1. Chapter 11 Coordinate Systems

2. Outline About coordinate systems Geographic coordinate systems Projected coordinate systems Raster coordinate systems Common projection systems Choosing projections

3. Coordinate systems Figure 1. An arbitrary coordinate system used for surveying a site 250 750 0,0 250 500750 175, 200 500 Fence Building A Building B

4. Types of coordinate systems Unprojected –Based on spherical globe coordinates –Degrees of latitude and longitude Projected –Converts spherical coordinates to planar –Set of mathematical equations –Projects 3D coordinates to 2D map

5. Topo maps show three different coordinate systems: One unprojected system GCS (degrees) And two projected systems UTM (meters) State Plane (feet) Same point has different x-y values depending on the coordinate system used

6. UTM Zone 13 GCS Same point— different x-y’s State Plane

7. The Spatial Reference Every data set requires a complete description of its coordinate system for proper display and analysis –Geographic coordinate system / datum –Projection (if one is used) –Storage units used to store the x-y values (degrees, feet, etc.) –Domain, or maximum allowable x-y values –Resolution, or the x-y precision

8. Geographic coordinate systems Measuring degrees Latitude measures the angle from the horizontal. It represents north- south distance from the equator. Longitude measures around the circle of the equatorial plane. It represents east- west distance from Prime Meridian.

9. GCS properties Measured in angular degrees Length of longitude degree varies with latitude Commonly portrayed as a planar coordinate system in GIS using decimal degrees, which introduces distortion. Prime Meridian Equator -180 0 +180 -90 +90 0

10. Precision for unprojected data Unprojected data are stored in degrees –Require a high resolution for good results –Keep in mind when recording and transmitting * At the equator 1 deg ≈ 110 km* 0.001 deg ≈ 110 m 0.000001 deg ≈ 0.1 meters

11. Ellipsoids and The Geoid However, the earth is neither a perfect sphere, nor a perfect ellipsoid. It has a topographic surface defined as the change in elevation from…what? From the geoid. The geoid is a theoretical surface defined by gravity measurements. It is described as “the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest, and extended through the continents”. It is too complex and irregular to map with, so the ellipsoid is used. 50° -45° 60° But the discrepancy between the geoid and ellipsoid produces another source of error to locations.

12. The Datum 50° -45° 60° To minimize the discrepancy between the geoid and ellipsoid, a datum is defined. A datum shifts the ellipsoid relative to the geoid to achieve a best fit between the two. Best fit for North America Worse fit for South America

13. Datum definition A datum definition includes –The particular ellipsoid (major and minor axis) chosen –The adjustment or fit (translation of center) Together these define the GCS

14. Datums used in North America North American Datum 1927 (NAD 1927 or NAD27) –Based on Clarke 1866 spheroid, common until the 1980’s and still used for some data sets. North American Datum 1983 (NAD 1983 or NAD83) –Current popular datum for most mapping. GRS80 spheroid. –First choice if you must assume an unknown datum for a set of undocumented data. North American Datum 1983 HARN (NAD 1983 HARN) –Updates NAD83 with a High Accuracy Regional Network of fitted points. World Geodetic Survey 1984 (WGS84) –Geocentric datum –Seems to be default datum for many GPS units.

15. Projections and datums Every projection is based on a GCS Every GCS has a datum Every projection has a datum –Projections based on different datums will be offset from one another –Amount of offset depends on region –Typically 0 – 300 meters UTM Zone 13 NAD 1983 ≠ UTM Zone 13 NAD 1927! Roads in NAD83 Photo in NAD27

16. Datum transformations Projections are exact mathematical formulas Converting one datum to another requires specialized fitting –Not exact; errors up to several meters may occur –Errors accumulate with repeated transformations –Several methods available Some better than others for particular changes Not all methods work for all transformations Converting datums should be done only when necessary, and care should be taken in choosing the best method

17. Projected coordinate systems Projections Mathematical projection of points on the earth surface to a flat plane (paper). The earth surface is generally defined by ellipsoid and datum. Different datum surface gives slightly different results on the plane. Courtesy of ESRI, Inc.

18. Projection parameters Many different projections are supported by GIS programs. Using a projection involves choosing the projection and then setting various parameters that define it for your particular map. More Changing the parameters customizes the projection for your particular needs.

19. Central meridian The longitude which serves as the x=0 origin of the map. X values to the right of the central meridian are positive. X values to the left of the central meridian are negative.

20. Reference latitude Latitude which serves as the y = 0 origin for the map. Y values above the reference latitude are positive. Y values below the reference latitude are negative. Often the equator is used. Reference latitude

21. Coordinate units Projecting changes the x-y values from degrees to meters or feet Units in decimal degrees Units in meters -103.567,44.628 -103.678,44.653 -103.765,44.732 … 2445678,654321 2445021,650001 2444823,649200 …

22. Distortion All map projections introduce distortion Type and degree of distortion varies with map projection When using a projection, one must take care to choose one with suitable properties Area Distance Shape Direction

23. Projection distortions MercatorEquidistant Conic Distorts distance and area Preserves direction and shape Distorts direction and shape Preserves distance and ~area

24. Compromise projections Robinson Distorts all four properties a little

25. Raster coordinate systems Raster georeferencing Rows Columns X, Y location Raster data file N rows by M columns X, Y location Georeferenced to earth’s surface Two issues: 1. Location (x,y) of the upper left corner of the raster. 2. The “shape” of the features stored as pixels in the raster.

26. Georeferenced rasters A raster that already has the coordinate system information ready for use is said to be georeferenced. ArcGIS rasters and other formats such as GeoTiff come ready to use. Some rasters require work on the part of the user. Two cases generally apply. –The coordinate system information is known but the user must properly label the data set for the GIS to be able to use it. –The coordinate system information is unknown.

27. Rectification Rectification permanently transforms an image to new coordinate space. Higher order transformations have more parameters and require more control points. Saves new file

28. Projecting rasters Rasters, like vectors, can be converted from one CS to another by projecting. Cell centers are converted to the new system. Does not preserve original rectilinear spacing of the cell grid, so a new cell size must be specified. Resampling, as described for rectification, must also occur.

29. Common projection systems Geographic coordinate system –Degrees of latitude and longitude Universal Transverse Mercator –Divides world into 60 zones State Plane –Divides each state into one or more zones –Larger states have more zones

30. Geographic Coordinate Systems Primary use is for data distribution. User obtains data and then projects it into the desired coordinate system for the application. Not desirable for maps or analysis because of distortion.

31. Zone 16 Universal Transverse Mercator Based on Transverse Mercator (cylindrical) projection World divided into 60 zones 6 degrees wide Distortion is minimal within each zone Maps of different areas use best zone Best for maps covering small area in one zone

32. State Plane System States divided into one or more zones identified by a unique FIPS number A projection and parameters are established for each zone to achieve desired accuracy –Transverse Mercator, Lambert Conformal Conic, and Oblique Mercator are standard projections used Several varieties in common use –State Plane NAD 1927 uses feet –State Plane NAD 1983 uses meters –Some choose to use NAD 1983 (feet)

33. State Plane Zones East-west zones typically Lambert Conformal Conic N-S zones usually Transverse Mercator

34. Choosing projections Projections for large scale maps Local, city, county maps, smaller states –Projection systems virtually eliminate distortion –Choose appropriate UTM or State Plane zone –For best results, map should lie in a single zone

35. Projections for small scales Continents and countries Distortion is inevitable, so purpose drives the choice –Equidistant maps when distances are important –Equal area maps when areas are important –Conformal or compromise projections for general purpose maps Coordinate system names generally indicate the locale and purpose it is optimized for. Use for clues to choice.

36. Problem solutions Oregon covers two UTM zones and two State Plane zones. No single zone is best. State has defined an Oregon Statewide Lambert coordinate system. Some other states or countries have similar specialized coordinate systems.

37. Problem solutions Louisiana is less than 6 degrees wide but not centered in UTM zone. Has two State Plane zones. It has no special state projection defined that you can simply use. For the state map, use the UTM zone parameters but adjust the central meridian of the zone. Adjust to - 91.5 to center the zone on LA Center of state about -91.5°

38. Caution These solutions will give you somewhat better accuracy for your maps, but there are some considerations. –You will need to take care to convert all data to your chosen coordinate system. –GPS units will not be able to collect data directly in your coordinate system. –When using non-standard projections you must be extra careful with your metadata so that users understand the differences.

39. References Price, M. (2013). Mastering ArcGIS (6th ed.). McGraw-Hill Price, M. (2013). Mastering ArcGIS (6th ed.). McGraw-Hill. Mastering ArcGIS, 6/e Instructor Edition Chapter 11: PowerPoint Notes and Figures Instructor Edition Chapter 11: PowerPoint Notes and Figures