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The Nature of
Geographic Data
The Paper Map
• A long and rich history
• Has a scale or representative fraction
– The ratio of distance on the map to distance on the ground
• Is a major source of data for GIS
– Obtained by digitizing or scanning the map and registering it
to the Earth’s surface
• Digital representations are much more powerful than
their paper equivalents
Representations
• Are needed to convey
information
• Fit information into a
standard form or model
• Almost always simplify
the truth that is being
represented
– There is no information in
the representation about
daily journeys to work and
shop, or vacation trips out
of town
Digital Representation
• Uses only two symbols, 0 and 1, to represent
information
– N symbols (bits)  2N distinct values
• Many standards allow various types of information to be
expressed in digital form
– MP3 for music
– JPEG for images
– ASCII for text
• GIS relies on standards for geographic data
Why Digital?
• Economies of scale
– One type of information technology for all types of
information
• Simplicity
– 0,1  on,off
• Reliability
– Systems can be designed to correct errors
• Easily copied and transmitted
– Perfect copies
– At close to the speed of light
Accuracy of Representations
• Representations can rarely be perfect
– Details can be irrelevant, or too expensive and
voluminous to record
• It’s important to know what is missing in a
representation
– Representations can leave us uncertain about the real
world
The Fundamental Problem
• Geographic information links a place, and often a time,
with some property of that place (and time)
– “The temperature at 34 N, 120 W at noon local time on
12/2/99 was 18 Celsius”
• The potential number of properties is vast
– In GIS we term them attributes
– Attributes can be physical, social, economic, demographic,
environmental, etc.
Types of Attributes
• Nominal, e.g. land cover class
– Distinction (“a” is/is not “b”)
• Ordinal, e.g. a ranking
– Significance (“a” is X-er than “b”)
• Interval, e.g. Celsius temperature
– Relative magnitude (“a” is N units X-er than “b”)
• interpolable
• Ratio, e.g. Kelvin temperature
– Absolute magnitude (“a” is N times X-er than “b”)
• scalable
Cyclic Attributes
• Do not behave as other attributes
– What is the average of two compass bearings, e.g. 350 and
10?
• Occur commonly in GIS
– Wind direction
– Slope aspect
– Flow direction
• Special methods are needed to handle and analyze
The Fundamental Problem
• The number of places and times is also vast
– Potentially infinite
• The more closely we look at the world, the more
detail it reveals
– Potentially ad infinitum
– The geographic world is infinitely complex
• Humans have found ingenious ways of dealing
with this problem
– Many methods are used in GIS to create
representations or data models
Types of Spatial Data
• Discrete: definitive; with concrete,
observable, boundaries
• Continuous: no easily discernable
boundaries, “fuzziness” depends on scale
Types of Spatial Data
• Continuous spatial data: geostatistics
– Samples may be taken at intervals, but the spatial process
is continuous
– e.g. soil quality
• Discrete data
– Irregular: zonal data, regions, states, districts, postcodes,
zipcodes
– Regular lattice data: constructed grid, ‘raster’
representation
Discrete Objects and Fields
• Two ways of conceptualizing geographic variation
– The most fundamental distinction in geographic
representation
• Discrete objects
– The world as a table-top
– Objects with well-defined boundaries
Discrete Objects
•
•
•
•
Points, lines, and areas
Countable
Persistent through time, perhaps mobile
Biological organisms
– Animals, trees
• Human-made objects
– Vehicles, houses, fire hydrants
Fields
• Properties that vary continuously over space
– Value is a function of location
– Property can be of any attribute type, including direction
• Elevation as the archetype
– A single value at every point on the Earth’s surface
– The source of metaphor and language
• Any field can have slope, gradient, peaks, pits
Examples of Fields
• Soil properties, e.g. pH, soil moisture
• Population density
– But at fine enough scale the concept breaks down
•
•
•
•
Name of county or state or nation
Atmospheric temperature, pressure
Pollution level
Groundwater quality information
Difficult Cases
• Lakes and other natural phenomena
– Often conceived as objects, but difficult to define or
count precisely
– “When is a heap of sand no longer a heap?”
• Weather forecasting
– Forecasts originate in models of fields, but are
presented in terms of discrete objects
• Highs, lows, fronts
Rasters and Vectors
• How to represent phenomena conceived as fields or
discrete objects?
• Raster
–
–
–
–
–
Divide the world into square cells
Register the corners to the Earth
Represent discrete objects as collections of one or more cells
Represent fields by assigning attribute values to cells
More commonly used to represent fields than discrete objects
Legend
Mixed conifer
Douglas fir
Oak savannah
Grassland
Raster representation. Each color
represents a different value of a nominalscale field denoting land cover class.
Characteristics of Rasters
• Pixel size
– The size of the cell or picture element, defining the
level of spatial detail
– All variation within pixels is lost
• Assignment scheme
– The value of a cell may be an average over the cell, or
a total within the cell, or the commonest value in the
cell
– It may also be the value found at the cell’s central
point
Vector Data
• Used to represent points, lines, and areas
• All are represented using coordinates
– One per point
– Areas as polygons
• Straight lines between points, connecting back to the start
• Point locations recorded as coordinates
• May have “holes” and “islands”
– Lines as polylines
• Straight lines between points
Raster vs Vector
• Volume of data
– Raster becomes more voluminous as cell size
decreases
• Source of data
– Remote sensing, elevation data come in raster form
– Vector favored for administrative or discrete data
• Software
– Some GIS better suited to raster, some to vector
Generalization
• GIS data may preserve data beyond what you
need or want
• ArcGIS can differentiate between incredibly small
values
– State Plane (feet) default is 0.003937 inches
• Software may have difficulties displaying overly
detailed data at smaller scales
Spatial Autocorrelation
• First law of geography: “everything is related to
everything else, but near things are more related than
distant things” – Waldo Tobler
• Many new geographers would say “I don’t understand
spatial autocorrelation” Actually, they don’t understand
the mechanics, they do understand the concept.
Spatial Autocorrelation
• Spatial Autocorrelation – correlation of a variable
with itself through space.
– If there is any systematic pattern in the spatial
distribution of a variable, it is said to be spatially
autocorrelated
– If nearby or neighboring areas are more alike, this is
positive spatial autocorrelation
– Negative autocorrelation describes patterns in which
neighboring areas are unlike
– Random patterns exhibit no spatial autocorrelation
Positive spatial autocorrelation
Overly dispersed - negatively
autocorrelated
Random - no spatial autocorrelation
Importance of Spatial Autocorrelation
• Most statistics are based on the assumption that
the values of observations in each sample are
independent of one another
• Positive spatial autocorrelation may violate this,
if the samples were taken from nearby areas
• Goals of spatial autocorrelation
– Measure the strength of spatial autocorrelation in a
map
– test the assumption of independence or randomness
Why does spatial auto correlation occur?
• Reaction functions?
• Spillovers, externalities?
• Unobserved similarities between places?
• Diffusion? (disease spread)
• Common activity in neighboring areas? (crime)
• Common policy across neighboring areas? (zoning)
Sampling
• The sampling density determines the resolution of the
data
• Samples taken at 1 km intervals will miss variation
smaller than 1 km
• Standard approaches to sampling:
– Random
– Systematic
– Stratified
Random samples
• Every location is equally likely to be chosen
Systematic samples
• Sample points are spaced at regular intervals
Stratified samples
• Requires knowledge about distinct, spatially defined
sub-populations (spatial subsets such as ecological
zones)
• More sample points are chosen in areas where higher
variability is expected
Stratified samples
Using (Geospatial) Statistics
• As always, error propagates and grows through
subsequent analyses
• Correlation does not mean causation
• Sampling method may introduce bias
• Models and measurements must be appropriate
for your dataset
• With GIS data, model must be geo-aware
Pearson’s r & r2
• r is the correlation value between two or
more sets of values
• Ranging from -1 to +1, r identifies the
degree of positive or negative correlation
• Squaring r produces a percentage to which
two sets of data share the same values
• r can be plotted as a “best-fit” or trend line
Plotting Correlation
Gravity Model
wG
pi p j
2
dij
• Gravity model applies concepts in physics to the
social sciences
• The “masses” and distance between two urban

places influences
the migratory bond between
two places
• Population (people, employment) and distance
decay effect the degree to which two places are
“bonded”
Self-similarity and fractals
The Koch Snowflake
Length  1
First iteration
4
Length 
3
After
2 iterations
4 
Length   
3 
2
After 3 iterations
3
4

Length   
3
After n iterations
n
4

Length   
3
After

iterations
(work with me here, people)

4

Length   
 3

The Koch snowflake is six of these put together to form . . .
. . . well, a snowflake.
Notice that the perimeter of the Koch snowflake is infinite . . .
. . . but that the area it bounds is finite (indeed, it is
contained in the white square).
Importance of Fractals
• The precision at which you measure linear features
influences the total length
• What measurement is “right”?
• Self-similarity of features
– A craggy shoreline will have a similar pattern at a small and
large scale
– An agglomeration of urban neighborhoods into a city mirrors
the pattern of cities creating a region
Coastline Paradox
• Just like the fractal
snowflake, the coastline
of an island does not
have a well-defined
length.