1、Chapter 3Coordinate SystemsCopyright McGraw-Hill Education.Permission required for reproduction or display.3-1Outline GIS Concepts About coordinate systems Geographic coordinate systems Projected coordinate systems Raster coordinate systems Common projection systems Choosing projections About ArcGIS
2、 Labeling coordinate systems On-the-fly projection Projecting data Troubleshooting coordinate systems Georeferencing rastersCopyright 2015 by Maribeth H.Price3-2GIS ConceptsChapter 3.Coordinate SystemsCopyright 2015 by Maribeth H.Price3-3About coordinate systemsCopyright 2015 by Maribeth H.Price3-4C
3、oordinate systemsCopyright 2015 by Maribeth H.Price3-5Figure 1.An arbitrary coordinate system used for surveying a site2507500,0250500750175,200500FenceBuilding ABuilding BTypes of coordinate systems Unprojected Based on spherical globe coordinates Degrees of latitude and longitude Projected Convert
4、s spherical coordinates to planar Set of mathematical equations Projects 3D coordinates to 2D mapCopyright 2015 by Maribeth H.Price3-6Copyright 2015 by Maribeth H.Price3-7Topo maps show three different coordinate systems:One unprojected systemGCS(degrees)And two projected systemsState Plane(feet)UTM
5、(meters)Same point has different x-y values depending on the coordinate system usedGCSUTMState PlaneCopyright 2015 by Maribeth H.Price3-8UTM Zone 13GCSState PlaneSame pointdifferent x-ysCoordinate systems and data Every feature class stores x-y values based on a specific CS.The CS may be projected o
6、r unprojected.The feature class also has a label documenting the CS parameters.Copyright 2015 by Maribeth H.Price3-9ROADS-103.567,44.628-103.678,44.653-103.765,44.732STATE445678,654321445021,650001444823,649200unprojectedprojectedThe Spatial Reference Every data set requires a complete description o
7、f its coordinate system for proper display and analysis Geographic coordinate system/datum Projection(if one is used)Storage units used to store the x-y values(degrees,feet,etc.)Domain,or maximum allowable x-y values Resolution,or the x-y precisionCopyright 2015 by Maribeth H.Price3-10Geographic coo
8、rdinate systemsCopyright 2015 by Maribeth H.Price3-11Measuring degreesCopyright 2015 by Maribeth H.Price3-12Latitude measures the angle from the horizontal.It represents north-south distance from the equator.Longitude measures around the circle of the equatorial plane.It represents east-west distanc
9、e from Prime Meridian.Measuring degreesCopyright 2015 by Maribeth H.Price3-13latitude50Prime MeridianLongitude=0EquatorLatitude=0-4560 longitudelongitudeLatitude measures the angle from the horizontal.It represents north-south distance from the equator.Longitude measures around the circle of the equ
10、atorial plane.It represents east-west distance from Prime Meridian.+(60,50)+(-45,50)GCS propertiesCopyright 2015 by Maribeth H.Price3-14Measured in angular degreesLength of longitude degree varies with latitudeCommonly portrayed as a planar coordinate system in GIS using decimal degrees,which introd
11、uces distortion.Prime MeridianEquator-1800+180-90+900Precision for unprojected data Unprojected data are stored in degrees Require a high resolution for good results Keep in mind when recording and transmittingCopyright 2015 by Maribeth H.Price3-15*At the equator1 deg 110 km*0.001 deg 110 m0.000001
12、deg 0.1 metersEllipsoidsCopyright 2015 by Maribeth H.Price3-1650-4560However,the earth is not a perfect sphere.Mapping a point at(-45,60)onto an ellipsoid better represents its position on the earths surface.Cartography defines the ellipsoid using a major and minor axis representing the longer and s
13、horter radii of the ellipsoid.These values have changed over time as we have developed better measurements of the earths shape.True sphere+The GeoidCopyright 2015 by Maribeth H.Price3-1750-4560The earth is not a perfect ellipsoid either.It has a topographic surface defined as the change in elevation
14、 fromwhat?From the geoid.The geoid is a theoretical surface defined by gravity measurements.It is described as“the mean ocean surface of the Earth,if the oceans were in equilibrium,at rest,and extended through the continents”(Wikipedia).It is too complex and irregular to map with,so the ellipsoid is
15、 used.+But the discrepancy between the geoid and ellipsoid produces another source of error to locations.The DatumCopyright 2015 by Maribeth H.Price3-1850-4560To minimize the discrepancy between the geoid and ellipsoid,a datum is defined.A datum shifts the ellipsoid relative to the geoid to achieve
16、a best fit between the two.A local datum optimizes the shift for the best fit at a particular location.It may also use a surveyed network of points to make further adjustments.A geocentric or world-centered datum optimizes the fit for the entire earth.+Best fit for North AmericaWorse fit for South A
17、mericaDatum definition A datum definition includes The particular ellipsoid(major and minor axis)chosen The adjustment or fit(translation of center)Together these define the GCSCopyright 2015 by Maribeth H.Price3-19Datums used in North America North American Datum 1927(NAD 1927 or NAD27)Based on Cla
18、rke 1866 spheroid,common until the 1980s and still used for some data sets.North American Datum 1983(NAD 1983 or NAD83)Current popular datum for most mapping.GRS80 spheroid.First choice if you must assume an unknown datum for a set of undocumented data.North American Datum 1983 HARN(NAD 1983 HARN)Up
19、dates NAD83 with a High Accuracy Regional Network of fitted points.World Geodetic Survey 1984(WGS84)Geocentric datum Seems to be default datum for many GPS units.Copyright 2015 by Maribeth H.Price3-20Projections and datums Every projection is based on a GCS Every GCS has a datum Every projection has
20、 a datum Projections based on different datums will be offset from one another Amount of offset depends on region Typically 0 300 metersCopyright 2015 by Maribeth H.Price3-21UTM Zone 13 NAD 1983 UTM Zone 13 NAD 1927!Roads in NAD83Photo in NAD27Note for GPS Users GPS units may be set to collect point
21、s in more than one datum and projection Often UTM or lon-lat units may be specified UTM NAD 1983 UTM NAD 1927 Lat-Lon NAD 1983 etc You MUST know and record the datum in order to use the data correctly later!Be carefulthe default datum setting might not be the one you wantCopyright 2015 by Maribeth H
22、.Price3-22Datum transformations Projections are exact mathematical formulas Converting one datum to another requires specialized fitting Not exact;errors up to several meters may occur Errors accumulate with repeated transformations Several methods available Some better than others for particular ch
23、anges Not all methods work for all transformationsCopyright 2015 by Maribeth H.Price3-23Converting datums should be done only when necessary,and care should be taken in choosing the best methodProjected coordinate systemsCopyright 2015 by Maribeth H.Price3-24ProjectionsMathematical projection of poi
24、nts on the earth surface to a flat plane(paper).The earth surface is generally defined by ellipsoid and datum.Different datum surface gives slightly different results on the plane.Copyright 2015 by Maribeth H.Price3-25Courtesy of ESRI,Inc.Types of projectionsCopyright 2015 by Maribeth H.Price3-26Cyl
25、indricalConicAzimuthalCylindrical projectionsCopyright 2015 by Maribeth H.Price3-27CylindricalTransverse cylindricalTransverse MercatorMercatorCylindrical Equal AreaEquirectangularConic projectionsCopyright 2015 by Maribeth H.Price3-28Lambert Conformal ConicAlbers Equal Area ConicEquidistant ConicPo
26、lyconicAzimuthal ProjectionsCopyright 2015 by Maribeth H.Price3-29Polar ObliqueAzimuthal EquidistantGnomicPolar StereographicLambert Azimuthal EqualareaSpecial projectionsCopyright 2015 by Maribeth H.Price3-30CubeFullerBonne PseudoconicProjection parameters Many different projections are supported b
27、y GIS programs.Using a projection involves choosing the projection and then setting various parameters that define it for your particular map.Copyright 2015 by Maribeth H.Price3-31MoreChanging the parameters customizes the projection for your particular needs.Central meridianCopyright 2015 by Maribe
28、th H.Price3-320-100The longitude which serves as the x=0 origin of the map.X values to the right of the central meridian are positive.X values to the left of the central meridian are negative.Reference latitudeCopyright 2015 by Maribeth H.Price3-33Latitude which serves as the y=0 origin for the map.
29、Y values above the reference latitude are positive.X values below the reference latitude are negative.Often the equator is used.Reference latitudeTangent vs secant projectionsCopyright 2015 by Maribeth H.Price3-34Cylinder/cone is tangent to the globe.Has a single standard parallel.No distortion alon
30、g parallel,increases with distance from it.Cylinder/cone is secant to the globe.Has two standard parallels.No distortion along parallels,increases with distance from them.Standard parallelsFalse easting and northingCopyright 2015 by Maribeth H.Price3-35Central meridianReference latitude0,0False nort
31、hingFalse eastingArbitrary values added to x and y values.Usually used to ensure that all x-y coordinates are positive.Coordinate units Projecting changes the x-y values from degrees to meters or feetCopyright 2015 by Maribeth H.Price3-36Units in decimal degreesUnits in meters-103.567,44.628-103.678
32、,44.653-103.765,44.7322445678,6543212445021,6500012444823,649200Distortion All map projections introduce distortion Type and degree of distortion varies with map projection When using a projection,one must take care to choose one with suitable propertiesCopyright 2015 by Maribeth H.Price3-37AreaDist
33、anceShapeDirectionProjection distortionsCopyright 2015 by Maribeth H.Price3-38MercatorEquidistant ConicDistorts distance and areaPreserves direction and shapeDistorts direction and shapePreserves distance and areaCompromise projectionsCopyright 2015 by Maribeth H.Price3-39RobinsonDistorts all four p
34、roperties a littleExtents The extent of a spatial data set indicates the range of x-y values present in the dataCopyright 2015 by Maribeth H.Price3-40Stored map units Raster coordinate systemsCopyright 2015 by Maribeth H.Price3-41Raster georeferencingCopyright 2015 by Maribeth H.Price3-42RowsColumns
35、X,Y locationRaster data fileN rows by M columnsX,Y locationGeoreferenced to earths surfaceTwo issues:1.Location(x,y)of the upper left corner of the raster.2.The“shape”of the features stored as pixels in the raster.Raster coordinatesCopyright 2015 by Maribeth H.Price3-43284096,414015 meters-104.480,4
36、6.005 degreesSouth Dakota State Plane SouthGeographic Coordinate SystemSouth Dakota topography in two coordinate systems.Note the significant difference in shape due to one being unprojected and the other projected.You can change the x-y value in the upper left corner,but it does not affect the unde
37、rlying shape of the actual coordinate system.Local rastersCopyright 2015 by Maribeth H.Price3-44UTM Zone 13NSouth Dakota State Plane SouthEven rasters of small areas(a quadrangle)can have significant differences based on the underlying coordinate system.So just knowing the upper left corner is not e
38、nough.You need to know the rest of the coordinate system information also.Georeferenced rasters A raster that already has the coordinate system information ready for use is said to be georeferenced.ArcGIS rasters and other formats such as GeoTiff come ready to use.Some rasters require work on the pa
39、rt of the user.Two cases generally apply.The coordinate system information is known but the user must properly label the data set for the GIS to be able to use it.The coordinate system information is unknown.Copyright 2015 by Maribeth H.Price3-45Case I The raster comes with a header or metadata with
40、 the coordinate system info,including the upper left x-y and the projection parameters.User creates a world file.User sets the raster properties so that ArcMap can access the information and use it.Copyright 2015 by Maribeth H.Price3-46A x pixel size in map unitsC x coord of center of upper left pix
41、elE -y pixel size in map unitsF y coord of center of upper left pixelB.D rotation termsA world file contains parameters to convert the pixel coordinates to real-world coordinates.Case II No georeferencing information is available The user must develop the transformation parameters.Copyright 2015 by
42、Maribeth H.Price3-47The parameters are determined by specifying pairs of identical locations on the raster and a reference layer to create matching pairs,known as control points.Then solve for the parameters A-F.A world file can be created from them,and stored with the image.Rectification Rectificat
43、ion permanently transforms an image to new coordinate space.Higher order transformations have more parameters and require more control points.Saves new fileCopyright 2015 by Maribeth H.Price3-48The RMS errorCopyright 2015 by Maribeth H.Price3-49The residual for each control point is the distance bet
44、ween the actual point and the modeled point after the transformation based on all the points.The Root Mean Square(RMS)error gives you an idea of the average accuracy(in map units)as long as you have more control points than the minimum needed.Control points(links)The RMS error should be reported in
45、the metadata created for the final raster.Resampling During rectification,a new cell size is specified for the output grid.The cell centers change location and cells may have gaps or overlaps.The new cell centers rarely align with the old cell centers,and must be resampled to fit the new grid.Copyri
46、ght 2015 by Maribeth H.Price3-50Resampling methodsCopyright 2015 by Maribeth H.Price3-51Nearest neighbor resampling grabs the value from the old cell that falls at the center of the new cell.It preserves the original value and should always be used with categorical data,or when the original data val
47、ues need to be preserved.It is the fastest method.Bilinear resampling calculates a new value from the four cells that fall closest to the center of the new cell.It uses a distance-weighted algorithm based on the old cell centers.It is best used with continuous data such as elevation.Cubic convolutio
48、n resampling calculates a new value from the sixteen cells that fall closest to the center of the new cell.It uses a distance-weighted algorithm based on the old cell centers.It is best used with continuous data such as elevation.It is the most time-consuming method.Projecting rastersRasters,like ve
49、ctors,can be converted from one CS to another by projecting.Cell centers are converted to the new system.Does not preserve original rectilinear spacing of the cell grid,so a new cell size must be specified.Resampling,as described for rectification,must also occur.Copyright 2015 by Maribeth H.Price3-
50、52South Dakota State Plane SouthGeographic Coordinate SystemEstimating GCS cell sizeCopyright 2015 by Maribeth H.Price3-53Geographic Coordinate SystemLatitude degrees,unlike longitude,are consistent in size.A single degree of latitude is 111.3 km.The height of a single cell is 0.00833 degrees 111.3
