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Cartograms and Data Visualisation. Mapping People. [email protected] http://www.nuim.ie/ncg. Outline. Map Projections Cartograms Population Cartogram of Ireland Population Change. Map Projections. A problem with maps arises because the earth is roughly spherical and maps are variously - PowerPoint PPT Presentation
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Cartograms and Data Visualisation Cartograms and Data Visualisation
Mapping PeopleMapping People
[email protected]://www.nuim.ie/ncg
[email protected]://www.nuim.ie/ncg
Map Projections
• A problem with maps arises because the earth is roughly spherical and maps are variously– printed on flat sheets of paper– bound into books for convenience of use– viewed on flat computer displays
Projections
• We therefore need some means of representing the 3-d nature of the Earth in two dimensions
• We might not need to represent the whole earth
• This is where map projections come in
Whole-Earth Projections
• There are hundreds of different map projections
• Usually named after their creator or method of construction
• Each has different properties…
Projection properties
• Relationships between areas are preserved (‘equal area’ projections)
• Relationships between angles are preserved (‘conformal’ projections)
• Some distance relationships are preserved
Projections: uses
• Navigation– Lineof constant bearing is a straight line on
Mercator’s projection
• Representing continents– Lambert’s conformal conic projection is used to
represent maps by the EU
• Representing countries– Relates to the extent of country (eg RoI and UK
choose a transverse cylindrical projection)
Projections: uses
• Political
– Peters’ Projection from 1973 claimed to represent the areas of the countries more truly than ‘Imperialistic’ Mercator projection
– (Although Gall came up with the same projection in 16xx!)
Places not people
• People tend not to spread themselves uniformly across land areas
• They tend to live where it’s more convenient to do so (lowland areas, near rivers, near raw materials)
• They’re also gregarious – live in settlements
• They don’t usually live in the middle of deserts or tundra
Showing people
• We’re so used to thinking in terms of the physical or political earth that we forget about the social earth.
• Our maps represent physical or administrative features (roads, trees, rivers, buildings) but not people
Showing people
• Showing the results of an election or incidence of a disease presents a problem
• In areas of high population density the physical size of the zones to be mapped is often small
• Large rural areas with low populations dominate the visual effect and give us a misleading impression of the underlying spatial pattern
People based maps
• Can we, therefore, come up with a map projection in which the sizes of the zones are in proportion to the number of people than live in them?
• Yes… they’re known as – Value-by-area maps– Density-equalising maps– Cartograms
Albers’ conic projection
Population based cartogram
Voting in the 2000 US Presidential election – proportion voting for each candidate [Gastner & Newman: 2004]
Lung cancer in males in New York State [Gastner & Newman: 2004]
If we plot the locations of lung cancer cases, we obtain a map which follows the underlying population distribution – there appears to be “clusters” (but these are spurious!)
However, if we use a map based on equal population density we see that the incidence of lung cancer is randomly spatially distributed
Joseph R. Grundy, Pennsylvania manufacturer, suggested in the Senate lobby committee that the present equal power of States in voting on tariff bills is unfair because of differences in voting strength. Here's a map of the United States showing the size of each State on the basis of population and Federal Taxes. Washington Post November 3, 1929. [Tobler: 2004]
Creating cartograms
• In the late 1950s the US geographer Waldo Tobler became interested in the possibilities of using computers to carry out the calculations for cartograms
• His PhD ‘Map Transformations of Geographic Space’ appeared in 1961
But…
• The process is rather complex and many solutions have been proposed among them:
• Tobler (1961)– slow , but prone to topological errors
• Dougenik, Chris & Niemeyer (1985)– faster, but still prone to error
• Dorling (1996)– based on cellular automata: unaesthetic results
• Kocmoud (1997)– “prohibitively slow”
Gastner & Newman
• Recently Michael Gastner and Michael Newman, both physicists, proposed another solution based on diffusion
• Like Dorling’s method it allows regions to ‘trade their area until a fair distribution is reached’
• However it is not tied to an underlying lattice – results don’t look “blocky”
Software
• Gaster and Newman’s C code is available for download from their website
• It can be compiled and run on a desktop/laptop PC…
• … or something more powerful
Irish Cartogram
• We use Garstner and Newman’s method to produce a density-equalized map of Irish counties
• The starting point is a list of coordinates for each county boundary in the Irish National Grid system…
• … and the populations of each county
Time required…
• The software runs quite quickly…
• There are 14000 coordinates for the counties of Ireland in the data I’m using
• Takes about 2 minutes to run on a Dell 270
Spaces
• We’ll refer to the original map as showing ‘physical space’
• We’ll refer to the transformed coordinates as being in ‘cartogram space’
• GIS software allows us to transform other data between these spaces
Rubbersheeting
• The transformation process is known colloquially as rubbersheeting
• We need a set of vectors…
• The next maps show the displacement vectors for the ‘centroids’ of each county
Changing Population
• We can use the county populations from previous Censuses to examine the effects of population change
• 1841• 1926• 1961 - 2002
Population Scaling
• The previous cartograms show how the segments of the Irish ‘cake’ are redistributed according the changes in population
• Using GIS we can scale the cartograms so that the land area is in proportion to the total population in each year
Population 1841-2002
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
1841 1851 1861 1871 1881 1891 1901 1911 1921 1931 1941 1951 1961 1971 1981 1991
Date
Po
pu
lati
on
Population by County 1841-2002
0
200000
400000
600000
800000
1000000
1200000
1841 1851 1861 1871 1881 1891 1901 1911 1926 1936 1946 1951 1956 1961 1966 1971 1979 1981 1986 1991 1996 2002
Date
Po
pu
lati
on
Carlow
Cavan
Clare
Cork
Donegal
Dublin
Galw ay
Kerry
Kildare
Kilkenny
Laois
Leitrim
Limerick
Longford
Louth
Mayo
Meath
Monaghan
Offaly
Roscommon
Sligo
Tipperary N.R.
Tipperary S.R.
Waterford
Westmeath
Wexford
Wicklow
Comparison
• (a) 1926 – after Independence• (b) 1961 – population starts
increasing• (c) 2002 – present day