Map Projections Red Rocks Community College Information Sources: Autodesk World User’s Manual ArcView User’s Manual GeoMedia user’s Manual MapInfo User’s Guide GIS and Computer Cartography, C. Jones

Map Projections Map 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 Projections Map 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 Projections A projection system is like wrapping a flat sheet of paper around the earth. Data are then projected from the earth’s 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 Projections The 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 Projections All map projections distort the earth’s surface to some extent. They all stretch and compress the earth in some direction. No projection is best overall.

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

Conformal Map Projections Projections 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 regions Examples: Mercator, Lambert Conformal Conic

Conformal Map Projections The 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. Greenland’s shape is distorted.

Map Projections For 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 Projections For 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 Projections For 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? Projection AreaDistan ce Directio n ShapeWorldRegionMediu m Scale Large Scale Topo grap hy Them ai Maps Prese ntati ons Transverse Mercator YPPYY Miller Cylindrical YY Lambert Azimuthal Equal Area YPYYY Lambert Equidistant Azimuthal PPPYPY Albers Equal Area Conic PPPYPY Y = Yes P = Partly

Coordinate Transformations Coordinate 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 Transformations Digital and paper maps are available in many projections and coordinate systems. Coordinate transformations allow you to transform other people’s 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 Projections World Projections –Behrmann –Equal-Area Cylindrical –Hammer-Aitoff –Mercator –Miller Cylindrical –Mollweide –Peters –Plate Carree –Robinson Sinusoidal –The World from Space (Orthographic) Hemispheric Projections –Equidistant Azimuthal –Gnomonic –Lambert Equal-Area Azimuthal –Orthographic –Stereographic

GeoMedia Projections –Albers Equal Area –Azimuthal Equidistant –Bipolar Oblique Conic Conformal –Bonne –Cassini-Soldner –Mercator –Miller Cylindrical –Mollweide –Robinson Sinusoidal –Cydrindrical Equirectangular Gauss-Kruger Ecket IV Krovak Laborde Lambert Conformal Conic Mollweide Sinusoidal Orthographic Simple Cylindrical Transverse Mercator Rectified Skew Orthomorphic Universal Polar Stereographic Van der Grinten Gnomonic Plus Others

ArcView Projections US Projections and Coordinate Systems –Albers Equal-Area –Equidistant Conic –Lambert Conformal Conic –State Plane (1927, 1983) –UTM International coordinate systems –UTM National Grids –Great Britain –New Zealand –Malaysia and Singapore –Brunei

Spheroids and Geoids

The 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 earth’s 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 Ellipsoid The ellipsoid is an approximation of the Earth’s shape that does not account for variations caused by non-uniform density of the Earth. Examples of Ellipsoids Clarke 1866Clarke 1880 GRS80WGS60 WGS66WGS72 WGS84Danish

The Geoid A calculation of the earth’s 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 Geoid Satellite 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 Geoid The maximum discrepancy between the geoid and the WGS-84 ellipsoid is 60 meters above and 100 meters below. Because the Earth’s radius is about 6,000,000 meters (~6350 km), the maximum error is one part in 100,000.

The UTM System

Universal Transverse Mercator In 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 Zones Zone 1 Longitude Start and End 180 W to 174 W Linear UnitsMeter False Easting500,000 False Northing0 Central Meridian 177 W Latitude of OriginEquator Scale of Central Meridian

UTM Zones Zone 2 Longitude Start and End 174 W to 168 W Linear UnitMeter False Easting500,000 False Northing0 Central Meridian 171 W Latitude of OriginEquator Scale of Central Meridian0.9996

UTM Zones Zone 13 Colorado Longitude Start and End 108 W to 102 W Linear UnitMeter False Easting500,000 False Northing0 Central Meridian 105 W Latitude of OriginEquator

Geodetic Datums

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

Geodetic Datums A datum is a mathematical model Provide a smooth approximation of the Earth’s surface. Some Geodetic Datums WGS60WGS66Puerto RicoIndian 1975Potsdam South American 1956 TokyoOld Hawaiian European 1979 Bermuda 1957

Common U S Datums North American Datum 1927 North American Datum 1983 Intergraph’s GeoMedia Professional allows transformation between two coordinate systems that are based on different horizontal geodetic datums. Pg. 33.