[ArcGIS地理信息系统教程-(3)[129页]课件

1、Chapter 3Coordinate SystemsCopyright McGraw-HillEducation.Permission required for reproduction or display.3-1OutlineGIS ConceptsAbout coordinate systemsGeographic coordinate systemsProjected coordinate systemsRaster coordinate systemsCommon projection systemsChoosing projectionsAbout ArcGISLabeling

2、coordinate systemsOn-the-fly projectionProjecting dataTroubleshooting coordinate systemsGeoreferencing rastersCopyright 2015 by Maribeth H. Price3-2GIS ConceptsChapter 3.Coordinate SystemsCopyright 2015 by Maribeth H. Price3-3About coordinate systemsCopyright 2015 by Maribeth H. Price3-4Coordinate s

3、ystemsCopyright 2015 by Maribeth H. Price3- 5Figure 1. An arbitrary coordinate system used for surveying a site2507500,0250500750175, 200500FenceBuilding ABuilding BTypes of coordinate systemsUnprojectedBased on spherical globe coordinatesDegrees of latitude and longitudeProjectedConverts spherical

4、coordinates to planarSet of mathematical equationsProjects 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 (meters

5、)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 dataEvery feature class stores x-y values based on a specific CS.The CS may be projected or unpr

6、ojected.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 ReferenceEvery data set requires a complete description of its

7、coordinate system for proper display and analysisGeographic 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 valuesResolution, or the x-y precisionCopyright 2015 by Maribeth H. Price3-10Geographic co

8、ordinate 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 d

9、istance from Prime Meridian.Measuring degreesCopyright 2015 by Maribeth H. Price3- 13latitude50Prime MeridianLongitude = 0EquatorLatitude = 0-4560longitudelongitudeLatitude measures the angle from the horizontal. It represents north-south distance from the equator.Longitude measures around the circl

10、e of the equatorial 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 deg

11、rees, which introduces distortion.Prime MeridianEquator-1800+180-90+900Precision for unprojected dataUnprojected data are stored in degreesRequire a high resolution for good resultsKeep in mind when recording and transmittingCopyright 2015 by Maribeth H. Price3-15* At the equator1 deg 110 km*0.001 d

12、eg 110 m0.000001 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 repres

13、enting the longer and shorter 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

14、as the change in elevation 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 irregul

15、ar to map with, so the ellipsoid is 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 ellip

16、soid relative to the geoid to achieve 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

17、 for North AmericaWorse fit for South AmericaDatum definitionA datum definition includesThe particular ellipsoid (major and minor axis) chosenThe adjustment or fit (translation of center)Together these define the GCSCopyright 2015 by Maribeth H. Price3-19Datums used in North AmericaNorth American Da

18、tum 1927 (NAD 1927 or NAD27)Based on Clarke 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.Nort

19、h American Datum 1983 HARN (NAD 1983 HARN)Updates NAD83 with a High Accuracy Regional Network of fitted points.World Geodetic Survey 1984 (WGS84)Geocentric datumSeems to be default datum for many GPS units.Copyright 2015 by Maribeth H. Price3-20Projections and datumsEvery projection is based on a GC

20、SEvery GCS has a datumEvery projection has a datumProjections based on different datums will be offset from one anotherAmount of offset depends on regionTypically 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 Use

21、rsGPS units may be set to collect points in more than one datum and projectionOften UTM or lon-lat units may be specifiedUTM NAD 1983UTM NAD 1927Lat-Lon NAD 1983 etcYou MUST know and record the datum in order to use the data correctly later!Be carefulthe default datum setting might not be the one yo

22、u wantCopyright 2015 by Maribeth H. Price3-22Datum transformationsProjections are exact mathematical formulasConverting one datum to another requires specialized fittingNot exact; errors up to several meters may occur Errors accumulate with repeated transformationsSeveral methods availableSome bette

23、r than others for particular changesNot 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. Price3-24Projecti

24、onsMathematical projection of points 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 projectionsCopy

25、right 2015 by Maribeth H. Price3- 26CylindricalConicAzimuthalCylindrical projectionsCopyright 2015 by Maribeth H. Price3- 27CylindricalTransverse cylindricalTransverse MercatorMercatorCylindrical Equal AreaEquirectangularConic projectionsCopyright 2015 by Maribeth H. Price3- 28Lambert Conformal Coni

26、cAlbers Equal Area ConicEquidistant ConicPolyconicAzimuthal ProjectionsCopyright 2015 by Maribeth H. Price3- 29Polar ObliqueAzimuthal EquidistantGnomicPolar StereographicLambert Azimuthal EqualareaSpecial projectionsCopyright 2015 by Maribeth H. Price3- 30CubeFullerBonne PseudoconicProjection parame

27、tersMany different projections are supported by 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

28、 needs.Central meridianCopyright 2015 by Maribeth 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- 33L

29、atitude which serves as the y = 0 origin for the map.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

30、globe.Has a single standard parallel.No distortion along 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

31、. Price3- 35Central meridianReference latitude0,0False northingFalse eastingArbitrary values added to x and y values.Usually used to ensure that all x-y coordinates are positive.Coordinate unitsProjecting changes the x-y values from degrees to meters or feetCopyright 2015 by Maribeth H. Price3-36Uni

32、ts in decimal degreesUnits in meters-103.567,44.628-103.678,44.653-103.765,44.7322445678,6543212445021,6500012444823,649200DistortionAll map projections introduce distortionType and degree of distortion varies with map projectionWhen using a projection, one must take care to choose one with suitable

33、 propertiesCopyright 2015 by Maribeth H. Price3-37AreaDistanceShapeDirectionProjection distortionsCopyright 2015 by Maribeth H. Price3- 38MercatorEquidistant ConicDistorts distance and areaPreserves direction and shapeDistorts direction and shapePreserves distance and areaCompromise projectionsCopyr

34、ight 2015 by Maribeth H. Price3-39RobinsonDistorts all four properties a littleExtentsThe 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 g

35、eoreferencingCopyright 2015 by Maribeth H. Price3- 42RowsColumnsX, 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 coordin

36、atesCopyright 2015 by Maribeth H. Price3- 43284096,414015 meters-104.480, 46.005 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 ch

37、ange the x-y value in the upper left corner, but it does not affect the underlying 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

38、 the underlying coordinate system.So just knowing the upper left corner is not enough. You need to know the rest of the coordinate system information also.Georeferenced rastersA raster that already has the coordinate system information ready for use is said to be georeferenced. ArcGIS rasters and ot

39、her formats such as GeoTiff come ready to use.Some rasters require work on the part 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

40、2015 by Maribeth H. Price3-45Case IThe raster comes with a header or metadata with 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 M

41、aribeth H. Price3-46A x pixel size in map unitsC x coord of center of upper left pixelE -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 IINo georeferencing information

42、is availableThe user must develop the transformation parameters.Copyright 2015 by 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 wo

43、rld file can be created from them, and stored with the image.RectificationRectification 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 errorCopyrigh

44、t 2015 by Maribeth H. Price3- 49The residual for each control point is the distance between 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 contr

45、ol points than the minimum needed.Control points (links)The RMS error should be reported in the metadata created for the final raster.ResamplingDuring 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 ce

46、nters rarely align with the old cell centers, and must be resampled to fit the new grid.Copyright 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 preserve

47、s the original value and should always be used with categorical data, or when the original data values 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

48、based on the old cell centers. It is best used with continuous data such as elevation.Cubic convolution 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

49、continuous data such as elevation. It is the most time-consuming method.Projecting rastersRasters, like vectors, 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

50、 be specified.Resampling, as described for rectification, must also occur.Copyright 2015 by Maribeth H. Price3-52South Dakota State Plane SouthGeographic Coordinate SystemEstimating GCS cell sizeCopyright 2015 by Maribeth H. Price3- 53Geographic Coordinate SystemLatitude degrees, unlike longitude, a

51、re consistent in size. A single degree of latitude is 111.3 km. The height of a single cell is 0.00833 degrees 111.3 km/degree = 0.927 km or about 900 m.At this latitude (45) the width of the cell would be about 600 m. GCS 964 columns and 422 rowsMap units: degreesCell size: 30 arc seconds 0.008333

52、degrees900m600 m0.0080.008So 900m or 1000m would be a reasonable choice for the new cell size.Common projection systemsCopyright 2015 by Maribeth H. Price3-54Commonly used CSGeographic coordinate systemDegrees of latitude and longitudeUniversal Transverse MercatorDivides world into 60 zonesState Pla

53、neDivides each state into one or more zonesLarger states have more zonesCopyright 2015 by Maribeth H. Price3-55Geographic Coordinate SystemsCopyright 2015 by Maribeth H. Price3-56Primary use is for data distribution.User obtains data and then projects it into the desired coordinate system for the ap

54、plication.Not desirable for maps or analysis because of distortion.Universal Transverse MercatorBased on Transverse Mercator (cylindrical) projectionWorld divided into 60 zones 6 degrees wideDistortion is minimal within each zoneMaps of different areas use best zoneBest for maps covering small area

55、in one zoneCopyright 2015 by Maribeth H. Price3-57Zone 16State Plane SystemStates divided into one or more zones identified by a unique FIPS numberA projection and parameters are established for each zone to achieve desired accuracyTransverse Mercator, Lambert Conformal Conic, and Oblique Mercator a

56、re standard projections usedSeveral varieties in common useState Plane NAD 1927 uses feetState Plane NAD 1983 uses metersSome choose to use NAD 1983 (feet)Copyright 2015 by Maribeth H. Price3-58Copyright 2015 by Maribeth H. Price3- 59State Plane ZonesEast-west zones typically Lambert Conformal Conic

57、N-S zones usually Transverse MercatorOblique MercatorChoosing projectionsCopyright 2015 by Maribeth H. Price3-60Selecting a projectionCopyright 2015 by Maribeth H. Price3- 61A map using a Geographic Coordinate system (GCS) appears distorted.Always use a projected coordinate system for mapping.Types

58、of projectionsCopyright 2015 by Maribeth H. Price3- 62CylindricalConicAzimuthalGenerally preserve direction and shape. Transverse cylindrical good for N-S oriented areas.Generally preserve area and distance. Preferred for E-W oriented areas.Generally preserve area and distance. Commonly used for sat

59、ellite data and polar regions.Projections for large scale mapsLocal, city, county maps, smaller statesProjection systems virtually eliminate distortionChoose appropriate UTM or State Plane zoneFor best results, map should lie in a single zoneCopyright 2015 by Maribeth H. Price3-63Projections for sma

60、ll scalesContinents and countriesDistortion is inevitable, so purpose drives the choiceEquidistant maps when distances are importantEqual area maps when areas are importantConformal or compromise projections for general purpose mapsCopyright 2015 by Maribeth H. Price3-64Coordinate system names gener