# Geography Lab 4

Geography 256/556

Exercise: Map Projections 1: Distortion in Maps: area and object (Shape) deformation

Purpose: to introduce concepts of distortion inherent in any map projection.

Problem: As graphical models of the world, maps contain various forms of exaggeration. One of the most obvious sources of exaggeration arises from projection of a 3-dimensional world onto a 2-dimensional surface. Projecting from 3-d to 2-d can exaggerate relative scale, size, orientation, and distance relations between any pair of objects. The ways in which projection exaggeration contribute to map misperception are especially evident on world maps. The Mercator, for example, shows Greenland as larger than South America though South America is more than three times the land area of Greenland.

In this exercise you will explore how projections can change our perception of the mapped world. This exercise focuses on two principal forms of map projection exaggeration: area and shape distortion.

Materials and Methods: The materials for this exercise consist of three world base maps with longitude-latitude grids in the ArcMap project, Exer4. The basic idea is to change the map projection and observe what happens to the shapes and sizes (area) of the latitude-longitude grid and the various continents. In order to be sure that the shape and area effects you see are the consequence of the new map projection, and not View window properties, you’ll need to make sure that all maps have the same scale. Notice the representative fraction (RF) map scale in the toolbar above the map. Click on each map and notice that each is currently set to a scale of 1:275,000,000. (Type 1:275,000,000 directly into the scale display window to change the map’s scale). Each time you change a projection, be sure to change the map scale back to 1:275,000,000.

Examine the composition of each map: GEOGRID is a graticule grid containing the Prime Meridian, the International Dateline, the Equator, tropics, and Arctic and Antarctic circles; the second graticule grid, latlong, maps meridians and parallels every 5. Notice that the first map projection creates a perfectly square grid of parallels and meridians; in other words, the length of 5 of latitude on this map equals the length of 5 of longitude. Of course, latitude and longitude do not form a regular square grid on the real globe. This first map, where the graticules form a square grid, is known as unprojected .

1: Make sure that you are in the View/View Layout window and then edit the text box in lower left corner of the layout window with your name. Notice that the three maps are unprojected.

2: Change the three map projections according to the instructions and sets of projections listed on the attached table (e.g., map sheet 1 should show one map as unprojected, the 2nd with the Mercator projection, and the 3rd with the Miller projection); verify the display scale (1:275,000,000); update each map title to reflect the new projection, and export the map as a JPEG to your course folder.

3: Use the 5 by 5 latitude-longitude grid and various continents to observe how the shapes and areas of map features change. Pay attention to all parts of the map—from the Equator to the Poles and from west to east. Think in distortion terms – i.e., elongated, squashed, stretched, etc. Use the attached table to organize your observations.

Lab Report: Fill in the table below with your observations, using terms such as preserved, distorted, and exaggerated with modifiers (adjectives) such as slightly or little or no or greatly. Note: As you recall in lecture Tissot’s Indicatrix can be used to assess distortion in shape and area. (You can review how TI works from the slides for week 5.). Also note where on the map the properties of shape and area are affected. Do this for each of the projections listed in the table. Discussion (answer below) Why might the nature of a map’s projection be cause for concern to elementary school (K-6) educators or curriculum developers? Discuss in the context of the projections you examined in this exercise. Submit your discussion (report), table with your JPEG maps inserted after the table (please make sure they are legible).

Another projections resource: http://desktop.arcgis.com/en/arcmap/10.3/guide-books/map-projections/robinson.htm

Feel free to explore other world map projections!

Points:

Table 6 points (.25 points for each answer)

Discussion 1 point

Maps: 3 points (.25 points for each map) Insert below the table.

Exercise 5

Summary table of map projections and apparent distortions

 shape area World Projections projection surface Map Sheet 1 1. unprojected plane 2. Mercator cylinder 3. Miller cylinder Map sheet 2 1. Robinson pseudo-cylinder 2.Craster Parabolic pseudo-cylinder 3. Loximuthal pseudo-cylinder Map sheet 3 1. Equidistant Cylindrical cylinder 2. Equidistant Conic cone 3. Cylindrical Equal Area cylinder Map sheet 4 1. Bonne cone 2. Cube plane 3. The World from Space sphere

To change the map projection:

1. Activate that map, right mouse click, select Properties and the Coordinate System tab.

2. Go to the lower window on the Coordinate System tab, click on Predefined, then on Projected Coordinate Systems, then on World.

3. Select the new projection from the list, click on the OK button, and then on the Yes button when the warning message appears.