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Cartograms and Data Visualisation

Cartograms and Data Visualisation. Mapping People. ncg@nuim.ie 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

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Cartograms and Data Visualisation

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

  2. Outline • Map Projections • Cartograms • Population Cartogram of Ireland • Population Change

  3. 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

  4. 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

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

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

  7. 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)

  8. 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!)

  9. Some World Projections

  10. Mercator

  11. Mollweide

  12. Robinson

  13. Peters

  14. 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

  15. 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

  16. 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

  17. 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

  18. Example Cartograms

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

  20. 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

  21. 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]

  22. Dorling: c1990 Levasseur: 1870

  23. 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

  24. 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”

  25. 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”

  26. 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

  27. 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

  28. 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

  29. Ireland as we know it

  30. County Boundaries

  31. County Boundaries with Road network

  32. … applying the cartogram projection gives us…

  33. Maps Compared Unemployment Rate: 2002

  34. Social Class 1 Households: 2002

  35. Households with Internet Access: 2002

  36. 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

  37. 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

  38. Displacement vector

  39. 2002 – Road Network

  40. 2002 – Rail Network

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

  42. 1841

  43. 1926

  44. 1961

  45. 1971

  46. 1981

  47. 1991

  48. 2002

  49. 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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