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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