Datums, Coordinate Systems, Coordinate Reference Systems ...

1 Datums, Coordinate Systems , Coordinate Reference Systems and datum TransformationsDean C. Mikkelsen, , Warmerdam, OSGeo, FWToolsFOSS4G2007 Sept. 2007 Victoria, BC ! " # $ % " # $ " # & ' " # " # ( # ) $ * # + , - .. $ . / ' 0" # 1 2 2 2 2 2 2 2 2 .. ! 3 # ! 3 # ! 3 # ! 3 # ! 3 # ! 3 # ! 3 # ! 3 # Latitude and Longitude areNOT UNIQUE!NOT UNIQUE!'# / .. # 0" # 1 0" # 1 ! 4 4 . 4 . * 4 . 4 - # "35 ! 6% - $ + ' / Geoid (MSL)SphereEllipsoid / SpheroidWGS72/84. 7 # . 7 # . 7 # . 7 # . 7 # . 7 # . 7 # . 7 # * * * * * * * * " # " # " # " # " # " # " # " # Used for a specific region North America, Europe, South America etc. A Coordinate frame is determined and an ellipsoid chosen to minimize the local geoid-ellipsoid separation.

2 Not Earth centered! Hundreds have been defined for countries all over the planetBEST FITTINGELLIPSOID FORTHE REGIOND atum datum = Coordinate FRAME + Reference ELLIPSOIDE llipsoidSemi Major AxisInv. FlatteningAiry 1841 (Namibia) (India 1830) (Sabah) (India 1956) (Malaysia 1969) (Malay. & Sing) (Pakistan) Fischer 19246378388297 Krassovsky American .. 8-9 . 8-9 . 8-9 . 8-9 . 8-9 . 8-9 . 8-9 . 8-9 Defined as :+ellps=<name> or+a=<semi_major_axis>+b=<semi_minor_axis>Or defined with:+a=<semi_major_axis>+rf=<inverse_flattening>Axis defined in meters .Examples : +ellps=WGS84 +a= + rf= Use cs2cs - le to get a list of known ellipsoids . " # " # " # " # " # " # " # " # datum Origin11 main stns (UK)many pts (global)1591+ pts (global) PotsdamLa Canoa, Ranch, KSGlobal, numerous ptsHerstmonceux, UKManoca Twr, stn, NigeriaITRF yyyywhereyyyy = adj.

3 Year+ Reference EllipsoidAiryWGS72 ellipsoidWGS84 ellipsoidInternational 1924 International 1924 Clarke 1886 GRS80 AiryClarke 1880 IGNC larke 1880 RGSGRS80= DatumOSGB36 WGS72 WGS84ED50 PSAD56 NAD27 NAD83OS(SN)70 MANOCAMINNAITRS Defined as :+ datum =<datum_name>+towgs84= <x_shift> ,< y_shift> ,< z_shift>+towgs84= < xs> ,< ys> ,< zs> ,< xr> ,< yr> ,< zr> ,<s>+nadgrids= < list of grid shift files>Examples : + datum =WGS84 +towgs84= , , + ellps=clark80 +nadgrids= +ellps= clrk66 Use cs2cs - ld to get a list of known datums.. 8-9 " . 8-9 " . 8-9 " . 8-9 " . 8-9 " . 8-9 " . 8-9 " . 8-9 " Common Coordinate Systems defined in dictionaries . Format : +init= <dictionary>:< name> Example: + init= epsg:4326 Dictionaries are text files in/ usr/ local/ share/ proj Search them with a text editor!

4 Declarations look like:# WGS 84<4326> +proj=longlat + datum =WGS84 +no_defs <> . 8-9 " . 8-9 " . 8-9 " . 8-9 " . 8-9 " . 8-9 " . 8-9 " . 8-9 " Distributed Dictionaries : epsg: Definitions for EPSG GCS and PCS. nad27: State plane zones keyed on USGS zone # nad83: State plane zones keyed on USGS zone # esri: ESRI extended EPSG database : OGC WMS EPSG extensions world : as sorted additional common projections OGC WKT is a standard for exchange of Coordinate Systems . Originally from Simple Features for SQL Variations used by ESRI Projection Engine , Oracle, AutoMap , Mapguide,GDAL/ OGR and PostGIS Not to be confused with WKT geometries . : ; . : ; . : ; . : ; . : ; . : ; . : ; . : ; PROJCS["NAD27 / New York Eas t ",GEOGCS["NAD27", datum ["Nor th _Amer ican _Datum_1927",SPHEROID["Clarke 1866", , ,AUTHORITY["EPSG","7008"]],AUTHORITY["EP SG","6267"]],PRIMEM["Greenwich ",0,AUTHORITY["EPSG","8901"]],UNIT["d egree", ,AUTHORITY["EPSG","9122"]],AUTHORITY["EP SG","4267"]],PROJECTION["Tran sver s e_Mercator "],PARAMETER["lat itud e_of_or igin ",40],PARAMETER["cen t ral_mer id ian ",- ],PARAMETER["s cale_factor ", ],PARAMETER["fals e_eas t in g",500000],PARAMETER["fals e_n or th in g",0],UNIT["US survey foot ", ,AUTHORITY["EPSG","9003"]],AUTHORITY["EP SG","32015"]]< # + < # + < # + < # + < # + < # + < # + < # + OabRotate 180 Flatteningaba=-()eaba2222=-()eabb ()2222=-!

5 4 : " # 3 , ! 4 : " # 3 , ! 4 : " # 3 , ! 4 : " # 3 , ! 4 : " # 3 , ! 4 : " # 3 , ! 4 : " # 3 , ! 4 : " # 3 , LuzonIndianHanoiHengYangNankingYushanHon gKongKweiyangAustralianKandawalaGandajik a BaseDjakartaIndianBukit RimpahTokyoTimbalaiKertauSouth AsiaPulkovoSouth AsiaNorth AmericaNorth AmericaNorth AmericaEuropeanEuropeanEuropeanPulkovoPu lkovoPulkovoSouth AmericaSouth AmericaSouth AmericaCape ArcCape ArcCape ArcAustralianAustralianAustralianTokyoTo kyoTokyoIndianIndianIndianOver 100 well-defined datums worldwide! % # % # % # % # Equatorial PlaneSpheroid ANormal AGeodeticLatitude ANormal BSpheroid BGeodeticLatitude B% (=%* >" ( >( 6> )% # % # > ?# )% # % # > ?# )* @*! % ( : * . &" # - = GeogCRS/ datum Latitude LongitudeManocaN 04 04' E 008 29' MinnaN 04 04' E 008 29' "WGS 84 N 04 04' E 008 29' (using GULF1977 transformation from Manoca to WGS84 and MPN 1994 transformation from Minna to WGS84) $$$$$$$$"" A "!)

6 "" A "! "" A "! "" A "! "" A "! "" A "! "" A "! "" A "! A Reference system using latitude and longitude A Reference system using latitude and longitude to define the location of points on the surface of a to define the location of points on the surface of a sphere or spheroidsphere or spheroiddecimal degrees (DD) decimal degrees (DD) (DMS) 92degrees/minutes/seconds (DMS) 92 3030 0000 WW Universal Coordinate system (lat/Universal Coordinate system (lat/lonlon)) Lat/Lat/lonlongood for locating positions on good for locating positions on surface of a globesurface of a globe Lat/Lat/lonlonis not efficient for measuring distances is not efficient for measuring distances and areas!and areas!

7 Latitude and longitude are not uniform units Latitude and longitude are not uniform units of measureof measure One degree of longitude at equator = One degree of longitude at equator = km (Clarke 1866 spheroid)km (Clarke 1866 spheroid) One degree of longitude at 60 One degree of longitude at 60 latitude = latitude = km km (Clarke 1866 spheroid)(Clarke 1866 spheroid)! " # ! " # ! " # ! " # ! " # ! " # ! " # ! " # West Texas Texas Central Zone NAD27 Lat: 32 N Long: 105 W NAD83 32 00 N 105 00 W Differences DE ft DN ft DR ft N ft Montana MontanaSouth Zone NAD27 Lat: 45 N Long: 112 W NAD83 44 59 N 112 00 W Differences DE ft DN ft DR ft N ft ( 3 B " #.)

8 - =GeogCRS/DatumLatitude LongitudeAratu20 36 N 38 56 WSAD69 20 36 N 38 56 W WGS84 20 36 N 38 56 WDifferences in Lat/Long coordinates are evident. But .. What if you didn t have the datum label?" " # A " " # A " " # A " " # A " " # A " " # A " " # A " " # A .. Where is? 20 36 N 38 56 W" " # " " # " " # " " # # ! # ! # ! # ! NNAD 27 WGS84or NAD 83 WGS72200m or 656 ft16m or 52 ftWGS 84:Lat: 27 00 N, Long: 92 14 NNAD 27 Lat: 27 00 NLong: 92 14 NNAD 27 minus WGS 84:DDDDL atitude = DLongitude = DDDDN orthing = m (-656 feet)DDDDE asting = + m (45 feet)C1 % # D EF-F C1 % # D EF-F C1 % # D EF-F C1 % # D EF-F While working in one GeogCRS ( datum )1 latitude = meters, 1 longitude = meters * cos (latitude)This is NOTvalid when geographic coordinates are on DIFFERENT datums.

9 The example NAD27 and WGS84 latitude on the previous slide differs by only C-FG1,whereas the physical offset is approximately CHH-H GIG Why is this the case? % # % # % # % # Equatorial PlaneSpheroid ANormal AGeodeticLatitude ANormal BSpheroid BGeodeticLatitude B%* >" ( >( 6> ) # ' J -- # ' J -- # ' J -- # ' J -- # ' J -- # ' J -- # ' J -- # ' J --Major Point to Remember :Latitudes and Longitudesare not uniqueare not uniqueunless qualified with a datum or GeogCRS name! " # " # " # " # " # " # " # " # 2 + + . " # Often, there are many choices available How do you choose the correct transformation? 2 + # # ' + / # . # Little sharing of geodetic information. Operators needed more accurate transformations.)

10 Satellite receivers could measure directly. " # # " # # " # # " # # " # # " # # " # # " # # : # # 7 + , 0 1 # . + # Most positioning work in the energy/mining/forestrysector is done by GPS measurements solely linked to the WGS 84 GeogCRS (& datum ) To obtain coordinates in a local Reference system , someone MUST transform from WGS 84 to that local GeogCRS. If different datum shifts are used, then different geographic coordinates will be obtained. ! ! ! ! ! ! ! ! 2 + # . C . 5 " # C " # 5 Geocentric Translation (3-parameters) 7-parameter transformations (Special caution MUST BE EXERCISED here!) Many other transformation methods exist, with limited applications # # ' + + . '# ' ' + + 4 4.