L 5 Map Projections

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Map projections are used to transfer or “project” geographical coordinates onto a flat surface. .There are many projections: Maine example:• NAD 27 Universal Transverse Mercator – Zone 19N• NAD 27 Maine State Plane

– East Zone– West Zone

• NAD 83 Universal Transverse Mercator– Zone 19N• NAD 83 Maine State Plane

– East Zone– Central Zone– West Zone

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Many Projections: Minnesota examplehttp://rocky.dot.state.mn.us/geod/projections.htm

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Projections may be categorized by:

1.The location of projection source

2.The projection surface

3.Surface orientation

4.Distortion properties

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Gnomonic - center of globe Stereographic - at the antipode Orthographic - at infinity

Source:http://www.fes.uwaterloo.ca/crs/geog165/mapproj.htm

Categorized by the Location of Projection Source

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Cone – Conic

Cylinder - Cylindrical Plane - Azimuthul

The projection surface:

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Projection Surfaces – “developable”

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The Tangent Case vs. The Secant Case

In the tangent case the cone, cylinder or plane just touches the Earth along a single line or at a point.

• In the secant case, the cone, or cylinder intersects or cuts through the Earth as two circles.

• Whether tangent or secant, the location of this contact is important because it defines the line or point of least distortion on the map projection.

• This line of true scale is called the standard parallel or standard line.

Standard Parallel

• The line of latitude in a conic or cylindrical projection where the cone or cylinder touches the globe.

• A tangent conic or cylindrical projection has one standard parallel.

• A secant conic or cylindrical projection has two standard parallels.

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The Orientation of the Surface

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Projections Categorized by Orientation:

Equatorial - intersecting equator 

Transverse - at right angle to equator 

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Specifying Projections

1. The type of developable surface (e.g., cone)

2. The size/shape of the Earth (ellipsoid, datum), and size of the surface

3. Where the surface intersects the ellipsoid

4. The location of the map projection origin on the surface, and the coordinate system units

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Defining a Projection – LCC(Lambert Conformal Conic)

• The LCC requires we specify an upper and lower parallel

• An ellipsoid• A central meridian• A projection origin

centralmeridian

origin

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• Locally preserves angles/shape.

• Any two lines on the map follow the same angles as the corresponding original lines on the Earth.

• Projected graticule lines always cross at right angles.

• Area, distance and azimuths change.

Conformal Projections

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Equidistant Projections

• A map is equidistant when the distances between points differs from the distances on Earth by the same scale factor.

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Equivalent/Equal Area Projection

• Equivalent/equal area projections maintain map areas proportional to the same areas of the Earth.

• Shape and scale distortions increase near points 90o from the central line.

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“Standard” Projections

• Governments (and other organizations) define “standard” projections to use

• Projections preserve specific geometric properties, over a limited area

•Imposes uniformity, facilitates data exchange, provides quality control, establishes limits on geometric distortion.

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National Projections

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Map Projections vs. Datum Transformations

• A map projections is a systematic rendering from 3-D to 2-D

• Datum transformations are from one datum to another, 3-D to 3-D or 2-D to 2-D

• Changing from one projection to another may require both.

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From one Projection to Another

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Common GIS Projections• Mercator- A conformal, cylindrical projection tangent to the

equator.  Originally created to display accurate compass bearings for sea travel. An additional feature of this projection is that all local shapes are accurate and clearly defined.

• Transverse Mercator - Similar to the Mercator except that the cylinder is tangent along a meridian instead of the equator. The result is a conformal projection that minimizes distortion along a north-south line, but does not maintain true directions.

• Universal Transverse Mercator (UTM) – Based on a Transverse Mercator projection centered in the middle of zones that are 6 degrees in longitude wide.  These zones have been created throughout the world.

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• Lambert Conformal Conic – A conic, confromal projection typically intersecting parallels of latitude, standard parallels, in the northern hemisphere.  This projection is one of the best for middle latitudes because distortion is lowest in the band between the standard parallels. It is similar to the Albers Conic Equal Area projection except that the Lambert Conformal Conic projection portrays shape more accurately than area.

• Lambert Equal Area - An equidistant, conic projection similar to the Lambert Conformal Conic that preserves areas.

• Albers Equal Area Conic - This conic projection uses two standard parallels to reduce some of the distortion of a projection with one standard parallel. Shape and linear scale distortion are minimized between standard parallels.

•  State Plane – A standard set of projections for the United States – based on either the Lambert Conformal Conic or transverse mercator

projection, depending on the orientation of each state.  Large states commonly require several state plane zones.

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Map Projections Summary

• Projections specify a two-dimensional coordinate system from a 3-D globe

• All projections cause some distortion• Errors are controlled by choosing the proper

projection type, limiting the area applied• There are standard projections• Projections differ by datum – know your

parameters

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Coordinate Systems

• Once map data are projected onto a planar surface, features must be referenced by a planar coordinate system.

• Coordinates in the GIS are measured from the origin point. However, false eastings and false northings are frequently used, which effectively offset the origin to a different place on the coordinate plane.

• The three most common systems you will encounter in the USA are: – State Plane– Universal Transverse Mercator (UTM)– Public Land Survey System (PLSS) – non-coordinate systems

Coordinate systems

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State Plane Coordinate Systems

• Uses Lambert conformal conic (LCC) and Transverse Mercator (TM, cylindrical)

• LCC when long dimension East-West

• TM when long dimension N-S

• May be mixed, as many zones used as needed

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State Plane Coordinate System

• Each state partitioned into zones

• Each zone has a different projection specified

• Distortion in surface measurement less than 1 part in 10,000 within a zone

CaliforniaState PlaneZones

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State Plane Coordinate System Zones

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Maine State Plane

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State Plane Coordinate System

e.g., Maine East State Plane Zone

Projection: Transverse_MercatorFalse_Easting: 700000.000000False_Northing: 0.000000Central_Meridian: -67.875000Scale_Factor: 0.999980Latitude_Of_Origin: 43.833333Linear Unit: Meter (1.000000)

Geographic Coordinate System: GCS_North_American_1983Angular Unit: Degree (0.017453292519943295)Prime Meridian: Greenwich (0.000000000000000000)Datum: D_North_American_1983 Spheroid: GRS_1980 Semimajor Axis: 6378137.000000000000000000 Semiminor Axis: 6356752.314140356100000000 Inverse Flattening: 298.257222101000020000

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UTM – Universal Transverse Mercator

• UTM define horizontal positions world-wide by dividing the surface of the Earth into 6o zones.

• Zone numbers designate the 6o longitudinal strips extending from 80o south to 84o north.

• Each zone has a central meridian in the center of the zone.

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Universal Transverse Mercator – UTM System

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UTM Zone Details

Each Zone is 6 degrees wide

Zone location defined by a central meridian

Origin at the Equator, 500,000m west of the zone central Meridian

Coordinates are always positive (offset for south Zones)

Coordinates discontinuous across zone boundaries

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Universal Transverse Mercator Projection – UTM Zones for the U.S.

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UTM Zone 19N• Projection: Transverse_Mercator• False_Easting: 500000.000000• False_Northing: 0.000000• Central_Meridian: -69.000000• Scale_Factor: 0.999600• Latitude_Of_Origin: 0.000000• Linear Unit: Meter (1.000000)

• Geographic Coordinate System: GCS_North_American_1983• Angular Unit: Degree (0.017453292519943295)• Prime Meridian: Greenwich (0.000000000000000000)• Datum: D_North_American_1983• Spheroid: GRS_1980• Semimajor Axis: 6378137.000000000000000000• Semiminor Axis: 6356752.314140356100000000• Inverse Flattening: 298.257222101000020000

False Easting/Northing

• False easting – the value added to the x coordinates of a map projection so that none of the values being mapped are negative.

• False northing are values added to the y coordinates.

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Central Meridian

• Every projection has a central meridian.• The line of longitude that defines the center

and often the x origin of the projected coordinate system.

• In most projections, it runs down the middle of the map and the map is symmetrical on either side of it.

• It may or may not be a line of true scale. (True scale means no distance distortion.)

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Central Meridian

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http://www.geography.hunter.cuny.edu/~jochen/GTECH361/lectures/lecture04/concepts/Map%20coordinate%20systems/Projection%20parameters.htm

Scale Factor

• 0 > scale factor < =1

• The ratio of the actual scale at a particular place on the map to the stated scale on the map.

• Usually the tangent line or secant lines.

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Coordinate Systems Notation

Latitude/LongitudeDegrees Minutes Seconds 45° 3' 38" NDegrees Minutes (decimal) 45° 3.6363' NDegrees (decimal) 45.0606° N

State Plane (feet) 2,951,384.24 N

UTM (meters) 4,996,473.72 N

ArcGISDatums and Projections

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Datum Transformations

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Moving your data between coordinate systems sometimes includes transforming between the geographic coordinate systems. Because geographic coordinate systems contain datums that are based on spheroids, a geographic transformation also changes the underlying spheroid

ArcGIS Help

Datum Transformations

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A geographic transformation is always defined in a particular direction.

When working with geographic transformations, if no mention is made of the direction, an application or tool like ArcMap will handle the directionality automatically.

For example, if converting data from WGS 1984 to NAD 1927, you can pick a transformation called NAD_1927_to_WGS_1984_3 and the software will apply it correctly.

(ArcMap automatically loads one geographic transformation. It's designed for the lower 48 states of the United States and converts between NAD 1927 and NAD 1983.)

ArcGIS Help

Graph the Following

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Distance Time

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Distance Time

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Graph the Following

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DistanceKm

TimeHr

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DistanceM

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Define The Projection

•Predefined

•Custom

•Import

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Predefined

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Custom & Import

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Custom & Import

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Reproject “On the Fly”

• Two or more layers with different DEFINED projections.

• First layer in the data frame defines the projection for the data frame.

• Next layer added, ArcGIS will automatically reproject it to the data frame.

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Defining The Projection for A Data Frame

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Project

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Project

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