Working with Map Projections

GLY 560: GIS and Remote Sensing for Earth Scientists

Class Home Page: http://www.geology.buffalo.edu/courses/gly560/

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Map Projection

•The transformation from the geographic grid to a plane coordinate system is referred to as map projection.

•Transformation from one plane coordinate system to another is referred to as re-projection.

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Ellipsoid (Global) Coordinate Systems

• Global coordinates based upon “spherical” coordinates modified to account for imperfect shape of earth.

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Latitude-Longitude System

oThe most commonly used coordinate system today is the latitude, longitude, and height system.

oThe Prime Meridian and the Equator are the reference planes used to define latitude and longitude.

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Equator and Prime Meridian

Meridian = (N-S Longitude); Parallel = (E-W Latitude)

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Latitude-Longitude Systems

•Degree-Minute-Second (DMS)

• 1 deg = 60 min

• 1 min = 60 sec

•Decimal Degrees (DD)

• 455230= 45.875

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Plane Coordinate Systems

• René Descartes (1596-1650) introduced systems of coordinates based on orthogonal (right angle) coordinates.

• These two and three-dimensional systems used in analytic geometry are often referred to as Cartesian systems.

• Similar systems based on angles from baselines are often referred to as polar systems.

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Plane Coordinate Systems

• 2-D Systems(1 plane)

• 3-D Systems(2 orthogonal planes)

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Projection Classes

•Conformal: preserves local shape

•Equivalent: preserves area

•Equidistant: preserves length

•Azimuthal: preserves directions

Map can have more that one property, but conformal and equivalent are mutually exclusive

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Projections Affect Maps

The greater the map area, the greater the impact of projection

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Conic Projection

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Cylindrical Projection

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Azimuthal Projection

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Common Map Projections

•Choice of map projection depends upon:

• Attribute to be preserved

• Scale to be represented

• Aspect of the map

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Transverse Mercator Projection

• Secant cylindrical projection

• Straight meridians and parallels intersect at right angles. Scale is true at the equator or at two standard parallels equidistant from the equator. Often used for marine navigation because all straight lines on the map are lines of constant azimuth.

• Requires:• Standard Parallels

• Central Meridian

• Latitude of Origin

• False Easting and Northing

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Lambert Conformal Conic

• Secant conic projection

• Area, and shape are distorted away from standard parallels. Directions true in limited areas. Used for maps of North America.

• Requires:

• Standard Parallels

• Central Meridian

• Latitude of Projection Origin

• False Easting and Northing

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Albers Equal-Area Conic

• Secant conic projection (similar to Lambert Conformal Conic but preserves area instead of shape)

• Distorts scale and distance except along standard parallels. Used in large countries with a larger east-west than north-south extent.

• Requires:• Standard Parallels

• Central Meridian

• Latitude of Projection Origin

• False Easting and Northing

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Unprojected Maps

• Unprojected maps consider longitude and latitude as a simple rectangular coordinate system.

• Scale, distance, area, and shape are all distorted with the distortion increasing toward the poles.

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Datum

•To project Earth to a flat plane we must choose an ellipsoid or spheroid to represent the Earth’s surface.

•Choosing an ellipsoid implies a horizontal datum for the projected map.

•Hundreds of datums have been used.

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Reference Ellipsoids

• Reference ellipsoids are usually defined by semi-major (equatorial radius) and flattening (the relationship between equatorial and polar radii).

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Selected Reference Ellipsoids

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Clarke 1866 Datum (NAD27)

•Land-based ellipsoid running through Meades Ranch Kansas

•Basis for North American Datum of 1927 (NAD27) still used today.

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World Geodetic System 1984

•Determined from satellite orbit data.

• Identical to GRS80

•Used for North American Datum 1983 (NAD83)

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NAD27 vs NAD83

•GIS Data providers switching from NAD27 to NAD83.

•NAD83 tied to global positioning system measurements

•Horizontal shift between NAD27 and NAD83 10-100 m in conterminous US and >200 m in Alaska.

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Coordinate Systems

•Map projections used for small-scale maps (<1:1,000,000).

•Plane coordinate systems used for large-scale maps (>1:24,000).

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US Plane Coordinate Systems

•Universal Transverse Mercator (UTM)

•Universal Polar Stereographic (UPS)

•State Plane Coordinate (SPC)

•Public Land Survey System (PLSS)

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Universal Transverse Mercator

• The National Imagery and Mapping Agency (NIMA) (formerly the Defense Mapping Agency) adopted UTM grid for military use.

• UTM divides earth’s surface between 84N and 80S into 60 zones about 360 km wide.

• Each of 60 zones mapped onto transverse mercator projection.

• False origin assigned to each UTM zone. In Northern Hemisphere, UTM measured from false origin at equator and 500,000 m West of central meridian.

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UTM Zones

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UTM Zones

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UTM on USGS Maps

• On 7.5-minute quadrangle maps the UTM grid lines are indicated at intervals of 1,000 meters, by blue ticks in the margins of the map or with full grid lines.

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State Plane System

• In United States, State Plane System developed in the 1930s and was based on NAD27.

• While the NAD-27 State Plane System has been superseded by the NAD-83 System, maps in NAD-27 coordinates (in feet) are still in use.

• Most USGS 7.5 Minute Quadrangles use several coordinate system grids including latitude and longitude, UTM kilometer tic marks, and State Plane coordinates.

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Public Land Survey System

• Public Land Rectangular Surveys have been used since the 1790s to identify public lands in the United States.

• Appears on large-scale USGS topographic maps

• Abbreviations used for Township (T or Tps), Ranges (R or Rs), Sections(sec or secs), and directions (N, E, S, W, NE, etc.).

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Public Land Survey System

• Each state has a principle meridian running N-S, and a baseline running E-W.

• When measuring in a N-S direction, each square is called a township.

• When measuring in an E-W direction, each of these squares is called a range.