Thematic maps - Università degli Studi di Trento

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Thematic maps
Thematic maps
Paolo Zatelli
Dipartimento di Ingegneria Civile ed Ambientale
Università di Trento
Paolo Zatelli | Università di Trento |
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Thematic maps
Outline
1
Thematic cartography
2
Data, features and representation
Data
Representation
Points, lines and areas
3
Attribute classification
Natural breaks - Equal intervals - Standard deviation
Quantiles - Equal areas - Progressions
User defined classes
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Thematic maps | Thematic cartography
Thematic maps
What are they used for?
Thematic maps are used to display a “thematism” of data, i.e. to
display an attribute of geometric features (points, lines, areas).
To create thematic maps we need:
graphics to choose line types and colors to display the attribute
symbols to display the attribute
statistics to choose the classes for the attribute’s values
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Thematic maps
An example
A thematic map is used to highlight the distribution of an attribute. The
example below displays the distribution of the world population.
Countries
Countries by population (n. of inhabitants)
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Vector and raster
Entities or fields
Usually thematic maps are created from vector data, however, it is
possible to user raster maps, modifying the color table or reclassifying
them.
DTM of the Spearfish County
Reclassified DTM (9 classes of 100m)
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Thematic maps | Data, features and representation | Data
Outline
1
2
Data
Representation
3
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Input data
What 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 table
associated to geometric features (points, lines and areas).
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Input data
Geometry
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Input data
Attributes
FIPS
AC
AG
AJ
AL
AM
AO
AQ
AR
AS
BA
BB
BD
BF
BG
BH
..
ISO2
AG
DZ
AZ
AL
AM
AO
AS
AR
AU
BH
BB
BM
BS
BD
BZ
..
ISO3
ATG
DZA
AZE
ALB
ARM
AGO
ASM
ARG
AUS
BHR
BRB
BMU
BHS
BGD
BLZ
..
UN
28
12
31
8
51
24
16
32
36
48
52
60
44
50
84
..
NAME
Antigua and Barbuda
Algeria
Azerbaijan
Albania
Armenia
Angola
American Samoa
Argentina
Australia
Bahrain
Barbados
Bermuda
Bahamas
Bangladesh
Belize
..
AREA
44
238174
8260
2740
2820
124670
20
273669
768230
71
43
5
1001
13017
2281
..
POP2005
83039
32854159
8352021
3153731
3017661
16095214
64051
38747148
20310208
724788
291933
64174
323295
15328112
275546
..
REGION
19
2
142
150
142
2
9
19
9
142
19
19
19
142
19
..
SUBREGION
29
15
145
39
145
17
61
5
53
145
29
21
29
34
13
..
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Population distribution by country
frequency
World populatione - 30 equal classes
data
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Thematic maps | Data, features and representation | Representation
Outline
1
2
Data
Representation
3
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Vector layer representation
Data distribution
The representation of a layer substantially depends on the type and on
the distribution of the attribute to be depicted.
Examples:
the attribute is qualitative (type of soil) or quantitative (pH of the
soil)?
the distribution (of pH) is uniform or some values have different
frequencies?
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Vector features and layers
How an attribute value is represented on the map
In a GIS three types of vector features are used, points, lines and
areas, which are represented by:
points
lines
areas
symbols
hatching
symbols
colors
colors
colors
dimensions
widths
dithering
An internal point (e.g. centroid) can be used to represent an attribute
of an area.
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Types of attributes - I
to create thematic maps
Representation of attributes depends on their properties:
1
Quantitative
nominal [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”.
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Types of attributes - II
2
Qualitative
ordinal 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 an
assessment (e.g. a forest in “good”, “fairly good”, ...,
“very bad” condition). In general arithmetic
operations 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 “year
zero”). Some arithmetic operations make sense (e.g.
difference of years), other do not (e.g. ratio between
years).
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Types of attributes - III
ratio attributes are quantitative, the origin is not arbitrary
but the interval is (e.g. age, field value). Arithmetic
operations are possible.
count such as ratio, but measurement units are not
arbitrary, therefore it is not always possible to rescale
the interval (e.g. dwellers in an area, number of
municipalities in a region).
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Choice of colors and dithering
General criteria
Some general rules:
how attributes are classified is fundamental
colors must be chosen to cater for color blind people
colors and dithering must be used in intuitive ways:
light colors correspond to lower values, darker ones to higher
values
thick dithering corresponds to higher values
continuous lines are used for certain boundaries, dashed lines for
uncertain ones
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Thematic maps | Data, features and representation | Points, lines and areas
Outline
1
2
Data
Representation
3
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Points and lines
IGMI symbols
IGMI: points - edifici di culto (churchs)
IGMI: lines - strade e ferrovie (roads and railroads)
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Areas - I
Types of thematic maps
For area features, the most used types of maps are:
area class areas’ boundaries depend on an attribute because all
areas with the same value are represented in the same
way, therefore common boundaries are dissolved (e.g.
land use).
coropleth boundaries are defined when data are
gathered/processed (e.g. census units).
dot the number of dots (randomly placed inside the area to
simulate a density) represents the attribute’s value.
proportional symbols symbols (usually placed in the center for the
area) proportional to the value of the attribute are used
(see lines and points).
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Areas - II
Types 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 (assuming
continuous or discrete values) simulating a “height”.
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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 phenomenon
are used (e.g. green -> forest, blue -> hydrography, etc.).
This kind of map can be used to evaluate the dispersion/concentration
of phenomena (e.g. same land use in different areas).
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Area class - II
Countries by region (continent)
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Dots map - I
A dot represents one unit (or multiple) of the attribute’s value (e.g. 1
airport, 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.
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Dots map - II
World population in 2005 - 1 dot = 500 000 inhabitants
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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 a
time; however, these are usually less readable than 2D symbols.
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Proportional symbols map - II
User perception of surface usually leads to underestimate them, with a
greater effect on large areas.
Possible solutions are:
to use the apparent scale method, where symbols’ surfaces grows
faster than direct proportionality (exponentials are used for circles,
usually r 1.14 instead of r )
to use symbols with discrete values of surface
to optimize the legend to remove this effect
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Proportional symbols map - III
World population in 2005
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Isarithmic - I
to represent scalar fields
The distribution of an attribute is represented using lines passing
through 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 3D
view.
Lines’ density must take into account the accuracy of the attribute’s
values (e.g. contour levels on maps with different scales have different
distances).
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Isarithmic - II
3D contour levels - Trento
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Isarithmic - III
Contour levels - Trento
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3D views- I
It is possible to use a 3D view (usually axonometric) to represent an
attribute 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 any
attribute (even not an extent).
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3D views- II
Scalar field - DTM 3D - Trento
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3D views- III
Entities - World population in 2005
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Thematic maps | Attribute classification
Most of the times an attribute has a large number of different values: if
each value is represented in a different way (by color, symbol, etc.) the
resulting 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 the
same class, while maximizing the differences with elements of the
other classes.
In some cases classes are chosen according to legal or de facto
standards.
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Thematic maps | Attribute classification
Classification methods
Different methods can be used to classify data, i.e. to chose the
intervals for grouping data.
The choice of the intervals depend on the attribute’s distribution:
natural breaks for non normal distributions
equal intervals for uniform or normal distributions
std deviation for normal distributions
quantile
for uniform or normal distributions
constant area for maps with areas with similar values
progressions for distributions with many values on the tails
user defined if the possibilities above are not satisfying
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Thematic maps | Attribute classification | Natural breaks - Equal intervals - Standard deviation
Outline
1
2
Data
Representation
3
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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 of
square differences inside each class and the sum of the square
difference with respect to the global mean is maximized (Jenks’
algorithm).
Advantages:
classes have the maximum possible internal homogeneity
this is a robust classification method
it is easy to implement an automatic procedure
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Natural breaks - II
Drawbacks:
results are good only if discontinuities do actually exist in the
distribution (at least a number of discontinuities equal to the
number 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 of
maps is usually difficult (because in general the same attribute in
different regions has different distribution and therefore different
classes)
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Natural breaks - III
frequency
break
break
break
break
Natural breaks - 5 classes
class 1
class 2
class 3
class 4
cl. 5
data
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Natural breaks - IV
World population in 2005 - natural breaks
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Equal intervals - I
Classes with equal width
This method is used for uniform or quasi uniform distributions.
Interval (constant) width is given by
max − min
n. of classes
Advantages:
it is easy to understand
if the absolute maximum and minimum are used, classes are
independent from the mapped region, therefore maps are
comparable
Drawbacks:
it is not suitable if the distribution is not uniform or quasi uniform
(empty classes/overcrowded classes)
it “hides” the differences between values
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Equal intervals - II
Classes with equal width
frequency
Equal intervals - 5 classes
class 1
class 2
class 3
class 4
class 5
data
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Equal intervals - III
World population in 2005 - equal intervals
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Standard deviation - I
for normal distributions
It is used when attribute’s distribution is nearly Gaussian.
Intervals are defined around the mean value, with amplitudes that are
multiples 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 mean
value.
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Standard deviation - II
for normal distributions
m + 1 std. dev.
Standard deviation - 5 classes
Values 1-30
m - 2 std. dev.
frequency
Std. dev. = 6.65
mean
m - 1 std. dev.
Mean = 18.30
class 1
class 2
class 3
class 4
class 5
data
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Standard deviation - III
World population in 2005 - standard deviation
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Thematic maps | Attribute classification | Quantiles - Equal areas - Progressions
Outline
1
2
Data
Representation
3
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Quantiles - I
Classes 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 the
amplitudes of the classes are very different).
In some cases, artificial discontinuities result, because similar values
can be placed in different classes (near the boundary between two
classes).
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Quantiles - II
Classes with equal numerosity
Quantiles - 5 classes
Data 240
Classes 5
frequenza
Elements per class 48
class 1
class 2
class 3
class 4
class 5
dati
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Quantiles - III
World population in 2005 - quantiles
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Equal areas
Classes with equal surface
A similar approach is to use equal areas: classes are chosen so that
for each class the surface is as much as possible the same.
When areas have similar surfaces, the result is the same of using
quantiles.
When areas have different surfaces, the differences between smaller
areas tend to vanish, because these areas are grouped together.
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Progressions
Classes with variable width
Attributes with arithmetic or geometric progressions can be
represented 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 the
tails.
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Thematic maps | Attribute classification | User defined classes
Outline
1
2
Data
Representation
3
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User defined classes:
it is used when the other approaches do not lead to satisfactory
results (e.g. “difficult” distributions)
it is used after the application of the other methods to round up
classes’ boundary values, to make the more readable
it can (but should not) be used to highlight or hide a certain feature
of an attribute (e.g. to “hide” areas with higher values)
the result depend on the user experience
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Comparison of thematic maps
Different classification methods
Natural breaks
Equal intervals
Standard deviation
Quantiles
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Surfaces proportional to the attribute
normalized
Some representation techniques distort areas so that their surface
represent 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
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Thematic maps | Appendice | License
c
This presentation is 2009
Paolo Zatelli, available as
Data for thematic maps are available at “the Mapping Hacks website”: http://www.mappinghacks.com/data/ with Creative
Commons 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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Thematic maps - Università degli Studi di Trento

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