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Longley et al. Chapters 3 and 4. The Nature of Geographic Data. What are Geographic Data?. “ Location, location, location! ” to map, to link based on the same place, to measure distances and areas Attributes physical or environmental soci-economic (e.g., population or income) Time
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Longley et al. Chapters 3 and 4 The Nature of Geographic Data
What are Geographic Data? • “Location, location, location!” • to map, to link based on the same place, • to measure distances and areas • Attributes • physical or environmental • soci-economic (e.g., population or income) • Time • height above sea level (slow?) • Sea surface temperature (fast)
Problems w/ Representing Geographic Data • Digital Earth • Entire Earth into single digital representation • Infinite complexity • What to leave in, what to leave out • Representations are partial (data models)
Discrete Objects and Fields( Vector and Raster Structures) DISCRETE • Well-defined boundaries in empty space • “Desktop littered w/ objects” • World littered w/ cars, houses, etc. • Counts • 49 houses in a subdivision
Dimensionality of Objects:A way of identifying them 0-D 1-D 2-D
The discrete object view leads to a powerful way of representing geographic information about objects Example of representation of geographic information as a table. The locations and attributes are for each of four grizzly bears in the Kenai Peninsula of Alaska. Locations, in degrees of longitude and latitude, have been obtained from radio collars. Only one location is shown for each bear, at noon on July 31, 2000.
Fieldsmuch easier to think of terrain as a continuous surface in which elevation can be defined rigorously at every cell. Not points, lines, areas, but what varies and how smoothly An image of part of the lower Colorado River in the southwestern USA. The lightness of the image at any point measures the amount of radiation captured by the satellite's imaging system. Image derived from a public domain SPOT image, courtesy of Alexandria Digital Library, University of California, Santa Barbara.
Data Models and Data Structures Data Models: fields and objects are no more than conceptualizations, or ways in which we think about geographic phenomena. They are not always designed to deal with the limitations of computers. Field & Object Data Models Data Structures: methods of representing the data model in digital form w/in the computer Raster and Vector Data Structures
Mixed Pixels Examples of the largest share rule, where a cell's value is on the value that occupies the largest share of the cell's area, and the central point rule, where a cell's value is based on the value that occupies the central point of the cell.
Vector Data Structure:Lines vs. Polygons An area (red line) and its approximation by a polygon (blue line).
Topology • Science and mathematics of geometric relationships • Simple features + topological rules • Connectivity • Adjacency • Shared nodes / edges • Topology needed by • Data validation • Spatial analysis (e.g. network tracing, polygon adjacency)
Vectors (Arcs) and Topology • Vectors without topology are spaghetti structures. • Points, lines, and areas • stored in their own files, with links between them. • stored w/ topology (i.e. the connecting arcs and left and right polygons). • Relationships are computed and stored
Connectedness, Adjacency, Contiguity, Geo-Relational 2, -7, 5, 6
Topology, GIS, and You • Topological data structures dominate GIS software. • Must BUILD topology from unconnected arcs • rarely are maps topologically clean when digitized, imported, or “GPSed.” • “Tolerances” important - features can move or disappear • “snapping”, elimination, merging, etc.
Sliver Slivers due to double digitizing and overlay can be eliminated.
(xmax, ymax) (xmin, ymin) The bounding rectangle
Why Topology Matters • allows automated error detection and elimination. • allows many GIS operations to be done without accessing the (x,y) files. • makes map overlay feasible. • makes spatial analysis possible.
TIN: Triangulated Irregular Network • Based on the Delaunay triangulation model of a set of irregularly distributed points. • Way to handle raster data with the vector data structure. • Common in most GISs. • More efficient than a grid.
triangulation TIN surface pseudo 3D Courtesy www.ian-ko.com/resources/triangulated_irregular_network.htm
Spatial Autocorrelation Tobler’s 1st Law of Geography:everything is related to everything else, but near things are more related than distant things S. autocorrelation: formal property that measures the degree to which near and distant things are related. Close in space Dissimilar in attributes Attributes independent of location Close in space Similar in attributes Arrangements of dark and light colored cells exhibiting negative, zero, and positive spatial autocorrelation.
Sampling: The Quest to Represent the Real World Field - selecting points from a continuous surface Object - selecting some discrete objects, discarding others a sampling scheme with periodic random changes in the grid width of a spatially systematic sample a spatially random sample a stratified random sample a spatially systematic (stratified) sample Spatially systematic sampling presumes that each observation is of equal importance in building a representation.
Spatial Interpolation:“Intelligent Guesswork” • the process of filling in the gaps between sample observations. • attenuating effect of distance between sample observations • selection of an appropriate interpolation function • Tobler’s law - nearer things are key, in a smooth, continuous fashion • Pollution from an oil spill • Noise from an airport, etc.
(Artificial) Smooth & Continuous Variation:contours equally spaced, along points of equal elevation
Is Variation in Nature Always Smooth and Continuous? Graduate Student’s Corollary to Tobler’s 1st Law of Geography • “The real world is infinitely complex, so why bother?” • For true nature of geographic data, use other interpolation methods and functions • IDW - nearer points given more importance • Sampling still important!!!
Same IDW Interpolation( but higher elevations skewed to right )
