0 and so on and so on and so on 701 700 000 0 702 0 1 000 703 1 000 1 000 704 2 000 1 000 and so on and so on and so on 876 948 697 000 1 250 000 876 949 698 000 1 250 000 876 950 699 000 1 250 000 876 951 700 000 1 250 000 Where 1 the record number is a sequential number starting at 1 for the origin point 0 0 and finishing at 876 951 for the north east corner 700 000 1 250 000 2 ETRS89 National Gri
6. these products provide the complete solution to these users at all Ordnance Survey mapping scales Chapter 2 Data overview Basic principles Specifications of OSTN02 horizontal transformation Transformation Transformation type Estimation method Grid resolution Grid interpolation Accuracy Extent horizontal datum transformation between ETRS89 and OSGB36 interpolated square grids of easting and northing shifts Delaunay triangulation 1 km bilinear 0 1 m RMS with respect to OSGB36 primary secondary and tertiary triangulation monuments 700 km east by 1 250 km north Specifications of OSi OSNI polynomial transformation Transformation Transformation type Accuracy Extent datum transformation between Irish Grid and ETRS89 3rd order polynomial 0 4 m 95 of data Republic of Ireland and Northern Ireland Specifications of OSGM02 Geoid model Transformation Transformation type Estimation method Grid resolution Grid interpolation Accuracy 015 vertical ETRS89 ellipsoid to orthometric height interpolated square grid of geoid heights above ETRS89 ellipsoid Spherical Fast Fourier transformation with modified Stokes kernels 1 km bilinear Area specific Mainland GB 2 rms Republic of Ireland 3 cm rms Northern Ireland 2 cm rms with respect to Ordnance Survey BMs Data structure OSTNO02 OSGM02 within Great Britain format and layout of the data Within Great Britain
7. completeness legality reliability quality or suitability of them other than those implied by statute Ordnance Survey and where relevant Ordnance Survey Northern Ireland and Ordnance Survey Ireland shall not be liable to a user or any third party for any losses costs claims or indirect special incidental punitive or consequential damages arising out of access downloading or use of OSTNO2 the OSi OSNI polynomial transformation or OSGMO2 Lois Data copyright Copyright and any database right or other intellectual property right in the OSTNO2 data available from this site however it is made available belongs to Ordnance Survey and is therefore Crown copyright Copyright and any database right or other intellectual property right in OSGMO 2 data available from this site however it is made available belongs jointly to Ordnance Survey Ordnance Survey Northern Ireland and is protected by Crown copyright and Ordnance Survey Ireland Ordnance Survey and where relevant Ordnance Survey Northern Ireland and Ordnance Survey Ireland permit users to copy or incorporate copyrighted material from both OSTNO2 the OSi OSNI polynomial transformation or OSGM02 either onto their own PCs or into their software However this is dependant on the appropriate copyright notice being displayed in the software The appropriate notices are Ordnance Survey Ireland 2002 or Crown copyright 2002 All rights reserved as applicable The appropr
8. ellipsoid and ITM projection see appendix Having located the correct cell find the values of the geoid undulations at the four corners of the cell sgy 54 Sg 59 and the offsets of the point dx dy from the bottom left corner of the cell y as shown in figure 1 above the se sn values are used to find the OSTNO2 eastings and northings shifts Lois The value of the geoid undulation at point x y is given as follows N 1 0 1 u sg 90 sg 9 u sg 1 9 u sg Where t dx 1 000 and u dy 1 000 The resulting geoid undulation is subtracted from the ellipsoidal height H to give orthometric height h Chapter 4 Quality statement Coverage OSTNO2 covers Great Britain and the Isle of Man The OSi OSNI polynomial transformation covers the Republic of Ireland and Northern Ireland It should be noted that the Irish Grid and the National Grid are two independent coordinate reference systems and that Irish Grid coordinates are not directly compatible with OSGB36 coordinates OSGM02 covers all of Great Britain Isle of Man Republic of Ireland and Northern Ireland The Geoid model comprises 14 patches in order to relate to mean sea level as defined by the specific vertical datum for each region The datum flag that forms part of each data record specifies to which datum the geoid ellipsoid separation value relates Both models have been cookie cutto a boundary that extends 10 km off
9. 00 V Ay UV 0 Ag V U V AUV AU V 0 AAU V A4SU V 3600 AA Boo BiU B1 UV BoU Bo V Bi UV AsoU Bos V B4 U V B UV B4U V B4U V B sU2 V 3600 Where A and B are the computed parameters and U and V are the normalised coordinates calculated as follows U ko n and V ko A An Where and are the coordinates of the approximate centre of the region The parameters Aj mand A are given in table 2 below The transformed geographical coordinates are then obtained as follows AA and AG The reverse transformation from ETRS89 to Irish Grid cannot be calculated directly and requires iteration ij Conversions between geographical and grid coordinates are computed using standard Transverse Mercator projection formulae in association with the published Irish Grid parameters Table of coefficients for OSi OSNI polynomial transformation Coefficient i Latitude Ai j Longitude Bi j 0 0 0 763 2 810 0 1 0 123 4 680 0 2 0 183 0 170 0 3 0 374 2 163 1 0 4 487 0 341 1 0 515 0 119 12 0 414 3 913 1 3 13 110 18 867 2 0 0 215 1 196 2 1 0 570 4 877 2 2 5 703 27 795 2 3 113 743 284 294 3 0 0 265 0 887 3 1 2 852 46 666 3 2 61 678 95 377 3 3 265 89
10. 000 500 000 3 402 000 500 000 and so on and so on and so on 351 750 000 500 000 352 400 000 501 000 353 401 000 501 000 354 402 000 501 000 355 403 000 501 000 and so on and so on and so on 175 848 747 000 1 000 000 175 849 748 000 1 000 000 175 850 749 000 1 000 000 175 851 750 000 1 000 000 Where 1 the record number is a sequential number starting at 1 for the origin point 0 0 and finishing at 175 851 for the north east corner 750 000 1 000 000 2 ETRS89 ITM projection grid intersection easting coordinate in metres 3 ETRS89 ITM projection grid intersection northing coordinate in metres 4 the height of the Geoid above the ETRS89 ellipsoid in metres at the intersection that is ETRS89 height OSGMO02 Geoid height orthometric height above mean sea level 5 the Geoid datum flag is a number from 1 to 14 representing the geoid datum to which OSGMO2 Geoid height relates for example this flag is 13 for Malin Head the orthometric height datum used in the Republic of Ireland See table 1 below for details of other datum flag references Table 1 Geoid datum flag Datum name Region 0 N A Outside model boundary 1 Newlyn UK mainland 2 St Marys Scilly Isles 3 Douglas02 Isle of Man 4 Stornoway Outer Hebrides 5 St Kilda St Kilda 6 Lerwick Shetland Isles 7 Newlyn Orkney Isles 8 Fair Isle Fair Isle 9 Flannan Isles Flannan Isles 10 North Rona North Rona 11 Sule Skerry Sule S
11. 5 the Geoid datum flag is a number from 1 to 14 representing the geoid datum to which OSGMO2 Geoid height relates for example this flag is 14 for Belfast the orthometric height datum used in Northern Ireland See table 1 page 17 for details of other datum flag references OSGMO02 within the Republic of Ireland format and layout of the data Within the Republic of Ireland OSGM02 is released as a single data file using a 1 km grid This grid covers an area 350 km east west and 500 km north south the origin is offset by 400 000 500 000 from the origin of the projected ETRS89 coordinates see appendix B As with the data for Great Britain and Northern Ireland the area to which the models are valid has been cookie cutto a polygon around the coastline and the border with Northern Ireland This means that any position more than 10 km offshore or 2 km over the border with Northern Ireland will have fields 4 and 5 see below set to zero It is strongly recommended that the transformation software be written to return an outside transformation boundary type error when a point outside this area is encountered Each record occupies a separate line with the south west corner being the first record in the file The format of each record is indicated by the following table Record no Easting m Northing m OSGM02 Geoid Geoid m datum flag 1 400 000 500 000 2 401
12. of the earth ETRF89 European Terrestrial Reference Frame 1989 the Europe fixed realisation of WGS84 Governed by EUREF as a standard reference frame for Europe ETRS89 European Terrestrial Reference System 1989 a coordinate system that is the Europe fixed precise version of WGS84 Governed by EUREF as the standard fixed reference system for Europe ETRS89 is related to the state of the art WGS84 consistent system ITRS2000 by a six parameter kinematic transformation published by IERS EUREF EUREF European Reference Frame a sub commission of the International Association of Geodesy Commission X geocentric datum A reference system that uses the centre of mass of the earth as its origin the popularity of these systems today derives from their usefulness in describing satellite orbits Lois Geoid model A model of the level surface which is closest to mean sea level over the oceans This surface is continued under land as the fundamental reference surface for height measurement GPS Global Positioning System an outdoor positioning technique using a constellation of US Department of Defense satellites and a portable receiver to dynamically determine coordinates For high precision several receivers are used and their relative positions are determined GRS80 A global reference ellipsoid used in the WGS84 coordinate system Also known as the WGS84 ellipsoid IERS International Earth Rotation Service ITRF Inter
13. 0 09 Isle of Man 0 03 St Kilda 0 06 Any discrepancy found between an Ordnance Survey levelled bench mark and a OSGMO2 computed orthometric height is likely to be due to bench mark subsidence or uplift and assuming precise GPS survey has been carefully carried out the orthometric height given by OSGMO2 should be considered correct in preference to archive bench mark heights Appendix A Transforming ETRS89 GPS coordinates to OSGB36 and orthometric height Worked example To convert the coordinates of Caister Water Tower at position given by ETRS89 geographical coordinates 52 39 28 8282 N 1 42 57 8663 E 108 05 m to OSGB36 and orthometric height Step 1 Compute ETRS89 eastings and northings see appendix B Latitude 52 39 28 8282 N 52 658007833 N Longitude 1 42 57 8663 E 1 716073973 E The parameters for the GRS80 ellipsoid are a 6 378 137 000 b 6 356 752 314 Following the procedure in appendix B the calculation steps yield the following 2 6 69437999e 03 V 6 38912542e 06 p 6 37332179 06 f 2 47965408 03 M 4 06772557 05 P 6 48577261 02 3 06772557 05 1 54055171 06 1 56081387e 05 2 06739447e 04 IV 3 87545974e 06 V 1 0023086e 05 VI 1 01356325 05 eastings 651 307 0031 northings 313 255 6859 Lois The ETRS89 eastings and northings to the nearest mm are therefore x 651 307 003 y 313 255 68
14. 01 1 For example to find the record for 2 1 OOON east_index integer part 2 000 1 000 2 north_index integer part 1 000 1 000 1 record_number east index north index x 701 1 2 1x701 1 704 Procedure for transforming ETRS89 to OSGB36 coordinates To convert an ETRS89 easting and northing x y obtained using appendix B to a National Grid easting and northing e n the easting and northing shifts from the data file should be added to the x and y coordinates respectively The point to be transformed is unlikely to lie exactly on one of the nodes of the grid so to calculate the shifts at any other points an interpolation is required The first stage in the transformation is to identify in which grid cell the ETRS89 point lies This simply requires an integer division of the x y coordinates where x and y are in metres east_index integer part of x 1 000 north index integer part of y 1 000 Having located the correct cell find the values of the shifts at the four corners of the cell se se se se for the shifts in eastings and sn sn sn sn for the shifts in northings and the offsets of the point x y from the bottom left corner of the cell shown in figure 1 below the sg values in the figure are used to find the vertical shift values from OSGMO 2 later on Lois 563 503 583 562 SI S22 Sei SN1 561 Figure 1 Calculating the O
15. 2000 313 177 448000 showing that for this example applying the algorithm in both directions gives the values that were started with To calculate the GRS80 ellipsoidal height from the orthometric height simply add the geoid ellipsoid separation Lois Appendix B Converting latitude and longitude to easting and northing The formulae in this appendix and appendix C require ellipsoid constants and projection constants given in the tables below Important note When converting OSGB36 coordinates between easting northing and latitude longitude in either direction use the Airy 1830 ellipsoid constants When converting ETRS89 coordinates between easting northing and latitude longitude in either direction use the GRS80 ellipsoid constants Use the same National Grid projection constants for both ETRS89 and OSGB36 coordinates The ITM Irish Transverse Mercator projection is required to obtain ETRS89 eastings and ETRS89 northings for use with the OSGMO2 Geoid model data files for Northern Ireland and the Republic of Ireland The ITM projection should only be used with the GRS80 ellipsoid Ellipsoid constants Used for the Ellipsoid Semi major axis Semi minor axis b following coordinate a metres metres system Airy 1830 6 377 563 396 6 356 256 910 OSGB36 National Grid GRS80t 6 378 137 000 6 356 752 3141 ETRS89 WGS84 t Also known as the WGS84 ellipsoid The ellipsoid squared ec
16. 6 Step 2 Convert ETRS89 eastings and northings to OSGB36 and ETRS89 height to orthometric height First calculate the grid cell in which the point lies east_index integer_part_of x 1 000 651 north_index integer_part_of y 1 000 313 The eastings and northings of the south west corner of the cell are therefore Yo 651 000 313 000 The easting northing and geoid shifts for the four corners of the cell are given by se sn sg shifts east index north index shifts 651 313 record 651 313 x 701 1 record 220 065 102 775 78 244 44 252 sn 89 shifts 652 313 record 220 066 102 813 78 246 44 236 se SN 89 shifts 652 314 record 220 767 102 822 78 227 44 224 se sn 89 shifts 651 314 record 220 766 102 783 78 216 44 240 Lois The offset values are given by dx X X 307 0032 dy y y 255 6860 t dx 1 000 0 3070032 u dy 1 000 0 2556860 The shifts are therefore se 1 t 1 u se 90 t u se 1 t se 102 789 sn 1 t 1 sn 901 sn t u sn 1 t u sn 78 238 sg 1 t 1 u sg 90 u sg u sg 1 0 u sg 44 244 And finally the National Grid OSGB36 eastings and northings coordinates are given by e x se 651 409 792 n y sn 313 177 448 The orthometric height h is given by h 108 05 sg
17. 8 853 950 Other parameters Om 53 5 Ag 77 0 1 The Ordnance Survey Geoid model OSGM02 Orthometric height h in the UK and Ireland can be found by the formula h H N Where H is the GRS80 ellipsoidal height and N is the geoid undulation geoid ellipsoid separation Please note some publications use the notations of h and H the other way round OSGMO uses a grid look up method with geoid undulation interpolated from a 1 km grid covering the UK and the Republic of Ireland Similar to the Ordnance Survey Great Britain OSTNO2 transformation the first stage in calculating the geoid undulation is to identify in which grid cell the ETRS89 point lies To identify the appropriate grid cell and record numbers in the GB data set follow the procedure given earlier Transforming ETRS89 coordinates to OSGB36 National Grid To identify the appropriate grid cell and record numbers in the Northern Ireland dataset use the following formulae east_index integer_part_of x 1000 550 north_index integer_part_of y 1000 800 record_number east_index north_index x 251 1 To identify the appropriate grid cell and record numbers in the Republic of Ireland dataset use east_index integer_part_of x 1000 400 north_index integer_part_of y 1000 500 record_number east_index north_index x 351 1 For both Irish datasets the ETRS89 eastings x and ETRS89 northings y must be computed using the GRS80
18. STNO2 se and sn horizontal shifts and the sg vertical shifts for OSGMO2 Shifts for x y are se east_shift east_index north_index NOTE recall that the record number in the data file will be east_index north_index x 701 1 east shift east index 1 north index se east shift east index 1 north index 1 east shift east index north index 1 sn north shift east index north index sn north shift east index 1 north index north shift east index 1 north index 1 sn north shift east index north index 1 Offsets are dx 2X X dy y y The value of the east shift se north t dx 1 000 u dy 1 000 se 1 t 1 se 1 se sn 1 t 1 u sn t 1 u sn shift sn at the point x y is given by the following formulae r 9 use 1 t u se r 9 u sn 1 t u sn These shifts must then be added to the point x y to give the National Grid position e n e x se n y sn Inverse transformation OSGB36 to ETRS89 To compute ETRS89 eastings and northings from OSGB36 coordinates an iterative procedure is required Step 1 To start the iteration compute the ETRS89 OSGB36 easting and northing shifts at the OSGB36 point using the OSGB396 easting and northing and the method described in procedure for transforming coordinates page 20 Subtract these shifts from the OSGB36 coordinates to obtain the first estima
19. al datums to the accuracies shown in the table below The Ordnance Surveys recommend the use of the Geoid model OSGM02 and the active GPS network to produce orthometric height compatible with Ordnance Survey mapping The standard error of the main datums are OSGM02 region Standard error m Great Britain 0 02 Republic of Ireland 0 03 Northern Ireland 0 02 Orkney 0 08 Shetland 0 03 Outer Hebrides 0 09 Isle of Man 0 03 St Kilda 0 06 Ordnance Survey Great Britain intend that OSGM02 is the official definition of the relationship between GPS ellipsoid heights and orthometric height in Great Britain In the way that GPS and the transformation model OSTNO2 define the horizontal coordinate system precise GPS surveying using the Ordnance Survey Great Britain active GPS Network in conjunction with the Geoid model will become the standard method of determining orthometric height ETRS89 explained Benefits The Ordnance Survey transformations and OSGMO link the Ordnance Survey coordinate reference systems and vertical datums to the GPS compatible coordinate system ETRS89 In Europe ETRS89 is a precise version of the better known WGS84 reference system optimised for use in Europe however for most purposes it can be considered equivalent to WGS84 Specifically the motion of the European continental plate is not apparent in ETRS89 which allows a fixed relationship to be established between this system and O
20. ate transformations between Irish Grid and ETRS89 Transformed ETRS89 coordinates will agree with Irish Grid coordinates derived from traditional survey control to within 0 4 m 95 data Accuracy of OSGM02 The heights output by precise GPS positioning in the ETRS89 coordinate system are geometric distance above the WGS84 GRS80 reference ellipsoid Note that GPS heights are typically two to three times less precise than horizontal positions OSGMO2 converts GPS ellipsoid heights to orthometric heights above mean sea level 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 OSGMO2 and hence OSGM02 is compatible with the products from each of the Ordnance Surveys Other geoid models may give mean sea level heights that are incompatible with the Ordnance Surveys products The estimated accuracies of OSGMO 2 for each regional vertical datum are included the table below The figures quoted assume precise ellipsoidal heights are used for lower quality GPS observations additional error budget must be included Regional datum Standard error m Great Britain 0 02 Republic of Ireland 0 03 Northern Ireland 0 02 Orkney 0 08 Shetland 0 03 Outer Hebrides
21. c XI ca E 2 tan 2 ae 54 28 tan 9 24 tan g _ Ov 61 662 tan 1320tan 720 tan 9 VIKE E y VIKE E IX E E 4 X E E XIKE E E C3 C4 Worked example using Airy 1830 ellipsoid and National Grid Intermediate values are shown here to 10 decimal places Compute all values using double precision arithmetic E 651 409 903 m N 313 177 270 m 9 2002324604e 01 rad M 4 1290347144 05 2nd 9 2006619470 01 rad M 4 1317717541e 05 3rd 9 2006620953e 01 rad M 4 1317726997 05 final 9 2006620954 01 rad 6 3885233415e 06 6 3728193094e 06 2 4642205195 03 VII 1 6130562490e 14 VIII 3 3395547442 28 IX 9 4198561719 42 2 5840062509e 07 XI 4 6985969968e 21 XII 1 61243166226 34 XIIA 6 6577316330 48 52 39 27 2531 N 4 1 43 4 5177 E Appendix D Glossary The following is a list of technical terms used in this user guide together with a fuller definition datum A point line surface or set of these with respect to which positions of objects can be stated as unique sets of coordinates de facto national standard A national standard by adoption rather than legally enforced ellipsoid biaxial The 3 D geometric figure obtained by rotating an ellipse about its minor axis Used in geodesy to approximate the shape
22. centricity constant e is computed from a and b by 2 2 2 a e Projection constants Projecti Scale factor True origin Map coordinates on central 4 of true origin m meridian F E and N National 0 9996012717 lat 49 N E 400 000 Grid long 2 W N 100 000 ITM 0 99982 Lat 53 30 N E 600 000 long 8 W N 750 000 To convert a position from the graticule of latitude and longitude coordinates A 9 to a grid of easting and northing coordinates E N using a transverse mercator projection for example OSGB36 National Grid ITM or UTM Universal Transverse Mercator compute the following formulae Remember to express all angles in radians You will need the ellipsoid constants a b and and the projection constants listed below northing of true origin E easting of true origin scale factor on central meridian latitude of true origin and A longitude of true origin and central meridian a b 2 B2 a v aF 1 e sin g B3 p 1 sin g B4 5 ren 2 eir 6 0 mew Zhi sing e x pu Sw Eu inte 2 0 4 1 sin 3 cos 3 9 I M N II 2 5 Sin Pecos 0 5 972 sp Sin cos 61 58 tan tan IV vcos V Lom 3 6 VI T 9 5 18tan2 tan 14g 58tan
23. d projection grid intersection easting coordinate in metres 3 ETRS89 National Grid projection grid intersection northing coordinate in metres 4 the shift in eastings at the intersection between ETRS89 and OSGB36 National Grid that is ETRS89 east OSTNO2 east shift OSGB36 National Grid easting 5 the shift in northings at the intersection between ETRS89 and OSGB36 National Grid that is ETRS89 north OSTNO2 north shift OSGB36 National Grid northing 6 the height of the Geoid above the ETRS89 ellipsoid in metres at the intersection that is ETRS89 height OSGM02 Geoid height orthometric height above mean sea level 7 the Geoid datum flag is a number from 1 to 14 representing the geoid datum to which OSGM02 Geoid height relates for example this flag is 1 for Ordnance Datum Newlyn the orthometric height datum used on the British mainland See table 1 page 17 for details of other datum flag references OSGMO02 within Northern Ireland format and layout of the data Within Northern Ireland OSGMO is released as a single data file using a 1 km grid This grid covers an area 250 km east west and 200 km north south the origin is offset by 550 000 800 000 from the origin of the projected ETRS89 coordinates see appendix B As with the data for Great Britain the area to which the models are valid has been cookie cutto a polygon around the coastline and the border with the Republic of Ireland This means that any position mor
24. e than 10 km offshore or 2 km over the border with the Republic of Ireland will have fields 4 and 5 see below set to Zero It is strongly recommended that the transformation software be written to return an outside transformation boundary type error when a point outside this area is encountered Each record occupies a separate line with the south west corner being the first record in the file The format of each record is indicated by the following table ETRS89 ETRS89 northing OSGM02 Geoid Geoid datum Record no m Ht m 1 550 000 800 000 2 551 000 800 000 3 552 000 800 000 and so on and so on and so on 251 800 000 800 000 252 550 000 801 000 253 551 000 801 000 254 552 000 801 000 255 553 000 801 000 and so on and so on and so on 50 448 797 000 1 000 000 50 449 798 000 1 000 000 50 450 799 000 1 000 000 50 451 800 000 1 000 000 Where 1 the record number is a sequential number starting at 1 for the origin point 550 000 800 000 and finishing at 50451 for the north east corner 800 000 1 000 000 2 ETRS89 ITM projection grid intersection easting coordinate in metres 3 ETRS89 ITM projection grid intersection northing coordinate in metres 4 the height of the Geoid above the ETRS89 ellipsoid in metres at the intersection that is ETRS89 height 5 2 Geoid height orthometric height above mean sea level
25. he precise relationship between the two vertical reference surfaces The resulting Ordnance Survey Geoid model OSGMO2 incorporates all the above vertical datums The Ordnance Survey of Great Britain has developed the horizontal transformation OSTNO2 This transformation consists of a 700 km by 1 250 km grid of translation vectors at 1 km resolution This provides a fit between the GPS coordinate system ETRS89 European Terrestrial Reference System 1989 and the OSGB36 National Grid OSTNO2 is in agreement with major triangulation stations at the level of 0 1 m root mean square error RMSE OSTNO 2 has been developed from the national primary secondary and tertiary triangulation station network It contains over 3 200 points directly observed by GPS and more than 1 000 from the original retriangulation observations adjusted on the ETRS89 datum Within Great Britain OSTNO2 the Ordnance Survey National Grid Transformation in conjunction with the ETRS89 positions of the active GPS network stations is now the official definition of OSGB36 National Grid coordinate system This means that using OSTNO2 with the National GPS Network surveyors using GPS have no need to occupy triangulation stations in order to relate GPS coordinates to National Grid coordinates OSi OSNI polynomial transformation Ordnance Survey Ireland and Ordnance Survey of Northern Ireland recommend the OSi OSNI polynomial transformation for all horizontal transformations in the Re
26. ial transformation which is the standard datum transformation for use throughout Ireland The Ordnance Survey of Great Britain has developed OSTNO2 the standard datum transformation for Great Britain Ordnance Survey mapping also includes height information that relates to a regional vertical datum Height information in Great Britain refers to Ordnance Datum Newlyn ODN which is established from mean sea level Although ODN is the national height datum used across mainland Great Britain there are a number of additional datums that are used on the surrounding islands for example Lerwick on the Shetland Islands Stornoway on the Outer Hebrides St Kilda Douglas02 on the Isle of Man St Marys on the Scilly Isles The Ordnance Survey of Northern Ireland relates heights within Northern Ireland to Belfast Lough datum and Ordnance Survey Ireland relates heights within the Republic of Ireland to the Malin Head datum OSTNO2 Orthometric heights in these systems have in the past been realised via a network of Ordnance Survey bench marks BMs These traditional levelling networks cover the whole of Great Britain Northern Ireland and the Republic of Ireland However heights from precise GPS surveying are relative to a reference ellipsoid that approximates to the shape of the earth but does not coincide with mean sea level To enable GPS to be used to determine orthometric heights the Ordnance Surveys have jointly developed a model to establish t
27. iate mapping agency logo must also appear next to the copyright notice Details of mapping agency logos are found in the style guides available on the web site User guide copyright Trademarks This user guide is Crown copyright 2002 All rights reserved It accompanies OSTNO2 and OSGMO data to allow you to make effective use of the data Any part of this guide may be copied for business use Business use is defined as actions related to business decision making or as part of day to day operations associated with the running of the business No part of the guide may be copied or incorporated in products services or publications a user generates for onward sale or as free promotional support material without the prior written permission of Ordnance Survey Ordnance Survey the OS Symbol and OSGB36 are registered trademarks and OSTNO2 is a trademark of Ordnance Survey the national mapping agency of Great Britain OSGM02 is a trademark of Ordnance Survey Ordnance Survey Northern Ireland and Ordnance Survey Ireland Ordnance Survey Northern Ireland OSNI and the OSNI Symbol are trademarks of Ordnance Survey Northern Ireland The OSi Symbol is a registered trademark of Ordnance Survey Ireland Ordnance Survey Ireland and OSi are trademarks of Ordnance Survey Ireland Contents Chapter 1 Chapter 2 Chapter 3 Chapter 4 6 Coordinate transformat
28. ions and the Geoid model 6 7 OSVOSNI Polynomial tANSTOMM ALON occides cene eei EE 7 Ordnance Survey Geoid 56 02 i C ce RE RER ET PER 8 589 retentis I NE eet 9 ence a aaaaa 9 PAD DIG AU OMS m c 10 BERT UU 11 Basic EE 11 HH EE 12 OSTNO2 OSGM02 within Great Britain format and layout of the 12 OSGMO 2 within Northern Ireland format and layout of the data sssssssssssseeeeeeemeeemene nennen enne 13 OSGMO 2 within the Republic of Ireland format and layout of the 15 Ordnance Survey transformations and OSGMO2 explained 18 Sasu nu u M UD ME M uM eU 18 Transforming ETRS89 coordinates to OSGB36 National Grid 18 Calculating whichidatarecord to i eR 18 Procedure for transforming ETRS89 to OSGB36 coordinates ennemi enne tnr enne tnn enne 19 Inverse transformation OSGB36 to ETRS89 u ile pau Pape axi
29. kerry 12 Foula Foula 13 Malin Head Republic of Ireland 14 Belfast Northern Ireland NOTE If the datum flag indicates a zero 0 then the coordinate falls more than 10 km offshore or 2 km beyond the Northern of Ireland border and is not covered by the model Chapter 3 OSTNO2 Ordnance Survey transformations OSGM02 explained This chapter explains the algorithms that must be coded to implement the Ordnance Survey transformations OSTNO2 and the OSi OSNI polynomial and OSGMO2 Transforming ETRS89 coordinates to OSGB36 National Grid overview To transform an ETRS89 value to OSGB36 the ETRS89 easting and northing is first obtained using the algorithm GRS80 ellipsoid parameters and National Grid projection parameters in appendix B Within the kilometre square where the point falls a bilinear interpolation is used to obtain the exact transformation value for the point from the values at the four corners of the kilometre square These values are added to the ETRS89 easting and northing to obtain the OSGB36 values The inverse transformation OSGB36 to ETRS89 is accomplished by an iterative procedure Calculating which data record to use To find the record number corresponding to a given ETRS89 easting and northing use the following algorithm east index jinteger part of easting 1 000 north index integer part of northing 1 000 record number east index north index x 7
30. mission or otherwise wish to make a suggestion as to how this user guide can be improved please contact us at the address shown under Contact details For users in Great Britain and the Isle of Man The Geospatial Development Team will be pleased to deal with your enquiries Email GIDTechSup ordsvy gov uk or write to The Geospatial Development Team Ordnance Survey Romsey Road SOUTHAMPTON United Kingdom SO16 4GU Web site www gps gov uk 015 For users in Northern Ireland Ordnance Survey of Northern Ireland Colby House Stranmillis Court Belfast Northern Ireland BT9 5BJ Web site www osni gov uk For users in the Republic of Ireland Ordnance Survey Ireland Phoenix Park Dublin 8 Ireland Web site www osi ie Liability OSTNO2 OSGMO2 are provided free of charge by Ordnance Survey and where relevant Ordnance Survey Northern Ireland and Ordnance Survey Ireland on an as is and as and when available basis to users A user of either OSTNO2 the OSi OSNI polynomial transformation or OSGMO 2 does so at their own risk Downloading of any dynamic link library dll files from this site is made without any representation or warranty or condition whether expressed or implied in particular it is without representation warranty or condition that OSTNO2 the OSi OSNI polynomial transformation and OSGMO2 are error free free from viruses or other harmful components or as to the accuracy content
31. national Terrestrial Reference Frame the state of the art global realisation of the WGS84 reference system using observations from worldwide networks of active geodetic stations of the VLBI SLR GPS and DORIS techniques ODN Ordnance Datum Newlyn the levelling based vertical reference frame for most of the British Isles with a single tide gauge constraint in Newlyn in Cornwall OSGB36 Ordnance Survey Great Britain 1936 the British horizontal mapping datum observed by triangulation from 1936 and traditionally realised on the ground by triangulation stations With the release of the definitive transformation OSTNO2 OSGB396 is now realised by the ETRS89 coordinates of the National GPS Network in conjunction with the OSTNO2 transformation Lois OSGM02 Ordnance Survey National Geoid Model 2002 a gravimetric Geoid model that is aligned with the national height datums of Great Britain Northern Ireland and Ireland OSTNO2 Ordnance Survey National Grid Transformation 2002 a grid shift type horizontal transformation between the ETRS89 datum and OSGB36 National Grid realisation A spatial reference system made real on the ground by monumented points with estimated coordinates and errors transformation A procedure to change from one coordinate system to another WGS84 World Geodetic System 1984 the global geodetic reference system used to describe the position of GPS satellites and ground stations
32. public of Ireland and Northern Ireland This transformation has been developed in association with the Institute of Engineering Surveying and Space Geodesy University of Nottingham The transformation is based on 183 points evenly distributed throughout Ireland and Northern Ireland The precise ETRS89 and Irish Grid coordinates of these points are determined by GPS and terrestrial survey methods and a one dimensional 3 order polynomial individually fitted to the latitude and the longitude The resulting polynomial allows calculation of the coordinate differences at additional points The polynomial transformation has an accuracy of 0 4 m 95 data Ordnance Survey Geoid model OSGM02 To provide the third dimension of the transformation the Ordnance Surveys have with others developed the Geoid model OSGM02 The model is derived from precise gravity surveys across UK Ireland and surrounding waters additionally the model includes data from the global geopotential model EGM96 Alignment to each regional vertical datum is based on precise GPS observations at Ordnance Survey levelling marks Within Great Britain these include the Ordnance Survey fundamental bench mark network The Geoid model consists of a 1 km grid with geoid ellipsoid separation values covering all of Great Britain Ireland and Northern Ireland This model can be used with GPS determined positions to establish height above mean sea level as defined by the respective vertic
33. rdnance Survey mapping coordinate systems Additional precise versions of WGS84 are currently in use notably ITRS these are not equivalent to ETRS89 The difference between ITRS and ETRS889 is in the order of 0 25 m in 1999 and growing by 0 025 m per year in UK and Ireland This effect is only relevant in international scientific applications For all navigation mapping GIS and engineering applications within the tectonically stable parts of Europe including UK and Ireland the term ETRS89 should be taken as synonymous with WGS84 Together the Ordnance Survey transformations and OSGM02 provide the complete solution to relating GPS WGS84 datasets to Ordnance Survey mapping in three dimensions Used with the active GPS network they allow GPS surveying within the National Grid or the Irish Grid and to the appropriate vertical datum without the need to visit any Ordnance Survey traditional control points These new standards bring the benefits of simplicity and uniformity Applications The Ordnance Survey transformations and OSGM02 are of interest to GPS surveyors who need to relate their survey to the National Grid or the Irish Grid and or OD orthometric heights used with the active GPS Network these products remove the need to visit traditional Ordnance Survey horizontal and vertical control points and GIS GPS CAD and navigation system developers who need to integrate GPS WGS84 datasets with Ordnance Survey mapping
34. shore and 2 km beyond the Northern Ireland Republic of Ireland border Any point outside this boundary will return null values in the shift and datum flag records It is strongly suggested that any software written to incorporate this data be capable of recognising a null value and to return an outside of model boundary error message Within Ireland and Northern Ireland OSGM02 returns orthometric heights relative to the Malin Head and Belfast Lough datums respectively OSGMO 2 will return orthometric height relative to either the Malin Head or the Belfast Lough datums for points within 2 km of the border between the Republic of Ireland and Northern Ireland Accuracy of Ordnance Survey transformations Within Great Britain OSTNO2 is the definitive OSGB36 ETRS89 transformation OSTNO2 in combination with the ETRS89 coordinates of the active GPS network stations rather than the fixed triangulation network now define the National Grid This means that for example the National Grid coordinates of an existing OSGB36 point refixed using GPS from the National GPS Network and OSTNO2 will be the correct ones The original archived OSGB36 National Grid coordinates of the point if different will no longer be true OSGB36 by definition but the two coordinates new and archived will agree on average to better than 0 1 m 6896 probability Within the Republic of Ireland and Northern Ireland the OSi OSNI polynomial transformation is recommended for coordin
35. te of the ETRS89 easting and northing Step 2 Use this estimate of the ETRS89 easting and northing to obtain improved values for the easting and northing shifts and subtract these from the OSGB36 coordinates to obtain improved values of the ETRS89 easting and northing Step 3 If the difference between the first shift value and second shift value is more than 0 0001 metres in either easting or northing repeat step 2 until this is not the case Step 4 If ETRS89 latitude and longitude coordinates are required obtain these from the ETRS89 easting and northing by the procedure described in appendix C The OSi OSNI polynomial transformation To some extent distortions within traditional triangulation networks are inevitable Within the triangulation network of the Republic of Ireland and Northern Ireland these distortions are not generally significant however regional distortions do occur 3 order polynomial transformation has been developed to model these distortions A polynomial expression was fitted to the coordinate differences of a number of points in the different coordinate reference systems This is a one dimensional fitting method that is applied to the geographical coordinate requiring independent parameters to be computed for both latitude and longitude In general the polynomial model can be expressed as A B A A The fully expanded forms of the 3 order polynomial are as follows Av
36. um TM ORDNANCE SURVEY MAPPING NORTHERN IRELAND Ordnance Survey Ireland Transformations and OSGMO2 User guide Preface Contact details This grid transformation software and user guide has been commissioned by a consortium comprising Ordnance Survey Great Britain Ordnance Survey Ireland OSi and Ordnance Survey of Northern Ireland OSNI These organisations are responsible for the official definitive topographic mapping of their respective countries This user guide contains all the information you need to make effective use of the Ordnance Survey Grid Transformations in the UK and Ireland and the Ordnance Survey Geoid model OSGM02 Within Great Britain coordinates are transformed using the Ordnance Survey National Grid Transformation OSTNO2 Within the Republic of Ireland and Northern Ireland the OSi OSNI Polynomial Transformation is used OSGM02 is used to transform heights throughout the UK and Ireland Users wishing to incorporate the pre prepared dll should refer to the Grid InQuest 6 0 user guide The intention of this guide is to help you understand the information contained in the data as well as providing detailed technical information and the data format specification however it is assumed that users have some appreciation of coordinate systems and datums This user guide has been checked and validated before issue and every endeavour made to ensure that the contents are accurate If you find an error o
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