Map Projections and Coordinate Systems Gerry Daumiller Montana State Library Natural Resource Information System.

Map Projections and Coordinate Map Projections and Coordinate SystemsSystems

Map Projections and Coordinate Map Projections and Coordinate SystemsSystems

Gerry DaumillerGerry Daumiller

Montana State LibraryMontana State LibraryNatural ResourceNatural Resource

Information SystemInformation System

Map ProjectionsMap ProjectionsMap ProjectionsMap ProjectionsWhy are they important?Why are they important?

An important thing to remember about map An important thing to remember about map projections is that you can not generally projections is that you can not generally measure distances and areas accurately measure distances and areas accurately from projected data. The next slides show from projected data. The next slides show some examples of this.some examples of this.

Robinson Projection -- 16,930 MilesRobinson Projection -- 16,930 Miles

Length of the Arctic Coastline of RussiaLength of the Arctic Coastline of RussiaLength of the Arctic Coastline of RussiaLength of the Arctic Coastline of RussiaOblique Mercator Projection -- Oblique Mercator Projection --

10,473 Miles10,473 Miles

Mercator Projection -- Mercator Projection -- 31,216 Miles31,216 Miles

Length Distortion on World MapsLength Distortion on World MapsLength Distortion on World MapsLength Distortion on World Maps

Mercator ProjectionMercator Projection

Lower 48 States -- 52,362,000 Sq Miles

Columbia -- 4,471,000 Sq Miles

Mollweide Projection Mollweide Projection (equal-area)(equal-area)

Lower 48 States -- 30,730,000 Sq Miles

Columbia -- 4,456,000 Sq Miles

Area Distortion on World MapsArea Distortion on World MapsArea Distortion on World MapsArea Distortion on World Maps

Albers Equal Area Projection -- 2564.3 Miles

Oblique Mercator Projection -- 2583.9 Miles

Difference = 19.6 MilesOne part in 132

0.76 Percent

Linear Distortion on National MapsLinear Distortion on National MapsLinear Distortion on National MapsLinear Distortion on National Maps

Lambert Conformal Projection -- 147,657 Square Miles

Albers Equal Area Projection -- 148,993 Square Miles

Difference = 1336 Square MilesOne part in 111

0.90 Percent

Area Distortion on National MapsArea Distortion on National MapsArea Distortion on National MapsArea Distortion on National Maps

Montana State Plane Coordinates – 39,189.6 feet

Oblique Mercator Projection – 38,212.1 feet

Difference = 27.5 feet One part in 1742 0.0574 Percent

Linear Distortion on Local MapsLinear Distortion on Local MapsLinear Distortion on Local MapsLinear Distortion on Local Maps

Montana State Plane Coordinates -- 122,314.3 Acres

Albers Equal Area Projection -- 122,425.2 Acres

Difference = 110.9 Acres One part in 1104 0.091 Percent

Area Distortion on Local MapsArea Distortion on Local MapsArea Distortion on Local MapsArea Distortion on Local Maps

Coordinate Systems vs.Coordinate Systems vs.Map ProjectionsMap Projections

Coordinate Systems vs.Coordinate Systems vs.Map ProjectionsMap Projections

• A map projection is a method or a type of equation A map projection is a method or a type of equation used to transform three-dimensional coordinates used to transform three-dimensional coordinates on the earth to two-dimensional coordinates on on the earth to two-dimensional coordinates on the map.the map.

• A coordinate system usually includes the A coordinate system usually includes the specification of a map projection, plus the three specification of a map projection, plus the three dimensional model of the Earth to be used, the dimensional model of the Earth to be used, the distance units to be used on the map, and distance units to be used on the map, and information about the relative positions of the two information about the relative positions of the two dimensional map and the model of the Earth.dimensional map and the model of the Earth.

Latitude-LongitudeLatitude-LongitudeLatitude-LongitudeLatitude-Longitude

Latitude-LongitudeLatitude-LongitudeLatitude-LongitudeLatitude-Longitude

• Not uniform units of measureNot uniform units of measure

• Meridians converge at the PolesMeridians converge at the Poles

1° longitude 1° longitude at Equator = 111 kmat Equator = 111 km at 60° lat. = 55.8 kmat 60° lat. = 55.8 km at 90° lat. = 0 kmat 90° lat. = 0 km

1° latitude 1° latitude at Equator = 111 kmat Equator = 111 km at 90° lat. = 112 kmat 90° lat. = 112 km

Projected CoordinatesProjected CoordinatesProjected CoordinatesProjected CoordinatesGeographic CoordinatesGeographic CoordinatesGeographic CoordinatesGeographic Coordinates

Using Geographic Coordinates as Plane CoordinatesUsing Geographic Coordinates as Plane CoordinatesUsing Geographic Coordinates as Plane CoordinatesUsing Geographic Coordinates as Plane Coordinates

SpheroidsSpheroidsSpheroidsSpheroids

• Set of parameters that represent a model of Set of parameters that represent a model of the earth’s size and shapethe earth’s size and shape

• Based on an ellipse with 2 radiiBased on an ellipse with 2 radii– Semimajor axis (longer) and the semiminor (shorter)Semimajor axis (longer) and the semiminor (shorter)

SpheroidsSpheroidsSpheroidsSpheroids

• The Earth is not a perfect The Earth is not a perfect spheroid. Different spheroids are spheroid. Different spheroids are used in different parts of the world used in different parts of the world to create the best possible model to create the best possible model of the Earth’s curvature in each of the Earth’s curvature in each location.location.

SpheroidsSpheroidsSpheroidsSpheroids

DatumsDatumsDatumsDatums

• A Datum is a spheroid, plus the A Datum is a spheroid, plus the definition of the relationship definition of the relationship between the Earth and the between the Earth and the coordinates on the spheroid.coordinates on the spheroid.

DatumsDatumsDatumsDatums

• There are four datums commonly There are four datums commonly used in Montana: NAD27, WGS84, used in Montana: NAD27, WGS84, NAD83, and NAD83 HARN. The NAD83, and NAD83 HARN. The latitude and longitude of a point on latitude and longitude of a point on the ground is different in each the ground is different in each datum.datum.

DatumsDatumsDatumsDatums• Difference (meters) between NAD27 and NAD83Difference (meters) between NAD27 and NAD83

DatumsDatumsDatumsDatums• Difference (meters) between NAD83 and NAD83 HARNDifference (meters) between NAD83 and NAD83 HARN

Projected Coordinate Projected Coordinate SystemsSystems

Projected Coordinate Projected Coordinate SystemsSystems

• Define locations on a 2-D surfaceDefine locations on a 2-D surface

• Traditional planar coordinatesTraditional planar coordinates

• Can allow easy measurement, Can allow easy measurement, calculation, and/or visual calculation, and/or visual interpretation of distances and interpretation of distances and areasareas

Visualize a light shining through Visualize a light shining through the Earth onto a surfacethe Earth onto a surface

Visualize a light shining through Visualize a light shining through the Earth onto a surfacethe Earth onto a surface

ESRI

Mercator ProjectionMercator ProjectionMercator ProjectionMercator Projection

Miller ProjectionMiller ProjectionMiller ProjectionMiller Projection

Cylindrical Equal-Area ProjectionCylindrical Equal-Area ProjectionCylindrical Equal-Area ProjectionCylindrical Equal-Area Projection

Mollweide Projection Mollweide Projection (equal-area,(equal-area,

psuedo-cylindrical) psuedo-cylindrical)

Mollweide Projection Mollweide Projection (equal-area,(equal-area,

psuedo-cylindrical) psuedo-cylindrical)

Perspective ProjectionPerspective ProjectionPerspective ProjectionPerspective Projection

Stereographic ProjectionStereographic ProjectionStereographic ProjectionStereographic Projection

Conic ProjectionsConic ProjectionsConic ProjectionsConic Projections

Lambert ConformalLambert ConformalLambert ConformalLambert Conformal Albers Equal AreaAlbers Equal AreaAlbers Equal AreaAlbers Equal Area

Conic ProjectionsConic ProjectionsConic ProjectionsConic Projections

Standardized Coordinate SystemsStandardized Coordinate SystemsStandardized Coordinate SystemsStandardized Coordinate Systems

There are an infinite number of coordinate systems possible, whichThere are an infinite number of coordinate systems possible, whichcan be created by choosing a projection and then tailoring itscan be created by choosing a projection and then tailoring itsparameters to fit any region on the globe.parameters to fit any region on the globe.

Standardized coordinate systems have been developed to simplifyStandardized coordinate systems have been developed to simplifythe process of choosing a system. The two most commonthe process of choosing a system. The two most commonstandard systems used in the United States are the State Planestandard systems used in the United States are the State PlaneCoordinate system and the Universal Transverse Mercator system.Coordinate system and the Universal Transverse Mercator system.

SPCS NAD27 & NAD83 Zones for the SPCS NAD27 & NAD83 Zones for the NorthwestNorthwest

SPCS NAD27 & NAD83 Zones for the SPCS NAD27 & NAD83 Zones for the NorthwestNorthwest

ESRI

UTMUTMUTMUTM

To find the true distance between two points: To find the true distance between two points: http://www.ngs.noaa.gov/cgi-bin/Inv_Fwd/inverse.prlhttp://www.ngs.noaa.gov/cgi-bin/Inv_Fwd/inverse.prl

Choosing a Projection:Choosing a Projection: Checking Accuracy Checking Accuracy

Choosing a Projection:Choosing a Projection: Checking Accuracy Checking Accuracy

To find the true area of polygons, project them to an To find the true area of polygons, project them to an equal-area projection and recalculate their areas.equal-area projection and recalculate their areas.

Accuracy of Projections – State Plane Single ZoneAccuracy of Projections – State Plane Single ZoneAccuracy of Projections – State Plane Single ZoneAccuracy of Projections – State Plane Single Zone

Accuracy of Projections – State Plane North ZoneAccuracy of Projections – State Plane North ZoneAccuracy of Projections – State Plane North ZoneAccuracy of Projections – State Plane North Zone

Accuracy of Projections – State Plane Central ZoneAccuracy of Projections – State Plane Central ZoneAccuracy of Projections – State Plane Central ZoneAccuracy of Projections – State Plane Central Zone

Accuracy of Projections – UTM Zone 12Accuracy of Projections – UTM Zone 12Accuracy of Projections – UTM Zone 12Accuracy of Projections – UTM Zone 12

Accuracy of Projections – Albers Equal AreaAccuracy of Projections – Albers Equal AreaAccuracy of Projections – Albers Equal AreaAccuracy of Projections – Albers Equal Area

Accuracy of Projections – Albers Equal AreaAccuracy of Projections – Albers Equal AreaAccuracy of Projections – Albers Equal AreaAccuracy of Projections – Albers Equal Area

Accuracy of Projections -- StatisticsAccuracy of Projections -- StatisticsAccuracy of Projections -- StatisticsAccuracy of Projections -- Statistics

Maximum error in Montana for each coordinate system:Maximum error in Montana for each coordinate system:

LENGTHLENGTH AREAAREAPercentPercent Ratio Ratio PercentPercent Ratio Ratio

UTM Zone 12UTM Zone 12 0.3340.334 299 299 0.5540.554 180 180State Plane 1983State Plane 1983 0.0750.075 1333 1333 0.1140.114 877 877State Plane NorthState Plane North 0.2690.269 372 372 0.4200.420 238 238 (within zone)(within zone) 0.0080.008 1250012500 0.0130.013 7962 7962State Plane CentralState Plane Central 0.1420.142 704 704 0.1980.198 505 505 (within zone)(within zone) 0.0080.008 1250012500 0.0390.039 2564 2564State Plane SouthState Plane South 0.1670.167 599 599 0.2360.236 424 424 (within zone)(within zone) 0.0130.013 7692 7692 0.0210.021 4761 4761

Projections and True NorthProjections and True NorthProjections and True NorthProjections and True North

http://nris.mt.gov/gis/gerry/true_north.txt