Working with Map Projections GLY 560: GIS and Remote Sensing for Earth Scientists Class Home Page: http://www.geology.buffalo.edu/courses/gly560/

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. 4/14/2017 GLY560: GIS and RS

Ellipsoid (Global) Coordinate Systems Global coordinates based upon “spherical” coordinates modified to account for imperfect shape of earth. 4/14/2017 GLY560: GIS and RS

Latitude-Longitude System The most commonly used coordinate system today is the latitude, longitude, and height system. The Prime Meridian and the Equator are the reference planes used to define latitude and longitude. 4/14/2017 GLY560: GIS and RS

Equator and Prime Meridian Meridian = (N-S Longitude); Parallel = (E-W Latitude) 4/14/2017 GLY560: GIS and RS

Latitude-Longitude Systems Degree-Minute-Second (DMS) 1 deg = 60 min 1 min = 60 sec Decimal Degrees (DD) 45°52¢30²= 45.875 ° 4/14/2017 GLY560: GIS and RS

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. 4/14/2017 GLY560: GIS and RS

Plane Coordinate Systems 2-D Systems (1 plane) 3-D Systems (2 orthogonal planes) 4/14/2017 GLY560: GIS and RS

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 4/14/2017 GLY560: GIS and RS

Projections Affect Maps The greater the map area, the greater the impact of projection 4/14/2017 GLY560: GIS and RS

Conic Projection 4/14/2017 GLY560: GIS and RS

Cylindrical Projection 4/14/2017 GLY560: GIS and RS

Azimuthal Projection 4/14/2017 GLY560: GIS and RS

Common Map Projections Choice of map projection depends upon: Attribute to be preserved Scale to be represented Aspect of the map 4/14/2017 GLY560: GIS and RS

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 4/14/2017 GLY560: GIS and RS

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 4/14/2017 GLY560: GIS and RS

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 4/14/2017 GLY560: GIS and RS

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. 4/14/2017 GLY560: GIS and RS

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. 4/14/2017 GLY560: GIS and RS

Reference Ellipsoids Reference ellipsoids are usually defined by semi-major (equatorial radius) and flattening (the relationship between equatorial and polar radii). 4/14/2017 GLY560: GIS and RS

Selected Reference Ellipsoids 4/14/2017 GLY560: GIS and RS

Clarke 1866 Datum (NAD27) Land-based ellipsoid running through Meades Ranch Kansas Basis for North American Datum of 1927 (NAD27) still used today. 4/14/2017 GLY560: GIS and RS

World Geodetic System 1984 Determined from satellite orbit data. Identical to GRS80 Used for North American Datum 1983 (NAD83) 4/14/2017 GLY560: GIS and RS

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. 4/14/2017 GLY560: GIS and RS

Coordinate Systems Map projections used for small-scale maps (<1:1,000,000). Plane coordinate systems used for large-scale maps (>1:24,000). 4/14/2017 GLY560: GIS and RS

US Plane Coordinate Systems Universal Transverse Mercator (UTM) Universal Polar Stereographic (UPS) State Plane Coordinate (SPC) Public Land Survey System (PLSS) 4/14/2017 GLY560: GIS and RS

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 84°N and 80°S 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. 4/14/2017 GLY560: GIS and RS

UTM Zones 4/14/2017 GLY560: GIS and RS

UTM Zones 4/14/2017 GLY560: GIS and RS

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. 4/14/2017 GLY560: GIS and RS

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. 4/14/2017 GLY560: GIS and RS

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.). 4/14/2017 GLY560: GIS and RS

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. 4/14/2017 GLY560: GIS and RS