Post on 22-Dec-2015
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.