Geographic data represents real world phenomena that can be measured at locations on Earth. It can describe discrete objects with boundaries or continuous fields without clear boundaries. Geographic data is represented digitally using data models like raster and vector structures. Vector data represents discrete objects while raster data divides space into a grid. Topology defines spatial relationships between geographic features that is important for analysis. Sampling and interpolation are used to generalize and estimate values across continuous surfaces from a finite set of sample points.

2. The Nature of Geographic
Data
Longley et al.
Chapters 3 and 4

3. 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)

4. 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)

5. 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

6. Dimensionality of Objects:
A way of identifying them
0-D
1-D
2-D

7. 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.
The discrete object view leads to a
powerful way of representing geographic
information about objects

8. Fields:
care to count every peak, valley,
ridge, slope???

9. Fields
much easier to think of terrain as a continuous surface in
which elevation can be defined rigorously at every cell.
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.
Not points, lines, areas,
but what varies and
how smoothly

10. 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

11. Raster Data Structure

12. 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.

13. Vector Data Structure:
Lines vs. Polygons
An area (red line) and its approximation by a polygon (blue line).

14. 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)

15. 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

16. 2, -7, 5, 6
Connectedness, Adjacency, Contiguity, Geo-
Relational

17. 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.

18. Nodes that are close together are snapped.

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

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

21. 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.

22. Issues w/ Raster & Vector

23. 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.

24. triangulation
Courtesy www.ian-ko.com/resources/triangulated_irregular_network.htm
TIN surface
pseudo 3D

25. 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

26. 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 points 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.

27. 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.

28. (Artificial) Smooth & Continuous Variation:
contours equally spaced, along points of equal
elevation

29. 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!!!

30. An Example from ArcGIS

31. Examine Attributes of Points

32. Choose Interpolation Parameters

33. IDW Interpolation

34. Hillshade ( hypothetical illumination )
to Better Visualize

35. Another set of sample points

36. Examine Attributes

37. Same Interpolation Parameters

38. Same IDW Interpolation
( but higher elevations skewed to right )

39. Hillshade

40. Comparison