The Nature of Geographic Data Based in part on Longley et al. Chapters 3 and 4

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 Continuous 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

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, The discrete object view leads to a powerful way of representing geographic information about objects

Fields: Not points, lines, areas, but what varies and how smoothly…. “What occurs everywhere” care to count every peak, valley, ridge, slope???

Object/Vector Feature Types

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 Data Models and Data Structures

Raster Data Structure

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).

Slivers due to double digitizing and overlay can be eliminated. Sliver

Rasters and Vectors Vector-based line Flat File Raster-based line Flat File Now YOU!

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)

An Object Model uses a Vector (Arc/Node) Data Structure Object data model evolved into the arc/node variation in the 1960s. Points in sequence build lines. Lines have a direction - nodes or ordering of the points. Lines in sequence build polygons.

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

2, -7, 5, 6 Connectedness, Adjacency, Contiguity, Geo-Relational

Topology, GIS, and You Topological data structures very important in 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.

Nodes that are close together are snapped.

The bounding rectangle (xmax, ymax) (xmin, ymin)

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.

Issues w/ Raster & Vector

“Rasters are faster, but vectors are correcter” What about a compromise? a TIN can be used to represent surfaces.

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 Courtesy TIN surface pseudo 3D

Spatial Autocorrelation Arrangements of dark and light colored cells exhibiting negative, zero, and positive 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

Sampling: The Quest to Represent the Real World a spatially random sample a spatially systematic (stratified) sample a stratified random sample a sampling scheme with periodic random changes in the grid width of a spatially systematic sample Field - selecting discrete objects from a continuous surface Object - selecting some discrete objects, discarding others 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!!!

An Example from ArcGIS

Examine Attributes of Points

Choose Interpolation Parameters

IDW Interpolation

Hillshade ( hypothetical illumination ) to Better Visualize

Another set of sample points

Examine Attributes

Same Interpolation Parameters

Same IDW Interpolation ( but higher elevations skewed to right )

Hillshade

Comparison