Spatial Data What is special about Spatial Data? Briggs Henan University 2012

What is needed for spatial analysis? Location information—a map An attribute dataset: e.g population, rainfall Links between the locations and the attributes Spatial proximity information Knowledge about relative spatial location Topological information Topology --knowledge about relative spatial positioning Topography --the form of the land surface, in particular, its elevation Briggs Henan University 2012

Berry’s geographic matrix Berry, B.J.L 1964 Approaches to regional analysis: A synthesis . Annals of the Association of American Geographers, 54, pp. 2-11 1990 location Attributes or variables Variable 1 Variable 2 … Variable P areal unit 1 areal unit 2 . areal unit n time 2000 location Attributes or variables Population Income … Variable P areal unit 1 areal unit 2 . areal unit n 2010 location Attributes or Variables Population Income … Variable P Henan Shanxi . areal unit n geographic associations geographic distribution geographic fact Briggs Henan University 2012

Briggs Henan University 2012

Briggs Henan University 2012 Types of Spatial Data Continuous (surface) data Polygon (lattice) data Point data Network data Briggs Henan University 2012

Spatial data type 1: Continuous (Surface Data) Spatially continuous data attributes exist everywhere There are an infinite number locations But, attributes are usually only measured at a few locations There is a sample of point measurements e.g. precipitation, elevation A surface is used to represent continuous data Briggs Henan University 2012

Spatial data type 2: Polygon Data polygons completely covering the area* Attributes exist and are measured at each location Area can be: irregular (e.g. US state or China province boundaries) regular (e.g. remote sensing images in raster format) *Polygons completely covering an area are called a lattice Briggs Henan University 2012

Spatial data type 3: Point data Point pattern The locations are the focus In many cases, there is no attribute involved Briggs Henan University 2012

Spatial data type 4: Network data Attributes may measure the network itself (the roads) Objects on the network (cars) We often treat network objects as point data, which can cause serious errors Crimes occur at addresses on networks, but we often treat them as points See: Yamada and Thill Local Indicators of network-constrained clusters in spatial point patterns. Geographical Analysis 39 (3) 2007 p. 268-292 Briggs Henan University 2012

Which will we study? Point data Polygon data* Continuous data* 1: Analyzing Point Patserns (clusterirg and dispersion) 2: Analyzing Polygons  (Spatial Autocorrelation and Spatial Regression models) 3Surface analysis: nterpolation, trend surface analysis and kriging) Which will 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) *in the fall semester Briggs Henan University 2012

Briggs Henan University 2012 Converting from one type of data to another. --very common in spatial analysis Briggs Henan University 2012

Converting point to continuous data: interpolation Briggs Henan University 2012

Briggs Henan University 2012 Interpolation Finding attribute values at locations where there is no data, using locations with known data values Usually based on Value at known location Distance from known location Methods used Inverse distance weighting Kriging Simple linear interpolation Unknown Known Briggs Henan University 2012

Converting point data to polygons using Thiessen polygons Briggs Henan University 2012

Thiessen or Proximity Polgons (also called Dirichlet or Voronoi Polygons) Polygons created from a point layer Each point has a polygon (and each polygon has one point) any location within the polygon is closer to the enclosed point than to any other point space is divided as ‘evenly’ as possible between the polygons Thiessen or Proximity Polygons A Briggs Henan University 2012

How to create Thiessen Polygons 1. Connect point to its nearest (closest) neighbor 2. Draw perpendicular line at midpoint 3. Repeat for other points 4. Thiessen polygons Briggs Henan University 2012

Converting polygon to point data using Centroids Centroid—the balancing point for a polygon used to apply point pattern analysis to polygon data More about this later Briggs Henan University 2012

Using a polygon to represent a set of points: Convex Hull No! the smallest convex polygon able to contain a set of points no concave angles pointing inward A rubber band wrapped around a set of points “reverse” of the centroid Convex hull often used to create the boundary of a study area a “buffer” zone often added Used in point pattern analysis to solve the boundary problem. Called a “guard zone” Briggs Henan University 2012

Models for Spatial Data: Raster and Vector two alternative methods for representing spatial data Briggs Henan University 2012

Briggs Henan University 2012 Concept of Vector and Raster house river trees Real World Raster Representation Vector Representation point line polygon Briggs Henan University 2012

Comparing Raster and Vector Models Raster Model area is covered by grid with (usually) equal-size, square cells attributes are recorded by giving each cell a single value based on the majority feature (attribute) in the cell, such as land use type or soil type Image 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 Model The fundamental concept of vector GIS is that all geographic features in the real work can be represented either as: points or dots (nodes): trees, poles, fire plugs, airports, cities lines (arcs): streams, streets, sewers, areas (polygons): land parcels, cities, counties, forest, rock type Because representation depends on shape, ArcGIS refers to files containing vector data as shapefiles Briggs Henan University 2012

Briggs Henan University 2012 Raster model Image Land use (or soil type) corn wheat fruit clover 186 21 Each cell (pixel) has a value between 0 and 255 (8 bits) 1 2 3 4 5 6 7 8 9 Briggs Henan University 2012

Briggs Henan University 2012 Vector Model point (node): 0-dimensions single x,y coordinate pair zero area tree, oil well, location for label line (arc): 1-dimension two connected x,y coordinates road, stream A network is simply 2 or more connected lines polygon : 2-dimensions four or more ordered and connected x,y coordinates first and last x,y pairs are the same encloses an area county, lake 1 2 7 8 . x=7 Point: 7,2 y=2 Line: 7,2 8,1 Polygon: 7,2 8,1 7,1 7,2 Briggs Henan University 2012

Using raster and vector models to represent surfaces Briggs Henan University 2012

Representing Surfaces with raster and vector models –3 ways Contour lines Lines of equal surface value Good for maps but not computers! Digital elevation model (raster) raster cells record surface value TIN (vector) Triangulated Irregular Network (TIN) triangle vertices (corners) record surface value Briggs Henan University 2012

Contour (isolines) Lines for surface representation Contour lines of constant elevation --also called isolines (iso = equal) Advantages Easy to understand (for most people!) Circle = hill top (or basin) Downhill > = ridge Uphill < = valley Closer lines = steeper slope Disadvantages Not good for computer representation Lines difficult to store in computer

Raster for surface representation Each cell in the raster records the height (elevation) of the surface 105 110 115 120 Raster cells with elevation value Surface Contour lines Raster cells (Contain elevation values) Briggs Henan University 2012

Triangulated Irregular Network (TIN): Vector surface representation a set of non-overlapping triangles formed from irregularly spaced points preferably, 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. valley ridge vertex 1 2 4 3 5

Draft: How to Create a TIN surface: from points to surfaces Thiessen3.jpg Thiessen4.jpg Links together all spatial concepts: point, line, polygon, surface Briggs Henan University 2012

Briggs Henan University 2012 Using raster and vector models to represent polygons (and points and lines) Briggs Henan University 2012

Briggs Henan University 2012 Representing Polygons (and points and lines) with raster and vector models X 1 2 3 4 5 6 7 8 9 Raster model not good not accurate Also a big challenge for the vector model but much more accurate the solution to this challenge resulted in the modern GIS system Briggs Henan University 2012

Using Raster model for points, lines and polygons --not good! For lines and polygons Line not accurate Point “lost” if two points in one cell Polygon boundary not accurate Point located at cell center --even if its not Briggs Henan University 2012

Briggs Henan University 2012 Using vector model to represent points, lines and polygons: Node/Arc/Polygon Topology The relationships between all spatial elements (points, lines, and polygons) defined by four concepts: Node-ARC relationship: specifies which points (nodes) are connected to form arcs (lines) Arc-Arc relationship specifies which arcs are connected to form networks Polygon-Arc relationship defines 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 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 from to Left Right from to New! Briggs Henan University 2012

Node/Arc/ Polygon and Attribute Data 1 II 2 Birch Node/Arc/ Polygon and Attribute Data Example of computer implementation Smith Estate I A34 III A35 4 IV 3 Cherry Attribute Data Spatial Data Briggs Henan University 2012

Briggs Henan University 2012 This 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 Redlands, CA, started a new company called ESRI Inc., and created the first commercial GIS system, ArcInfo, in 1971 Modern GIS was born! Briggs Henan University 2012

Other ways to represent polygons with vector model 2. Whole polygon structure 3. Points and Polygons structure Used in earlier GIS systems before node/arc/polygon system invented Still used today for some, more simple, spatial data (e.g. shapefiles) Discuss these if we have time! Briggs Henan University 2012

Vector Data Structures: Whole Polygon Whole Polygon (boundary structure): list coordinates of points in order as you ‘walk around’ the 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 overlap all lines are ‘double’ (except for those on the outside periphery) no topological information about polygons which are adjacent and have a common boundary? used by the first computer mapping program, SYMAP, in late 1960s used by SAS/GRAPH and many later business mapping programs Still used by shapefiles. Topology --knowledge about relative spatial positioning -- knowledge about shared geometry Topography --the form of the land surface, in particular, its elevation Briggs Henan University 2012

Whole Polygon: illustration Data File A 3 4 A 4 4 A 4 2 A 3 2 B 4 4 B 5 4 B 5 2 B 4 2 C 3 2 C 4 2 C 4 0 C 3 0 C 3 2 D 4 2 D 5 2 D 5 0 D 4 0 E 1 5 E 5 5 E 5 4 E 3 4 E 3 0 E 1 0 5 E A B C D 4 3 2 1 1 2 3 4 5 Briggs Henan University 2012

Vector Data Structures: Points & Polygons Points and Polygons: list ID numbers of points in order as you ‘walk around’ the outside boundary a second file lists all points and their coordinates. solves the duplicate coordinate/double border problem still no topological information Do not know which polygons have a common border first used by CALFORM, the second generation mapping package, from the Laboratory for Computer Graphics and Spatial Analysis at Harvard in early ‘70s Briggs Henan University 2012

Points and Polygons: Illustration Points File 1 3 4 2 4 4 3 4 2 4 3 2 5 5 4 6 5 2 7 5 0 8 4 0 9 3 0 10 1 0 11 1 5 12 5 5 Polygons File 12 A 1, 2, 3, 4, 1 B 2, 5, 6, 3, 2 C 4, 3, 8, 9, 4 D 3, 6, 7, 8, 3 E 11, 12, 5, 1, 9, 10, 11 5 11 2 5 1 4 3 A B E 3 4 2 6 C D 1 10 9 8 7 1 2 3 4 5 Briggs Henan University 2012

Monday, we will begin talking about Spatial Statistics Hopefully, you now have a better understanding of what is special about spatial data! Monday, we will begin talking about Spatial Statistics Briggs Henan University 2012

Briggs Henan University 2012