M AP P ROJECTIONS AND S CALE

1. MAP PROJECTIONSAND SCALE OUTLINE: scale definition types of scale projection definition projection properties and classification choosing a map projection

2. PROJECTIONS

3. THE GLOBE Advantages: • most accurate map • latitude and longitude lines Disadvantages • expensive to make • cumbersome to handle and store • difficult to measure • not fully visible at one

4. Flat Map Curved Earth PROJECTIONS • process of transforming earth’s spherical surface to a flat map while maintaining spatial relationships.

5. PROJECTIONS • projection process involves stretching and distortion

6. PROJECTIONS • no matter how the earth is divided up, it can not be unrolled or unfolded to lie flat (undevelopable shape).

7. PROJECTION PROCESS • most projections are combinations of the following characteristics: • characteristic of earth features that are maintained • shape of the projection plane (developable shape) • aspect of the projection plane • points or lines of tangency or secancy • location of the false ‘illumination source’

8. PROJECTION PROPERTIES • properties in which distortion is minimized when producing a map Area • equal area or equivalent • area sizes are correct everywhere on map • shapes greatly distorted

9. PROJECTION PROPERTIES Distance • equidistant • distance is correct in all directions from a point i.e. equidistant projection centered on Winnipeg would show the correct distance to any other location on the map, from Winnipeg only • distorting area and/or direction

10. PROJECTION PROPERTIES Equidistant

11. PROJECTION PROPERTIES Direction • azimuthal • compass bearing is maintained in all directions only from a point • shapes, distances and areas are badly distorted

12. PROJECTION PROPERTIES Shape • conformal • shape maintains its shape across the map • distorting area • latitude and longitude cross at right angles • used for navigation

13. PROJECTION PROPERTIES

14. Equal-Area projection Mercator projection PROJECTION PROPERTIES Tissot’s Indicatrix • convenient way of showing distortion • size and shape of the indicatrix will vary from one part of the map to another

15. Mercator: PROJECTIONS • made by projecting a globe onto a surface – developable surface • distortion is least where developable surface touches the earth • accomplished by use of geometry and mathematics

16. PROJECTION CLASSIFICATION • Tangent case – shape just touches the earth along a single line or at point. • Secant case – shape intersects or cuts through earth as two circles.

17. PROJECTION CLASSIFICATION Conical • globe sits under a cone, touching along pre-selected line of latitude • projection developed by cutting cone lengthwise and unrolling

18. PROJECTION CLASSIFICATION normal case: • parallels – concentric circular arcs, meridians – straight equally spaced lines

19. PROJECTION CLASSIFICATION

20. Lambert conformal conic projection Albers equal-area conic projection PROJECTION CLASSIFICATION

21. PROJECTION CLASSIFICATION Conical Distortion

22. PROJECTION CLASSIFICATION Conical Polyconic – envelopes globe with an infinite number of cones, each with its own standard parallel

23. PROJECTION CLASSIFICATION Cylindrical • projected onto a cylinder which is also cut lengthwise and unrolled

24. PROJECTION CLASSIFICATION Cylindrical • evenly spaced network of straight, horizontal parallels and straight vertical meridians (grid like)

25. PROJECTION CLASSIFICATION

26. parallels become further apart and poles can not be seen PROJECTION CLASSIFICATION Cylindrical Distortion • projection of the entire world, significant distortion occurs at the higher latitudes

27. Mercator Projection True size PROJECTION CLASSIFICATION Cylindrical Distortion • sizes of Greenland vs. Africa

28. PROJECTION CLASSIFICATION Cylindrical • straight line between any two points follows a single direction called a rhumb line • useful in construction of navigational charts

29. PROJECTION CLASSIFICATION Planar/Azimuthal • portion of earth’s surface is transformed from a perspective point to a flat surface

30. Light rays PROJECTION CLASSIFICATION Planar/Azimuthal • perspective point/light source

31. PROJECTION CLASSIFICATION Planar/Azimuthal • true direction only between center and other locations • most often used to map polar regions

32. NORMAL TRANSVERSE OBLIQUE PROJECTION CLASSIFICATION

33. Planar Conic Cylindrical CANADA PROJECTED

34. Pseudocylindrical PROJECTION CLASSIFICATION Pseudo map projections • pseudoconic and pseudocylindrical projections - have curved meridians instead of straight ones

35. PROJECTION CLASSIFICATION Pseudo map projections • modified projections - changes have been made to reduce the pattern of distortion or add more standard parallels • modified to reduce the distortion in the size of areas

36. Goode’s Projection PROJECTION CLASSIFICATION Pseudo map projections • individual or unique projections – can not be easily related to one of the three developable geometric forms

37. CHOOSING PROJECTION • depends on: • purpose for which the data is to be used • property in which distortion is minimized • extent and location of area

38. CHOOSING PROJECTION steps: • size of area of interest • small area has little distortion, any projection. • latitude of area of interest • low-latitudes – cylindrical • mid-latitudes – conical • polar latitudes - planar

39. CHOOSING PROJECTION • shape of area of interest: • E-W extent: conic or cylindrical • N-S extent: cylindrical • square or circular: planar • purpose: • navigation – planar or cylindrical • world distributions – cylindrical • specific locations - planar

40. COMMON PROJECTIONS Albers Equal-Area Conic • equal area, secant conical projection (two standard parallels) • resembles earth graticule

41. COMMON PROJECTIONS Mercator • cylindrical, conformal projection • angular relationships are preserved • parallels and meridians appear as straight lines • parallels are farther apart with increased distance from equator

42. COMMON PROJECTIONS Mercator • change in N-S scale exactly offset change in E-W direction (shapes preserved) • scale is true at equator or at two standard parallels equidistant from equator • all rhumb lines appear as straight lines, while great circle arcs are not (except equator and meridians) • used primarily for navigation and large scale maps

43. COMMON PROJECTIONS Transverse Mercator • cylindrical, conformal projection • similar to Mercator except the axis of projection cylinder is rotated 90o from polar axis • scale is true along central meridian or along two straight lines equidistant from and parallel to central meridian • used to portray areas with larger N-S than E-W extent.

44. COMMON PROJECTIONS Lambert Conformal Conic • conformal, secant conical projection with two standard parallels • possesses true shape of small areas with area distortion • concentric parallels (increasing intervals) and equally-spaced straight meridians

45. COMMON PROJECTIONS

46. COMMON PROJECTIONS

47. COMMON PROJECTIONS Mollweide • pseudocylindrical, equal-area projection • N-S scale is decreased in high latitudes, increased in low latitudes; opposite in E-W direction • parallels are straight, spaced closer together from equator

48. COMMON PROJECTIONS Polar Stereographic • directions are true from center point • conformal projection: over a small area, angles in the map are the same as the corresponding angles on Earth's surface • meridians are straight and radiating; parallels are concentric circles • shows only one hemisphere

49. COMMON PROJECTIONS Polar Stereographic • preserves circles - all great and small circles are shown as concentric arcs or straight lines • scale true only where the central parallel and meridian cross • used in polar aspect for topographic maps of polar regions, regions that are circular in shape

50. COMMON PROJECTIONS Eckert IV Equal Area • pseudocylindrical and equal-area • scale is true along the parallel at 40:30 North and South