Map ProjectionsRed Rocks Community CollegeInformation Sources: Autodesk World Users ManualArcView Users ManualGeoMedia users ManualMapInfo Users GuideGIS and Computer Cartography, C. Jones

Map ProjectionsMap projections refer to the techniques cartographers and mathematicians have created to depict all or part of a three-dimensional, roughly spherical surface on two-dimensional, flat surfaces with minimal distortion.

Map ProjectionsMap projections are representations of a curved earth on a flat map surface. A map projection defines the units and characteristics of a coordinate system.The three basic types of map projections are azimuthal, conical, and cylindrical.

Map ProjectionsA projection system is like wrapping a flat sheet of paper around the earth.Data are then projected from the earths surface to the paper.Select a map projection based on the size area that you need to show.Base your selection on the shape of the area.

Mercator ProjectionsThe Mercator projection is the only projection in which a straight line represents a true direction, On Mercator maps, distances and areas are greatly distorted near the poles.Continents are greatly distorted

Map ProjectionsAll map projections distort the earths surface to some extent. They all stretch and compress the earth in some direction. No projection is best overall.

Equal Area ProjectionsProjections that preserve area are called equivalent or equal area.Equal area projections are good for small scale maps (large areas)Examples: Mollweide and GoodeEqual-area projections distort the shape of objects

Conformal Map ProjectionsProjections that maintain local angles are called conformal. Conformal maps preserve angles Conformal maps show small features accurately but distort the shapes and areas of large regionsExamples: Mercator, Lambert Conformal Conic

Conformal Map ProjectionsThe area of Greenland is approximately 1/8 that of South America. However on a Mercator map, Greenland and South America appear to have the same area.Greenlands shape is distorted.

Map ProjectionsFor a tall area, extended in north-south direction, such as Idaho, you want longitude lines to show the least distortion.

You may want to use a coordinate system based on the Transverse Mercator projection.

Map ProjectionsFor wide areas, extending in the east-west direction, such as Montana, you want latitude lines to show the least distortion.

Use a coordinate system based on the Lambert Conformal Conic projection.

Map ProjectionsFor a large area that includes both hemispheres, such as North and South America, choose a projection like Mercator.

For an area that is circular, use a normal planar (azimuthal) projection

When to use a Projection?Y = YesP = Partly

Coordinate TransformationsCoordinate transformation allows users to manipulate the coordinate system using mathematical projections, adjustments, transformations and conversions built into the GIS. Because the Earth is curved, map data are always drawn in a way in which data are projected from a curved surface onto a flat surface.

Coordinate TransformationsDigital and paper maps are available in many projections and coordinate systems.Coordinate transformations allow you to transform other peoples data into the coordinate system you want.Generally transformation is required when existing data are in different coordinate systems or projections. It is important to include the map projection and coordinate system in your metadata documents.

You cannot destroy or damage data by transforming it to another projection or datum.

GIS Software Projections

ArcView ProjectionsWorld ProjectionsBehrmannEqual-Area CylindricalHammer-AitoffMercatorMiller CylindricalMollweidePetersPlate CarreeRobinson SinusoidalThe World from Space (Orthographic)Hemispheric ProjectionsEquidistant Azimuthal GnomonicLambert Equal-Area AzimuthalOrthographicStereographic

GeoMedia ProjectionsAlbers Equal AreaAzimuthal EquidistantBipolar Oblique Conic ConformalBonneCassini-SoldnerMercatorMiller CylindricalMollweideRobinson SinusoidalCydrindrical Equirectangular

Gauss-KrugerEcket IVKrovakLabordeLambert Conformal ConicMollweideSinusoidalOrthographicSimple CylindricalTransverse MercatorRectified Skew OrthomorphicUniversal Polar StereographicVan der GrintenGnomonicPlus Others

ArcView ProjectionsUS Projections and Coordinate SystemsAlbers Equal-AreaEquidistant ConicLambert Conformal ConicState Plane (1927, 1983)UTMInternational coordinate systemsUTMNational GridsGreat BritainNew ZealandMalaysia and SingaporeBrunei

Spheroids and Geoids

Spheroids and GeoidsThe rotation of the earth generates a centrifugal force that causes the surface of the oceans to protrude more at the equator than at the poles.This causes the shape of the earth to be an ellipsoid or a spheroid, and not a sphere.The nonuniformity of the earths shape is described by the term geoid. The geoid is essentially an ellipsoid with a highly irregular surface; a geoid resembles a potato or pear.

The EllipsoidThe ellipsoid is an approximation of the Earths shape that does not account for variations caused by non-uniform density of the Earth.Examples of Ellipsoids

The GeoidA calculation of the earths size and shape differ from one location to another.For each continent, internationally accepted ellipsoids exist, such as Clarke 1866 for the United States and the Kravinsky ellipsoid for the former Soviet Union.

The GeoidSatellite measurements have led to the use of geodetic datums WGS-84 (World Geodetic System) and GRS-1980 (Geodetic Reference System) as the best ellipsoids for the entire geoid.

The GeoidThe maximum discrepancy between the geoid and the WGS-84 ellipsoid is 60 meters above and 100 meters below.Because the Earths radius is about 6,000,000 meters (~6350 km), the maximum error is one part in 100,000.

The UTM System

Universal Transverse MercatorIn the 1940s, the US Army developed the Universal Transverse Mercator System, a series of 120 zones (coordinate systems) to cover the whole world.The system is based on the Transverse Mercator Projection. Each zone is six degrees wide. Sixty zones cover the Northern Hemisphere, and each zone has a projection distortion of less than one part in 3000.

UTM ZonesZone 1

Longitude Start and End 180 W to 174 WLinear UnitsMeterFalse Easting500,000False Northing0Central Meridian 177 WLatitude of OriginEquatorScale of Central Meridian 0.9996

UTM ZonesZone 2

Longitude Start and End 174 W to 168 WLinear UnitMeterFalse Easting500,000False Northing0Central Meridian 171 WLatitude of OriginEquatorScale of Central Meridian0.9996

UTM ZonesZone 13 Colorado

Longitude Start and End 108 W to 102 WLinear UnitMeterFalse Easting500,000False Northing0Central Meridian 105 WLatitude of OriginEquator

Geodetic Datums

Geodetic DatumDefined by the reference ellipsoid to which the geographic coordinate system is linkedThe degree of flattening f (or ellipticity, ablateness, or compression, or squashedness) f = (a - b)/af = 1/294 to 1/300

Geodetic DatumsA datum is a mathematical modelProvide a smooth approximation of the Earths surface.

Some Geodetic Datums

Common U S DatumsNorth American Datum 1927North American Datum 1983

Intergraphs GeoMedia Professional allows transformation between two coordinate systems that are based on different horizontal geodetic datums. Pg. 33.