## Measuring Scale Distortion

Table of Contents

- Exploring Error and Uncertainty Related to Datums and Projections Using ArcGIS
- Skill Drill: Setting Up Your Workspace
- Skill Drill: Downloading Data from Natural Earth
- Skill Drill: Connect to Your Workspace Folder in ArcMap
- Creating a File Geodatabase
- Creating Feature Classes from Shapefiles
- Adding XY Data using the ArcCatalog Window
- Skill Drill: Creating Indicatrices Using the Buffer Tool
- Evaluate Distortion Patterns in Map Projections
- Measuring Scale Distortion
- Skill Drill: Evaluate and Measure Distortion
- Troubleshooting Datum Shift
- Repairing Corrupted Data Using the Define Projection Tool
- Skill Drill: Repairing Incorrect Coordinate System Definitions

In ArcMap, activate the *Snapping* toolbar (**Figure 2.3**2).

On the *Snapping* toolbar, be sure that only the *Point Snapping* is active (**Figure 2.33**). If necessary, click the others to disable them. Point snapping will make measurements easier in a later step.

Turn on the labels for the populated places layer so that the map displays the name of each city. On the *Tools* toolbar, find the *Measure* tool (**Figure 2.34**).

Earlier, you created the circles on the indicatrix layer by using a buffer with a radius of five hundred kilometers. For consistency, change the units in the *Measure* tool to kilometers (**Figure 2.35**).

The first measurements need to establish an accurate baseline. To do this, change the *Measurement Type* to *Geodesic* (**Figure 2.36**). Recall that a geodesic measurement uses the spherical model of Earth when calculating distances.

Practice using the *Measure* tool on one of the circles on the indicatrix layer. Zoom into the circle closest to Alaska. It has a shape that is nearly a perfect circle. Then, with the Measure tool active, move the mouse cursor over one side of the circle and click once. Then, move the cursor to the opposite side of the circle and double-click to complete the line segment. The *Measure* tool records the information on the dialog box (**Figure 2.37**).

Don’t worry about getting it perfect. This step helps you practice using the Measure tool while also demonstrating the accuracy of a geodesic measurement.

Next, measure the distance between Tokyo and Vancouver. You may need to zoom out to see both cities clearly (**Figure 2.38**). The point snapping setting should help with the accuracy of the measurement.

Open a blank Microsoft Excel workbook and record the geodesic length in kilometers between Tokyo and Vancouver. Also, record the scale factor by entering the following formula in the cell next to the distance in kilometers (**Figure 2.39**). Be sure to include the dollar signs in the second half of the equation.

- =B2/$B$2

On the *Measure* tool dialog box, change the *Measurement Type* to *Planar* (**Figure 2.40**).

Once again, measure the distance from Tokyo and Vancouver. You should notice a slight difference in the distance value (**Figure 2.41**).

Record the planar distance from Tokyo and Vancouver into your Excel table (**Figure 2.42**). Copy and paste the scale factor formula into the cell next to the distance in kilometers for *The World from Space* projection.

As you learned previously, the **scale factor** is the relationship between the *principal scale* and the *actual scale* (**Figure 2.43**). One uses the **principal scale**, based on the scale of the generating globe, to construct the map projection. Cartographers refer to a map scale measured locally as an **actual scale**.

In this instance, you are *not* using scale ratios for actual and principal scale. Instead, you are dividing the planar map projection measurement by the geodesic measurement (**Figure 2.44**). Like the principal scale, the geodesic measurement is based on the scale of the generating globe. The results are similar.

A scale factor of 1 means that the planar map projection distance and the spherical geodesic distance are the same. A scale factor of less than one indicates that the planar map projection distance is less than spherical geodesic distance. Therefore, the map projection is distorting distances by making them smaller. A scale factor of greater than one means that the planar map projection distance is greater than spherical geodesic distance. Thus, the map projection is distorting distances by making them larger. Knowing the range of the scale factor throughout the map is a good indicator of error and uncertainty related to size and distance.

On your Microsoft Word document, record the answer to the following question as it applies to *The World from Space* projection:

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

Save the Excel workbook to your *final* folder. In
later steps, you enter additional measurements and scale factors for multiple
map projections.

As you can see, the difference between the geodesic measurement and the planar measurement of each map projection are significant. Understanding how map projections influence accuracy is especially important when conducting spatial analysis.