Word of the Month - Map Scale

In the August edition of Word of the Month, I drew a parallel between map scale and the stated accuracy of a geospatial dataset according to the USGS National Mapping Accuracy Standards (NMAS). In this Word of the Month, I elaborate on the map scale discussion by focusing on a visual representation of this concept; but first a bit of background on the topic before we jump into the comparison images.

Map scale relates a distance on a printed/digital map to its distance in the real world. Map scale can be stated in various fashions:

1. Perhaps the most common is the representative fraction (RF). When scale is stated by the RF it looks like 1:50,000 or 1/50,000. Put into words, this means that 1 unit on the map – be it millimeters, centimeters or inches – equals 50,000 of those same units on the surface of our planet; so that 1 inch on this map would equal 50,000 inches in the real world (or roughly 0.8 miles).
2. A verbal statement is another common way to represent map scale and to continue our example above it would look like this: “1 inch equals 50,000 inches.”
3. On printed and digital maps, scale is typically represented as a bar or graph. Below is an example bar scale for a printed/digital map with a 1 inch equal 50,000 inches scale.

When speaking about map scale, cartographers have defined terminology based on the geographic extent of the map. A small scale map actually covers a large area such as a single county; and while this might not be intuitive, it does make sense when you consider scale by the RF. A small scale map could have a scale of 1/500,000 which expressed in numbers is just 0.000002; and hence the term small scale for a map covering a large area. A large scale map covers a small area, such as a city. A large scale map could have a scale of 1/500 or 0.002 (which is a very large number in comparison to 0.000002). To explain the difference between large and small scale maps, let’s take a look at a series of maps of the Chicago, Illinois area. In this first map, we are looking at 1:250,000 scale view of the Greater Chicagoland metro region. This 15-meter Landsat mosaic (and subsequent images) comes to us courtesy of DigitalGlobe’s ArcGIS ImageConnect extension:

In the next image, the scale is now set to 1:50,000 with a source DigitalGlobe image from July 2008. Notice the detail that is now apparent, for instance in the downtown Loop area located on the shores of Lake Michigan:

In this final image, the scale is zoomed to 1:4,800 which is nearly full resolution for this 30-cm aerial data collected in July 2008. We have zoomed in on the Navy Pier in Chicago (which is on the upper right-hand side of the above image) and you can now see individual boats, buildings and roads at this scale:

In the last edition of Word of the Month, we related map scale and accuracy through a mathematical equation that was developed by the USGS for all federal geospatial projects. While this equation may have seemed a bit obscure, in this final section of the September Word of the Month, I present a visual interpretation of the relationship between map scale and accuracy. In a small scale map, the geographic area that is covered is large and thus the detail that one can show (and interpret) on such a map is limited. Take for example a polyline file that follows the center of a river channel. In the screengrabs below (taken from ArcGIS), we focus on the Lower Yellowstone River. The first screengrab shows a section of the river channel at 1:250,000 scale. At this small scale, the need to be accurate with the river channel is diminished as you simply could not show any more detail than is already displayed here.

Now here is a zoomed in screengrab of the same river channel at 1:12,000 map scale. We have zoomed in on the red square indicated above. In this second screengrab, you can see how complex the river channel really is in this section of the Lower Yellowstone. Since the map is more complex, you expect and need a higher level of accuracy for this data to have any validity. If we zoomed in even further on a 50-foot stretch of this river (unfortunately data at this scale was not available), we would see very small undulations in the river channel that are missed in this 1:12,000 scale map:

As you can see from these two opposing previews, one with a small scale and the other with a large scale, the relationship between map scale and positional accuracy is rather intuitive: as map scale increases, the features seen in the map will be more detailed; and thus the positional accuracy of these features must also increase or else the map would have little real world value.

Brock Adam McCarty
Chief Operating Officer
Map Wizard