The Nature of Geographic Data

1
The Nature of Geographic Data
2
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 Earths surface
• Digital representations are much more powerful
  than their paper equivalents

3
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

4
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

5
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

6
Accuracy of Representations

• Representations can rarely be perfect
• Details can be irrelevant, or too expensive and
  voluminous to record
• Its important to know what is missing in a
  representation
• Representations can leave us uncertain about the
  real world

7
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.

8
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

9
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

10
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

11
Types of Spatial Data

• Discrete definitive with concrete, observable,
  boundaries
• Continuous no easily discernable boundaries,
  fuzziness depends on scale

12
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

13
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

14
Discrete Objects

• Points, lines, and areas
• Countable
• Persistent through time, perhaps mobile
• Biological organisms
• Animals, trees
• Human-made objects
• Vehicles, houses, fire hydrants

15
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 Earths
  surface
• The source of metaphor and language
• Any field can have slope, gradient, peaks, pits

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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

17
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

18
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

19
Legend
Mixed conifer
Douglas fir
Oak savannah
Grassland
Raster representation. Each color represents a
different value of a nominal-scale field denoting
land cover class.
20
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 cells
  central point

21
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

22
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

23
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

24
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 dont
  understand spatial autocorrelation Actually,
  they dont understand the mechanics, they do
  understand the concept.

25
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

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Positive spatial autocorrelation
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Overly dispersed - negatively autocorrelated
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Random - no spatial autocorrelation
29
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

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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)

31
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

32
Random samples

• Every location is equally likely to be chosen

33
Systematic samples

• Sample points are spaced at regular intervals

34
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

35
Stratified samples
36
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

37
Pearsons 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

38
Plotting Correlation
39
Gravity Model

• 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

40
Self-similarity and fractals
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The Koch Snowflake
First iteration
After 2 iterations
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After 3 iterations
43
After n iterations
44
(work with me here, people)
45
The Koch snowflake is six of these put together
to form . . .
. . . well, a snowflake.
46
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).
47
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

48
Coastline Paradox

• Just like the fractal snowflake, the coastline of
  an island does not have a well-defined length.