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Cartograms and Data Visualisation Mapping People ncg@nuim.ie http://www.nuim.ie/ncg ncg@nuim.ie http://www.nuim.ie/ncg

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Outline Map Projections Cartograms Population Cartogram of Ireland Population Change

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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

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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

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Whole-Earth Projections There are hundreds of different map projections Usually named after their creator or method of construction Each has different properties…

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Projection properties Relationships between areas are preserved (‘equal area’ projections) Relationships between angles are preserved (‘conformal’ projections) Some distance relationships are preserved

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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)

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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!)

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Some World Projections

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Mercator

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Mollweide

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Robinson

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Peters

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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

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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

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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

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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

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Example Cartograms

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Albers’ conic projection Population based cartogram Voting in the 2000 US Presidential election – proportion voting for each candidate [Gastner & Newman: 2004]

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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

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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]

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Levasseur: 1870 Dorling: c1990

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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

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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”

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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”

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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

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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

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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

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Ireland as we know it

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County Boundaries

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County Boundaries with Road network

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… applying the cartogram projection gives us…

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Maps Compared Unemployment Rate: 2002

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Social Class 1 Households: 2002

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Households with Internet Access: 2002

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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

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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

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Displacement vector

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2002 – Road Network

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2002 – Rail Network

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Changing Population We can use the county populations from previous Censuses to examine the effects of population change 1841 1926 1961 - 2002

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1841

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1926

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1961

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1971

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1981

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1991

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2002

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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

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1841

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1851

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1861

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1871

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1881

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1891

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1901

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1911

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1926

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1936

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1946

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1951

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1961

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1971

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1981

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1991

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2002

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Comparison (a) 1926 – after Independence (b) 1961 – population starts increasing (c) 2002 – present day

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1926 1951 2002

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Cartograms Cartograms provide another way of communicating data They make us think about people space and not physical space They make us think about the underlying processes

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