Exploring Error and Uncertainty Related to Datums and Projections Using ArcGIS

Evaluate Distortion Patterns in Map Projections

Table of Contents

  1. Exploring Error and Uncertainty Related to Datums and Projections Using ArcGIS
  2. Skill Drill: Setting Up Your Workspace
  3. Skill Drill: Downloading Data from Natural Earth
  4. Skill Drill: Connect to Your Workspace Folder in ArcMap
  5. Creating a File Geodatabase
  6. Creating Feature Classes from Shapefiles
  7. Adding XY Data using the ArcCatalog Window
  8. Skill Drill: Creating Indicatrices Using the Buffer Tool
  9. Evaluate Distortion Patterns in Map Projections
  10. Measuring Scale Distortion
  11. Skill Drill: Evaluate and Measure Distortion
  12. Troubleshooting Datum Shift
  13. Repairing Corrupted Data Using the Define Projection Tool
  14. Skill Drill: Repairing Incorrect Coordinate System Definitions

As learned previously, a map projection is the geometric transformation of the spherical earth onto a flat plane using mathematical equations. One cannot perform this transformation without a high degree of distortion. However, some map projections can maintain a high degree of accuracy of particular geometric characteristics called preserved properties. Distortion occurs in one or more of the following properties:

  • Area
  • Shape
  • Distance
  • Direction
  • Continuity

A map projection may be able to maintain more than one of these properties, but no map projection can preserve all of them at once.

A Note on Continuity

Recall that geographic space is a continuous phenomenon modeling the shape of the earth. Meaning, a globe has a continuous surface without breaks. All flat maps break this continuity of shape, some more obvious than others. For example, looking at the orthographic projection, especially on screen, a map reader may mistake it for a three-dimensional globe. While there are digital globes that can turn dynamically, the orthographic projection is a flat map. The continuity is broken in this instance because you can only look at one hemisphere at a time.

The orthographic projection breaks continuity because you can only view one hemisphere of Earth.

Take a moment to capture a screenshot of your ArcMap window. You can do this by pressing the Alt key and the Print Screen key on your keyboard while the ArcMap window is active.

Alternatively, you may use the Microsoft Windows Snip and Sketch app to capture a portion of your screen.

Open a blank Microsoft Word document. In Microsoft Word, press Ctrl V to paste the screenshot into the document. Right-click the image and choose Insert Caption (Figure 2.31). Type the name of the map projection as the figure caption.

Next, copy the following table into your word document and fill in your answers to the questions below.

Map Projection

Which of the five properties appear to be preserved based on the size and shape of the indicatrices?

Which of the five properties appear to be distorted based on the size and shape of the indicatrices?

Where on the map does there appear to be minimal distortion?

Where on the map does there appear to be the most distortion?

What does the scale factor indicate in terms of distortion for this map projection in the region between Tokyo and Vancouver?

The World from Space (Orthographic)

Cylindrical Equal Area (world)

Goode Homolosine (Ocean)

Mercator (world)

North America Lambert Conformal Conic

North Pole Azimuthal Equidistant

With Tissot’s indicatrices, you may only be able to determine distortion patterns in area and shape. Do not worry about distance, direction, or continuity.

  1. Which of the five properties appear to be preserved based on the size and shape of the indicatrices?
  2. Which of the five properties appear to be distorted based on the size and shape of the indicatrices?
  3. Where on the map does there appear to be minimal distortion?
  4. Where on the map does there appear to be the most distortion?
Figure 2.31: You should be prepared to discuss the answers to these questions at a later time.

Save your Word document to your final folder. You answer these same questions for other map projections in a later step.