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! 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)!

7 " # ! " # ! " # ! " # ! " # ! " # ! " # ! " # 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 " # . - =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" " # " " # " " # " " # # !)

8 # ! # ! # ! 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. 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!)

9 " # " # " # " # " # " # " # " # 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. 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!)

10 Many other transformation methods exist, with limited applications # # ' + + . '# ' ' + + 4 4 . KK ZYXG reenwichMeridian% = * # % = * # % = * # % = * # % = * # % = * # % = * # % = * # From the perspective of a geographic software design three From the perspective of a geographic software design three Coordinate Coordinate systemssystemscan potentially be addressed. Each differ either in the order ocan potentially be addressed. Each differ either in the order of f the Coordinate the Coordinate tupletupleor in the direction of increasing values. or in the direction of increasing values. Mathematical Mathematical Axis Order (X,Y) Axis Order (X,Y) Signed values, increase to the right und upwards Signed values, increase to the right und upwards Computer Graphics Computer Graphics Axis Order (X,Y) Axis Order (X,Y) Unsigned values increase to the bottom and to the right.