Map Projections Red Rocks Community College Information Sources: Autodesk World User’s Manual ArcView User’s Manual GeoMedia user’s Manual MapInfo User’s.

Map ProjectionsRed 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 Area Distan

ceDirection

Shape World Region Medium Scale

Large Scale

Topography

Themai Maps

Presentations

Transverse Mercator

Y P P Y Y

Miller Cylindrical

Y Y

Lambert Azimuthal Equal Area

Y P Y Y Y

Lambert Equidistant Azimuthal

P P P Y P Y

Albers Equal Area Conic

P P P Y P Y

Y = YesP = 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

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 EllipsoidsClarke 1866 Clarke 1880

GRS80 WGS60

WGS66 WGS72

WGS84 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 6,000,000 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 WLinear Units MeterFalse Easting 500,000False Northing 0Central Meridian 177 WLatitude of Origin EquatorScale of Central Meridian 0.9996

UTM Zones

• Zone 2

Longitude Start and End 174 W to 168 WLinear Unit MeterFalse Easting 500,000False Northing 0Central Meridian 171 WLatitude of Origin EquatorScale of Central Meridian 0.9996

UTM Zones

• Zone 13 Colorado

Longitude Start and End 108 W to 102 W

Linear Unit Meter

False Easting 500,000

False Northing 0

Central Meridian 105 W

Latitude of Origin 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 DatumsWGS60 WGS66 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 GeoMedia Professional allows transformation between two coordinate systems that are based on different horizontal geodetic datums. Pg. 33.