3Definitions: Ellipsoid Also referred to as Spheroid, although Earth is not a sphere but is bulging at the equator and flattened at the polesFlattening is about 21.5 km difference between polar radius and equatorial radiusEllipsoid model necessary for accurate range and bearing calculation over long distances GPS navigationBest models represent shape of the earth over a smoothed surface to within 100 meters
4The Spheroid and Ellipsoid The sphere is about 40 million meters in circumference.An ellipsoid is an ellipse rotated in three dimensions about its shorter axis.The earth's ellipsoid is only 1/297 off from a sphere.Many ellipsoids have been measured, and maps based on each. Examples are WGS84 and GRS80.
6WGS 84 Geoid defines geoid heights for the entire earth Geoid: the true 3-D shape of the earth considered as a mean sea level extended continuously through the continentsApproximates mean sea levelWGS 84 Geoid defines geoid heights for the entire earth
8Definition: DatumA mathematical model that describes the shape of the ellipsoidCan be described as a reference mapping surfaceDefines the size and shape of the earth and the origin and orientation of the coordinate system used.There are datums for different parts of the earth based on different measurementsDatums are the basis for coordinate systemsLarge diversity of datums due to high precision of GPSAssigning the wrong datum to a coordinate system may result in errors of hundreds of meters
9Commonly used datums Datum Spheroid Region of use NAD 27 Clark 1866 Canada, US, Atlantic/Pacific Islands, Central AmericaNAD 83GRS 1980Canada, US, Central AmericaWGS 84Worldwide
10The DatumAn ellipsoid gives the base elevation for mapping, called a datum.Examples are NAD27 and NAD83.The geoid is a figure that adjusts the best ellipsoid and the variation of gravity locally.It is the most accurate, and is used more in geodesy than GIS and cartography.
12Map ScaleThe ratio of the distance between two points on the map and the real world (earth) distance between the same two pointsMap measurement / Real world measurement
13Map ScaleMap scale is based on the representative fraction, the ratio of a distance on the map to the same distance on the ground.Most maps in GIS fall between 1:1 million and 1:1000.A GIS is scaleless because maps can be enlarged and reduced and plotted at many scales other than that of the original data.To compare or edge-match maps in a GIS, both maps MUST be at the same scale and have the same extent.The metric system is far easier to use for GIS work.
14Types of ScaleGraphicalVerbalRepresentative Fraction
22Relative Location Systems Real world descriptionsCorner of 34th and Fifth
23Absolute Location Systems Absolute descriptionUses mathematical coordinates to define the position of grid intersections with respect to a defined (accepted) origin
24Absolute Location Systems Common Absolute Location SystemsGlobal Coordinate SystemCartesian Coordinate SystemsUniversal Transverse Mercator (UTM) Coordinate SystemState Plate Coordinate System
25Geographic Coordinates Geographic coordinates are the earth's latitude and longitude system, ranging from 90 degrees south to 90 degrees north in latitude and 180 degrees west to 180 degrees east in longitude.A line with a constant latitude running east to west is called a parallel.A line with constant longitude running from the north pole to the south pole is called a meridian.The zero-longitude meridian is called the prime meridian and passes through Greenwich, England.A grid of parallels and meridians shown as lines on a map is called a graticule.
26The Global Coordinate System Spherical coordinate systemUnprojectedExpressed in terms of two angleslatitudelongitudeLatitude and longitude are traditionally measured in degrees, minutes, and seconds (DMS).
27Origin for the Global Coordinate System Latitudepositive in northern hemispherenegative in southern hemisphereLongitudepositive east of Prime Meridiannegative west of Prime Meridian
29The Global Coordinate System LongitudeAngle formed by a line going from the intersection of the prime meridian and the equator to the center of the earth, and a second line from the center of the earth to the point in question
30The Global Coordinate System LatitudeAngle formed by a line from the equator toward the center of the earth, and a second line perpendicular to the reference ellipsoid at the point in question
31Cartesian Coordinate Systems Computationally, it is much simpler to work with Cartesian coordinates than with spherical coordinatesx,y coordinatesreferred to as “eastings” & “northings”defined units, e.g. meters, feet
32Map ProjectionsA transformation of the spherical or ellipsoidal earth onto a flat map is called a map projection.The map projection can be onto a flat surface or a surface that can be made flat by cutting, such as a cylinder or a cone.If the globe, after scaling, cuts the surface, the projection is called secant. Lines where the cuts take place or where the surface touches the globe have no projection distortion.
33Map Projections (cont.) Projections can be based on axes parallel to the earth's rotation axis (equatorial), at 90 degrees to it (transverse), or at any other angle (oblique).A projection that preserves the shape of features across the map is called conformal.A projection that preserves the area of a feature across the map is called equal area or equivalent.No flat map can be both equivalent and conformal. Most fall between the two as compromises.To compare or edge-match maps in a GIS, both maps MUST be in the same projection.
34ProjectionMethod of representing data located on a curved surface onto a flat planeAll projections involve some degree of distortion of:DistanceDirectionScaleAreaShapeDetermine which parameter is importantProjections can be used with different datums
35ProjectionsThe earth is “projected” from an imaginary light source in its center onto a surface, typically a plate, cone, or cylinder.Planar or azimuthalConicCylindrical
36Cylindrical Projections Secancy: projection surface cuts through globe, this reduces distortion of larger land areasTangency: only one point touches surfaceUsed for entire worldParallels and meridians form straight lines
37Example Cylindrical Projections Shapes and angles within small areas are true (7.5’ Quad)Distances only true along equator
38Conic Projections Can only represent one hemisphere Often used to represent areas with east-west extent (US)
39Lambert is used in State Plane Coordinate System Albers is used by USGS for state maps and all US maps of 1:2,500,000 or smallerLambert is used in State Plane Coordinate SystemSecant at 2 standard parallelsDistorts scale and distance, except along standard parallelsAreas are proportionalDirections are true in limited areas
40Azimuthal Projections Often used to show air route distancesDistances measured from center are trueDistortion of other properties increases away from the center point
41Orthographic:Used for perspective views of hemispheresArea and shape are distortedDistances true along equator and parallelsLambert:Specific purpose of maintaining equal areaUseful for areas extending equally in all directions from center (Asia, Atlantic Ocean)Areas are in true proportionDirection true only from center pointScale decreases from center point
42Other Projections Pseudocylindrical Unprojected or Geographic projection: Latitude/LongitudeThere are over 250 different projections!
43Pseudocylindrical:Used for world mapsStraight and parallel latitude lines, equally spaced meridiansOther meridians are curvesScale only true along standard parallel of 40:44 N and 40:44 SRobinson is compromise between conformality, equivalence and equidistance
44Mathematical Relationships ConformalityScale is the same in every directionParallels and meridians intersect at right anglesShapes and angles are preservedUseful for large scale mappingExamples: Mercator, Lambert Conformal ConicEquivalenceMap area proportional to area on the earthShapes are distortedIdeal for showing regional distribution of geographic phenomena (population density, per capita income)Examples: Albers Conic Equal Area, Lambert Azimuthal Equal Area, Peters, Mollweide
45Mathematical Relationships EquidistanceScale is preservedParallels are equidistantly placedUsed for measuring bearings and distances and for representing small areas without scale distortionLittle angular distortionGood compromise between conformality and equivalenceUsed in atlases as base for reference maps of countriesExamples: Equidistant Conic, Azimuthal EquidistantCompromiseCompromise between conformality, equivalence and equidistanceExample: Robinson
47Local Coordinate Systems A coordinate system is a standardized method for assigning codes to locations so that locations can be found using the codes alone.Standardized coordinate systems use absolute locations.A map captured in the units of the paper sheet on which it is printed is based on relative locations or map millimeters.In a coordinate system, the x-direction value is the easting and the y-direction value is the northing. Most systems make both values positive.
49Coordinate Systems for the US Some standard coordinate systems used in the United States aregeographic coordinatesuniversal transverse Mercator systemmilitary gridstate planeTo compare or edge-match maps in a GIS, both maps MUST be in the same coordinate system.
51The Universal Transverse Mercator Coordinate System 60 zones, each 6° longitude wideZones run from 80° S to 84° NPoles covered by Universal Polar System (UPS)
52UTM Zone Projection Transverse Mercator Projection applied to each 6o zone tominimize distortion
53UTM Coordinate Parameters UnitmetersZones:6o longititueN and S zonesseparate coordX-origin500,000 m eastof central meridianY-originequator
54Advantage of UTM Settings Zone central meridian Eastings = 500,000 metersNorth pole Northings = 10,000,000 metersallows overlap between zones form mapping purposesgive all eastings positive numberstell if we are to the east or west of the central meridianprovide relationship between true north and grid north
55State Plane Coordinate System Each state has one or more zonesZones are either N-S or E-W oriented (except Alaska)Each zone has separate coordinate system and appropriate projectionUnit: feetNo negative numbers
56Map Projections for State Plane Coordinate System E-W zones: Lambert conformal conic projectionN-S zones: Transverse Mercator Projection
57Pros and Cons of SPCS Advantages: The system is used primarily for engineering applicationse.g. utility companies, local governments to do accuratesurveying of facilities network (sewers, power lines)More accurate than UTM.feet vs. metersSPCS deals with smaller areaDisadvantages:Lack of universality cause problems for mapping over large areas such as across zones and states
58Projections and Datums Projections and datums are linkedThe datum forms the reference for the projection, so...Maps in the same projection but different datums will not overlay correctlyTens to hundreds of metersMaps in the same datum but different projections will not overlay correctlyHundreds to thousands of meters.
59Determining datum or projection for existing data MetadataData about dataMay be missingSoftwareSome allow it, some don’tComparisonOverlay may show discrepanciesIf locations are approx. 200 m apart N-S and slightly E-W, southern data is in NAD27 and northern in NAD83
60Selecting Datums and Projections Consider the following:Extent: world, continent, regionLocation: polar, equatorialAxis: N-S, E-WSelect Lambert Conformal Conic for conformal accuracy and Albers Equal Area for areal accuracy for E-W axis in temperate zonesSelect UTM for conformal accuracy for N-S axisSelect Lambert Azimuthal for areal accuracy for areas with equal extent in all directionsOften the base layer determines your projections
61GIS Capability A GIS package should be able to move between map projections,coordinate systems,datums, andellipsoids.
62SummaryThere are very significant differences between datums, coordinate systems and projections,The correct datum, coordinate system and projection is especially crucial when matching one spatial dataset with another spatial dataset.