Introduction to Coordinate Introduction to Coordinate SystemsSystems

andandWorking with Coordinate Systems Working with Coordinate Systems

in ArcGISin ArcGIS

Amanda HenleyAmanda HenleyGIS LibrarianGIS Librarian

Davis Library ReferenceDavis Library ReferenceSeptember 2006September 2006

…what to do?Orange County, NC

Today’s PresentationToday’s Presentation Introduction to Map Projections and Coordinate Introduction to Map Projections and Coordinate

SystemsSystems• Modeling the earthModeling the earth• Geographic Coordinate SystemsGeographic Coordinate Systems• DatumsDatums• Projected Coordinate SystemsProjected Coordinate Systems• Examples of common coordinate systemsExamples of common coordinate systems

Working with Coordinate Systems in ArcGISWorking with Coordinate Systems in ArcGIS• On the fly projectionsOn the fly projections• ““Geographic Coordinate System: Geographic Coordinate System:

GCS_Assumed_Geographic_1”GCS_Assumed_Geographic_1”

Additional resourcesAdditional resources

Modeling the EarthModeling the Earth The Earth is not a perfect sphereThe Earth is not a perfect sphere It is an It is an Oblate SpheroidOblate Spheroid Different Spheroids have been Different Spheroids have been

devised to model the earth- they are devised to model the earth- they are distinguished by the length of their distinguished by the length of their axes:axes:

Semi-MajorAxis

Semi-MinorAxis

Geographic Coordinate SystemsGeographic Coordinate Systems

Locations are Locations are defined on a 3-D defined on a 3-D spherical surfacespherical surface

Made up of Made up of graticules rather graticules rather than grid cellsthan grid cells

Units are in degreesUnits are in degrees

Image Source: Understanding Coordinate Systems, ESRI 2000:http://its.unc.edu/gis/arcgis/pc_documentation_83/Understanding_Map_Projections.pdf

Geographic Coordinate SystemsGeographic Coordinate Systems

Not uniform:Not uniform:• Distances and Distances and

measures are not measures are not accurateaccurate

Meridians Meridians Converge Near Converge Near PolesPoles

1° longitude:1° longitude:• @ Equator= 111 km@ Equator= 111 km• @ 60@ 60°° lat. = 55.8 km lat. = 55.8 km• @ 90@ 90°° lat. = 0km lat. = 0km

Original Image Source: www.learner.org/jnorth/tm/DistanceLatLong.html

Distance of 60° long at equatorvs.

Distance of 60° long at 40° latitude

Geographic Coordinate SystemsGeographic Coordinate Systems

Image Source: [http://support.esri.com/index.cfm?fa=knowledgebase.techarticles.articleShow&d=29129].

Use Decimal Degrees (angles), 3 digits or lessUse Decimal Degrees (angles), 3 digits or less North America:North America:

• West of the Prime Meridian, so Longitude (X) is negativeWest of the Prime Meridian, so Longitude (X) is negative• North of the Equator, so Latitude (Y) is positiveNorth of the Equator, so Latitude (Y) is positive

Converting between degrees, minutes Converting between degrees, minutes seconds and decimal degreesseconds and decimal degrees

GIS Software takes Geographic Coordinates in Decimal Degrees, GIS Software takes Geographic Coordinates in Decimal Degrees, not degrees, minutes, secondsnot degrees, minutes, seconds

Converting is easyConverting is easy

Divide each value by the number of minutes or seconds in a Divide each value by the number of minutes or seconds in a degree. degree.

ExampleExample 37 degrees 36 ' 30"37 degrees 36 ' 30" Divide 36 minutes by 60:Divide 36 minutes by 60: 36/60=.6036/60=.60

Divide 30 seconds by 3600Divide 30 seconds by 3600 30/3600=.0083330/3600=.00833

Add up the degrees to get the answerAdd up the degrees to get the answer 37 degrees + .60 + .0083 = 37.60833 DD37 degrees + .60 + .0083 = 37.60833 DD

Components of a Geographic Components of a Geographic Coordinate SystemCoordinate System

Geographic Coordinate Systems Geographic Coordinate Systems includeinclude• A DatumA Datum• An angular Unit of Measure (degrees)An angular Unit of Measure (degrees)• A Prime MeridianA Prime Meridian

Datums Described Datums Described

Links a spheroid to a location on the earthLinks a spheroid to a location on the earth Define the origin and orientation of the Define the origin and orientation of the

coordinate systems used to map the earthcoordinate systems used to map the earth

A datum is “a fixed, three-dimensional A datum is “a fixed, three-dimensional surface, an oblate spheriod, that is surface, an oblate spheriod, that is approximately the size and shape of the approximately the size and shape of the Earth. From this surface, Latitude, Longitude, Earth. From this surface, Latitude, Longitude, and Elevation are computed”and Elevation are computed”(Source Below)(Source Below)..

Source: http://www.connect.net/jbanta/FAQ.htmlhttp://www.connect.net/jbanta/FAQ.html

Datums Described, Cont.Datums Described, Cont. A spheroid is an earth model, a datum is a A spheroid is an earth model, a datum is a

practical application of the model practical application of the model (souce below).(souce below).

A spheroid model of the earth is fixed to a A spheroid model of the earth is fixed to a base pointbase point• Example: Example: • The USGS decided that the Clarke 1866 spheroid The USGS decided that the Clarke 1866 spheroid

was a good approximation for the shape of the was a good approximation for the shape of the earth within the US, so they linked it to Meade’s earth within the US, so they linked it to Meade’s Ranch Kansas.Ranch Kansas.

Thus we have NAD27Thus we have NAD27 It is wrong- as you move away from the fixed point It is wrong- as you move away from the fixed point

errors increaseerrors increase We have many datums because we keep re-measuring We have many datums because we keep re-measuring

the earth, hopefully getting closer each timethe earth, hopefully getting closer each time

Source: http://www.connect.net.jbanta/FAQ.htmlSource: http://www.connect.net.jbanta/FAQ.html

Geodetic DatumsGeodetic Datums

There are many datums There are many datums • Local:Local:

NAD 27 Datum, uses Clarke 1866 spheroidNAD 27 Datum, uses Clarke 1866 spheroid NAD 83 Datum, uses GRS 1980 spheroidNAD 83 Datum, uses GRS 1980 spheroid Used in US and Canada OnlyUsed in US and Canada Only

• GlobalGlobal WGS 84 Datum, uses WGS 1984 spheroidWGS 84 Datum, uses WGS 1984 spheroid *Very* similar to NAD 83*Very* similar to NAD 83

In addition to being in the same projection, data In addition to being in the same projection, data themes must also be in the same datum.themes must also be in the same datum.

Source: Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder [http://www.colorado.edu/geography/gcraft/notes/datum/datum_f.html]Accessed: 01/25/06

Datum Differences May Be Difficult to SeeIn this case, the boundaries are roughly 32 meters off: datum shifts are not uniform

Errors up to 1 km can result from confusing one datum for another

Datum Differences ContinuedDatum Differences Continued Latitude and Longitude are Latitude and Longitude are

measurements based on a datummeasurements based on a datum They are not absolute locationsThey are not absolute locations Latitude Longitude coordinates alone Latitude Longitude coordinates alone

are not enoughare not enough Example Davis Library:Example Davis Library: NAD83: -79.04790, 35.91097NAD83: -79.04790, 35.91097 NAD27: -79.04816, 35.91083NAD27: -79.04816, 35.91083

• (almost 29 meters away)(almost 29 meters away)

Datum Transformations Datum Transformations ArcGIS 9.1ArcGIS 9.1

NAD 1927 to NAD 1983 NAD 1927 to NAD 1983 -for areas in the 48 contiguous states-for areas in the 48 contiguous states

NameName CodeCode Area of UseArea of UseNAD_1927_To_NAD_1983_NADCONNAD_1927_To_NAD_1983_NADCON 12411241 United States (contiguous 48 states - CONUS)United States (contiguous 48 states - CONUS)

WGS 1984 to NAD 1983 WGS 1984 to NAD 1983 -for areas in the 48 contiguous states-for areas in the 48 contiguous states

NameName CodeCode Area of UseArea of UseNAD_1983_To_WGS_1984_5NAD_1983_To_WGS_1984_5 15151515 United StatesUnited States

There are five transformations to chose from, each is appropriate for different areas. 5 Supercedes There are five transformations to chose from, each is appropriate for different areas. 5 Supercedes 4.4.

Data in a Geographic Coordinate System:Data in a Geographic Coordinate System:United StatesUnited States

Data in a Geographic Coordinate System:Data in a Geographic Coordinate System: North Carolina North Carolina

Projected Coordinate SystemsProjected Coordinate Systems

Projected Coordinate Systems Projected Coordinate Systems mathematically transform the 3 mathematically transform the 3 dimensional earth so that it can be dimensional earth so that it can be modeled in 2 dimensions. modeled in 2 dimensions.

This results in distortionThis results in distortion

Different projections are used for Different projections are used for different areas and purposesdifferent areas and purposes

Different Projections Preserve Different Different Projections Preserve Different Properties of the EarthProperties of the Earth

DirectionsDirections DistancesDistances Shapes Shapes AreasAreas

If some properties are maintained, If some properties are maintained, errors in others may be exaggeratederrors in others may be exaggerated

Commonly Used Projected Commonly Used Projected Coordinate SystemsCoordinate Systems

State Plane- a coordinate system State Plane- a coordinate system that divides the United States, Puerto that divides the United States, Puerto Rico and U.S. Virgin Islands into Rico and U.S. Virgin Islands into >120 zones.>120 zones.

North Carolina State Plane Meters, North Carolina State Plane Meters, NAD83 is used by the North Carolina NAD83 is used by the North Carolina CGIACGIA

NC State Plane Feet, NAD83 is used NC State Plane Feet, NAD83 is used by most local data providers.by most local data providers.

U.S. State Plane ZonesU.S. State Plane Zones

Image Source: http://www.warnercnr.colostate.edu/class_info/nr502/lg3/datums_coordinates/spcs.html, Accessed January 27, 2006.

Georgia State Plane Meters Georgia State Plane Meters East and WestEast and West

North Carolina State PlaneNorth Carolina State PlaneMeters and FeetMeters and Feet

Commonly Used Projected Commonly Used Projected Coordinate Systems Cont.Coordinate Systems Cont.

UTM- Universal Transverse Mercator UTM- Universal Transverse Mercator divides the globe into 60 zones, each divides the globe into 60 zones, each 6° longitude.6° longitude.

Transverse Mercator is accurate for Transverse Mercator is accurate for narrow zonesnarrow zones

Often used for large scale scientific Often used for large scale scientific mappingmapping

Units are in metersUnits are in meters

UTM Zones in North CarolinaUTM Zones in North Carolina

Spatial Data for Orange County, Spatial Data for Orange County, NC in two different UTM ZonesNC in two different UTM Zones

Commonly Used Projected Commonly Used Projected Coordinate Systems Cont.Coordinate Systems Cont.

Albers Equal Area Conic:Albers Equal Area Conic:• ““Used by USGS for maps showing the Used by USGS for maps showing the

conterminous United States (48 states) or large conterminous United States (48 states) or large areas of the United States. Well suited for large areas of the United States. Well suited for large countries or other areas that are mainly east-countries or other areas that are mainly east-west in extent and that require equal-area west in extent and that require equal-area representation. Used for many thematic representation. Used for many thematic maps.”maps.”

Source: USGS http://erg.usgs.gov/isb/pubs/MapProjections/projections.html Accessed, 1/27/06.

Albers Equal Area ConicAlbers Equal Area Conic

Data in Albers Equal Area Conic and Data in Albers Equal Area Conic and Geographic Coordinate SystemGeographic Coordinate System

Working With Coordinate Systems Working With Coordinate Systems in ArcGISin ArcGIS

• On the Fly ProjectionOn the Fly Projection• ““Geographic Coordinate System: Geographic Coordinate System:

GCS_Assumed_Geographic_1”GCS_Assumed_Geographic_1”• DemonstrationsDemonstrations

Defining a Layer’s Coordinate System Using Defining a Layer’s Coordinate System Using ArcCatalogArcCatalog

Defining a Layer’s Coordinate System Using Defining a Layer’s Coordinate System Using ArcToolboxArcToolbox

Projecting a layer in ArcToolboxProjecting a layer in ArcToolbox Projecting a layer in ArcMapProjecting a layer in ArcMap