Each month I will explore a geospatial topic of interest in this regular feature, the Geospatial Frequently Asked Question (G-FAQ). G-FAQ will be written in a down to earth fashion with an emphasis on illustrations, tables and imagery as is required to explain the topic. I will also provide links to each of the references used to write this piece so that you can dig deeper on your own. I hope you enjoy G-FAQ and please do send along any feedback/questions you might have about my monthly topics.
For the first G-FAQ, I will focus on a topic that made me scratch my head for the first few months of working with satellite imagery:
Why does a mathematical expression of ‘scale’ (e.g., 1:12,000) have two meanings to geospatial professionals? Some use scale to describe my zoom level in ArcGIS; others use it to describe the accuracy of orthorectified imagery; and still others use it to mean both at the same time – what gives?!
Before I jump into the answer to this question, let me explain the concept in a bit more detail. For this G-FAQ, we will focus on this expression of scale – 1:12,000. In some cases, 1:12,000 is used to describe the zoom I set in ArcGIS to define what level of detail is apparent in my imagery (i.e. map scale). In other cases, 1:12,000 is a definition of a map’s horizontal accuracy as 10-meter Circular Error 90% (or CE90%). And to a smaller minority, 1:12,000 implies both map scale and horizontal accuracy.
According to the NMAS, for a paper map with a map scale (I define this term in some detail below) of 1:20,000 or larger, the accuracy of 90% of the depicted features must be within 1/30 inch of the scale. And for maps with a smaller scale, 90% of the features must be within 1/50 inch of the scale. Now to put that into terms that are easier to understand, if you have a paper map at 1:12,000 scale, the features depicted on this map must be within 400 inches (or 12,000 / 30) of their actual positions on the planet; while a map at 1:50,000 scale must have an accuracy of 1,000 inches (or 50,000 / 50) to meet the NMAS standards. As a side note, Circular Error 90% also has its roots in the NMAS as CE90% is defined as the distance within which 90% of the points in an image fall from their actual positions. While the standards established in the NMAS have been revised multiple times since 1941, perhaps most notable in 1998 by the Federal Geographic Data Committee, the concept of tying horizontal accuracy to map scale was established during the early days of mapping technology.
Now to move on to the second part of this month’s topic we focus on map scale, starting with a simple definition: it is a fraction or ratio that expresses the distance on a map as its distance in the real world. So put into words, a map scale of 1:12,000 would mean that 1 inch on a paper map or computer screen represents 12,000 inches (or 1,000 feet) in the real word. In an era of static, tangible paper maps, the concept of map scale was more intuitive as you could bring one into the field to get a reminder on scale and its tie to a real world distance. But in the world of the computer monitor, with its ability to zoom in and out on a true ‘photo’ of the planet, this relationship has lost some of its tangibility. To many, map scale is now the number you enter in ArcGIS to zoom in and out on your imagery: when you use a larger number (such as 1:12,000), you zoom out; when you use a smaller number (such as 1:2,400), you zoom in. If you use too small of a number (such as 1:120), you zoom in too close and get a fuzzy, pixilated looking image.
In this series of previews, you see a visual representation of map scale with the same location shown at varying scales: 1:12,000, then 1:2,400 and finally 1:1,200. We have used a sample of 50-cm Natural Color WorldView-2 imagery collected on September 3, 2011 over Greene County, Pennsylvania. This data has been processed with our color balancing technique, Photo Enhancement. (Image Courtesy: DigitalGlobe)
To wrap up this month’s G-FAQ, let’s bring all of these concepts together. Scale is a geospatial term with two different but related definitions. When used to explain the accuracy of a map, image or other geospatial dataset, scale is tied to the CE90% horizontal accuracy standards established by the NMAS in 1941. CE90% is inherently tied to map scale as you saw in the discussion above; and this link is the reason geospatial professionals tend to use scale interchangeably when chatting about imagery and vector data. When used to explain the zoom level of a map, scale is defined as map scale which has a distinct visual impact as can be seen in the series of WorldView-2 previews above [NOTE: MAKE SURE PREVIEWS ARE ABOVE, CHANGE IF NOT]. As we learned in our elementary school writing classes, context matters when you decide how scale is defined in your conversation.
Do you have an idea for a future G-FAQ? If so, let me know by email at email@example.com.
Find Out More About This Topic Here:
- Federal Geographic Data Committee National Standard for Spatial Data Accuracy (NSSDA)
- Rice University’s Mathematics of Cartography – Scale
- United States National Map Accuracy Standards (NMAS)
Brock Adam McCarty