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

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

Robinson Projection -- 16,930 Miles Length of the Arctic Coastline of Russia Oblique Mercator Projection -- 10,473 Miles Mercator Projection -- 31,216 Miles Length Distortion on World Maps

Mercator Projection Lower 48 States -- 52,362,000 Sq Miles Columbia -- 4,471,000 Sq Miles Mollweide Projection (equal-area) Lower 48 States -- 30,730,000 Sq Miles Columbia -- 4,456,000 Sq Miles Area Distortion on World Maps

Albers Equal Area Projection Miles Oblique Mercator Projection Miles Difference = 19.6 Miles One part in Percent Linear Distortion on National Maps

Lambert Conformal Projection ,657 Square Miles Albers Equal Area Projection ,993 Square Miles Difference = 1336 Square Miles One part in Percent Area 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 Percent Linear Distortion on Local Maps

Montana State Plane Coordinates ,314.3 Acres Albers Equal Area Projection ,425.2 Acres Difference = Acres One part in Percent Area Distortion on Local Maps

Coordinate Systems vs. Map Projections A map projection is a method or a type of equation used to transform three-dimensional coordinates on the earth to two-dimensional coordinates on the map.A map projection is a method or a type of equation used to transform three-dimensional coordinates on the earth to two-dimensional coordinates on the map. A coordinate system usually includes the specification of a map projection, plus the three dimensional model of the Earth to be used, the distance units to be used on the map, and information about the relative positions of the two dimensional map and the model of the Earth.A coordinate system usually includes the specification of a map projection, plus the three dimensional model of the Earth to be used, the distance units to be used on the map, and information about the relative positions of the two dimensional map and the model of the Earth.

Latitude-LongitudeLatitude-Longitude

Latitude-LongitudeLatitude-Longitude Not uniform units of measureNot uniform units of measure Meridians converge at the PolesMeridians converge at the Poles 1° longitude at Equator = 111 km at Equator = 111 km at 60° lat. = 55.8 km at 60° lat. = 55.8 km at 90° lat. = 0 km at 90° lat. = 0 km 1° latitude at Equator = 111 km at Equator = 111 km at 90° lat. = 112 km at 90° lat. = 112 km

Projected Coordinates Geographic Coordinates Using Geographic Coordinates as Plane Coordinates

SpheroidsSpheroids Set of parameters that represent a model of the earth’s size and shapeSet of parameters that represent a model of the 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)

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

SpheroidsSpheroids

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

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

DatumsDatums Difference (meters) between NAD27 and NAD83Difference (meters) between NAD27 and NAD83

DatumsDatums Difference (meters) between NAD83 and NAD83 HARNDifference (meters) between NAD83 and NAD83 HARN

Projected Coordinate Systems Define locations on a 2-D surfaceDefine locations on a 2-D surface Traditional planar coordinatesTraditional planar coordinates Can allow easy measurement, calculation, and/or visual interpretation of distances and areasCan allow easy measurement, calculation, and/or visual interpretation of distances and areas

Visualize a light shining through the Earth onto a surface ESRI

Mercator Projection

Miller Projection

Cylindrical Equal-Area Projection Mollweide Projection (equal-area, psuedo-cylindrical)

Perspective Projection

Stereographic Projection

Conic Projections

Lambert Conformal Albers Equal Area Conic Projections

Standardized Coordinate Systems There are an infinite number of coordinate systems possible, which can be created by choosing a projection and then tailoring its parameters to fit any region on the globe. Standardized coordinate systems have been developed to simplify the process of choosing a system. The two most common standard systems used in the United States are the State Plane Coordinate system and the Universal Transverse Mercator system.

SPCS NAD27 & NAD83 Zones for the Northwest ESRI

UTMUTM

To find the true distance between two points: Choosing a Projection: Checking Accuracy To find the true area of polygons, project them to an equal-area projection and recalculate their areas.

Accuracy of Projections – State Plane Single Zone

Accuracy of Projections – State Plane North Zone

Accuracy of Projections – State Plane Central Zone

Accuracy of Projections – UTM Zone 12

Accuracy of Projections – Albers Equal Area

Accuracy of Projections -- Statistics Maximum error in Montana for each coordinate system: LENGTHAREA Percent RatioPercent Ratio UTM Zone State Plane State Plane North (within zone) (within zone) State Plane Central (within zone) (within zone) State Plane South (within zone) (within zone)

Projections and True North