Copyright, 1998-2005 © Qiming Zhou
GEOG1150. Cartography
Thematic MappingThematic Mapping
Thematic Mapping 2
Thematic mapsThematic maps A map showing qualitative and /or
quantitative information on specific features or concepts in relation to the necessary topographic details
The main objectives is to portray geographical relationships regarding particular distributions
Emphasize spatial pattern of one or more geographic attributes
Aimed at a specific group of users to whom spatial information must be efficiently communicated
Thematic Mapping 3
See notes Thematic.pdfSee notes Thematic.pdf
Thematic Mapping 4
ClassificationClassification
Degree of generalization Function Subject
Thematic Mapping 5
Degree of generalizationDegree of generalization
An analytic map-showing distribution of one or more elements of the phenomenon using nominal data
A complex map- superimposition of several more or less mutually related spatial distribution each with its own respective nominal or ordinal data
A synthesis map-integrated spatial structure, maps that answers questions at all levels
Thematic Mapping 6
FunctionFunction
Inventory Educational Analytical
Thematic Mapping 7
SubjectSubject Decimal indexing 0-base maps 1-Natural phenomena 2-Population &culture 3-Economic 4-Communication 5-Political-administrative 6-Historical 7-Planning &environmental management 8-Cosmological 9-Composite &miscellaneous content-ecological,
tourists
Thematic Mapping 8
Base mapsBase maps
A map containing topographic information and on which the thematic information can be plotted
Base map has to be made functional to the thematic map
Application of detailed or generalized base map depends on the scale, purpose and subject of the thematic map
Better to use as a source document for base map - a map on a larger scale than the final thematic map than on a smaller scale
Thematic Mapping 9
Elements of base mapsElements of base maps
Graticule/grid Drainage pattern Relief Settlements Communication system Administrative units Geographical names Projection-scale, purpose, place, size of area
to be presented
Thematic Mapping 10
Thematic MappingThematic Mapping
Objectives of map design Data measurement Basic statistical concepts and processes Thematic map representations
Thematic Mapping 11
Objectives of Map DesignObjectives of Map Design
Geographical variables are so diverse and complex, we must understand their essential nature.
Geographical ordering - locational relationships. Discrete phenomena. Continuous phenomena.
Thematic Mapping 12
Discrete phenomenaDiscrete phenomena
A distribution that does not occur everywhere in the mapped area
Can only occupy a given point in space at any time
Can be measured in integers, categories Discontinuous phenomena that can only be
ascertained at particular location and not elsewhere e.g. Vegetation types, population
Thematic Mapping 13
Continuous phenomenaContinuous phenomena
Data that are distributed continuously without interruption across the surface
Describes data that can be measured everywhere e.g. temperature, air pressure, elevation
Thematic Mapping 14
See notes j.b.krygierSee notes j.b.krygier
Thematic Mapping 15
Data MeasurementData Measurement
Scales of measurement Nominal Ordinal Interval Ratio
Use of the scales of measurement in thematic mapping
Thematic Mapping 16
Nominal Scales of Nominal Scales of MeasurementMeasurement
Point Line Area
Town River Swamp
Mine Road Desert
Church Graticule Forest
Bench mark
BoundaryCensus regions
Examples of differentiation of point, line and area features on a nominal scale of measurement.
After Robinson, et al., 1995
Thematic Mapping 17
Ordinal Scales of Ordinal Scales of MeasurementMeasurement
Examples of differentiation of point, line and area features on an ordinal scale of measurement.
After Robinson, et al., 1995
Point Line (roads) Area
Large
Medium
Small
National
Provincial
County
Township
Industrial regions
Major Minor
Smoke pollution
Thematic Mapping 18
Interval-Ratio Scales of Interval-Ratio Scales of MeasurementMeasurement
Examples of differentiation of point, line and area features on an interval or ratio scale of measurement.
After Robinson, et al., 1995
Point Line (roads) Area
Thematic Mapping 19
Basic Statistical Concepts Basic Statistical Concepts and Processesand Processes It is often necessary to manipulate raw
data prior to mapping. Pre-map data manipulation stage:
Making data to be mapped comparable.
Thematic Mapping 20
Absolute and Derived DataAbsolute and Derived Data
Absolute qualities or quantities: observed, measured or counted quantities
“raw data” maps showing land use categories, production of goods, elevations above sea level, etc.
Derived/relative values. Calculated, Summarisation or relationship
between features. Four classes of relationships: averages, ratios,
densities and potentials.
Thematic Mapping 21
AveragesAverages
Measures of central tendency Three commonly used averages in
cartography: Arithmetic mean Median Mode
Thematic Mapping 22
Arithmetic MeanArithmetic Mean
N
xx
n
ii
1
Arithmetic mean
Geographical mean
A
xax
n
iii
1
Thematic Mapping 23
Median and ModeMedian and Mode
Median - the attribute value in the middle of all ordered attribute values Geographic median - the attribute value
below which and above which half the total area occurs
Mode - the value that occurs most frequently in a distribution Area modal class - the class which
occupies the greatest proportion of an area
Thematic Mapping 24
RatiosRatios
Something per unit of something else
Quantities that are not comparable should never be made the basis for a ratio
b
a
n
nx
Ratio or rate Proportion Percentage
N
nx a 100
N
nx a
Thematic Mapping 25
DensitiesDensities
Relative geographical crowding or sparseness of discrete phenomena
A
nD
Thematic Mapping 26
PotentialsPotentials Individuals comprising a distribution (e.g. people or
prices) interact or influence one another. The gravity concept: the degree of interaction is directly
proportional to the magnitudes of the phenomena and inversely proportional to the distance between their locations
Pi-potential of place i, X j-value of X at each place, D I j-distance between place I and j
Repeat calculation at each place
jiD
xxP
n
j ji
jii
1 ,
Thematic Mapping 27
Thematic Map Thematic Map RepresentationsRepresentations Indices of variation
Mode - variation ratio
Median - quantile range (quartiles, ceciles or centiles (percentiles))
Arithmetic mean - standard deviation
N
xxn
ii
1
2
A
aV
N
fV mm 1;1
Thematic Mapping 28
Scaling SystemsScaling Systems
Scale Average Index of Variation
Nominal Mode Variation ratio
Ordinal Median Decile range
Interval Arithmetic mean Standard deviation
Ratio Arithmetic mean Standard deviation
Thematic Mapping 29
Some Basic Statistical Some Basic Statistical RelationsRelations Regression analysis Correlation analysis
Spatial autocorrelation
n
ii
n
ii
n
iii
yyxx
yyxxr
1
2
1
2
1
Thematic Mapping 30
Regression analysisRegression analysis The description of the nature of the relationship between two or
more variables; it is concerned with the problem of describing or estimating the value of the dependent variable on the basis of one or more independent variables.
Statistical technique used to establish the relationship of a dependent variable, such as the sales of a company, and one or more independent variables, such as family formations, Gross Domestic Product per capita income, and other Economic Indicators. By measuring exactly how large and significant each independent variable has historically been in its relation to the dependent variable, the future value of the dependent variable can be predicted. Essentially, regression analysis attempts to measure the degree of correlation between the dependent and independent variables, thereby establishing the latter's predictive value.
Thematic Mapping 31
Correlation analysisCorrelation analysis
A causal, complementary, parallel, or reciprocal relationship, especially a structural, functional, or qualitative correspondence between two comparable entities: a correlation between drug abuse and crime.
Statistics. The simultaneous change in value of two numerically valued random variables: the positive correlation between cigarette smoking and the incidence of lung cancer; the negative correlation between age and normal vision.
An act of correlating or the condition of being correlated.
Thematic Mapping 32
ExampleExampleArea Per Capita Personal
Income ($)Per Capita Educational Expenditure ($)
Number of First-degree Graduates ($)
A 3882 273 330
B 4395 266 910
C 3870 240 500
D 5695 333 40
E 4282 273 870
F 4082 276 70
G 3952 210 240
H 5770 357 2920
J 5938 340 530
K 5550 390 1760
L 5304 314 460
M 4840 280 1670
N 4830 360 580
P 5745 376 0
Q 4570 287 2500
(Source: Robinson, et al., 1995)
Thematic Mapping 33
Regression AnalysisRegression Analysis
200
220
240
260
280
300
320
340
360
380
400
3500 4000 4500 5000 5500 6000 6500
Per Capita Personal Income ($)
Per
Cap
ita E
du
catio
nal
Exp
end
iture
($)
85.0
5883.085.19ˆ
r
XY
Scattergrams with fitted linear regression line.
0
500
1000
1500
2000
2500
3000
3500 4000 4500 5000 5500 6000 6500
Per Capita Personal Income ($)
Nu
mb
er o
f F
irst
-deg
ree
Gra
du
ates
($) 21.0
2533.067.335ˆ
r
XY
Thematic Mapping 34
Areal UnitsAreal Units
Thematic Mapping 35
Observed, Predicted and Observed, Predicted and ResidualsResiduals
Maps showing observed per capita educational expenditures, predicted per capita educational expenditures based on per capita income, and residuals from the regression.
From Robinson, et al., 1995
Thematic Mapping 36
Observed, Predicted and Observed, Predicted and Residuals Residuals (Cont.)(Cont.)
Maps showing observed numbers of first-degree graduates, predicted numbers of first-degree graduates based on per capita income, and residuals from the regression.
From Robinson, et al., 1995
Thematic Mapping 37
Data ClassificationData Classification
Systematically grouping data based on one or more characteristics
Arrange data before displaying them 3 reasons why we classify data: Technical constraints: manual vs digital Data accuracy: classification smooth out data
inaccuracy Perceptional demands -Classification result in clearer
map image, Classification enables selective perception of seeing groups and patterns, Classifications is helpful to enhance insight in the data
Classification is a generalization process-improve understanding and readability
Thematic Mapping 38
Data classificationData classification classification is a key method of abstracting
reality into simplified map method of classification is important as effects
‘look’ of the map classification scheme can easily be experimented
with (manipulated?) to give the pattern you want classification should ‘match’ data distribution number of classes. can reader interpret between
them? recommended max of 6 distribution of zones into classes
Thematic Mapping 39
Same data plusdifferent classificationequal different lookingchoropleth map!
Thematic Mapping 40
ClassificationClassification
Tobler(1973)-unnecessary to classify data- (unclassed data)
Resulting image not generalized Those oppose to Tobler: reason –
virtually impossible to perceive differences between neighbourhoods that are further apart geographically
Thematic Mapping 41
To classify or not to To classify or not to classify?classify? What is the map purpose? Interested in: to be able to determine
values of each area? or is it just an overview?
If decides to classify: nature of data What types of data are available?
Thematic Mapping 42
Conditions for Clear Conditions for Clear OverviewOverview The final map should approach the statistical
surface as closely as possible A statistical surface exists for any distribution that
is mathematically continuous over an area and is measured on an ordinal, interval or ratio scale. (Robinson)
A statistical surface is a 3-D representation of the data in which the height is made proportional to the values of data
Visualization allows cartographic induction 2 types: i.stepped-derived from choropleth
ii.smooth- derived from isoline maps
Thematic Mapping 43
Thematic Mapping 44
General Conditions for Clear General Conditions for Clear OverviewOverview The final map should display those
patterns or structures that are characteristics for the mapped phenomenon. Extreme high or low values should not disappear.
Each class should contain its share of the observed values
Thematic Mapping 45
Cont..Cont.. Encompass the full range of data- Class interval must
cover from the lowest to the highest value Classes may not overlap No class interval should be vacant The accuracy of the classification may not exceed the
accuracy of the original data If possible have a logical mathematical relationship
between class interval Rounded off class limits are better understood and
memorized The no. of classes must give good portrayal of the
distribution
Thematic Mapping 46
Primary Types of Primary Types of ClassificationClassification There is no one best way to classify data – depends
on the purpose of the map Simplicity is the top goal, no matter if the end result is
visual or mathematicalExogenous Values not related to the actual data set are used to
subdivide into groups Example: A specific income level used to define
'poverty level'Arbitrary Constant, rounded values having no relation to the
distribution of data values are used to divide the data Usually used as a matter of convenience - easy to
implement Example: 10, 20, 30, 40, 50, etc.
Thematic Mapping 47
Cont..Cont..Idiographic A long-used technique, most preferred by
cartographers Classes are determined by the "natural breaks" in the
data set Example: Given the data set, 1 2 3 6 7 8 11 12 14, the
breaks could occur between 3 and 6, 8 and 11Serial Uses standard deviation, equal intervals, and
arithmetic and geometric progressions to divide up the data sets
Example: data showing a bell curve distribution
Thematic Mapping 48
Jenks and Coulson (1963)Jenks and Coulson (1963)
Choose a map type Limit the number of classes. Research
revealed that humans can handle up to max 7 classes to get an overview. The exact no. of classes is influenced by: the type of symbolization, the theme’s geog. distribution and the data range
Define the class limits
Thematic Mapping 49
General steps in Data General steps in Data Classification -RobinsonClassification -Robinson
Need to determine the no. of classes, the sizes of the class intervals, the class limits
Put data into array Construct a dispersal graph/scatter diagram Produce graphic array (curve) Compare graphic array curve with theoretical
(mathematical) curve Determine the classification methods, select
most appropriate classification Decide no. of class, calculate class limits,
adjust class limits
Thematic Mapping 50
Thematic Mapping 51
How many How many Classes/category?Classes/category? Factors User requirements Visual variables used No. of data values Size of areal units/symbols Distribution of data Grouping of data around the middle
value
Thematic Mapping 52
No. of Classes-ITCNo. of Classes-ITCPoint Line Area
Size 4 4 5
Value 3 4 5
Texture 2 4 5
Suggestion for CHECKING: C=Log N/Log 2 (Wang Zhe Shen) where C= no. of classes, N = no. of observationsN : 4-7 8-15 16-31 32- 36 64-127 128-255C : 2 3 4 5 6 7
7(+-)2 = 5 to 9
Thematic Mapping 53
Classification-Class limitsClassification-Class limits
2 approaches Graphic Mathematic methods
Thematic Mapping 54
Classification-Graphic Classification-Graphic approachapproach Natural breaks/break points
Sort observed values Observe discontinuities/break points-
function as class boundaries
Frequency diagram Cumulative frequency diagram
Thematic Mapping 55
Classification-Mathematic Classification-Mathematic approach (Robinson)approach (Robinson) Constant series or Equal steps/Equal interval
Based on range Parameters of normal distribution Quantiles
Systematically Unequal Stepped Class limits Arithmetic series Geometric series
Irregular Stepped Class limits Frequency graph Clinographic curve Cumulative frequency curve
Thematic Mapping 56
Thematic Mapping 57
Thematic Mapping 58
Natural Breaks Natural Breaks
A method preferred by many cartographers because it captures the character of the data set
Natural groupings in the data are sought and their obvious breaks are used as the class boundaries
Thematic Mapping 59
Thematic Mapping 60
QuantilesQuantiles This method divides the data set into equal number of values in
each class This minimizes the importance of class boundaries, but it can be
misleading because one class could have widely differing values Common methods: quartiles (4 classes), quintiles (5 classes),
deciles (10 classes) This differs from constant intervals; in this you divide up the
number of values in the data set, not the values themselves as with constant
Choose the number of classes, then compute limits using difference of domain ranking
rank the attribute data values in ascending order # of data observations / # of classes = # of
observations in each class apply symbolization to “mimic” the increasing/decreasing
magnitudes
Thematic Mapping 61
Thematic Mapping 62
Equal Interval/equal stepsEqual Interval/equal steps This is a common method and very easy to use Imagine passing planes of an equal distance through a
data set (like elevation) This method encloses equal amounts of the total data
range into each class interval Choose the number of classes, then compute limits
using difference of range max data value – min data value =
range range / # of classes = class interval the # of classes establishes how many “equal
intervals” will be used apply symbolization to “mimic” the
increasing/decreasing magnitudes
Thematic Mapping 63
Equal intervalEqual interval
Ex: Data set range from 0-36 and no. of class is 4
Class 1 0-9 Class 2 10-18 Class 3 19-27 Class 4 28-36
Thematic Mapping 64
Thematic Mapping 65
Standard Deviations Standard Deviations
If a data set displays a normal frequency distribution, then this method can be used
Measure for the spread of data around the mean
The mean is calculated and then the standard deviation using statistical mathematics
Usually no more than 6 classes are necessary to convey the information
Thematic Mapping 66
Cont..Cont..
Working from the mean outwards in units of S, which gives an even no. of classes
Class 1 <(mean-S) Class 2 (mean-S) to mean Class 3 mean to (mean+S) Class 4 >(mean+S)
Where S = Standard deviation
Thematic Mapping 67
Thematic Mapping 68
Arithmetic/Geometric Arithmetic/Geometric Progressions Progressions Both of systematic/mathematical
classification methods Arithmetic is used only when the
shape of the data set approximates the shape of a typical arithmetic progression
Geometric is used when the frequency of the data declines with increasing magnitude - something typical in geographic data
Thematic Mapping 69
Arithmetic Progressions Arithmetic Progressions
The width of class increases with constant value .
Example: Class 1 0-2 width=2 or I Class 2 2-6 width=4 or 2I Class 3 6-12 width=6 or 3I
Thematic Mapping 70
Arithmetic progressionArithmetic progression
If no. of class is known,
Xmin+I+2I+3I+4I+…..=Xmax If Xmin & Xmax , n are known Calculate I= Xmax-Xmin/(n(n+1)/2)
Where Xmax=max value
Xmin=min value
I=class interval
n=no. of class
Thematic Mapping 71
Geometric progressionGeometric progression
Upper class limit increase in size by multiplying with a constant factor
Example Class 1 1-10 10¹ Class 2 11-100 10² Class 3 101-1000 10³ etcIn the eg. the factor is 10. The upper limit is always 10
times bigger than the previous upper limit
Thematic Mapping 72
Geometric progressionGeometric progression
Determine the number of class, n Then calculate the interval, I I=sqrt(xmax/xmin)*n
Where Xmax=Max value
Xmin= Min value
n = no. of class
Thematic Mapping 73
Geometric progressionGeometric progression
Classes then: Class 1 (Xmin) – (Xmin*I) Class 2 (Xmin*I ) –(Xmin*I²) Class 3 (Xmin*I²) –(Xmin*I³) etc
Thematic Mapping 74
Reciprocal progressionReciprocal progression
For very skewed distributions Class 1 (Xmin) to (1/Xmin-I) ¹־ Class 2 (1/Xmin-I) ¹־ to (1/Xmin-2I) ¹־
Etc I =((1/xmin) – (1/Xmax))/n Where Xmin = min value of data range
Xmax = max value of data range
n = no. of class
Thematic Mapping 75
Jenks’ Optimization Jenks’ Optimization Method Method Cartographer George Jenks developed this
optimization system The goal: forming groups that are internally
homogeneous while assuring heterogeneity among classes
This has proven to be a very useful method, next to natural breaks - but requires computing power to perform
A statistical approach based on “Min & Max” of data variance
data variance – how much data values vary in magnitude among each other
start with a single class: range (a single class) = max data value – min data value
introduce another group whereby: minimize within group variance (member data
values closer in value) maximize between group variance (difference in
group averages as great as possible)
Thematic Mapping 76
Procedure The Jenks optimization method is also known as the goodness of variance fit (GVF). It is used to minimize the squared deviations of the class means. Optimization is achieved when the quantity GVF is maximized:
1. Calculate the sum of squared deviations between classes (SDBC).
GVF = -------------------
2. Calculate the sum of squared deviations from the array mean (SDAM).
3. Subtract the SDBC from the SDAM (SDAM-SDBC). This equals the sum of the squared deviations from the class means (SDCM).
The method first specifies an arbitary grouping of the numeric data. SDAM is a constant and does not change unless the data changes. The mean of each class is computed and the SDCM is calculated. Observations are then moved from one class to another in an effort to reduce the sum of SDCM and therefore increase the GVF statistic. This process continues until the GVF value can no longer be increased.
Thematic Mapping 77
Thematic Mapping 78
Standard curvesStandard curves
Thematic Mapping 79
Example: World Example: World Population DensityPopulation Density
0
5000
10000
15000
20000
25000
30000
Po
pu
lati
on
Den
sity
(p
erso
ns/
sqkm
)
Maximum = 30127
Minimum = 0
Mean = 291.3
Std = 1947.1
Thematic Mapping 80
Natural BreaksNatural Breaks
0
200
400
600
800
1000
Po
pu
lati
on
Den
sity
(p
erso
ns/
sqkm
)
Class 1 Class 2
Thematic Mapping 81
Natural BreaksNatural Breaks(Cont.)(Cont.)
0
5
10
15
20
25
30
35
2 6 10 30 50 70 90 150 250 350 450 600 800 1000 3000 5000
Fre
qu
en
cy
Thematic Mapping 82
Equal IntervalEqual Interval
0
200
400
600
800
1000
Po
pu
lati
on
Den
sity
(p
erso
ns/
sqkm
)
Class 1
Thematic Mapping 83
Equal IntervalEqual Interval(Cont.)(Cont.)
0
5
10
15
20
25
30
35
2 6 10 30 50 70 90 150 250 350 450 600 800 1000 3000 5000
Fre
qu
en
cy
Thematic Mapping 84
Equal AreaEqual Area
0
200
400
600
800
1000
Po
pu
lati
on
Den
sity
(p
erso
ns/
sqkm
)
Cla
ss
1 Class 5
Cla
ss
2 Class 3 Class 4
Thematic Mapping 85
Equal Area Equal Area (Cont.)(Cont.)
0
5
10
15
20
25
30
35
2 6 10 30 50 70 90 150 250 350 450 600 800 1000 3000 5000
Fre
qu
en
cy
Thematic Mapping 86
QuartileQuartile
0
200
400
600
800
1000
Po
pu
lati
on
Den
sity
(p
erso
ns/
sqkm
)
Class 1 Class 5Class 2 Class 3 Class 4
Thematic Mapping 87
Quartile Quartile (Cont.)(Cont.)
0
5
10
15
20
25
30
35
2 6 10 30 50 70 90 150 250 350 450 600 800 1000 3000 5000
Fre
qu
en
cy
Thematic Mapping 88
Standard DeviationStandard Deviation
0
200
400
600
800
1000
Po
pu
lati
on
Den
sity
(p
erso
ns/
sqkm
)
0 - 1 Std
-1 Std - 0
Mea
n
Mean = 291.3
SD = 1947.1
Thematic Mapping 89
Standard DeviationStandard Deviation
0
5
10
15
20
25
30
35
2 6 10 30 50 70 90 150 250 350 450 600 800 1000 3000 5000
Fre
qu
en
cy
Mean = 291.3
SD = 1947.1
Mean +1 Std +2
Thematic Mapping 90
Symbolising Geographical Symbolising Geographical FeaturesFeatures Point symbolisation
Qualitative Quantitative
Line symbolisation Qualitative Quantitative
Area symbolisation Qualitative Quantitative
Thematic Mapping 91
Qualitative Qualitative Point Point SymbolisationSymbolisation
Nominally scaled pictorial symbols on a map promoting winter activities in a portion of the state of Wisconsin. The map legend lists 14 symbols.
Cited in Robinson, et al., 1995
Thematic Mapping 92
Qualitative Point Symbolisation Qualitative Point Symbolisation (Cont.)(Cont.)
Nominally scaled symbols are used to indicate four classes of climatic stations. Left: the use of orientation of symbols. Right: the use of the visual variable, shape.
From Robinson, et al., 1995
Thematic Mapping 93
Quantitative Point Quantitative Point SymbolisationSymbolisation Various techniques are available to
the cartographer What technique to use depend on: Character of the feature to be mapped Type and complexity of the quantitative
information The purpose of the map and the map user Scale of the map Place/space available on the map
Thematic Mapping 94
Quantitative Point Quantitative Point SymbolisationSymbolisation Symbols with value indication Repeating principle The dot principle- each dot represent a unit value,
gives visual impression of distribution differences, factors: unit value of dot, size of dot, location of dot
Proportional symbols - sizes proportional to the quantity they represent, 3 methods to calculate: sqrt method, J.J. Flannery, range-graded (see notes Dotmap . pdf)
Graphs and diagrams - Line graphs, Bar graphs, Population pyramid, Pie graphs,Triangular graphs, Circular/clock graphs
Adjacent symbols
Thematic Mapping 95
Quantitative Point Quantitative Point SymbolisationSymbolisation See Diagrams in Quantitative Point
Folder
Thematic Mapping 96
Symbols are proportionally scaled so that areas of the symbols are in the same ratio as the population numbers they represent.
From Robinson, et al., 1995
Quantitative Point Quantitative Point SymbolisationSymbolisation
Thematic Mapping 97
Quantitative Point Symbolisation Quantitative Point Symbolisation (Cont.)(Cont.)
Left: symbols are range-graded to denote the population of the cities. Right: symbols are ordinally scaled. The legends are different due to the different levels or measurement.
From Robinson, et al., 1995
Thematic Mapping 98
Quantitative Point Quantitative Point Symbolisation Symbolisation (Cont.)(Cont.)
Three legends whose symbols are identical. The added information in the form of text puts one legend on an ordinal scale, one on a range-graded scale, and one on a ratio scale.
From Robinson, et al., 1995
Thematic Mapping 99
Use of Use of Visual Visual VariableVariable
Symbols use the visual variable value (colour) to order the data.
From Robinson, et al., 1995
Thematic Mapping 100
Use of Visual Variable Use of Visual Variable (Cont.)(Cont.)
Left: total population is symbolised by size, while percentage of black inhabitants is symbolised by the value (colour). Right: Percentage of black inhabitants is symbolised by the size, while total population is symbolised by the value (colour).
From Robinson, et al., 1995
Thematic Mapping 101
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Qualitative Line Qualitative Line SymbolisationSymbolisation
Examples of lines of differing character (the visual variable shape) which are useful for the symbolisation of nominal linear data.
From Robinson, et al., 1995
Thematic Mapping 103
Ordinal PortrayalOrdinal Portrayal
The use of line width (visual variable size) enhanced by the use of line character (visual variable shape) to denote the ordinal portrayal of civil administrative boundaries.
From Robinson, et al., 1995
Thematic Mapping 104
Quantitative Line Quantitative Line SymbolisationSymbolisation
Arrow Symbol map Short arrow represents direction, thickness or tone
represents the quantity. Flow Line map Quantitative information is given by lines of varying
sizes/widths. The width is proportional to the value. 3 types of flow lines: smooth curved ‘origin-
destination’ lines, straight ‘origin-destination’ lines, irregular lines more or less following the routes.
Flow lines with indication of direction of movement
Thematic Mapping 105
Arrow symbolArrow symbol
Thematic Mapping 106
Arrow symbol mapArrow symbol mapUsing Arrows to identify the strength (width), orientation and temperature values (blue=cold, red=warm) of ocean currents around New Zealand
Thematic Mapping 107
Flow Lines- legendFlow Lines- legend
Thematic Mapping 108
Flow LinesFlow Lines
Thematic Mapping 109
Flow LinesFlow Lines
Thematic Mapping 110
Flow Lines-with specific Flow Lines-with specific directiondirection
Thematic Mapping 111
Flow LinesFlow Lines Maps Maps
Thematic Mapping 112
Migration Migration between between different different regionsregions
Thematic Mapping 113
Range-graded line symbols. On this map of immigrants from Europe in 1900, lines of standardised width are used to represent a specified range of numbers of immigrants.
From Robinson, et al., 1995
Quantitative Line Quantitative Line SymbolisationSymbolisation
Thematic Mapping 114
Charles Joseph Minard: Mapping Napoleon's Charles Joseph Minard: Mapping Napoleon's March, 1861.March, 1861.
Thematic Mapping 115
Edward Tufte, in his praise of Minard's map,
identified 6 separate variables that were captured within it. First, the line width continuously marked the size of the army. Second and third, the line itself showed the latitude and longitude of the army as it moved. Fourth, the lines themselves showed the direction that the army was traveling, both in advance and retreat. Fifth, the location of the army with respect to certain dates was marked. Finally, the temperature along the path of retreat was displayed. Few, if any, maps before or since have been able to coherently and so compellingly weave so many variables into a captivating whole. (See Edward Tufte's 1983 work, The Visual Display of Quantitative Information.)
Thematic Mapping 116
Qualitative Area SymbolisationQualitative Area Symbolisation
Some standardised symbols for indicating lithologic data as suggested by the International Geographical Union Commission on Applied Geomorphology.
From Robinson, et al., 1995
Thematic Mapping 117
Qualitative Qualitative Area Area Symbolisation Symbolisation (Cont.)(Cont.)
Portrayal of North American air masses and their source regions. Although data have quantitative characteristics, the intent of this illustration is simply to portray location of air masses. This can be accomplished by using nominal area symbolisation.
Cited in Robinson, et al., 1995
Thematic Mapping 118
Quantitative Area SymbolisationQuantitative Area Symbolisation Choropleth mapping Objective: to show the quantities within
administrative unit areas Dasymetric mapping Objective: to show uniform quantities
regardless of unit area boundaries Isarithmic mapping Objective: to show the gradients , their size
and distribution Cartogram
Thematic Mapping 119
See notes thematic mapping See notes thematic mapping quantitative.pdf for map typesquantitative.pdf for map types
Thematic Mapping 120
Choropleth dasymetric isometricChoropleth dasymetric isometric
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Quantitative Area SymbolisationQuantitative Area Symbolisation
Terms referring to Line symbols Terms referring to Area symbols
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Terms referring to line symbolsTerms referring to line symbols Isolines/ Isarithm/ Isogram Isolines/ Isarithm/ Isogram
Isometric lines Metron = measurement Lines that portray absolute values.
The values they represent can exist at any point of the line.
Eg. Lines of equal elevation (isohypse/contour) temperature (isotherm), rainfall (isohyet), pressure (isobar)
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Isolines/ Isarithm/ Isogram Isolines/ Isarithm/ Isogram
Isopleths Plethos = magnitude Lines the represent relative values.
They represent concepts that are function of element and space.
Eg. Density. The values on which the lines are based cannot actually exist at points.
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Isometric lines Isometric lines
IsoplethsIsopleths
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Isoline mappingIsoline mapping
Step 1: exact location of control points Step 2: determination of class interval Step 3: interpolation of Isolines Step 4: shading or coloring of the
zones
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Control points-Control points- assume to represent area.
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Isoline mappingIsoline mapping
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Terms referring to Area symbolsTerms referring to Area symbols Chorogram Chorogram
Choros = area, space 2 groups i. Choropleth – Area symbol
applied to an administrative unit.
ii. Chorisogram- a system of shading or colour applied between two successive isolines.
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ChoroplethChoropleth
Quantitatve information is shown within administrative units. (districts, states)
Quantity mapped is normally of relative values such as ratios or percentages
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ChoroplethChoropleth
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Choropleth mapsChoropleth maps counterpart of histogram aggregate data, usually ratio or percentage data map for discrete spatial units choro from choros (place) and pleth (value) practical Issues
choice of intervals - number and their breaks equal interval, equal share (quantiles),
standard deviational, … choice of colors
important for perception of patterns misleading role of area of spatial units
larger areas “seem” more important
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very widely used. the ‘default’ mapping, especially for social data (e.g. census)
most mapping tools produce choropleth maps easy produced in GIS, stats software not necessarily the best solution problems. can easily promote false notions of
homogeneity inside the zones and sharp cut-off at the borders. real phenomena (e.g. Internet access) do not fit neat set of units
should be used for ratio data and not absolute counts as most spatial units are variable in size
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Choropleth mappingChoropleth mapping
Step 1: Plotting of boundaries Step 2: Calculation of ratios or
percentages from statistics Step 3: Choosing proper class interval Step 4:Plot quantities using graded
series of shadings
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Limitations of choroplethLimitations of choropleth
Assumption that distribution of the phenomena over unit area is uniform
Inaccuracy caused by difference in sizes of units
The choice of class interval affects the visual impression of the map
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Quantitative Area SymbolisationQuantitative Area Symbolisation Choropleth -exampleChoropleth -example
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Quantitative Area SymbolisationQuantitative Area Symbolisation Choropleth -exampleChoropleth -example
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Quantitative Area Quantitative Area SymbolisationSymbolisation
Map illustrating the range-graded classification of Florida counties. The use of the visual variable value (colour) creates a stepped surface.
Cited in Robinson, et al., 1995
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Dasymetric mappingDasymetric mapping
Technique as an improvement of the choropleth mapping technique for phenomena that have an uneven distribution
Using other geographical factors to determine the cause of uneven distribution
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Cont..Cont..
Use the same type of data as choropleth, but involve some analysis beyond the administrative districts
Do not assume homogeneity within districts
May look the same as isarithmic technique but ..
Values can go from high to low without going through intermediate values as in isarithmic technique
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J.K.Wright method of J.K.Wright method of calculating densitiescalculating densities
Dn = (D/1-Am) – ((Dm * Am)/1-Am)Where
Dn = Density in area n
Dm = estimated density in area m
D = density over the whole area (m+n)
(from choropleth map data)
Am = the fraction of m of the total area
n
m
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Dasymetric mappingDasymetric mapping Suppose n is land and m is area with water. Area has 80% land, 20% water If D (from choropleth) = 40 people/km sq. Assume water has no inhabitant, Dm = 0 Hence population should only be on n only Am = 0.2, Dn = to be calculated
So Dn = (40/1-0.2) – ((0*0.2/1-0.2))
= 40/0.8
= 50n =0.8
Land
m =0.2
Water
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Dasymetric Dasymetric mappingmapping
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http://geography.wr.usgs.gov/science/dasymetric/
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1)
Cartogram – What is it?Cartogram – What is it? A diagram highly abstracted on which locations or
outlines are distorted A small diagram on the face of a map showing
quantitative information. An abstracted and simplified map the base of which is
not true to scale. Unique representations of geographical space Are map transformations that distort area or
distance in the interest of some objective Have strong visual impact, attract reader attention Often concerned with magnitude and want to make
stronger impression than conventional choropleth or isarithmic mapping
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A cartogram is a type of graphic that depicts attributes of geographic objects as the object's area.
Because a cartogram does not depict geographic space, but rather changes the size of objects depending on a certain attribute, a cartogram is not a true map.
Cartograms vary on their degree in which geographic space is changed; some appear very similar to a map, however some look nothing like a map at all.
There are three main types of cartograms, each have a very different way of showing attributes of geographic objects- Non-contiguous Contiguous Dorling cartograms.
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Cartogram ..contCartogram ..cont Mapping requirements include the
preservation of shape, orientation contiguity, and data that have suitable variation.
Successful communication depends on how well the map reader recognizes the shapes of the internal enumeration units, the accuracy of estimating these areas, and effective legend design.
Cartogram construction may be by manual or computer means.
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Cartogram – example Cartogram – example Alter area sizes of countries to reflect
their pop. Sizes.
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Cartogram- Cartogram- NON-CONTIGUOUS CARTOGRAMSNON-CONTIGUOUS CARTOGRAMS
A non-contiguous cartogram is the simplest and easiest type of cartogram to make.
In a non-contiguous cartogram, the geographic objects do not have to maintain connectivity with their adjacent objects. This connectivity is called topology.
By freeing the objects from their adjacent objects, they can grow or shrink in size and still maintain their shape.
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an example of two non-contiguous cartograms of population in California's counties
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The difference between these two types of non-contiguous cartograms- The cartogram on the left has maintained the object's centroid (a centroid is the weighted center point of an area object.) Because the object's center is staying in the same place, some of the objects will begin to overlap when the objects grow or shrink depending on the attribute (in this case population.)
In the cartogram on the right, the objects not only shrink or grow, but they also will move one way or another to avoid overlapping with another object. Although this does cause some distortion in distance, most prefer this type of non-contiguous cartogram. By not allowing objects to overlap, the depicted sizes of the objects are better seen, and can more easily be interpreted as some attribute value
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Cartogram-Cartogram- CONTIGUOUS CARTOGRAMSCONTIGUOUS CARTOGRAMS
In a non-contiguous cartogram the connectivity between objects, or topology was sacrificed in order to preserve shape.
In a contiguous cartogram, the reverse is true- topology is maintained (the objects remain connected with each other) but this causes great distortion in shape.
The cartographer must make the objects the appropriate size to represent the attribute value, but he or she must also maintain the shape of objects as best as possible, so that the cartogram can be easily interpreted..
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an example of a contiguous cartogram of an example of a contiguous cartogram of population in California's counties. population in California's counties. Compare this to the previous non-Compare this to the previous non-contiguous cartogramcontiguous cartogram
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DORLING CARTOGARMSDORLING CARTOGARMS
This type of cartogram was named after its inventor, Danny Dorling of the University of Leeds.
A Dorling cartogram maintains neither shape, topology nor object centroids, though it has proven to be a very effective cartogram method.
To create a Dorling cartogram, instead of enlarging or shrinking the objects themselves, the cartographer will replace the objects with a uniform shape, usually a circle, of the appropriate size.
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DORLING CARTOGARMSDORLING CARTOGARMS
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See also notes in See also notes in visualization.ppt visualization.ppt
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Appropriate Appropriate Uses of the Uses of the Visual Visual VariablesVariables
Feature Dimension
Level of Measurement
Nominal Ordinal/Interval/Ratio
Qualitative Quantitative
Point Hue (colour) Size
shape Value (colour)
Orientation Chroma (colour)
Line Hue (colour) Size
Shape Value (colour)
Orientation Chroma (colour)
Area Hue (colour) Value (colour)
Shape Chroma (colour)
Pattern Size
Orientation
Volume Hue (colour) Value (colour)
Shape Chroma (colour)
Pattern Size
Orientation
Appropriate uses of the visual variables for symbolisation. The visual variable in italics are of secondary importance.
From Robinson, et al., 1995
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