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)

Timeheight above sea level (slow?) Sea surface temperature (fast)

Problems w/ Representing Geographic Data

Digital EarthEntire Earth into single digital representation

Infinite complexityWhat to leave in, what to leave outRepresentations are partial (data models)

Discrete Objects and Continuous Fields( Vector and Raster Structures)

DISCRETEWell-defined boundaries in empty space“Desktop littered w/ objects”World littered w/ cars, houses, etc.Counts49 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, 2000.

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 VectorsVector-based line

4753456 6234124753436 6234244753462 6234784753432 6234824753405 6234294753401 6235084753462 6235554753398 623634

Flat File

Raster-based line

00000000000000000001100000100000101010000101000011001000010100000000100010001000000010001000010000010001000000100010000100000001011100100000000100001110000000000000000000000000

Flat File

Now YOU!

TopologyScience and mathematics of geometric relationships

Simple features + topological rulesConnectivityAdjacencyShared nodes / edges

Topology needed byData validationSpatial 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 TopologyVectors 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

A

C B

1

2

3

4

5

0

D6

ab

c

d

e7

Arc

ID

L e f t

Poly

R t

Poly

From

n o d e

T o

n o d e

1 A 0 c a

2 A B b c

3 C A b a

4 0 C d a

5 C B d b

6 B D e e

7 B 0 d c

Poly

ID

No. of

arcs

List of

arcs

A 3 - 1 , - 2 , 3

B 4 2, -7, 5, -6

C 3 - 3 , - 5 , 4

D 1 6

2, -7, 5, 6

Connectedness, Adjacency, Contiguity, Geo-Relational

Topology, GIS, and YouTopological 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

Issue Raster Vector

Volume of Data Depends on cell size Depends on density

of vertices

Sources of data Remote sensing,

imagery

Socio-economic,

environ. sampling

Applications Resources,

enviromental

Socio-economic,

administrative

Software Raster GIS, image

processing

Vector GIS, autom.

Cartography

Resolution Fixed Variable

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 www.ian-ko.com/resources/triangulated_irregular_network.htm

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 functionTobler’s law - nearer things are key, in a smooth, continuous fashion

Pollution from an oil spillNoise 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 functionsIDW - nearer points given more importanceSampling 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