GEOG 486
Cartography and Visualization

Part III: Map scale, projection and the area of polygons


Different map projections are appropriate for different representations of spatial data. Here we investigate one quantitative aspect of spatial data — area, and see, at one particular scale (determined by the area in question), how much variation there is from one projection to another.

Concept Gallery

Add to what you have already learned about choosing a map projection in the Concept Gallery.

For this Part of the lesson we will continue to work with the data that we have displayed in our eightymilemap document.

A. Change the projection of the 80-mile buffer zone polygon

  1. Open the eightymilemap document that you created in Part II.
    When you see the phrase, change the projection, I want you to realize, if you have not already, that the implications are: Create a new dataset from an existing one, one that is in terms of a different map projection. It most definitely does not mean, go into ArcCatalog or ArcToolbox and change the definition of the projection on an existing dataset.
  2. Open the ArcToolbox pane in ArcMap.
  3. Expand Data Management Tools > Projections and Transformations and double-click on the Project tool.
  4. In the Project dialog box, control the settings such that you create a new feature class:
    • based on the Buffer_of_fl_gaPlaces layer,
    • named buffer_ed ("ed" for equidistant) and placed in your eightymilebuf.mdb geodatabase.
    • and setting the output coordinate system to the Equidistant Conic projection with projection parameters established in Part II.  This modified projection should be available in the Layers folder (that appears beneath the Projected Coordinate Systems folder) because it is what we used to create the pirateRadioPlaces feature class. Check the projection parameters that appear in the Current coordinate system area to make sure they are properly modified.
  5. Add the new buffer to the current map session, if it is not automatically added.
  6. Open the attribute table of the buffer_ed feature class.
  7. Note the value in the Shape_Area field. _______________________
    What are the units? ___________ If necessary, check the coordinate system properties of the feature class to find out.

B. Create two more versions of the Buffer Zone feature class and assess the area of the polygons

You should be able to do the following without step-by-step instructions:

  1. Create a version of the buffer zone feature class that is in USA Contiguous Albers Equal Area. Name it buffer_ea, and save it to your eightymilebuf.mdb geodatabase. (There is a USGS version of this projection in the list. Do not use that one.) The USA Contiguous Albers Equal Area is a conic projection — use the same projection parameters we used above for the equidistant conic projection.
  2. Create yet another version of the buffer zone feature class that is in the UTM system. Name it buffer_utm, and save it to your eightymilebuf.mdb geodatabase. (You will have to figure out which UTM zone this portion of Florida is in.)
    For the sake of the comparison you are about to make, independent of the GIS software, I calculated the area of what is referred to as a Spherical Cap having a radial dimension of 80 miles. I performed the calculation in the context of the GRS80 spheroid. So, hopefully, it is a fairly accurate estimate of what the buffer zone area would actually be on the curved surface of Earth.
    The number I came up, which is 52297287179.046 square meters.
  3. Compare the values in the Shape_Area fields of the three new buffer feature classes to each other and to the Spherical Cap area value above.
    Calculate the percentage difference between the Spherical Cap value provided and the three area values you found. Which projection do you think should be used to assess area?
    What can you say about the difference between the projections at this scale when it comes to area?
  4. Assuming the extent of the buffer does not change, would the differences in distortion between these projections be increased on a larger scale map such as 1:50,000 or 1:24,000 representing a smaller area or on a smaller scale map such as 1:1,000,000 or 1:50,000,000 reprsenting a larger area? Discuss this in your deliverables document.

C. Save the map document

That is it for Part III

You have just completed Part III of this project, which involved reinforcing the fact that "changing the projection" means creating a new dataset and also illustrating the degree to which the same data, cast in different map projections, portrays the world differently, or not....

The deliverables from this part of the lesson will be the buffer_ed, buffer_ea and buffer_utm feature classes in your eightymilebuf.mdb geodatabase, and a comparison of your area calculations and comments on map projection, map scale, and area (see section B-3). These comments can be in a .txt file or Word document.