1. GEOG 268: Cartography Map Projections

2. Distortions resulting from map transformations  Transformation of:  angles (shapes)  areas  distances  direction

3. Transformation of angles  On globe: compass rose the same at each point (directions 90 o apart)  correct angles maintained ?  Conformal (correct form) map projection  cannot be equal-area

4. Transformation of areas  Retain area representation:  all regions shown in correct relative size  equal area or equivalent projection  no map projection can be conformal and equivalent  conformal? Similar earth regions with unequal sizes,  equivalent? Equal area but deform angles

5. Transformation of distances  Maintain consistency of scale:  scale same along line connecting points  Two options:  maintain scale along one or more parallel lines  standard parallels,  maintain scale along one or two points  equidistant map projections  standard points

6. Transformation of directions  True direction along a sphere is actually along a Great Circle & not a rhumb line  Correct direction on map?  Great Circle shown as a straight line  several possible representations:  great circles as straight lines in limited area  standard parallels,  great circles w/ correct azimuths shown as straight lines from one point  azimuthal map projections

7. Visual analysis: “just look”  way graticule appears on reference globe vs. projection  parallels are parallel  parallels are spaced equally on meridians  meridians and great circles appear as straight lines when looking orthogonally  meridians converge towards poles  spacing of meridians decrease towards poles  meridians & parallels equally spaced at equator  at 60 o latitude, meridians are half as far apart as parallels  parallels & meridians always intersect at right angles  surface area between parallels and meridians same along same latitude interval

8. Choosing a map projection  Visualizing distortion helps you to:  select a suitable map projection  evaluate information already in map format  Cartographers need to be familiar with map projections  example: never measure area on Mercator  cartographers frequently transfer data from one map projection to another  fit characteristics of data to be mapped

9. Choosing a map projection  Factors influencing choice?:  geographers, historians, ecologists interested in mapping areas - relative sizes of regions  navigators, meteorologists, engineers concerned with angles and distances  atlas map maker often wants compromise  map projections have many advantages over globes:  convey concepts of distributions undesirable to be shown on a globe  no good or bad projection, just poor choices

10. Guidelines in choosing a map projection  Projection’s major property?  conformality  equivalency  azimuthality  reasonable appearance, etc.  example :  small scale map of temperatures across globe? More effective if...  Parallels are parallel  parallels straight lines: compare temps

11. Guidelines in choosing a map projection  Amount and arrangement of distortion?  Good match between shape of area being mapped & shape of area of low distortion on the projection  general classes of map projections  specific arrangements of their distortion  Series of maps / atlases?  Large and small scale maps need to show same pattern of distortion  use projections showing meridians & parallels at right angles to each other

12. Guidelines in choosing a map projection  Overall shape of an area important?  Shape and size of the page on which the map will be shown is a constraint  find a good projection fit - better detail  can create your own projection to fit need  request a transformation to minimize error within a particular region.  Many classed as “miscellaneous”  devised for special purposes  easy to create new types; become “fads”  Peter’s cylindrical