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Fundamentals of GIS Lecture materials by Austin Troy 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 ESRI’s online course on projections Using GIS--

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Fundamentals of GIS The Earth’s Size and Shape It is only relatively recently that we’ve been able to say what both are Estimates 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 sphere By the fifth century BCE, this was firmly established. But how big was it? Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS Spheroids The International 1924 and the Bessel 1841 spheroids are used in Europe while in North America the GRS80, and decreasingly, the Clarke 1866 Spheroid, are used In 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 noted

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Fundamentals of GIS Spheroids Two common spheroids use slightly different major and minor axis lengths Source: ESRI Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Spheroids One 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 simple For 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 noted

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Fundamentals of GIS Geoid While 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 ellipsoid Overall these differences are small ~ 100 meters Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Geoid The geoid is actually measured and interpolated, using gravitational measurements. Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Spheroids and Geoids We have several different estimates of spheroids because of irregularities in the earth surface: there are slight deviations and irregularities in different regions Before remote satellite observation, had to use a different spheroid for different regions to account for irregularities (see Geoid, ahead) to avoid positional errors That 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 noted

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Fundamentals of GIS The Geographic Grid Once 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 noted

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Fundamentals of GIS The Geographic Grid 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 0º longitude (Greenwich, England) Equator is at 0º latitude Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS The Geographic Grid This is like a planar coordinate system, with an origin at the point where the equator meets the prime meridian The difference is that it is not a grid because grid lines must meet at right angles; this is why it’s called a graticule instead Each 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 noted

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Fundamentals of GIS The Geographic Grid Latitude 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 decimal Example: 45° 52’ 30” = ° Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS The Geographic Grid Latitude lines form parallel circles of different sizes, while longitude lines are half-circles that meet at the poles Latitude 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 noted

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Fundamentals of GIS Datums Three dimensional surface from which latitude, longitude and elevation are calculated Allows us to figure out where things actually are on the graticule since the graticule only gives us a framework for measuring, not actual locations Frame of reference for placing specific locations at specific points on the spheroid Defines the origin and orientation of latitude and longitude lines. Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Datums A datum is essentially the model that is used to translate a spheroid into locations on the earth 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 Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Surface-Based Datums 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 sub-refence points came to be known as the datum. Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Surface-Based Datums 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 required Problem: errors compound with distance Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS c Surface-Based Datums These 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 noted

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Fundamentals of GIS Satellite-Based Datums 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 SurveyNational Geodetic Survey Yields 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 noted

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Fundamentals of GIS Common Datums 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 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 noted

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Fundamentals of GIS Lat / Long and Datums Pre-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 noted

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Fundamentals of GIS Lat / Long and Datums Lat / 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’ ”, 34 º 01’ ” in NAD83 and -117º 12’ ” 34 º 01’ ” in NAD27 Click here for a chart of the different coordinates for the Capital Dome center under different datums (Peter Dana)Click here Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Datum Shift When we go from a surface-oriented datum to a spheroid-based datum, the estimated position of survey benchmarks improves; this is called datum shiftdatum shift That shift varies with location: 10 to 100 m in the continental US, 400 m in Hawaii, 35 m in Vermont Source: Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Map Projection 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 3D 2D Think about projecting a globe onto a wall Source: ESRI Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS Map Projection: Distortion By definition, projections distorts: Shape Area Distance Direction Some 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 noted

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Fundamentals of GIS Shape Distortion Shape: 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 noted

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Fundamentals of 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 Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Area Distortion Area: 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 map No 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 noted

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Fundamentals of GIS Area Distortion 827,000 square miles 6.8 million square miles Mercator Projection Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Distance Distortion Distance: 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 noted

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Fundamentals of GIS Distance Distortion 4,300 km: Robinson 5,400 km: Mercator Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Direction Distortion Direction: 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 noted

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Fundamentals of GIS Map Projection: Distortion 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. Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Projection Specific Distortion Mercator 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 noted

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Fundamentals of GIS Projection Specific Distortion Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted Mercator—goes on forever Robinson Sinusoidal

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Fundamentals of GIS Quantifying Distortion Tissot’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 noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS Map Projection: Cylindrical Created by wrapping a cylinder around a globe The meridians (longitude) in cylindrical projections are equally spaced, while the spacing between parallel lines (latitude) increases toward the poles Meridians never converge so poles can’t be shown Source: ESRI Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of 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: Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Cylindrical Map Types Secant 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 globe The distance from map surface to projection surface is described by a scale factor, which is 1 where they touch Earth surface Projection surface Central meridian Standard meridians Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Cylindrical Map Types 3. 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 noted

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Fundamentals of GIS 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 globe Scale 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 latitude Requires alternating Scale Bar based on latitude Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 meridians Hence, 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 noted

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Fundamentals of GIS Cylindrical Map Distortion X miles 0 ◦ atitude 25 ◦ latitude 50 ◦ latitude Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 constant

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Fundamentals of GIS Map Projection: 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 Source: ESRI Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Map Projection: Conic Is most accurate where globe and cone meet—at the standard parallel Distortion generally increases north or south of it, so poles are often not included Conic 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 noted

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Fundamentals of GIS Map Projection: Conic Can be tangent or secant Secants are more accurate for reasons given earlier Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Map Projection: Planar /Azimuthal 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 Source: ESRI Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 Because 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 noted

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Fundamentals of GIS Map Projection: Mercator Specific type of cylindrical projection Invented by Gerardus Mercator during the 16 th 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 Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Map Projection: Mercator Not so good for preserving area Enlarges high latitude features like Greenland & Antarctica and shrinks mid latitude features. Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS Map Projection: Transverse Mercator Transverse 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 noted

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Fundamentals of GIS 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: ESRI

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Fundamentals of GIS Map Projection: Lambert Conformal Conic 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 Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 tangent There is no distortion along those two lines Distortion increases with distance from secants Source: ESRI Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS Map Projection: Albers Equal Area Conic Developed by Heinrich Christian Albers in the early nineteenth century for European maps Conic projection, using secants as standard parallels Differences between Albers and Lambert Lambert preserves shape Albers preserves area 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. Useful for portraying large land units, like Alaska or all 48 states Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS 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 ° northBehrmann cyclindrical equal-area Gall’s stereographic: secant intersecting at 45° north and 45 ° southGall’s stereographic: Peter’s: de-emphasizes area exaggerations in high latitudes; standard parallels at 45 or 47 °Peter’s: 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 noted

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Fundamentals of GIS Other Selected Projections Azimuthal projections: Azimuthal equidistant: preserves distance property; used to show air route distancesAzimuthal equidistant Lambert Azimuthal equal area: Often used for polar regions; central meridian is straight, others are curvedLambert Azimuthal equal area Oblique Aspect Orthographic North 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 noted

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Fundamentals of GIS Other Selected Projections More conic projections Equidistant Conic: used for showing areas near to, but on one side of the equator, preserves only distance propertyEquidistant Conic Polyconic: 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 curvesPolyconic 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 noted

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Fundamentals of GIS 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 curves Mollweide: used for world maps; is equal-area; 90 th meridians are semi-circlesMollweide: Robinson:based on tables of coordinates, not mathematical formulas; distorts shape, area, scale, and distance in an attempt to make a balanced mapRobinson 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 noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS 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 Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS Coordinate Systems The four most commonly used coordinate systems in the US: Universal Transverse Mercator (UTM) grid system State Plane Coordinate System (SPC) Others: The Universal Polar Stereographic (UPS) grid system The Public Land Survey System (PLSS) Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS UTM Universal Transverse Mercator 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 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 noted

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Fundamentals of GIS 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. 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 noted

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Fundamentals of GIS United States UTM Zones Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS UTM Scale factors are in the middle and 1 at the secants 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 Earth surface Projection surface Central meridian Standard meridians Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS UTM In the northern hemisphere, coordinates are measured from a false origin at the equator and 500,000 meters west of the central meridian In 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 meridian Accuracy: 1 in 2,500 Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS 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 Zones are much smaller—many states have two or more zones Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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 noted

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Fundamentals of GIS 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 NAD83Vermont State Plane Coordinate System In 1997, VCGI converted all their data from SPC27 to SPC83 Vermont uses Transverse Mercator because of its north-south orientation Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS State Plane Zone Map of New England Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS State Plane Zone Map of the Northwest Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted

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Fundamentals of GIS 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

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