Lecture 4

1. Lecture 4 Understanding Coordinate Systems

2. Geographic Coordinate systems • Spherical • Ellipsoidal • Curved GCS

3. Projected coordinate systems • (PCS) • 2D • Flat • Planar • Cartesian GCS PCS

4. GCS has angular units of measure • Degrees • 360 per circle • Decimal degrees • Degree, minute, second • Radians • 2 pi per circle • ~6.3 per circle (~57 degrees each) • Gradian • 400 per circle • Gon • Same as gradians • To some grad = degree

5. PCS has linear units of measure • Linear units • Meters • Feet • X and Y coordinates • Length, angles, and areas are constant Y Data usually here X + Y + X - Y + X X - Y - X + Y -

6. Map projection • Math to transform GCS

7. Map projection • Math to transform GCS to PCS • Flattening the earth – round to flat • Distortions make geographers SADD • Shape, Area, Distance, and Direction Plate Carrée projection

8. PCS properties example • Name – NAD 1983 UTM Zone 11N • GCS– NAD 1983 • Map Projection – Mercator • Projection parameters • Central meridian, latitude of origin, scale factor, false easting • Linear unit of measure (i.e., meters)

9. Geographic coordinate systems • Mathematical model of a planetary body - spheroid • Parameters describe the spheroid shape • Smooth, without imperfections • GCS for earth, planets, and more Earth Mars IO

10. GCS properties • Spheroid • Major and minor axis • Units (lat/long, radians, grads)

11. GCS properties • Spheroid • Major and minor axis • Units (lat/long, radians, grads) • Datum • Spheroid’s position in relation to actual earth • Local datum: spheroid touches edge of earth, good fit there Great fit here Bad fit here Local datum

12. GCS properties • Spheroid • Major and minor axis • Units (lat/long, radians, grads) • Datum • Spheroid’s position in relation to actual earth • Local datum: spheroid touches edge of earth, good fit there • Earth-centered: spheroid and earth center match All around best fit for the entire planet Great fit here Bad fit here Local datum Earth-centered datum

13. GCS properties example • Name • European Datum 1950 • Datum • European Datum 1950 • Spheroid • International 1924 • Prime Meridian • Greenwich • Angular unit of measure • Degrees

14. GCS with a local datum • Spheroid

15. GCS with a local datum • Datum • Spheroid’s position in relation to actual earth

16. GCS with a local datum • Datum • Spheroid’s position in relation to actual earth

17. GCS with a local datum • Datum • Spheroid’s position in relation to actual earth

18. GCS with a local datum • Datum • Spheroid’s position in relation to actual earth

19. GCS with a local datum • Datum • Spheroid’s position in relation to actual earth

20. GCS with a local datum • Datum • Spheroid’s position in relation to actual earth • Local datum: spheroid touches edge of earth, good fit there • Bad fit on the other side

21. GCS with an Earth Centered datum • Spheroid

22. GCS with an Earth Centered datum • Datum • Spheroid’s center matched to earth center

23. GCS with an Earth Centered datum • Datum • Spheroid’s center matched to earth center

24. GCS with an Earth Centered datum • Datum • Spheroid’s center matched to earth center

25. GCS with an Earth Centered datum • Datum • Spheroid’s center matched to earth center

26. GCS with an Earth Centered datum • Datum • Spheroid’s center matched to earth center

27. GCS with an Earth Centered datum • Datum • Spheroid’s center matched to earth center • Best fit all around the earth

28. Common GCS parameters in use today (US) • As measurement gets better, new GCS are defined • NAD27 – parameters defined in 1866 (log tables) • NAD83 – parameters defined in 1979 (pre-GPS) • WGS84 – parameters defined in 1984 (GPS) North American Datum 1927 North American Datum 1983 World Geodetic Survey 1984

29. Warning: different geographic coordinate system…

30. Geographic transformation • Math to transform from one GCS to another ESRI-Redlands 117 Degrees 11 Minutes 39.2 Seconds West 34 Degrees 3 Minutes 23.1 Seconds North NAD 27

31. Geographic transformation • Math to transform from one GCS to another • Changing GCS changes the lat/long for same point • The same spot on earth has differing coordinates ESRI-Redlands 117 Degrees 11 Minutes 42.36 Seconds West ESRI-Redlands 117 Degrees 11 Minutes 39.2 Seconds West 34 Degrees 3 Minutes 23.14 Seconds North 34 Degrees 3 Minutes 23.1 Seconds North NAD 83 NAD 27

32. ArcMap’s GCS and PCS behavior • Data frame - has both • Spatial data - has GCS, may have PCS • Metadata - prj, XML, mdb, or none • Tools that help

33. On-the-fly projection • ArcMap data frames have a GCS and a PCS • You should set them • If not set, data frames take first layer’s GCS/PCS Data frame: Bonne PCS

34. On-the-fly projection • ArcMap data frames have a GCS and a PCS • You should set them • If not set, data frames take first layer’s GCS/PCS • If needed, new layers are projected on-the-fly (to match) • If no CS metadata, new layer cannot be projected on-the-fly Input layer: Robinson PCS Data frame: Bonne PCS ArcMap projects data on-the-fly into a data frame

35. GCS and PCS metadata for spatial data • Stored in internal geodatabase tables • Stored in projection files • Shapefiles can have a .prj text file (e.g., streets.prj) • Coverages can have a prj.adf text file (e.g., /rivers/prj.adf) • Stored optionally in XML files created by ArcCatalog • Non-native ESRI datasets use various other formats

36. Warning! • GCS and PCS metadata is NOT required • You might get data that is missing its coordinate system metadata • If researched and discovered, you can add it • If not, use Spatial Adjustment to move the data into place

37. Problem Solution Spatial reference problems and solutions  You know the coordinate system information, but it is missing  Define Projection tool • Project tool or data frame project on-the-fly • The PCS is defined correctly, but is not the one you need  The GCS is defined, but it is not NAD27 or NAD83 • Project tool or set a geographic transformation in the data frame properties