coordinate reference systems jim graham & alex daniels colorado state university warner college...
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Coordinate Reference Systems
Jim Graham & Alex Daniels
Colorado State University
Warner College of Natural Resources
Coordinate Reference Systems
• Coordinate System– Cartesian or Rectangular– Spherical
• Projection– Geographic or Un-projected– UTM– State Plane
• Datum– Can contain a Spheroid
Geographic Coordinate Systems• Spherical coordinate system
• Units are in degrees
Spherical Coordinates• Longitude:
Degrees East or West from the prime meridian
• Latitude: Degrees North or South from the Equator
Longitude: -180° to 180°
Polar View
0°
NorthPole
Prime Meridian
90°
180°-180°
-90°WEST EAST
Longitude: 180° W to 180° E
Polar View
0°
Pole
Prime Meridian
90° E
180° E180° W
90° WWEST EAST
Longitude: 0° to 360°
Polar View
0°
Pole
Prime Meridian
90°
180°
270°
360°
EAST
Latitude: 90° to -90°
Equatorial View
-90°
Equator 0°
90°
~40°N
Latitude: 90° N to 90° S
Equatorial View
-90°
Equator 0°
90°
Degrees, Minutes, Seconds (DMS)• Each degree contains 60 minutes
• Each minute contains 60 seconds
• 40° 31’ 21” North by 105° 5’ 39” West
• 40 31 21 N, 105 5 39 W
• 403121N, 1050539W
See the GNIS web site for coordinates of locations in the US
Geographic Accuracy in DMS
• The earth is about 40,000 km around
• 40,000 / 360 degrees ~ – 111 km/degree
• 111 km/degree / 60 minute/degree ~– 1.85 km/minute
• 1.85 km/degree / 60 seconds/minute ~ 0.03 km/second or 30 meters/second
• To maintain 1 meter accuracy we need to keep 2 digits after the seconds decimal!
Decimal DegreesLatitudeLongitudeLocation
Wagar 231 -105.082° 40.5750°
New Belgium -105.069° 40.5930°
Paris
South Pole
2.2945° 48.8582°
? -90°
Bird's Nest (China) 116.391° 39.9915°
Decimal Degrees
• The earth is about 40,000 km around
• 40,000 / 360 degrees ~– 111 km/degree or 111,111 meters/degree
• To keep 1 meter accuracy we need to keep 6 or more digits after the decimal!
Finding Coordinates
• Go to: http://geonames.usgs.gov/
• Search for a name
• What format are the coordinates in?
• What is the accuracy of the data?
Converting Decimal Degrees to DMS and back again• Start with our Latitude: 40.5852778° N
– We know already there are 40 whole degrees
• Next we calculate the minutes – 60 minutes/degree so...– .5852778° x 60 min/degree = 35.116668 min
• Last we calculate the seconds– 60 seconds/minute so...– .116668 min x 60 sec/min = 7.00 seconds
• ~ 40° 35' 7” North Latitude
Projected Coordinate Systems
• Use projection to display 3 dimensional locations on to a surface in 2D
• Uses Cartesian coordinates (rectangular)
Cartesian Coordinates(Rectangular)
• X,Y
• Easting, Northing
• Miles, Meters, Feet, Nautical Miles
YNorth
XEast
Cogito Ergo Sum
Projections
• A projection is made by:– Taking a 3 dimensional world and
representing it in 2 dimensions.
http://welcome.warnercnr.colostate.edu/class_info/nr502/lg1/lg1_master.html
Projections
• Different orientations, different projections
http://welcome.warnercnr.colostate.edu/class_info/nr502/lg1/lg1_master.html
Projections and Distortion
• Where the 2D surface touches the earth model there is no distortion
• Point of Tangency ~
• Line of Tangency ~
http://welcome.warnercnr.colostate.edu/class_info/nr502/lg1/lg1_master.html
Projections
• There are hundreds of projections
• 98% of the time you will be using:– Geographic (Un-Projected)– Universal Trans-Mercator (UTM)– State Plane
UTM Coordinate Systems
• Universal Trans-Mercator Projection– Line of tangency runs north south
• Broken up into 120 Zones (60North/60South)
• Each zone has its own UTM projection with line of tangency running up the middle
• Minimizes distortion in each zone
• Units are in meters
UTM Zones (Northern Hemisphere)
X
Y
500,000 meters
Equator
500,000 Easting (X)4,000,000 Northing (Y)
84° N Latitude
Be careful!
• Don’t use “N” for “North” and “S” for “South”. In UTM the “N” region is in the south and the “S” region is in the north!
• Use “North” and “South”
• Yes, ESRI uses “13N” for our region!
State Plane
• Each state has one or more zones
• Each zone has its own axes and origin– May be based on different projections
• Zones usually by county boundaries
• Units are in feet
Reference System Standards
• European Petrolum Standards Group– EPSG
• Well Known Text Form (WKT)
• Arc PRJ files
• Proj 4
How to Determine Projection
• Enter “GoogleMaps Projection” into Google
What is a datum?
• According to the textbooks:• "A geodetic datum is any numerical or geometrical
quantity or set of such quantities that serves as a reference or base for other quantities." (James R. Smith, 1997, Introduction to Geodesy, page 83)
• Essentially a datum is a reference
Datum
• Shape of the earth• Minor/Major Axis• Spheroid Based• Local Survey (Grid)• North American Datum 1927 (NAD 27)• North American Datum 1983 (NAD 83)• World Geodetic System 1984 (WGS 84)• High Accuracy Reference Network (HARN)
http://www.ngs.noaa.gov/faq.shtml#WGS84
Datums
• There are hundreds of Datums
• If you only work in the US, 98% of the time you will be using:– NAD 27– NAD 83– WGS 84– HARN
Projections
• Area preserving projections– UTM, Lambert Cylindrical Equal-Area
• Equidistant projections– UTM, Geographic for North-South
• Conformal preserves local shapes– UTM, Lambert Conformal conic
Appropriate Projections
Projection to Use Area/Location/Extent
Albers Equal Area Conic contiguous US
Universal Transverse Mercator state governments
State Plane Coordinate System
county and city governments
Cylindrical projection low latitude areas
Conical Projection mid-latitude areas
Planar/Azimuthal Projection polar regions
Conical Projection broad east-west area
Cylindrical projection broad north-south area
ArcLand Definitions• Spatial Reference = Coordinate
Reference System (CRS)• Horizontal Coordinate System
– Geographic Coordinate System• Always Latitude/Longitude
– Projected Coordinate System• UTM• State Plane• Etc.
• Bottom line: ESRI confuses, CRS, Spatial Reference, Coordinate System, and Projection
Determining Spatial Reference• “prj” files
– If missing, the data is not spatially referenced
– If exists look inside (scary!)
• ArcCatalog– Navigate to the dataset– Check the “Spatial” tab
• ArcMap– Right click on the layer: Properties ->
Source
Defining Spatial Reference• Must be based on pre-existing
knowledge (i.e. don’t guess)
• To determine: – Check metadata, – Talk to original creator– Check against known CRS (last resort)
• To define:– ArcToolBox:
• Data Management Tools -> • Projections and Transforms -> • Define Projection
Projecting
• ArcMap: Toolbox– Accessible from ArcMap or :
• Data Management Tools -> • Projections and Transforms -> • Feature ->• Project
– Select a “Geographic Transformation” if needed
Really Important:• All spatial data is in a reference system
• NOT ALL DATA HAS A DEFINED REFERENCE SYSTEM!– To keep from ending up with major problems
you need to make sure all your data has a DEFINED REFERENCE SYSTEM
• To check: ArcMap: Properties -> Source• To define: Toolbox: Data Management Tools ->
Projections and Transformations -> Define Projection
• To change: Toolbox: Data Management Tools -> Projections and Transformations ->
GIS Definitions• Geo-referencing:
– Defining the position of something on the earth. Must include coordinates, projection, datum.
• Projection: – How geographic data is translated to be on a plane
• Datum:– How coordinates are referenced (shape of the
earth)
• Coordinate System:– How points are interpreted (i.e. rectangular,
spherical)
• Coordinate Reference System (CRS): – A specific projection and datum
PRJ file
• GEOGCS["GCS_WGS_1984",– DATUM["D_WGS_1984",
• SPHEROID["WGS_1984",– 6378137.0,298.257223563]],
– PRIMEM["Greenwich",0.0],– UNIT["Degree",0.0174532925199433]]
PRJ File 2
• PROJCS["WGS_1984_UTM_Zone_13N"– GEOGCS["GCS_WGS_1984”…
• PROJECTION["Transverse_Mercator"],
• PARAMETER["False_Easting",500000],
• PARAMETER["False_Northing",0],
• PARAMETER["Central_Meridian",-105],
• PARAMETER["Scale_Factor",0.9996],
• PARAMETER["Latitude_Of_Origin",0],
• UNIT["Meter",1]]