Geography 38:286 Computer Cartography

1
Geography 38286Computer Cartography

• Topic 5
• Choropleth Mapping
• Chapter 7 Dent

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Mapping TechniquesLecture Format

• Description
• Definition
• Types/variations
• Data characteristics
• Type of data
• Raw or Derived
• Spatial characteristics
• Discrete or Continuous
• Design Considerations
• Projection
• Legend
• Symbology
• Classification
• Colour scheme
• Scale
• Other

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What is Choropleth Mapping?

• Uses distinct
• Colour
• Shade
• Texture
• . . . to represent differences in value from one
  area to another
• Areal units typically administrative
• Can also be natural
• Also called enumeration area mapping

4
Two Types of Choropleth Maps

• 1. Conventional or Simple
• Areal units grouped into classes
• Minimum four
• Maximum 6 to 8
• Five most common
• By far the more common method

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Two Types of Choropleth Maps

• 2. Classless, Unclassed, or Tonal
• Each area assigned unique colour, shade or
  texture pattern
• Directly proportional to value
• No grouping into classes
• Difficult to detect spatial patterns

6
Three Types of Spatial Data

• Choice of mapping technique is often determined
  by type of spatial data
• While there are two general categories, in this
  course we consider three
• discrete
• areally discrete
• continuous

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Discrete Data

• Data values occur at
• a point
• a line
• or polygon
• No data occurs between features
• Phenomena is absent, nothing to measure
• Ex. hog barns, hydro lines, water quality

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Areally Discrete Data

• Special type of discrete data
• Represent aggregate values of discrete areas
• Values may be
• Totals
• Averages
• Rates/Proportions
• Represent entire area but do not necessarily
  occur across entire area

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Continuous

• Values occur continuously across area of interest
• BUT are measured/sampled at specific locations
  points
• Values vary continuously
• Sometimes represented at points
• Includes most naturally occurring phenomena
• Precipitation, elevation, temperature

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Spatial Characteristics of Data

• Choropleth technique can be used when data are
  aggregated by discrete areal units
• Each areal unit has one value
• Assumed constant across the area
• So, data are lost
• Not appropriate for mapping
• discrete point or line data
• continuously distributed data

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Two Aspatial Data Types

• Certain maps require specific aspatial data
  characteristics
• Ex. Totals cant be used, must use a proportion
• May necessitate some preliminary data processing
• Convert totals to an appropriate rate/proportion

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Aspatial Data Types

• Totals or Raw Values
• Actual values of areal unit
• total population
• number farms
• Ukrainian first language
• Misleading since size of areal units may vary
  significantly
• Consequently, raw values not used

13
Aspatial Data Types

• Derived Data
• Data expressed as a rate or proportion
• Typically normalized by either population or land
  area
• Wheat as a percentage of total cropland
• Population per square kilometre
• Elderly as a percentage of total population
• Crime as a percentage of . . . ?
• Curlers as a . . . ?
• ArcGIS can do this for you, but be careful

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Two Types of Areal Units

• Natural Areal Units
• Areas corresponding with naturally occurring
  discrete phenomena
• Drainage basins
• Ecoregions
• Land cover/Land use areas
• Soil boundaries
• Boundaries are finite and inherently associate
  with phenomena concerned

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Types of Area Units

• Artificial Areal Units
• Areas created to spatially organize the Earths
  surface
• political, administrative regions, census areas
• Used for the purposes of collecting and analyzing
  data
• Boundaries are often arbitrary

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Modifiable Areal Unit Problem

• Since arbitrary boundaries are . . . well,
  arbitrary, any artificial regionalization may be
  equally valid
• However, resulting areal units could yield very
  different aggregate data
• What are the implications with regard
• to choropleth mapping??
• regionalization of space???

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Modifiable Areal Unit Problem
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Considerations Scale

• Scale must be large enough so that smallest areal
  unit visible
• This dictates
• the geographic extent shown on the map
• or size of the final map composition
• or hierarchical level represented (next slide)

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Considerations Number Size of Areal Units

• Areal units are often nested
• Data reported at mulitple levels
• Provinces, CD, CSD, CMA, FED, CT, EA
• Ecozones, regions, provinces, districts
• We may be able to choose at what level data are
  mapped

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Number Size of Areal Units

• This has implication in terms of
• level of aggregation/loss of data
• choice of symbolization
• perceived accuracy/appearance
• fewer/large areas appear coarse/inaccurate
• more/small areas appear finer/more accurate

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Number Size of Areal Units

• Choice usually dependent on
• purpose of the map
• acceptable level of generalization
• data availability
• scale, geographic extent, size of final map

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Considerations Classification Technique

• Significantly impacts message
• More than one version can be presented but not
  common
• Should use most appropriate method not one that
  produces desire effect
• Statement indicating technique should be included

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Data Classification

• Method of cartographic abstraction
• Inevitable loss of information
• Purposes is to
• Reduce observations to manageable size
• Identify groupings of observations
• Reveal information otherwise obscured
• Regionalization is a means of spatial
  classification

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Classification Schemes

• Two classification schemes of classifications
• First identifies four types
• Exogenous
• Boundaries not related to data array
• But related to theme
• Often based on established critical or standard
  values
• poverty line
• age groups
• soil salinity

25
Classification Schemes

• Arbitrary
• Boundaries also unrelated to data array
• Used for convenience
• Usually round numbers
• Less than 10, 10 to 30, greater than 30

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Classification Schemes

• Idiographic
• Boundaries are based on qualities of the data
  array
• Naturally occurring groups
• Serial
• Boundaries based on mathematical or statistical
  characteristics
• standard deviations
• equal intervals
• arithmetic and geometric progressions

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Classification Schemes

• Second classification based on resulting
  intervals
• Constant Intervals
• Analogous to passing a series of planes through a
  3D model, each plane equal distance apart
• Variable Intervals
• Planes are unequal distances apart
• Either can be used to accentuate or mask outliers

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Equal Steps

• Each class represents equal proportion of the
  range of data values
• Procedure
• Data range R H - L
• Interval I R / n ( classes)
• Class boundaries are then determined by
• L, L (1 x I), L (2 x I), . . . L (n x CD)

Lower Boundary
Upper Boundary
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Equal Steps
1
2
3
4
5
Five Classes 0.02 4.76 4.77 9.51 9.52
14.26 14.27 19.01 19.02 23.77
R 23.77 0.02 23.75 I 23.75 / 5
4.75 Class Boundaries are 0.02, 4.77, 9.52,
14.27, 19.02, 23.77 Note No overlapping classes
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Equal Steps

• Most appropriate when
• Frequency distribution is rectangular/even
• Areal units of equal size
• Neither is a common occurrence
• Accentuates outliers when distribution is not
  rectangular

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Equal Steps
4.75
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Standard Deviations

• Limits based on mean and standard deviation
• Normally 1, 2, and 3 SDs above below mean
• Each class equal proportion of total deviation
• constant interval scheme
• Used when data displays normal distribution
• Common distribution

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Standard Deviations

• Procedure
• mean value m ?x / n
• SD ? (xi - m)2 / n-1-1/2
• Class boundaries are then determined by
• m (1 x SD) and m - (1 x SD)
• Usually 6 classes
• 3 above mean
• and 3 below mean

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Standard Deviations
-1
1
2
3
Mean 82.01/12 6.83 SD 7.5 Note No
overlapping classes
Six Classes lt1 SD 0 6.82 gt1 SD 6.83
14.32 gt2 SD 14.33 21.15 gt3 SD 21.16 27.99
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Standard Deviations

• Creates a more even looking distribution
• Even when distribution is skewed
• Masks outliers
• May present interpretation issues
• E.g. does map reader understand SD?

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Standard Deviations
- 1 SD
1 SD
2 SD
3 SD
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Geometric Intervals

• Mathematically defined class limits based on
  arithmetic or geometric properties of data
• Used when distribution approximates geometric
  progression
• Class intervals are progressively smaller or
  larger toward one end of the distribution so a
  variable interval technique
• Less common

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Quantiles

• Boundaries are selected such that same number of
  EAs occurs in each class
• However, intervals not constant

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Quantiles

• Procedure
• arrange all values in ascending order
• determine number of obs in each class (K) by
  K obs/ classes
• Starting at the lowest value, place an equal
  number of observations in each class
• Class limit is mean value between adjacent
  observations in different classes

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Quantiles
1
2
3
4
K 12 obs / 4 classes 3 obs/class Class
boundaries are mean values on either side of
class limits Still, no overlapping classes
Four Classes 0.02 1.60 1.61 4.19 4.20
11.01 11.02 23.77
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Quantiles

• Produces an even looking map
• A sense of diversity when there is little
• Masks outliers

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Quantiles
3 obs each
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Natural Breaks (Manual)

• Based on visual inspection of data using
• Histogram
• Cumulative percent curve
• Class limits identified where natural groupings
  or breaks occur
• Number of classes determined by number of natural
  breaks
• Subjective technique, but can be effective
• The manual scheme in ArcMap

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Natural Breaks
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Jenks Optimization Method

• An iterative technique
• Based on a measure called the goodness of
  variance fit (GVF)
• Maximizes
• between class heterogeneity
• and within class homogeneity
• You pick number of classes
• The way ArcMap calculates natural breaks

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Jenks Optimization Method
Natural Breaks 5 classes
1
?
2
?
3
?
4
?
5
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Jenks Optimization Method

• GVF SDAM - SDCM / SDAM
• Where
• SDAM sum of squared deviations from array mean
• SDCM sum of squared deviations from class means
• When SDCM is lowest then GVF will be closest to 1
• This is the best set of five classes

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Jenks Optimization Method
(x xi)2
SDAM ?(x xi)2 Where x the array mean
6.83 Xi each data value
?(x xi)2
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Jenks Optimization Method
(zc xi)2
SDCM ??(zc xi)2 Where zc the class mean Xi
each data value
??(zc xi)2
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Jenks Optimization Method
GVF 616.95 5.42 / 616.95 0.99
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Jenks Optimization Method
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Jenks Optimization Method
1
2
3
4
(zc xi)2
Quantiles with 4 classes GVF 616.95 99.87 /
616.95 0.84
??(zc xi)2
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Considerations Legend Design

• Significant interpretation error can occur when
  range graded class boundaries used
• Range grading refers to use of classes with
  continuous intervals
• E.g. 1-10, 11-20, 21-30, 31-40,
• In reality, continuous range of data may not exist

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Legend Design
Effect of range grading Non-continuous data
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Legend Design/Ancillary Data

• Legend boxes should be
• 2/3 as tall as they are wide
• not square boxes
• can also use irregular shapes
• Appropriate ancillary data include
• histogram or cumulative curve
• indication of classification technique

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Considerations Symbol Selection

• Symbols indicate relative change in value
• Achieved by varying symbol
• Arrangement
• Texture
• Orientation
• Colour saturation/chroma
• Colour value/intensity
• Colour hue

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Considerations Map Projection

• Relative proportion of map area represented by
  different symbols affects interpretation
• Consequently, an equivalent projection is most
  appropriate
• More important when mapping at smaller scale
  (i.e. large geographic areas)

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MIDTERM TO HERE Questions?