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Thematic maps

Thematic maps

Paolo Zatelli

Dipartimento di Ingegneria Civile ed Ambientale

Università di Trento

Paolo Zatelli | Università di Trento | 1 / 58

Thematic maps

Outline

1 Thematic cartography

2 Data, features and representationDataRepresentationPoints, lines and areas

3 Attribute classificationNatural breaks - Equal intervals - Standard deviationQuantiles - Equal areas - ProgressionsUser defined classes


Thematic maps | Thematic cartography

Thematic mapsWhat are they used for?

Thematic maps are used to display a “thematism” of data, i.e. todisplay an attribute of geometric features (points, lines, areas).

To create thematic maps we need:

graphics to choose line types and colors to display the attributesymbols to display the attributestatistics to choose the classes for the attribute’s values



Thematic mapsAn example

A thematic map is used to highlight the distribution of an attribute. Theexample below displays the distribution of the world population.

Countries Countries by population (n. of inhabitants)



Vector and rasterEntities or fields

Usually thematic maps are created from vector data, however, it ispossible to user raster maps, modifying the color table or reclassifyingthem.

DTM of the Spearfish County Reclassified DTM (9 classes of 100m)


Thematic maps | Data, features and representation | Data

Outline






Input dataWhat is needed to create a thematic map

To create thematic maps we need:1 geometry (features: points, lines, areas)2 attributes to be displayed on the map (obviously connected to the

features)

In the vector model an attributes corresponds to a column in the tableassociated to geometric features (points, lines and areas).



Input dataGeometry



Input dataAttributes

FIPS ISO2 ISO3 UN NAME AREA POP2005 REGION SUBREGIONAC AG ATG 28 Antigua and Barbuda 44 83039 19 29AG DZ DZA 12 Algeria 238174 32854159 2 15AJ AZ AZE 31 Azerbaijan 8260 8352021 142 145AL AL ALB 8 Albania 2740 3153731 150 39AM AM ARM 51 Armenia 2820 3017661 142 145AO AO AGO 24 Angola 124670 16095214 2 17AQ AS ASM 16 American Samoa 20 64051 9 61AR AR ARG 32 Argentina 273669 38747148 19 5AS AU AUS 36 Australia 768230 20310208 9 53BA BH BHR 48 Bahrain 71 724788 142 145BB BB BRB 52 Barbados 43 291933 19 29BD BM BMU 60 Bermuda 5 64174 19 21BF BS BHS 44 Bahamas 1001 323295 19 29BG BD BGD 50 Bangladesh 13017 15328112 142 34BH BZ BLZ 84 Belize 2281 275546 19 13.. .. .. .. .. .. .. .. ..



Population distribution by country

freq

uenc

y

data

World populatione - 30 equal classes


Thematic maps | Data, features and representation | Representation

Outline






Vector layer representationData distribution

The representation of a layer substantially depends on the type and onthe distribution of the attribute to be depicted.

Examples:the attribute is qualitative (type of soil) or quantitative (pH of thesoil)?the distribution (of pH) is uniform or some values have differentfrequencies?



Vector features and layersHow an attribute value is represented on the map

In a GIS three types of vector features are used, points, lines andareas, which are represented by:

pointssymbolscolorsdimensions

lineshatchingcolorswidths

areassymbolscolorsdithering

An internal point (e.g. centroid) can be used to represent an attributeof an area.



Types of attributes - Ito create thematic maps

Representation of attributes depends on their properties:

1 Quantitativenominal [or categorical] groups have names (“labels”) but not

values (e.g. land use, country, etc.).fuzzy sets like nominal attributes, but each element belongs to a

category to a given “degree”.



Types of attributes - IIto create thematic maps

2 Qualitativeordinal quantities do not have a numeric meaning, still it

possible to sort them, therefore to assign a number.This is often the case of categories expressing anassessment (e.g. a forest in “good”, “fairly good”, ...,“very bad” condition). In general arithmeticoperations make no sense, logical operations do(e.g. reclassification).

interval attributes are numeric and distributed on an interval,however the origin and the interval are arbitrary (e.g.years: different calendars use different years as “yearzero”). Some arithmetic operations make sense (e.g.difference of years), other do not (e.g. ratio betweenyears).



Types of attributes - IIIto create thematic maps

ratio attributes are quantitative, the origin is not arbitrarybut the interval is (e.g. age, field value). Arithmeticoperations are possible.

count such as ratio, but measurement units are notarbitrary, therefore it is not always possible to rescalethe interval (e.g. dwellers in an area, number ofmunicipalities in a region).



Choice of colors and ditheringGeneral criteria

Some general rules:

how attributes are classified is fundamentalcolors must be chosen to cater for color blind peoplecolors and dithering must be used in intuitive ways:

light colors correspond to lower values, darker ones to highervaluesthick dithering corresponds to higher values

continuous lines are used for certain boundaries, dashed lines foruncertain ones


Thematic maps | Data, features and representation | Points, lines and areas

Outline






Points and linesIGMI symbols

IGMI: points - edifici di culto (churchs) IGMI: lines - strade e ferrovie (roads and railroads)



Areas - ITypes of thematic maps

For area features, the most used types of maps are:

area class areas’ boundaries depend on an attribute because allareas with the same value are represented in the sameway, therefore common boundaries are dissolved (e.g.land use).

coropleth boundaries are defined when data aregathered/processed (e.g. census units).

dot the number of dots (randomly placed inside the area tosimulate a density) represents the attribute’s value.

proportional symbols symbols (usually placed in the center for thearea) proportional to the value of the attribute are used(see lines and points).



Areas - IITypes of thematic maps

isarithmic are used to represent scalar fields (e.g. height, pressure),using contour levels.

3D views can be used to represent an attribute (assumingcontinuous or discrete values) simulating a “height”.



Area class - I

All areas with the same value are represented in the same way,therefore boundaries change depending on the attribute’s value.

Whenever possible, colors and dithering appealing to the phenomenonare used (e.g. green -> forest, blue -> hydrography, etc.).

This kind of map can be used to evaluate the dispersion/concentrationof phenomena (e.g. same land use in different areas).



Area class - II

Countries by region (continent)



Dots map - I

A dot represents one unit (or multiple) of the attribute’s value (e.g. 1airport, 100000 inhabitants).

Dots are randomly placed in each area, to simulate a density.

There is no need to split the attribute’s range into classes.



Dots map - II

World population in 2005 - 1 dot = 500 000 inhabitants



Proportional symbols map - I

Symbol’s dimension is indicative of the value of the attribute.

Symbols with simple shapes are used (circles, squares and triangles);their surface is scaled as a function of the attribute’s value.

3D symbols can be used to represent more than one attribute at atime; however, these are usually less readable than 2D symbols.



Proportional symbols map - II

User perception of surface usually leads to underestimate them, with agreater effect on large areas.Possible solutions are:

to use the apparent scale method, where symbols’ surfaces growsfaster than direct proportionality (exponentials are used for circles,usually r1.14 instead of r )

to use symbols with discrete values of surface

to optimize the legend to remove this effect



Proportional symbols map - III

World population in 2005



Isarithmic - Ito represent scalar fields

The distribution of an attribute is represented using lines passingthrough points with the same attribute’s value.

Usually lines correspond to fixed increment of the attribute’ value (e.g.a contour level each 10 meters), in this way it is possible to mimic a 3Dview.

Lines’ density must take into account the accuracy of the attribute’svalues (e.g. contour levels on maps with different scales have differentdistances).



Isarithmic - IIto represent scalar fields

3D contour levels - Trento



Isarithmic - IIIto represent scalar fields

Contour levels - Trento



3D views- I

It is possible to use a 3D view (usually axonometric) to represent anattribute using a “height” associated to the geometric features.

This approach can be used for scalar fields (e.g. DTM) and for entities(e.g. areas representing countries).

The “height” can be a real height (e.g. DTM, buildings’ height) or anyattribute (even not an extent).



3D views- II

Scalar field - DTM 3D - Trento



3D views- III

Entities - World population in 2005


Thematic maps | Attribute classification

Attribute classification

Most of the times an attribute has a large number of different values: ifeach value is represented in a different way (by color, symbol, etc.) theresulting map is impossible to read.

For this reason, attribute’s values are grouped together in classes.Usually, no more than 5 - 7 classes are used at the same time.

A method to set the intervals identifying the classes must be chosen.Such method must minimize the differences between elements of thesame class, while maximizing the differences with elements of theother classes.

In some cases classes are chosen according to legal or de factostandards.


Thematic maps | Attribute classification

Classification methods

Different methods can be used to classify data, i.e. to chose theintervals for grouping data.

The choice of the intervals depend on the attribute’s distribution:

natural breaks for non normal distributionsequal intervals for uniform or normal distributionsstd deviation for normal distributionsquantile for uniform or normal distributionsconstant area for maps with areas with similar valuesprogressions for distributions with many values on the tailsuser defined if the possibilities above are not satisfying


Thematic maps | Attribute classification | Natural breaks - Equal intervals - Standard deviation

Outline






Natural breaks - I

This approach is used for non normal nor uniform distributions.Classes’ boundaries are placed at discontinuities of the distribution.

Given the number of classes, the difference between the sum ofsquare differences inside each class and the sum of the squaredifference with respect to the global mean is maximized (Jenks’algorithm).

Advantages:

classes have the maximum possible internal homogeneitythis is a robust classification methodit is easy to implement an automatic procedure



Natural breaks - II

Drawbacks:

results are good only if discontinuities do actually exist in thedistribution (at least a number of discontinuities equal to thenumber of classes-1)

the outcome depends on the number of classes

the procedure is iterative and can be computationally intensive

classes depend on the distribution, therefore the comparison ofmaps is usually difficult (because in general the same attribute indifferent regions has different distribution and therefore differentclasses)



Natural breaks - III

freq

uenc

y

data

Natural breaks - 5 classes

brea

k

brea

k

brea

k

brea

k

class 1 class 2 class 3 class 4 cl. 5



Natural breaks - IV

World population in 2005 - natural breaks



Equal intervals - IClasses with equal width

This method is used for uniform or quasi uniform distributions.Interval (constant) width is given by

max − minn. of classes

Advantages:it is easy to understandif the absolute maximum and minimum are used, classes areindependent from the mapped region, therefore maps arecomparable

Drawbacks:it is not suitable if the distribution is not uniform or quasi uniform(empty classes/overcrowded classes)it “hides” the differences between values



Equal intervals - IIClasses with equal width

freq

uenc

y

data

Equal intervals - 5 classes

class 1 class 2 class 3 class 4 class 5



Equal intervals - III

World population in 2005 - equal intervals



Standard deviation - Ifor normal distributions

It is used when attribute’s distribution is nearly Gaussian.

Intervals are defined around the mean value, with amplitudes that aremultiples of the standard deviation (e.g. 1, 2, 3 times the std. dev.).

It is useful to highlight the distribution of the values around the meanvalue.



Standard deviation - IIfor normal distributions

freq

uenc

y

data

Standard deviation - 5 classes

Values 1-30

Mean = 18.30

Std. dev. = 6.65

mea

n

m -

2 s

td. d

ev.

m -

1 s

td. d

ev.

m +

1 s

td. d

ev.




Standard deviation - III

World population in 2005 - standard deviation


Thematic maps | Attribute classification | Quantiles - Equal areas - Progressions

Outline






Quantiles - IClasses with equal numerosity

Classes are chosen so that they have the same number of elements.

It is useful for distributions not having similar values (in this case theamplitudes of the classes are very different).

In some cases, artificial discontinuities result, because similar valuescan be placed in different classes (near the boundary between twoclasses).



Quantiles - IIClasses with equal numerosity

freq

uenz

a

dati

Quantiles - 5 classes

Data 240

Classes 5

Elements per class 48




Quantiles - III

World population in 2005 - quantiles



Equal areasClasses with equal surface

A similar approach is to use equal areas: classes are chosen so thatfor each class the surface is as much as possible the same.

When areas have similar surfaces, the result is the same of usingquantiles.

When areas have different surfaces, the differences between smallerareas tend to vanish, because these areas are grouped together.



ProgressionsClasses with variable width

Attributes with arithmetic or geometric progressions can berepresented with classes with this type of distributions.

The width is different for each class, but this is systematic.

This approach is often used for distributions with many values on thetails.


Thematic maps | Attribute classification | User defined classes

Outline






User defined classes

User defined classes:

it is used when the other approaches do not lead to satisfactoryresults (e.g. “difficult” distributions)it is used after the application of the other methods to round upclasses’ boundary values, to make the more readableit can (but should not) be used to highlight or hide a certain featureof an attribute (e.g. to “hide” areas with higher values)the result depend on the user experience



Comparison of thematic mapsDifferent classification methods

Natural breaks Equal intervals

Standard deviation Quantiles



Surfaces proportional to the attributenormalized

Some representation techniques distort areas so that their surfacerepresent the attribute’s value with respect to the total value.

World population in 2000 - surface of each area is proportional to its population

c©2006 SASI Group and Mark Newman


Thematic maps | Appendice | License

This presentation is c©2009 Paolo Zatelli, available as

Data for thematic maps are available at “the Mapping Hacks website”: http://www.mappinghacks.com/data/ with CreativeCommons Attribution-Share Alike license.World population in 2000 map is available with Attribution-Noncommercial-No Derivative Works 3.0 Unported license,c©Copyright 2006 SASI Group (University of Sheffield) and Mark Newman (University of Michigan).

All maps and charts have been created using only Free Software under GNU license.


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