Map Projections Red Rocks Community College Information Sources

Map Projections Red Rocks Community College Information Sources: Autodesk World User’s Manual Arc. View User’s Manual Geo. Media user’s Manual Map. Info 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 threedimensional, 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 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 Transverse Mercator Area Distan ce Directio n Y Shape World P P Miller Cylindrical Lambert Azimuthal Equal Area Y P Region Mediu m Scale Large Scale Y Y = Yes P = Partly Topo grap hy Them ai Maps Prese ntatio ns Y Y Y Lambert Equidistant Azimuthal P P P Y Albers Equal Area Conic P P P Y Y

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

Arc. View 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

Geo. Media 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

Arc. View 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

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 1866 Clarke 1880 GRS 80 WGS 66 WGS 72 WGS 84 Danish

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 meters (~6350 km), the maximum error is one part in 100, 000.

The UTM System

Universal Transverse Mercator • In the 1940 s, 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 Linear Units False Easting False Northing Central Meridian Latitude of Origin Scale of Central Meridian 180 W to 174 W Meter 500, 000 0 177 W Equator 0. 9996

UTM Zones • Zone 2 Longitude Start and End Linear Unit False Easting False Northing Central Meridian Latitude of Origin Scale of Central Meridian 174 W to 168 W Meter 500, 000 0 171 W Equator 0. 9996

UTM Zones • Zone 13 Colorado Longitude Start and End Linear Unit False Easting False Northing Central Meridian Latitude of Origin 108 W to 102 W Meter 500, 000 0 105 W Equator

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 WGS 60 WGS 66 Puerto Rico Indian 1975 Potsdam South American 1956 Tokyo Old Hawaiian European 1979 Bermuda 1957

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