and Brian Voigt 2011 except where noted Lecture 6 Introduction to Projections and Coordinate Systems By Austin Troy and Brian Voigt University of Vermont with sections adapted from ESRIs online course on projections ID: 298723
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Slide1
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Lecture 6:Introduction to Projections and Coordinate SystemsBy Austin Troy and Brian Voigt, University of Vermont,with sections adapted from ESRI’s online course on projections
------Using GIS--Slide2
The Earth’s Size and Shape
It is only relatively recently that we’ve been able to say what both areEstimates of shape by the ancients have ranged from a flat disk, to a cube to a cylinder to an oyster.Pythagoras was the first to postulate the Earth was a sphereBy the fifth century BCE, this was firmly established.But how big was it?
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide3
The Earth’s Size
It was Posidonius who used the stars to determine the earth's circumference. “He observed that a given star could be seen just on the horizon at Rhodes. He then measured the star's elevation at Alexandria, Egypt, and calculated the angle of difference to be 7.5 degrees or 1/48th of a circle. Multiplying 48 by what he believed to be the correct distance from Rhodes to Alexandria (805 kilometers or 500 miles), Posidonius calculated the earth's circumference to be 38,647 kilometers (24,000 miles)--an error of only three percent.” -source: ESRI
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide4
The Earth’s Shape
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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide5
The Earth’s Shape
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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide6
SpheroidsThe International 1924 and the Bessel 1841 spheroids are used in Europe while in North America the GRS80, and decreasingly, the Clarke 1866 Spheroid, are usedIn Russia and China the Krasovsky spheroid is used and in India the Everest spheroid
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide7
SpheroidsTwo common spheroids use slightly different major and minor axis lengths
Source: ESRI
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide8
SpheroidsOne more thing about spheroids: If your mapping scales are smaller than 1:5,000,000 (small scale maps), you can use an authalic sphere to define the earth's shape to make things more simpleFor maps at larger scale (most of the maps we work with in GIS), you generally need to employ a spheroid to ensure accuracy and avoid positional errors
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide9
GeoidWhile the spheroid represents an idealized model of the earth’s shape, the geoid represents the “true,” highly complex shape of the earth, which, although “spheroid-like,” is actually very irregular at a fine scale of detail, and can’t be modeled with a formula (the DOD tried and gave up after building a model of 32,000 coefficients)It is the 3 dimensional surface of the earth along which the pull of gravity is a given constant; ie. a standard mass weighs an identical amount at all points on its surface The gravitational pull varies from place to place because of differences in density, which causes the geoid to bulge or dip above or below the ellipsoidOverall these differences are small ~ 100 meters
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide10
Geoid
www.esri.com/news/arcuser/0703/geoid1of3.html
The geoid is actually measured and interpolated, using gravitational measurements.
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide11
Spheroids and GeoidsWe have several different estimates of spheroids because of irregularities in the earth surface: there are slight deviations and irregularities in different regionsBefore remote satellite observation, had to use a different spheroid for different regions to account for irregularities (see Geoid, ahead) to avoid positional errorsThat is, continental surveys were isolated from each other, so ellipsoidal parameters were fit on each continent to create a spheroid that minimized error in that region, and many stuck with those for years
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide12
The Geographic GridOnce you have a spheroid, you also define the location of poles (axis points of revolution) and equator (midway circle between poles, spanning the widest dimension of the spheroid), you have enough information to create a coordinate grid or “graticule” for referencing the position of features on the spheroid.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide13
The Geographic GridThis is a location reference system for the earth’s surface, consisting of:Meridians: lines of longitude andParallels: lines of latitude
Source: ESRI
Prime meridian is at
0º longitude (Greenwich, England)
Equator is at 0º latitude
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide14
The Geographic GridThis is like a planar coordinate system, with an origin at the point where the equator meets the prime meridianThe difference is that it is not a grid because grid lines must meet at right angles; this is why it’s called a graticule insteadEach degree of latitude represents about 110 km, although, that varies slightly because the earth is not a perfect sphere
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide15
The Geographic GridLatitude and longitude can be measured either in degrees, minutes, seconds (e.g. 56° 34’ 30”), where minutes and seconds are base-60 (like on a clock)Can also use decimal degrees (more common in GIS), where minutes and seconds are converted to a decimalExample: 45° 52’ 30” = 45.875 °
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide16
The Geographic GridLatitude lines form parallel circles of different sizes, while longitude lines are half-circles that meet at the polesLatitude goes from 0 to 90º N or S and longitude to 180 º E or W of meridian; the 180 º line is the date line
Source: ESRI
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide17
DatumsThree dimensional surface from which latitude, longitude and elevation are calculatedAllows us to figure out where things actually are on the graticule since the graticule only gives us a framework for measuring, not actual locationsFrame of reference for placing specific locations at specific points on the spheroidDefines the origin and orientation of latitude and longitude lines.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide18
Datums A datum is essentially the model that is used to translate a spheroid into locations on the earthA 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 spheroidTwo things are needed for datum: spheroid and set of surveyed and measured points
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide19
Surface-Based DatumsPrior 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 sub-refence points came to be known as the datum.
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide20
Surface-Based DatumsStarting points need to be very central relative to landmass being measuredIn 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 requiredProblem: errors compound with distance
Lecture materials by Austin Troy and Brian Voigt © 2011,
except where notedSlide21
c
Surface-Based DatumsThese were largely done without having to measure distances. How?Using high-quality celestial observations and distance measurements for the first two observations, could then use trigonometry to determine distances.
a
b
A
With b and c and A known,
determine
a’s location through solving for B and C by the law of
sines
B=A(sin(b))/(sin(a))
B
C
D
E
Mead’s Ranch
Secondary
Measured
point
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide22
Satellite-Based DatumsCenter of the spheroid can be matched with the center of the earth.Satellites started collecting geodetic information in 1962 as part of National Geodetic SurveyYields a spheroid that when used as a datum correctly maps the earth such that all lat / lon measurements from all maps created with that datum agree.Rather than linking points through surface measures to initial surface point, are measurements are linked to reference point in outer space
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide23
Common DatumsPreviously, 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 AmericaWorld Geodetic System 1984 (WGS84) is newer spheroid / datum, created by the US DOD; it is more or less identical to Geodetic Reference System 1980 (GRS80). GPS uses WGS84
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide24
Lat / Long and DatumsPre-satellite datums are surface-based. A given datum has the spheroid meet the earth in a specified location.Datum is most accurate near the contact point, less accurate as move away (remember, this is different from a projection surface because the ellipsoid is 3D).
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide25
Lat / Long and DatumsLat / long coordinates calculated with one datum are valid only with reference to that datum.This means those coordinates calculated with NAD27 are in reference to a NAD27 earth surface, not a NAD83 earth surface.Example: the DMS control point in Redlands, CA is -117º 12’ 57.75961”, 34 º 01’ 43.77884” in NAD83 and -117º 12’ 54.61539” 34 º 01’ 43.72995” in NAD27Click here for a chart of the different coordinates for the Capital Dome center under different datums (Peter Dana)
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide26
Datum ShiftWhen we go from a surface-oriented datum to a spheroid-based datum, the estimated position of survey benchmarks improves; this is called datum shiftThat shift varies with location: 10 to 100 m in the continental US, 400 m in Hawaii, 35 m in Vermont
Source: http
://www.ngs.noaa.gov/TOOLS/Nadcon/Nadcon.html
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide27
Map ProjectionThis is the method by which we transform the earth’s spheroid (real world) to a flat surface (abstraction), either on paper or digitallyBecause we can’t take our globe everywhere with us!Remember: most GIS layers are 2-D
3D
2D
Think about projecting a
globe
onto a wall
Source: ESRI
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide28
Map Projection
The earliest and simplest map projection is the plane chart, or plate carrée, invented around the first century; it treated the graticule as a grid of equal squares, forcing meridians and parallels to meet at right angles
If applied to the world as mapped now, it would look like
:
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide29
Map Projection: DistortionBy definition, projections distorts:Shape Area Distance DirectionSome projections specialize in preserving one or several of these features, but none preserve all
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide30
Shape DistortionShape: projection can distort the shape of a feature. Conformal maps preserve the shape of smaller, local geographic features, while general shapes of larger features are distorted. That is, they preserve local angles; angle on map will be same as angle on globe. Conformal maps also preserve constant scale locally.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide31
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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide32
Area DistortionArea: projection can distort the property of equal area (or equivalent), meaning that features have the correct area relative to one another.Map projections that maintain this property are often called equal area map projections.For instance, if S America is 8x larger than Greenland on the globe, it will be 8x larger on mapNo map projection can have conformality and equal area >>> sacrifice shape to preserve area and vice versa.
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide33
Area Distortion827,000 square miles6.8 million square miles
Mercator Projection
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide34
Distance DistortionDistance: projection can distort measures of true distance. Accurate distance is maintained for only certain parallels or meridians unless the map is localized. Maps are said to be equidistant if distance from the map projection's center to all points is accurate.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide35
Distance Distortion
4,300 km: Robinson
5,400 km: Mercator
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide36
Direction DistortionDirection: projection can distort true directions between geographic locations; that is, it can mess up the angle, or azimuth between two features. Some azimuthal map projections maintain the correct azimuth between any two points. In a map of this kind, the angle of a line drawn between any two locations on the projection gives the correct direction with respect to true north.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide37
Map Projection: DistortionWhen 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.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide38
Projection Specific DistortionMercator maintains shape and direction, but sacrifices area accuracy.The Sinusoidal and Equal-Area Cylindrical projections both maintain area, but look quite different from each other. The latter distorts shape.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.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide39
Projection Specific Distortion
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Mercator—goes on forever
Robinson
SinusoidalSlide40
Quantifying DistortionTissot’s indicatrix, made up of ellipses, is a method for measuring distortion of a map; here is Robinson
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide41
Quantifying Distortion
Sinusoidal
Area of these ellipses should be same as those at equator, but shape is different
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide42
Map Projection: Cylindrical
Created by wrapping a cylinder around a globeThe meridians (longitude) in cylindrical projections are equally spaced, while the spacing between parallel lines (latitude) increases toward the polesMeridians never converge so poles can’t be shown
Source: ESRI
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide43
Cylindrical Map Types
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 accurateIf 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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide44
Cylindrical Map TypesSecant projections are more accurate because projection is more accurate the closer the projection surface is to the globe and a when the projection surface touches twice, that means it is on average closer to the globeThe distance from map surface to projection surface is described by a scale factor, which is 1 where they touch
Earth surface
Projection surface
0.9996
Central meridian
Standard meridians
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide45
Cylindrical Map Types3. Transverse cyclindrical projections: in this type the cylinder is turned on its side so it touches a line of longitude; these can also be tangent
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide46
Cylindrical Map Distortion
A north-south cylindrical Projections cause major distortions in higher latitudes because those points on the cylinder are further away from from the corresponding point on the globeScale is constant in north-south direction and in east west direction along the equator for an equatorial projection but non constant in east-west direction as move up in latitudeRequires alternating Scale Bar based on latitude
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide47
Cylindrical Map Distortion
If such a map has a scale bar, know that it is only good for those places and directions in which scale is constant—the equator and the meridiansHence, the measured distance between Nairobi and the mouth of the Amazon might be correct, but the measured distance between Toronto and Vancouver would be off; the measured distance between Alaska and Iceland would be even further off
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide48
Cylindrical Map Distortion
X miles
0
◦
atitude
25
◦
latitude
50
◦
latitude
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide49
Cylindrical Map Distortion
Why is this? Because meridians are all the same length, but parallels are not.This sort of projection forces parallels to be same length so it distorts them As move to higher latitudes, east-west scale increases (2 x equatorial scale at 60° N or S latitude) until reaches infinity at the poles; N-S scale is constantSlide50
Map Projection: Conic
Projects a globe onto a coneIn simplest case, globe touches cone along a single latitude line, or tangent, called standard parallelOther latitude lines are projected onto coneTo flatten the cone, it must be cut along a line of longitude (see image)
The opposite line of longitude is called the
central
meridian
Source: ESRI
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide51
Map Projection: Conic
Is most accurate where globe and cone meet—at the standard parallelDistortion generally increases north or south of it, so poles are often not includedConic projections are typically used for mid-latitude zones with east-to-west orientation. They are normally applied only to portions of a hemisphere (e.g. North America)
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide52
Map Projection: Conic
Can be tangent or secantSecants are more accurate for reasons given earlier
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide53
Map Projection: Planar /AzimuthalProject a globe onto a flat planeThe simplest form is only tangent at one pointAny point of contact may be used but the poles are most commonly used
Source: ESRI
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide54
When another location is used, it is generally to make a small map of a specific areaWhen the poles are used, longitude lines look like hub and spokesBecause the area of distortion is circular around the point of contact, they are best for mapping roughly circular regions, and hence the poles
Source: ESRI
Map Projection: Planar /Azimuthal
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide55
Map Projection: Mercator
Specific type of cylindrical projectionInvented by Gerardus Mercator during the 16th CenturyIt 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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide56
Map Projection: MercatorNot so good for preserving areaEnlarges high latitude features like Greenland & Antarctica and shrinks mid latitude features.
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide57
Map Projection:Transverse Mercator
Invented by Johann Lambert in 1772, this projection is cylindrical, but the axis of the cylinder is rotated 90°, so the tangent line is longitudinal, rather than the equator 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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide58
Map Projection:Transverse MercatorTransverse Mercator projection is not used on a global scale but is applied to regions that have a general north-south orientation, while Mercator tends to be used more for geographic features with east-west axis.Commonly used in the US with the State Plane Coordinate system, with north-south features
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide59
Lecture materials by Austin Troy © 2008, except where noted
Map Projection:Lambert Conformal Conic
Invented
in 1772, this is a form of a 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: ESRISlide60
Map Projection:Lambert Conformal ConicVery good for middle latitudes with east-west orientation. It portrays the pole as a pointIt 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
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide61
Map Projection:Lambert Conformal Conic
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 tangentThere is no distortion along those two linesDistortion increases with distance from secants
Source: ESRI
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide62
Map Projection: Albers Equal Area Conic
Developed by Heinrich Christian Albers in the early nineteenth century for European mapsConic projection, using secants as standard parallelsDifferences between Albers and Lambert Lambert preserves shape Albers preserves areaPoles are not represented as points, but as arcs, meaning that meridians don’t convergeLatitude lines are unequally spaced concentric circles, whose spacing decreases toward the poles. Useful for portraying large land units, like Alaska or all 48 states
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide63
Map Projection: Albers Equal Area Conic
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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide64
Other Selected Projections
More Cylindrical equal area: (have straight meridians and parallels, the meridians are equally spaced, the parallels unequally spaced) Behrmann cyclindrical equal-area: single standard parallel at 30 ° northGall’s stereographic: secant intersecting at 45° north and 45 ° southPeter’s:
de-emphasizes area exaggerations in high latitudes; standard parallels at 45 or 47
°
Thanks to Peter Dana,
The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder
for links
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide65
Other Selected Projections
Azimuthal projections:Azimuthal equidistant: preserves distance property; used to show air route distancesLambert Azimuthal equal area: Often used for polar regions; central meridian is straight, others are curvedOblique Aspect OrthographicNorth Polar Stereographic
Thanks to Peter Dana,
The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder
for links
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide66
Other Selected Projections
More conic projectionsEquidistant Conic: used for showing areas near to, but on one side of the equator, preserves only distance propertyPolyconic: used for most of the early USGS quads; based on an infinite number of cones tangent to an infinite number of parallels; central meridian straight but other lines are complex curves
Thanks to Peter Dana,
The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder
for links
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide67
Other Selected Projections
Pseudo-cylindrical projections: resemble cylindrical projections, with straight, parallel parallels and equally spaced meridians, but all meridians but the reference meridian are curvesMollweide: used for world maps; is equal-area; 90th meridians are semi-circles Robinson:based on tables of coordinates, not mathematical formulas; distorts shape, area, scale, and distance in an attempt to make a balanced map
Thanks to Peter Dana,
The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder
for links
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide68
Coordinate Systems
Map projections 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)
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide69
Coordinate Systems
Projections are designed to minimize distortions of the four properties we talked about, because as scale decreases, error increasesCoordinate 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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide70
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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide71
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
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide72
Coordinate Systems
The four most commonly used coordinate systems in the US:Universal Transverse Mercator (UTM) grid systemState Plane Coordinate System (SPC)Others:The Universal Polar Stereographic (UPS) grid systemThe Public Land Survey System (PLSS)
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide73
UTM
Universal Transverse MercatorUTM 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 datums, so you will often see a layer as projected in “UTM83” or “UTM27”UTM is used for large scale mapping applications the world over, when the unit of analysis is fairly small, like a state
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide74
UTM
UTM divides the earth between 84°N and 80°S into 60 zones, each of which covers 6 degrees of longitudeZone 1 begins at 180 ° W longitude.Each UTM zone is projected separately There is a false origin (zero point) in each zone
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide75
United States UTM Zones
Lecture materials by Austin Troy and Brian Voigt © 2011, except where notedSlide76
UTM
Scale factors are 0.9996 in the middle and 1 at the secantsIn 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 0.9996
Earth surface
Projection surface
0.9996
Central meridian
Standard meridians
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide77
UTM
In the northern hemisphere, coordinates are measured from a false origin at the equator and 500,000 meters west of the central meridianIn the southern hemisphere, coordinates are measured from a false origin 10,000,000 meters south of the equator and 500,000 meters west of the central meridianAccuracy: 1 in 2,500
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide78
UTM
Because each zone is big, UTM can result in significant errors as get further away from the center of a zone, corresponding to the central line
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide79
SPC System
State Plane Coordinate System is one of the most common coordinate systems in use in the USIt was developed in the 1930s to record original land survey monument locations in the USMore accurate than UTM, with required accuracy of 1 part in 10,000Zones are much smaller—many states have two or more zones
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide80
SPC System
Transverse Mercator projection is used for zones that have a north south access. Lambert conformal conic is used for zones that are elongated in the east-west direction. Why?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 SPC83 is in meters, while SPC27 is in feet
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide81
SPC System
Many States have their own version of SPCVermont has the Vermont State Plane Coordinate System, which is in meters and based on NAD83In 1997, VCGI converted all their data from SPC27 to SPC83Vermont uses Transverse Mercator because of its north-south orientation
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where notedSlide82
State Plane Zone Map of New Englandhttp://www.ems-i.com/smshelp/General_Tools/Coordinates/new_england_state_plane.htm
Lecture materials by Austin Troy and Brian Voigt © 2011,
except where notedSlide83
State Plane Zone Map of the Northwesthttp://www.ems-i.com/smshelp/General_Tools/Coordinates/northwest_state_plane.htm
Lecture materials by Austin Troy and Brian Voigt © 2011,
except where notedSlide84
SPC System
Note how a conic projection is used here, since the errors indicate an east-west central line
Polygon errors-state plane
Lecture materials by Austin Troy
and Brian Voigt © 2011,
except where noted