Exploring Error and Uncertainty Related to Datums and Projections Using ArcGIS

Troubleshooting Datum Shift

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

Now that you have explored how different projections distort the geometric characteristics of features on a map, you will now investigate how the ArcGIS software handles multiple datasets with distinct spatial reference systems. Earlier, you changed the display projection to determine distortion patterns of the indicatrix layer visually. Each time you changed the data frame spatial reference properties on the Coordinate System tab, the spatial reference of the feature classes in your geodatabase remained untouched. ArcMap makes this possible through a process called project-on-the-fly.

When you first open a blank map document, the data frame has no spatial reference properties assigned to it. When you add your first layer to the Table of Contents, ArcMap adopts that layer’s spatial reference information and uses it for the data frame display. When you add the next layer to the Table of Contents, ArcMap checks the second layers spatial reference information. When it encounters a different spatial reference, ArcMap usually provides a warning message. If you accept the new layer, ArcMap tries to dynamically line up the two layers by performing a datum transformation on the fly.

A datum transformation is a mathematical process in which the geographic coordinates of one datum are converted into the geographic coordinates of another datum. Recall that geodetic datums are the reference ellipsoid and origin point that model Earth and form the basis for geographic coordinates such as latitude and longitude (Figure 2.47). You can’t have latitude and longitude coordinates without a datum. Additionally, each datum uses different latitude and longitude values due to their position relative to the geoid model of Earth.

Figure 2.47: The brown area represents the surface of the Earth. The dotted line represents the geoid model of Earth. The smooth grey surface represents the reference ellipsoid model of Earth. The lower section of this graph depicts the geoid-ellipsoid surfaces overlaid on top of each other. Double-click or tap twice to view the image in a larger size.

Some datums are optimized to increase accuracy over a specific region, such as North America or Europe. Other earth-centered datums, such as WGS 1984, try to average out their fit uniformly across the globe (Figure 2.48).

Figure 2.48: In places where the geoid, shown in yellow, separate from the ellipsoid, measurements are less accurate. The blue ellipsoid is a good fit for North America but does not work as well for other regions of the world. Likewise, the purple ellipsoid works well for Europe.  The orange earth-centered ellipsoid is optimal for global applications such as global navigation satellite systems. Double-click or tap twice to view the image in a larger size.

Typically, the ArcGIS software does a decent job when transforming the latitude and longitude coordinates from one datum to another. However, there are multiple ways to perform this transformation mathematically. In some cases, the method of transformation does not always provide the best results and can introduce spatial error into your analysis.

Navigate to the Humboldt County GIS Data Download page. Under Frequently Requested Data Sets, download the Humboldt County GIS Roadway Centerline shapefile(Figure 2.49). Save the zip file to your original folder. When done, decompress the file and delete the zip.

Figure 2.49: In Chrome, you can right-click on a link to save a downloaded file to a specific location. Double-click or tap twice to view the image in a larger size.

In ArcMap, add the roads shapefile to the map. Open the data frame properties and navigate to the coordinate system tab. Match the spatial reference of the data frame to the new road layer. You can do so by opening the Layers folder, which displays all of the spatial reference systems currently loaded into the Table of Contents (Figure 2.50). Select NAD 1927 State Plane California I FIPS 0401 from the list. When ready, click OK. The data frame now matches the spatial reference of the road layers.

Figure 2.50: The Layers folder provides a shortcut to spatial references for layers currently in the Table of Contents.

Return to the Humboldt County GIS Data Download page and download the Fire Hydrants Shapefile under Fire Plan Data (Figure 2.51). Save the file to your original folder and decompress it. When ready, add the fire hydrants shapefile to the map.

Figure 2.51: The Humboldt County website provides free GIS data related to Humboldt County. Double-click or tap twice to view the image in a larger size.

Zoom in to the Humboldt Bay and along the waterfront just north of Downtown Eureka (Figure 2.52). You should see the location of the fire hydrants relative to the streets. Most are located alongside the street segments and near intersections.

Figure 2.52: In this image, the green dots represent the fire hydrants. The pink rectangle marks the area of interest for this step. Double-click or tap twice to view the image in a larger size.

Next, use the Project tool to transform the fire hydrants layer from NAD 1927 State Plane California I FIPS 0401 to GCS WGS 1984. Recall that the Project tool does not alter the original data. Instead, it creates a copy of the data during the transformation process.

In the Catalog Window, click the plus sign next to Toolboxes. Expand the System Toolboxes, then Data Management Tools. Scroll down and expand Projections and Transformations and double-click the Project tool (Figure 2.53).

Figure 2.53: The Project tool is used for vector data. Double-click or tap twice to view the image in a larger size.

For the Input Dataset or Feature Class, use the drop-down menu to select the layer representing fire hydrants. For the Output Dataset or Feature, name the feature class hydrantWGS84 and save it to your geodatabase. For the Output Coordinate System, click the button on the right. When the Spatial References Properties window opens, open the Layers folder and GCS WGS 1984 and click OK. You may leave all other default settings and click OK (Figure 2.54).

Figure 2.54: Check to make sure that your settings match the image above. Double-click or tap twice to view the image in a larger size.

When the geoprocessing completes, you should see your hydrants feature class in your geodatabase. ArcMap may automatically add it to the map. If not, you should do so now. Zoom in close and compare the original fire hydrant layer with the new hydrant feature class. Change the colors of the point symbols for clarity if necessary (Figure 2.55). You may notice that the original layer and the new layer do not align.

Figure 2.55: The pink arrows indicate the shift in location from the original dataset, indicated by the green points, to the new dataset, indicated by the orange points, after the transformation process. Double-click or tap twice to view the image in a larger size.

Geospatial scientists call this difference in location a datum shift. This datum shift is caused by the differences in the geodetic datums between the two datasets as well as the mathematical equations used by the GIS software when trying to perform on-the-fly transformations. In other words, ArcMap knows that the two layers have different spatial reference system properties, and it works to line them up in the data frame using project-on-the-fly. However, the process is not perfect, and spatial errors are introduced.

In ArcMap, activate the Measure tool and change the units to meters. Measure the extent of the datum shift from a point on the original fire hydrant layer to the new one. In your Microsoft Word document, answer the following question:

  • How many meters of spatial error did the datum shift introduce?
  • How might such an error impact an application of geospatial analysis, such as for city planning?

Take a moment to consider the implications. Imagine if you didn’t have two copies of the same data set to compare. For example, suppose you downloaded the street layer from the Humboldt County website and obtained the fire WGS 84 hydrant layer from a different source, such as from a friend or coworker. How would you notice the spatial error introduced by the datum shift? Most readers would likely be unaware of the spatial error. A potential datum shift is why it is essential to use a consistent spatial reference system for every dataset when conducting spatial analysis.

The best way to avoid spatial errors when conducting an analysis is to make sure that every layer in the Table of Contents has the same spatial reference properties as the data frame.