1. Cartograms and Data Visualisation Mapping People ncg@nuim.ie http://www.nuim.ie/ncg 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. Levasseur: 1870 Dorling: c1990

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

40. 2002 – Road Network

41. 2002 – Rail Network

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

43. 1841

44. 1926

45. 1961

46. 1971

47. 1981

48. 1991

49. 2002

50. 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

53. 1841

54. 1851

55. 1861

56. 1871

57. 1881

58. 1891

59. 1901

60. 1911

61. 1926

62. 1936

63. 1946

64. 1951

65. 1961

66. 1971

67. 1981

68. 1991

69. 2002

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

71. 1926 1951 2002

72. 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