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
°
-180
°
180
°
WEST -90
°
North
Pole
Prime
Meridian
0
°
90
°
EAST
Polar View

Longitude: 180
°
W to 180
°
E
180
°
W 180
°
E
WEST 90
°
W
Pole
Prime
Meridian
0
°
90
°
E EAST
Polar View

Longitude: 0
° to 360
°
180
°
270
°
Pole
Prime
Meridian
360
°
0
°
90
° EAST
Polar View

Latitude: 90
° to -90
°
90
°
~40
°
N
0
°
Equator
-90
°
Equatorial View

Latitude: 90
°
N to 90
°
S
90
°
0
°
Equator
-90
°
Equatorial View

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 Degrees
Location Longitude
Wagar 231 -105.082
°
New Belgium -105.069
°
Paris
2.2945
°
South Pole ?
Bird's Nest
(China)
116.391
°
Latitude
40.5750
°
40.5930
°
48.8582
°
-90
°
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
Cogito Ergo
Sum
Y
North
X
East

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

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

Mercator Distortion

Projections
• There are hundreds of projections
• 98% of the time you will be using:
– Geographic (Un-Projected)
– Universal Trans-Mercator (UTM)
– State Plane

Global UTM Zones

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)
84
°
N Latitude
500,000 meters
X
Y
500,000 Easting (X)
4,000,000 Northing (Y)
Equator

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!

Global UTM Zones

US UTM Zones

State Plane

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

GoogleMaps
• Uses Mercator Projection

How to Determine Projection
• Enter “GoogleMaps Projection” into
Google

GoogleEarth

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

Earth is an oblate Spheroid

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
Albers Equal Area Conic
Universal Transverse
Mercator
State Plane Coordinate
System
Area/Location/Extent contiguous US state governments county and city governments
Cylindrical projection
Conical Projection low latitude areas 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

GeoReferencing: Unprojected

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

GeoReferencing: Geographic

GeoReferencing: Projected

Projecting
• ArcMap: Toolbox
– Accessible from ArcMap or :
• Data Management Tools ->
• Projections and Transforms ->
• Feature ->
• Project
– Select a “Geographic Transformation” if needed

Projecting

Spatial Reference

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]]