Introduction to GIS ©2008 Austin Troy. Introduction to GIS Map Projection Slide courtesy of Leslie...

Introduction to GIS

©2008 Austin Troy

Introduction to GIS

Map Projection

Slide courtesy of Leslie Morrissey

Introduction to GIS

So, what shape IS the earth?

©2008 Austin Troy

•Earth is not a sphere, but an ellipsoid, because the centrifugal force of the earth’s rotation “flattens it out”.

•This was finally proven by the French in 1753

•The earth rotates about its shortest axis, or minor axis, and is therefore described as an oblate ellipsoid

Source: ESRI

Introduction to GIS

And it’s also a….

©2008 Austin Troy

•Because it’s so close to a sphere, the earth is often referred to as a spheroid: that is a type of ellipsoid that is really, really close to being a sphere

•These are two common spheroids used today: the difference between its major axis and its minor axis is less than 0.34%....

Source: ESRI

Introduction to GIS

Spheroids

©2008 Austin Troy

•Spheroid: An ellipsoid which is very nearly a sphere

•Common spheroids for North America:

•2 dimensions!

•Sphere vs. Spheroid? Scale!!

Source: ESRI

Introduction to GIS

Geoid

©2008 Austin Troy

www.esri.com/news/arcuser/0703/geoid1of3.html

• The geoid is actually measured and interpolated, using gravitational measurements.

Introduction to GIS

The Geographic Graticule/Grid

©2008 Austin Troy

•This is a location reference system for the earth’s surface, consisting of:

•Meridians: lines of longitude and

•Parallels: lines of latitude

Source: ESRI

• Prime meridian is at Greenwich, England (that is 0º longitude)

• Equator is at 0º latitude

• Degrees, minutes, seconds or decimal degrees

Introduction to GIS

Horizontal Datums

©2008 Austin Troy

• Datum: model used to translate a spheroid into locations on the earth; a 3D surface or frame of reference; defines origin & orientation of graticule

• A spheroid only gives you a shape—a datum gives you locations of specific places on that shape.

• Hence, a different datum is generally used for each spheroid

• Two things are needed for datum: spheroid and set of surveyed and measured points

Introduction to GIS

Surface-Based Datums

©2008 Austin Troy

• Prior to satellites, datums were realized by connected series of ground-measured survey monuments

• A central location was chosen where the spheroid meets the earth: this point was intensively measured using pendulums, magnetometers, sextants, etc. to try to determine its precise location.

• Originally, the “datum” referred to that “ultimate reference point.”

• Eventually the whole system of linked reference and subrefence points came to be known as the datum.

Introduction to GIS

Surface Based Datums

©2008 Austin Troy

• Starting points need to be very central relative to landmass being measured

• In NAD27 center point was Mead’s Ranch, KS• NAD27 resulted in lat/long coordinates for about 26,000 survey points in the US and Canada.

• Limitation: requires line of sight, so many survey points were required

• Problem: errors compound with distance from the initial reference. This is why central location needed for first point

Introduction to GIS

Satellite Based Datums

©2008 Austin Troy

• With satellite measurements the center of the spheroid can be matched with the center of the earth.

• Satellites started collecting geodetic information in 1962 as part of National Geodetic Survey

• This gives a spheroid that when used as a datum correctly maps the earth such that all Latitude/Longitude measurements from all maps created with that datum agree.

• Rather than linking points through surface measures to initial surface point, measurements are linked to reference point in outer space

Introduction to GIS

Common Datums

©2008 Austin Troy

• Previously, the most common spheroid was Clarke 1866; the North American Datum of 1927 (NAD27) is based on that spheroid, and has its center in Kansas.

• NAD83 is the new North American datum (for Canada/Mexico too) based on the GRS80 geocentric spheroid. It is the official datum of the USA, Canada and Central America

• World Geodetic System 1984 (WGS84) is a newer spheroid/datum, created by the US DOD; it is more or less identical to Geodetic Reference System 1980 (GRS80). The GPS system uses WGS84.

Introduction to GIS

Lat/Long and Datums

©2008 Austin Troy

• These pre-satellite datums are surface based.

• A given datum has the spheroid meet the earth in a specified location somewhere.

• Datum is most accurate near the touching point, less accurate as move away (remember, this is different from a projection surface because the ellipsoid is 3D)

• Different surface datums can result in different lat/long values for the same location on the earth.

• So, just giving lat and long is not enough!!!

Introduction to GIS

©2008 Austin Troysource;: http://gallery.geocaching.com.au/Maps/DatumShift andhttp://www.ngs.noaa.gov/TOOLS/Nadcon/Nadcon.html

Introduction to GIS

Map Projection


Introduction to GIS

Review


Introduction to GIS

Map Projection

© 2005, Austin Troy

• This is the method by which we transform the earth’s spheroid (real world) to a flat surface (abstraction), either on paper or digitally

• Because we can’t take our globe everywhere with us!

• Remember: most GIS layers are 2-D

3D2D

Think about projecting a see-through globe onto a wall

Source: ESRI

Developable surface, a.k.a.

Projection surface

Introduction to GIS

Map Projection-distortion


• The problem with map projection is that it distorts one or several of these four properties of a surface:

• Shape (conformal) **

• Area (equal area) **

• Distance (equidistant)

• Direction (azimuthal)

** mutually exclusive

• Some projections specialize in preserving one or several of these features, but none preserve all

Introduction to GIS

Map Projection-distortion


• Hence, when choosing a projection, one must take into account what it is that matters in your analysis and what properties you need to preserve

• Conformal and equal area properties are mutually exclusive but some map projections can have more than one preserved property. For instance a map can be conformal and azimuthal

• Conformal and equal area properties are global (apply to whole map) while equidistant and azimuthal properties are local and may be true only from or to the center of map

Introduction to GIS

Area Distortion827,000 square miles6.8 million square

miles


Mercator Projection

Introduction to GIS


•4,300 km: Robinson•5,400 km: Mercator

Introduction to GIS

Shape distortion


• Mercator (left)• World Cylindrical Equal Area

(above)• The distortion in shape above is

necessary to get Greenland to have the correct area

• The Mercator map looks good but Greenland is many times too big

Introduction to GIS

Some Examples of distortion


Mercator—goes on foreverRobinson

sinusoidal

Introduction to GIS

Some examples of distortion


• Mercator maintains shape and direction, but sacrifices area

Introduction to GIS



• The Sinusoidal and Equal-Area Cylindrical projections both maintain area, but look quite different from each other. The latter distorts shape Lambert Equal-area Cylindrical

Sinusoidal

Introduction to GIS



• The Robinson projection does not enforce any specific properties but is widely used because it makes the earth’s surface and its features look somewhat accurate

Introduction to GIS

Map Projection-Distortion


• Tissot’s indicatrix, made up of ellipses, is a method for measuring distortion of a map

Introduction to GIS



• Tissot’s indicatrix; here is the Robinson projection

Introduction to GIS



• Tissot’s indicatrix; here is the Mercator projection

Introduction to GIS



• Tissot’s indicatrix; here is SinusoidalArea of these ellipses should be same as those at equator, but shape is different

Introduction to GIS

General Map Projection: Cylindrical


• Created by wrapping a cylinder around a globe and, in theory, projecting light out of that globe

• Meridians in cylindrical projections are equally spaced, while the spacing between parallel lines of latitude increases toward the poles

• Meridians never converge so poles can’t be shown

• Does not distort local shape (conformal) or direction

Source: ESRI

Introduction to GIS

Cylindrical Map Types


1. Tangent to great circle: in the simplest case, the cylinder is North-South, so it is tangent (touching) at the equator; this is called the standard parallel and represents where the projection is most accurate

2. If the cylinder is smaller than the circumference of the earth, then it intersects as a secant in two places

Source: http://nationalatlas.gov/articles/mapping/a_projections.html

Introduction to GIS

Cylindrical Map TypesSecant projections are more accurate because when the

projection surface touches the globe twice, the average distance from globe to projection surface is smaller

The distance from map surface to projection surface is described by a scale factor, which is the ratio of local scale at a given point to the nominal or “true” scale

Scale factor is 1 where the two surfaces touch


Projection surface.9996

Central meridianStandard meridians

Introduction to GIS

Cylindrical Map Types3. Transverse cylindrical projections: in this type the

cylinder is turned on its side so it touches a line of longitude; these can also be tangent


Introduction to GIS

Cylindrical map distortion


• North-south (equatorial) cylindrical projections cause major distortions at higher latitudes because points on the cylinder are further away from the corresponding point on the globe

• East-west distances are true along the equator but not as distance from the equator (latitude) changes

• Requires alternating scale bar based on latitude

Introduction to GIS

Cylindrical Map Distortion

© 2005, Austin TroyX miles

0 ◦ latitude

25 ◦ latitude

50 ◦ latitude

Straight line direction matches compass bearing (think Navigation)

Introduction to GIS

General Projection Types: Conic


• Projects a globe onto a cone

• In simplest case, globe touches cone along a single latitude line, or tangent, called standard parallel

• Other latitude lines are projected onto cone

• To flatten the cone, it must be cut along a line of longitude (see image)

• The opposite line of longitude is called the central meridian

• Good for mid-latitude areas w/ East-west orientationSource: ESRI

Introduction to GIS

Map Projection-General Types


Conic projections:

• Can be tangent or secant

• Secant are more accurate for reasons given earlier

Introduction to GIS



• Planar or Azimuthal Projections: simply project a globe onto a flat plane

• The simplest form is only tangent at one point

• Any point of contact may be used but the poles are most commonly used

• When another location is used, it is generally to make a small map of a specific area

• When the poles are used, longitude lines look like hub and spokes

Source: ESRI, wikipedia

Introduction to GIS



• Planar or Azimuthal Projections:

• Because the area of distortion is circular around the point of contact, they are best for mapping roughly circular regions, and hence the poles

Introduction to GIS

©2006 Austin Troy

Map Projection-Specific Types• Mercator: This is a specific type of cylindrical projection

• Invented by Gerardus Mercator during the 16th Century

• It was invented for navigation because it preserves azimuthal accuracy—that is, if you draw a straight line between two points on a map created with Mercator projection, the angle of that line represents the actual bearing you need to sail to travel between the two points

Source: ESRI

Introduction to GIS

©2006 Austin Troy

Map Projection-Specific Types• Mercator: Of course the Mercator projection is not so good for preserving area.

Notice how it enlarges high latitude features like Greenland and Antarctica relative to mid-latitude features

Introduction to GIS

©2006 Austin Troy

Map Projection-Specific Types• Transverse Mercator: cylindrical, but the axis of the cylinder is rotated 90°; tangent line is longitudinal, rather than equatorial

• Used for regions with north-south orientations (used in State Plane coordinate system)

• In this case, only the central longitudinal meridian and the equator are straight lines All other lines are

represented by complex curves: that is they can’t be represented by single section of a circle

Source: ESRI

Introduction to GIS

©2006 Austin Troy

Map Projection-Specific Types• Lambert Conformal Conic: invented in 1772, this is a type of conic projection

• Latitude lines are unequally spaced arcs that are portions of concentric circles. Longitude lines are actually radii of the same circles that define the latitude lines.

Source: ESRI

Introduction to GIS

©2006 Austin Troy

Map Projection-Specific Types• The Lambert Conformal Conic projection is very good for middle latitudes with east-west orientation.

• It portrays the pole as a point

• It portrays shape more accurately than area and is commonly used for North America.

• The State Plane coordinate system uses it for east-west oriented features

Introduction to GIS

©2006 Austin Troy

Map Projection-Specific Types• The Lambert Conformal Conic projection is a slightly more complex form of conic projection because it intersects the globe along two lines, called secants, rather than along one, which would be called a tangent

• There is no distortion along those two lines

• Distortion increases with distancefrom the secants

Source: ESRI

Introduction to GIS

©2006 Austin Troy

Map Projection-Specific Types• Albers Equal Area Conic projection: Again, this is a conic projection, using secants as standard parallels but while Lambert preserves shape Albers preserves area

• It also differs in that poles are not represented as points, but as arcs, meaning that meridians don’t converge

• Latitude lines are unequally spaced concentric circles, whose spacing decreases toward the poles.

• Developed by Heinrich Christian Albers in the early nineteenth century for European maps

Introduction to GIS

©2006 Austin Troy

Map Projection-Specific Types• Albers Equal Area Conic: It preserves area by making the scale factor of a meridian at any given point the reciprocal of that along the parallel.

• Scale factor is the ratio of local scale of a point on the projection to the reference scale of the globe; 1 means the two are touching and greater than 1 means the projection surface is at a distance

Introduction to GIS

©2006 Austin Troy

Plane Coordinate Systems• Map projections, as we discussed in last lecture provide the means for viewing small-scale maps, such as maps of the world or a continent or country (1:1,000,000 or smaller)

• Plane coordinate systems are typically used for much larger-scale mapping (1:100,000 or bigger)

• Very large scale (local) maps have distortions that are not measurable … effectively non-existent

Introduction to GIS

©2006 Austin Troy

Plane Coordinate Systems• Projections are designed to minimize distortions of the four properties we talked about, because as scale decreases, error increases

• Coordinate systems are more about accurate positioning (relative and absolute positioning)

• To maintain their accuracy, coordinate systems are generally divided into zones where each zone is based on a separate map projection that is optimized for each zone Group of projections!

Introduction to GIS

©2006 Austin Troy

Reason for PCSs• Remember from before that projections are most accurate where the projection surface is close to the earth surface. The further away it gets, the more distorted it gets

• Hence a global or even continental projection is bad for accuracy because it’s only touching along one (tangent) or two (secant) lines and gets increasingly distorted

Introduction to GIS

©2006 Austin Troy

Reason for PCSs• Plane coordinate systems get around this by breaking the earth up into zones where each zone has its own projection center and projection.

• The more zones there are and the smaller each zone, the more accurate the resulting projections

• This serves to minimize the scale factor, or distance between projection surface and earth surface to an acceptable level

Introduction to GIS

©2006 Austin Troy

Coordinate Systems• The four most commonly used coordinate systems in the US:

• Universal Transverse Mercator (UTM) grid system

• The Universal Polar Stereographic (UPS) grid system

• State Plane Coordinate System (SPC)

• And the Public Land Survey System (PLSS)

Introduction to GIS

©2006 Austin Troy

UTM• Universal Transverse Mercator is a very common coordinate system

• UTM is based on the Transverse Mercator projection (remember, that’s using a cylinder turned on its side)

• It generally uses either the NAD27 or NAD83 datum, so you will often see a layer as projected in “UTM83” or “UTM27”

• U.S. Federal agency data format

Introduction to GIS

©2006 Austin Troy

UTM• UTM divides the earth between 84°N and 80°S into 60 zones, each of which covers 6 degrees of longitude

• Zone 1 begins at 180 ° W longitude.

World UTM zones

Introduction to GIS

©2006 Austin Troy

UTM• US UTM zones

Introduction to GIS

©2006 Austin Troy

UTM• Each UTM zone is projected separately

• There is a false origin (zero point) in each zone

• In the transverse Mercator projection, the “cylinder” touches at two secants, so there is a slight bulge in the middle, at the central meridian. This bulge is very very slight, so the scale factor is only .9996

• The standard meridians are where the cylinder touches

Introduction to GIS

©2006 Austin Troy

UTM• Because each

zone is big, UTM can result in significant errors further away from the center of a zone, corresponding to the central and standard meridians

Introduction to GIS

©2006 Austin Troy

UTM• Scale factors are .9996 in the middle and 1 at the secants

Earth surface

Projection surface

.9996

Central meridian

Standard meridians

Introduction to GIS

©2006 Austin Troy

UTM• UTM is used for large scale mapping applications the world over, when the unit of analysis is fairly small, like a state

• Good choice for multi-state projects, but its best to stay within a single zone

• Its accuracy is 1 in 2,500

• For portraying very large land units, like Alaska or the 48 states, a projection is usually used, like Albers Equal Area Conic

Introduction to GIS

©2006 Austin Troy

SPC System• State Plane Coordinate System is one of the most common coordinate systems in use in the US

• It was developed in the 1930s to record original land survey monument locations in the US

• More accurate than UTM, with required accuracy of 1 part in 10,000

• Hence, zones are much smaller—many states have two or more zones

• Best choice for map extents within a single state

Introduction to GIS

©2006 Austin Troy

SPC System• Transverse Mercator projection is used for zones that have a north-south axis (taller than wide).

• Lambert conformal conic is used for zones that are elongated in the east-west direction. Why?

• Original units of measurement are feet, which are measured from a false origin.

• SPC maps are found based on both NAD27 and NAD83, like with UTM, but SPC 83 is in meters, while SPC 27 is in feet

Introduction to GIS

©2006 Austin Troy

SPC System• Note how a

conic projection is used here, since the errors indicate an east-west central line

Polygon errors -- state plane

Introduction to GIS

©2006 Austin Troy

SPC System• Many States have their own version of SPC

• Vermont has the Vermont State Plane Coordinate System, which is in meters and based on NAD83

• In 1997, VCGI converted all their data from SPC 27 to SPC 83

• Vermont uses Transverse Mercator because of its north-south orientation

Introduction to GIS

©2006 Austin Troy

• Here are some State Plane zone maps

SPC System

Introduction to GIS

©2006 Austin Troy

• Here are some State Plane zone maps

SPC System

Introduction to GIS

©2006 Austin Troy

• Primary purpose of GIS database?

• Acreage summaries, navigation, cartography….

• Location (polar, equatorial, middle latitudes?)

• Extent (world, state, local?)

• Source data projection (check metadata!)

• Map scale … large or small

• Match projection of existing GIS database (master)

• Match projection to requirements (e.g., contract)

Which to use?

Introduction to GIS

©2006 Austin Troy

Bottom line


Introduction to GIS

©2006 Austin Troy Slide courtesy of Leslie Morrissey

Projection applied in ArcGIS

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