空间统计书单3spatdata

1、Spatial DataWhat is special about Spatial Data?Briggs Henan University 20121What is needed for spatial analysis?Location informationa mapAn attribute dataset: e.g population, rainfallLinks between the locations and the attributesSpatial proximity informationKnowledge about relative spatial locationT

2、opological informationBriggs Henan University 20122Topology-knowledge about relative spatial positioningTopography-the form of the land surface, in particular, its elevation Berrys geographic matrixlocationAttributes or variablesVariable 1Variable 2Variable Pareal unit 1areal unit 2.areal unit nloca

3、tionAttributes or variablesPopulation eVariable Pareal unit 1areal unit 2.areal unit nlocationAttributes or VariablesPopulation eVariable PHenanShanxi.areal unit ntimegeographicassociationsgeographicdistributiongeographicfactBerry, B.J.L 1964 Approaches to regional analysis: A synthesis . Annals of

4、the Association of American Geographers, 54, pp. 2-112010199020003Briggs Henan University 2012Briggs Henan University 20124Types of Spatial DataContinuous (surface) dataPolygon (lattice) dataPoint dataNetwork dataBriggs Henan University 20125Spatial data type 1: Continuous (Surface Data)Spatially co

5、ntinuous dataattributes exist everywhereThere are an infinite number locationsBut, attributes are usually only measured at a few locationsThere is a sample of point measurementse.g. precipitation, elevationA surface is used to represent continuous dataBriggs Henan University 20126Spatial data type 2

6、: Polygon Datapolygons completely covering the area*Attributes exist and are measured at each locationArea can be: irregular (e.g. US state or China province boundaries) regular (e.g. remote sensing images in raster format)Briggs Henan University 20127*Polygons completely covering an area are called

7、 a latticeSpatial data type 3: Point dataPoint patternThe locations are the focusIn many cases, there is no attribute involvedBriggs Henan University 20128Spatial data type 4: Network dataAttributes may measure the network itself (the roads)Objects on the network (cars)We often treat network objects

8、 as point data, which can cause serious errorsCrimes occur at addresses on networks, but we often treat them as pointsBriggs Henan University 20129See: Yamada and Thill Local Indicators of network-constrained clusters in spatial point patterns. Geographical Analysis 39 (3) 2007 p. 268-292Which will

9、we study? Point data(point pattern analysis: clustering and dispersion)Polygon data* (polygon analysis: spatial autocorrelation and spatial regression)Continuous data*(Surface analysis: interpolation, trend surface analysis and kriging) Briggs Henan University 2012101: Analyzing Point Patserns (clus

10、terirg and dispersion)2: Analyzing Polygons (Spatial Autocorrelation and Spatial Regression models)3Surface analysis: nterpolation, trend surface analysis and kriging)*in the fall semesterConverting from one type of data to another.-very common in spatial analysisBriggs Henan University 201211Conver

11、ting point to continuous data:interpolation12Briggs Henan University 2012InterpolationFinding attribute values at locations where there is no data, using locations with known data valuesUsually based onValue at known locationDistance from known locationMethods usedInverse distance weightingKrigingBr

12、iggs Henan University 201213Simple linear interpolationUnknownKnownConverting point data to polygons using Thiessen polygons 14Briggs Henan University 2012Thiessen or Proximity Polgons(also called Dirichlet or Voronoi Polygons)Polygons created from a point layer Each point has a polygon (and each po

13、lygon has one point)any location within the polygon is closer to the enclosed point than to any other pointspace is divided as evenly as possible between the polygonsAThiessen or Proximity Polygons15Briggs Henan University 2012How to create Thiessen PolygonsBriggs Henan University 2012161. Connect p

14、oint to its nearest (closest) neighbor2. Draw perpendicular line at midpoint3. Repeat for other points4. Thiessen polygonsConverting polygon to point data using CentroidsCentroidthe balancing point for a polygonused to apply point pattern analysis to polygon dataMore about this laterBriggs Henan Uni

15、versity 201217Using a polygon to represent a set of points: Convex Hullthe smallest convex polygon able to contain a set of pointsno concave angles pointing inwardA rubber band wrapped around a set of points “reverse” of the centroidConvex hull often used to create the boundary of a study areaa “buf

16、fer” zone often added Used in point pattern analysis to solve the boundary problem.Called a “guard zone”No!Briggs Henan University 201218Models for Spatial Data:Raster and Vectortwo alternative methods for representing spatial dataBriggs Henan University 201219Real WorldVector RepresentationRaster R

17、epresentationConcept of Vector and Rasterlinepolygonpoint20Briggs Henan University 2012houserivertreesComparing Raster and Vector ModelsRaster Modelarea is covered by grid with (usually) equal-size, square cellsattributes are recorded by giving each cell a single value based on the majority feature

18、(attribute) in the cell, such as land use type or soil typeImage data is a special case of raster data in which the “attribute” is a reflectance value from the geomagnetic spectrum cells in image data often called pixels (picture elements)Vector ModelThe fundamental concept of vector GIS is that all

19、 geographic features in the real work can be represented either as:points or dots (nodes): trees, poles, fire plugs, airports, citieslines (arcs): streams, streets, sewers,areas (polygons): land parcels, cities, counties, forest, rock type Because representation depends on shape, ArcGIS refers to fi

20、les containing vector data as shapefiles21Briggs Henan University 2012Raster modelBriggs Henan University 201222cornwheatfruitcloverfruit012345678901234567891111144555111114455511111445551111144555111114455522222223332222222333222222233322442223332244222333Land use (or soil type)18621Each cell (pixe

21、l) has a value between 0 and 255 (8 bits)ImageVector Modelpoint (node): 0-dimensionssingle x,y coordinate pairzero areatree, oil well, location for label line (arc): 1-dimensiontwo connected x,y coordinatesroad, streamA network is simply 2 or more connected linespolygon : 2-dimensionsfour or more or

22、dered and connected x,y coordinates first and last x,y pairs are the sameencloses an areacounty, lake 1278.x=7Point: 7,2y=2Line: 7,2 8,1Polygon: 7,2 8,1 7,1 7,21278121127823Briggs Henan University 2012Using raster and vector models to represent surfacesBriggs Henan University 201224Representing Surf

23、aces with raster and vector models 3 waysContour linesLines of equal surface valueGood for maps but not computers!Digital elevation model (raster)raster cells record surface valueTIN (vector)Triangulated Irregular Network (TIN)triangle vertices (corners) record surface valueBriggs Henan University 2

24、01225Contour (isolines) Lines for surface representationAdvantagesEasy to understand (for most people!)Circle = hill top (or basin) Downhill = ridgeUphill = valleyCloser lines = steeper slopeDisadvantagesNot good for computer representationLines difficult to store in computer Contour lines of consta

25、nt elevation-also called isolines (iso = equal)Raster for surface representationEach cell in the raster records the height (elevation) of the surface Briggs Henan University 201227Raster cells(Contain elevation values)Surface105110115120Raster cells with elevation valueContour linesa set of non-over

26、lapping triangles formed from irregularly spaced pointspreferably, points are located at “significant” locations, bottom of valleys, tops of ridges Each corner of the triangle (vertex) has: x, y horizontal coordinates z vertical coordinate measuring elevation.Triangulated Irregular Network (TIN):Vec

27、tor surface representationvalleyridgevertex12435Draft: How to Create a TIN surface:from points to surfaces Briggs Henan University 201229Thiessen3.jpgThiessen4.jpgLinks together all spatial concepts: point, line, polygon, surfaceUsing raster and vector models to represent polygons(and points and lin

28、es)Briggs Henan University 201230Representing Polygons (and points and lines) with raster and vector modelsBriggs Henan University 201231Raster model not goodnot accurateAlso a big challenge for the vector modelbut much more accuratethe solution to this challenge resulted in the modern GIS system012

29、345678901234567891111144555111114455511111445551111144555111114455522222223332222222333222222233322442223332244222333XUsing Raster model for points, lines and polygons-not good!Briggs Henan University 201232Polygon boundary not accurateLine not accuratePoint located at cell center-even if its notPoi

30、nt “lost” if two points in one cellFor pointsFor lines and polygonsUsing vector model to represent points, lines and polygons:Node/Arc/Polygon TopologyThe relationships between all spatial elements (points, lines, and polygons) defined by four concepts: Node-ARC relationship:specifies which points (

31、nodes) are connected to form arcs (lines)Arc-Arc relationship specifies which arcs are connected to form networks Polygon-Arc relationshipdefines polygons (areas) by specifying which arcs form their boundary From-To relationship on all arcs Every arc has a direction from a node to a node This allows

32、This establishes left side and right side of an arc (e.g. street) Also polygon on the left and polygon on the right for every side of the polygon LeftRightfromto33Briggs Henan University 2012fromtoNew!BirchCherryIIIIIIIV143Node/Arc/ Polygon and Attribute DataExample of computer implementationSpatial

33、 DataAttribute DataA35SmithEstateA34234Briggs Henan University 2012This is how a vector GIS system works!This data structure was invented by Scott Morehouse at the Harvard Laboratory for Computer Graphics in the 1960s.Another graduate student named Jack Dangermond hired Scott Morehouse, moved to Red

34、lands, CA, started a new company called ESRI Inc., and created the first commercial GIS system, ArcInfo, in 1971Modern GIS was born! Briggs Henan University 201235Other ways to represent polygons with vector model2. Whole polygon structure3. Points and Polygons structureUsed in earlier GIS systems b

35、efore node/arc/polygon system inventedStill used today for some, more simple, spatial data (e.g. shapefiles)Discuss these if we have time!Briggs Henan University 201236Vector Data Structures: Whole PolygonWhole Polygon (boundary structure): list coordinates of points in order as you walk around the

36、outside boundary of the polygon.all data stored in one file coordinates/borders for adjacent polygons stored twice; may not be same, resulting in slivers (gaps), or overlapall lines are double (except for those on the outside periphery)no topological information about polygons which are adjacent and

37、 have a common boundary?used by the first computer mapping program, SYMAP, in late 1960sused by SAS/GRAPH and many later business mapping programsStill used by shapefiles.Topology-knowledge about relative spatial positioning - knowledge about shared geometryTopography-the form of the land surface, in particular, its elevati