SUG243 - Cartography (Thematic Mapping)

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.


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.


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.

http://www.answers.com/topic/gross-domestic-product

http://www.answers.com/topic/economic-indicator

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.


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

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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


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


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

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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.


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.


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.


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.


Thematic Mapping 99

Use of Use of Visual Visual VariableVariable

Symbols use the visual variable value (colour) to order the data.


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).




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.



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.



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


Arrow symbolArrow symbol


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


Flow Lines- legendFlow Lines- legend


Flow LinesFlow Lines


Flow LinesFlow Lines


Flow Lines-with specific Flow Lines-with specific directiondirection


Flow LinesFlow Lines Maps Maps


Migration Migration between between different different regionsregions


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.


Quantitative Line Quantitative Line SymbolisationSymbolisation


Charles Joseph Minard: Mapping Napoleon's Charles Joseph Minard: Mapping Napoleon's March, 1861.March, 1861.


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.)


Qualitative Area SymbolisationQualitative Area Symbolisation

Some standardised symbols for indicating lithologic data as suggested by the International Geographical Union Commission on Applied Geomorphology.



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.



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


See notes thematic mapping See notes thematic mapping quantitative.pdf for map typesquantitative.pdf for map types


Choropleth dasymetric isometricChoropleth dasymetric isometric


Quantitative Area SymbolisationQuantitative Area Symbolisation

Terms referring to Line symbols Terms referring to Area symbols


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)


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.


Isometric lines Isometric lines

IsoplethsIsopleths


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


Control points-Control points- assume to represent area.


Isoline mappingIsoline mapping


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.


ChoroplethChoropleth

Quantitatve information is shown within administrative units. (districts, states)

Quantity mapped is normally of relative values such as ratios or percentages


ChoroplethChoropleth


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


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



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


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


Quantitative Area SymbolisationQuantitative Area Symbolisation Choropleth -exampleChoropleth -example


Quantitative Area SymbolisationQuantitative Area Symbolisation Choropleth -exampleChoropleth -example


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.



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


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


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


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


Dasymetric Dasymetric mappingmapping


http://geography.wr.usgs.gov/science/dasymetric/


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


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.


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.


Cartogram – example Cartogram – example Alter area sizes of countries to reflect

their pop. Sizes.


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.


an example of two non-contiguous cartograms of population in California's counties

http://www.ncgia.ucsb.edu/projects/Cartogram_Central/cartogram_examples/noncontiguous.jpg


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


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..


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

http://www.ncgia.ucsb.edu/projects/Cartogram_Central/cartogram_examples/contiguous.jpg


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.


DORLING CARTOGARMSDORLING CARTOGARMS

http://www.ncgia.ucsb.edu/projects/Cartogram_Central/cartogram_examples/dorling3.jpg


See also notes in See also notes in visualization.ppt visualization.ppt


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.


Documents

SUG243 - Cartography (Thematic Mapping)