Environmental GISEnvironmental 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 ImportanceProjection 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 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 EastingsNorthings and Eastings

Northings• 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 SystemMilitary 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