Imagery & Remote Sensing

# On map scale and raster resolution

By Rajinder Nagi, Esri Cartographic Product Engineer

I am sure if you have used any imagery data to make maps then you have at one time or another asked yourself, “What resolution should the image be for me to be able to detect features in it?” Well, you don’t need to guess, because there is a mathematical relationship between the map scale and the image resolution.

In 1987, Waldo Tobler, renowned analytical cartographer (now emeritus from University of California-Santa Barbara) wrote, “The rule is: divide the denominator of the map scale by 1,000 to get the detectable size in meters. The resolution is one half of this amount.” Tobler goes on to note, “Of course the cartographer fudges. He makes things which are too small to detect much larger on the map because of their importance. But this cannot be done for everything so that most features less than resolution size get left off the map. This is why the spatial resolution is so critical.”

So here is the appropriate resolution for a select set of map scales:

For example, if you were not sure what resolution imagery you needed to acquire to detect features at a map scale of 1:50,000, using Tobler’s rule above, you can determine that imagery of approximately 25m [50000/ (1000*2)] resolution would be sufficient.

Similarly, if you need to find out the mapping scale from a known imagery resolution you can do so using the formula below:

Map Scale = Raster resolution (in meters) * 2 * 1000

Two, as used in the equation above, doubles the resolution. Then that number is multiplied by 1000 to get the map scale.

Here’s an example. Say you have a raster with a resolution of 30 meters. Each pixel is 30 meters on a size (an area of 900 square meters). You double that to get four pixels (two rows and two columns) with a resolution of 60 meters on a size (an area of 3600 square meters). Then you multiply that 60 meter resolution by 1000 to get a map scale of 60,000.

This would be helpful if you were going to acquire satellite imagery for your data creation or you already have imagery and are wondering, “What scale of map I can use that for?”

Hopefully this simple mathematical formula will help you the next time you need to digitize features from imagery.

References:

Tobler, Waldo. 1987. “Measuring Spatial Resolution”, Proceedings, Land Resources Information Systems Conference, Beijing, pp. 12-16.
Tobler, Waldo. 1988. “Resolution, Resampling, and All That”, pp. 129-137 of H. Mounsey and R. Tomlinson, eds., Building Data Bases for Global Science, London, Taylor and Francis.
Thanks to Steve Kopp and Aileen Buckley for their help with this blog entry.

### Rajinder Nagi

Rajinder has more than 20 years of experience in GIS and Remote Sensing. In his current role, he leads the community elevation program at Esri and has wide experience in cartographic visualization, image processing, databases and geo-processing. Rajinder has developed a multi-directional hillshade (esriurl.com/NextGenHillshade) algorithm to improve terrain visualization in Esri basemaps. He has also developed a fusion technique (esriurl.com/NAGIfusion) which maintains details and colors when integrating colored rasters with hillshades. Rajinder holds a Master of Science degree in Geoinformatics and a Bachelor of Science degree in Urban & Regional Planning.

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