Nicholas A. Procopio, Ph.D, GISP Environmental GIS Nicholas A. Procopio, Ph.D, GISP nick@drexel.edu

Ptolemy’s Projection URL: http://www.henry-davis.com/MAPS/Ancient%20Web%20Pages/119G.html

The Size and Shape of the Earth Earth’s ellipsoid is about 1/300 off from the sphere Clarke, Getting Started with Geographic Information Systems, prentice-Hall, 2001

Geodetic Datum An estimate of the ellipsoid allows calculation of the elevation of every point on earth, including sea level, and is often called a datum

Geodetic Datum Definition The National Geodectic Survey defines a geodetic datum as “a set of constants specifying the coordinate system used for geodetic control, i.e., for calculating the coordinates of points on the Earth” Base reference level for the third dimension of elevation for the earth’s surface Can depend on the ellipsoid, the earth model, and the definition of sea level Recent datums use the center of the earth as a reference point rather than a point on the ground surface

Geodetic Datum Hundreds of different datums have been used to frame position descriptions since the first estimates of the earth's size were made Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems, precise positioning systems, and navigation systems Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters

Importance of Datums Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems, precise positioning systems, and navigation systems

Variations in Datums Elevations referenced to a sphere, ellipsoid, geoid, or local sea level will all be different Even horizontal locations may vary

Clarke Ellipsoid In 1866, the US was mapped based on an ellipsoid measured by Sir Alexander Ross Clarke Ellipsoid derived from measurements taken in Europe, Russia, India, South Africa, and Peru The Clarke ellipsoid had an equatorial radius of 6,378,206.4 meters and a polar radius of 6,356,538.8 meters

Clarke Ellipsoid In 1924, a simpler measure of 1/297 was adopted as the international standard The US adopted the older values and became known as the North American Datum 1927 (NAD 1927)

NAD 1927 A horizontal control datum for the U.S. defined by a location and azimuth on the Clarke spheroid of 1866, with an origin at the survey station Meades Ranch, Kansas Geoidal height at Meades Ranch was assumed to be zero

NAD 1983 Horizontal control datum for the U.S., Canada, Mexico, and Central America, based on a geocentric origin Based on measurements taken in 1980 and accepted internationally as the geodetic reference system (GRS80 ellipsoid)

NAD 1928 vs. NAD 1983 NAD 27 based on Clarke Ellipsoid of 1866 NAD 27 computed with a single survey point (Meades Ranch) as the datum point Difference about 300m in places NAD 83 based on the Geodetic Reference System (GRS) of 1980 NAD 83 computed as a geocentric reference system with no datum point Difference about 300m in places

World Geodetic System U.S. military references an ellipsoid known as the GRS80 ellipsoid Refined the values slightly in 1984 to make the world geodetic system (WGS84) Significant because of GPS

Vertical Datums A level surface to which heights are referenced National Geodetic Vertical Datum of 1929 (NGVD 29) - vertical control datum in the U.S. NGVD 29 is defined by the observed (fixed) heights of MSL at 26 tide gauges and by the set of elevations of all benchmarks resulting from the adjustment

Vertical Datums North American Vertical Datum of 1988 (NAVD 88) - vertical control datum est. in 1991 by the minimum-constraint adjustment of the Canadian-Mexican-U.S. leveling observations Held fixed the height of the primary tidal benchmark at Father Point/Rimouski, Quebec, Canada.

Map Projections Cartographer’s tool for taking curved surface of reality (the globe) and placing it on a flat surface such as a piece of paper or a computer screen

Projection Importance Maps are a common source of input data for a GIS It is not uncommon to input various maps into a GIS that are based on individual projections In order to maintain accuracy of the input data, the input maps must be referenced from the same projection

Importance of Understanding Projections When displaying various data, it is important that they are all referenced to the same coordinate system Data displayed in varying coordinate systems will be located incorrectly relative to each other Very important factor data accuracy is critical

Global Projections The most complete projection is the globe Scale remains constant everywhere Little to no distortion

Map Projections A map projection is used to portray all or part of the round Earth on a flat surface Every map projection will distort one or more of the following attributes: Shape Area Distance Direction

Distortion of Map Projections No flat map can be simultaneously conformal (shape-preserving) and equal-area (area-preserving) in every point In most projections, at least one specific region (usually the center of the map) suffers little or no distortion If the represented region is small enough (and if necessary suitably translated in an oblique map), the projection choice may be of little importance

Distortion of Map Projections Summary Projections that minimize distortion of shape are referred to as conformal Projections that minimize distortion of area are referred to as equal-area Projections that minimize distortion of distance are referred to as equidistant Projections that minimize distortion of direction are referred to as true-direction

Projection Distortion Some projections minimize distortions in some of these properties at the expense of maximizing errors in others Others attempt to only moderately distort all of these properties Every projection has its own set of advantages and disadvantages

Types of Map Projections Conformal The scale of a map at any point on the map is the same in any direction Meridians (longitude) and parallels (latitude) intersect at right angles Shape is preserved locally on conformal maps Found mostly for maps used for measuring directions, because they preserve directions around any given point Examples - Lambert Conformal Conic & the Mercator projections

Lambert Conformal Projection URL: http://members.shaw.ca/quadibloc/maps/mco0301.htm

Mercator Projection URL http://math.rice.edu/~lanius/pres/map/maphis.html

Types of Projections Equivalent (Equal-Area) Preserves the property of area All parts of the earth’s surface are shown with the correct area Examples – Albers and Sinusoidal

Albers Projection URL; http://www.cnr.colostate.edu/class_info/nr502/lg2/projection_descriptions/albers.html

Types of Map Projections Equidistant Portrays distances from the center of the projection to any other place on the map Useful only if distances are critical Infrequently used in GIS Simple conic & azimuthal equidistant projections

The basis for three types of map projections—cylindrical, planar, and conic. In each case a sheet of paper is wrapped around the Earth, and positions of objects on the Earth’s surface are projected onto the paper. The cylindrical projection is shown in the tangent case, with the paper touching the surface, but the planar and conic projections are shown in the secant case, where the paper cuts into the surface. (Reproduced by permission of Peter H. Dana)

Examples of some common map projections The Mercator projection is a tangent cylindrical type, shown here in its familiar equatorial aspect (cylinder wrapped around the equator). The Lambert Conformal Conic projection is a secant conic type. In this instance, the cone onto which the surface was projected intersected the Earth along two lines of latitude: 20 North and 60 North.

(A) The so-called unprojected or Plate Carrée projection, a tangent cylindrical projection formed by using longitude as x and latitude as y. (B) A comparison of three familiar projections of the United States. The Lambert Conformal Conic is the one most often encountered when the United States is projected alone and is the only one of the three to curve the parallels of latitude, including the northern border on the 49th Parallel.

Coordinate Systems

A Cartesian coordinate system, defining the location of the blue cross in terms of two measured distances from the origin, parallel to the two axes

Coordinate Systems Relative location - references to locations given with respect to another place Absolute location – a location in geographic space given with respect to a known origin and standard measurement system, such a coordinate system

Locations to Numbers We must choose a standard way to encode locations on the earth Locations on paper map can be given in map millimeters or inches starting at the lower left-hand corner  Locations can then be given in (x, y) format – east-west followed by north-south  Standard ways of listing coordinates are then called coordinate systems

Locations to Numbers A system with all the necessary components to locate a position in 2- or 3-dimensional space; that is, an origin, a type of unit distance, and two axes Many different coordinate systems, based on a variety of geodetic datums, units, projections, and reference systems in use today

Coordinate Systems Latitude and Longitude Most common coordinate system The Prime Meridian and the Equator are the reference planes used to define latitude and longitude Hurvitz, P., University of Washington, CFR 250 Lecture Notes, 1999-2002

Latitude and Longitude Start with a line connecting N and S pole through the point The line is called a meridian Latitude measures angle between the point and the equator along the meridian Longitude measures the angle on the equatorial plane between the meridian of the point and the central meridian (through Greenwich, England)

Coordinate Systems Universal Transverse Mercator Earth divided into pole-to-pole zones Zones are each 6o of longitude wide First zone starts at 180oW, at the international date line and runs east (180oW to 174oW) Final zone (zone 60) runs from 174oE to the date line

The system of zones of the Universal Transverse Mercator system The system of zones of the Universal Transverse Mercator system. The zones are identified at the top. Each zone is six degrees of longitude in width (Reproduced by permission of Peter H. Dana)

Universal Transverse Mercator URL: http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

UTM Zones for the United States URL: http://mac.usgs.gov/mac/isb/pubs/factsheets/fs07701.html

Northings and Eastings Earth ~40,000,000 m around, thus northings in a zone go from 0 to 10 million meters Southern hemisphere – 0 northing is the South Pole; 10 million meter northing at equator Northern hemisphere – 0 northing at equator and 10 million meter northing at North Pole Eastings False origin established beyond the westerly limit of each zone (about half a degree) Central meridian has an easting of 500,000m Advantages: Allows overlap between zones for mapping purposes Gives all eastings positive numbers

UTM Zones Clarke, Getting Started with Geographic Information Systems, prentice-Hall, 2001

UTM Advantages Frequently used Consistent for the globe Provides a universal approach to accurate georeferencing

UTM Disadvantages Not used beyond 84oN & 80oS Full georeference requires the zone number, easting and northing (unless the area of the data base falls completely within a zone) Rectangular grid superimposed on zones defined by meridians causes axes on adjacent zones to be skewed with respect to each other problems arise in working across zone boundaries no simple mathematical relationship exists between coordinates of one zone and an adjacent zone

Coordinate Systems State Plane Coordinate System Based on both the transverse Mercator & the Lambert conformal conic projections w/ units in feet (metric versions now as well) Based upon a different map of each state E-W elongated states drawn on a Lambert conformal conic projection N-S elongated states drawn on a transverse Mercator projection Except Alaska – Lambert conformal conic, transverse Mercator, & oblique Mercator

Coordinate Systems State Plane Coordinate System Based upon a different map of each state E-W elongated states drawn on a Lambert conformal conic projection N-S elongated states drawn on a transverse Mercator projection Except Alaska – Lambert conformal conic, transverse Mercator, & oblique Mercator

State Plane Coordinate System URL: http://www.pipeline.com/~rking/spc.htm

Coordinate Systems State Plane Coordinate System Each zone has an arbitrarily determined origin that is usually some given number of feet west and south of the southernmost point on the map Means that the eastings and northings all come out as positive numbers System then simply gives eastings and northings in feet

State Plane Advantages Slightly more precise than UTM Foot rather than meter scale SPCS can be more accurate over small areas SPCS is used by surveyors all over the U.S.

State Plane Disadvantages Lack of universality Problems may arise at the boundaries of projections

Military Grid Coordinate System Adopted by U.S. Army in 1947  Uses a lettering & numbering system  West to east zones numbered from 1 to 60 Within zones, 8o strips of latitude lettered from C (80o to 72o S) to X (72o to 84o N)

Military Grid Coordinate System Clarke, Getting Started with Geographic Information Systems, prentice-Hall, 2001

Set coordinates to Lat/Long

Set coordinates to State Plane

Set coordinates to UTM