# Figuring out map scale when you know the spatial resolution of a Satellite Image?

I'm interested in figuring out how map scale and satellite pixel size (spatial resolution) are related.

For example the TM or ETM+ has roughly 30m ground resolution, then, what could be the finest scale of the extracted map?

Is there any formula or rule of thumb for converting the satellite pixel size to map scale?

• I'm a little confused by the question, if the ground resolution is 30m, then that is the finest scale available to map? One might look to aggregate the data to a larger scale to gain confidence in the signal, but that would be task dependent. – AnserGIS Sep 6 '13 at 7:13
• @AnserGIS: What the OP is asking, is that if you create a LULC map based on TM/ETM+ of 3m resolution, what would be the scale of the extracted vector? i.e. will be the LULC be accurate at 1:50,000 or 1:25000 or some other value? Is there a formula to calculate the scale upto which the Vectors are correct/Accurate? – Devdatta Tengshe Sep 6 '13 at 11:51

I assume you need to produce a paper map because the term "scale" nowadays makes sense only when talking about paper maps.

There is a formula that calculates the scale of the paper map:

1/x = 1 / (30 m/pixel × 4000 pixels/m) = 1:120,000 So, you would produce a map with a scale of a 1:120 000 using your 30 m images.

• on a paper map, you also need to take into account the print resolution in DPI, example, a 150dpi will have doubled sized considering a 300dpi print – MCunha Nov 18 '17 at 9:45

If the question is at what scale a vector of change can be considered reliable given the 30m sampling. Well that partly depends on the data values - i.e. its a question of noise to signal.

If the amount of change is quite high, i.e. the reflectance values between two classes quite distinct, one would be happy with a finer scale of map.

As to the absolute minimum for Landsat, in reality each 30m pixel is really a representation of light gathered from a fuzzy circle on the ground around its center. The corners of the pixel are the radius of that circle. Beyond that point, reflected light is having more influence on neighbouring pixels. A bit of trig shows the radius to be about 42m. Thus there is an overlap of up to 12 meters each way for both axes. So any attempt to draw a vector along a line of change cannot be meaningful at less than a smallest object of 42m assuming that adjacent pixels received very different signals. The smallest scale is thus the smallest one can physically draw a map and still represent that size of object.

However, usually the signals are not that clear cut between individual pixels, the noise from the overlap is significant relative to the difference in spectral response. So the true smallest scale will be that at which the classification produces statistically distinct differences between landscape patches. Demanding that each class be statistically distinct from its neighbours aggregates similar pixels together. Once that is achieved, the smallest patch left defines the smallest scale which can be clearly seen.

I suspect what you really wanted was Ardit Sulce's answer which I also liked, but perhaps this was at least interesting!

I understand the question that has been asked as the following:

(1) "What is the cartographic formula between scale and pixel size (spatial resolution)? (2) What is the finest scale that can be extracted for a map from an image with 30m pixels? (3) Is there any thumb rule for relating the satellite pixel size to map scale?

Answers: (1) For a pixel size of p meters, the cartographic scale of a map is 1:2000p. (2) Hence, for an image with 30m pixels, the finest scale is 1:2000(30) = 1:60000 (3) The thumb rule is Answer 1 (for the most appropriate size of the thumb)

References:

Hengl T (2006) Finding the right pixel size. Computers & Geosciences, 32(9): 1283-1298.

Tobler W (1988) Resolution, Resampling, and All That. In: Mounsey H, Tomlinson R (Eds.), Building Databases for Global Science, Taylor and Francis: London, pp. 129–137.

The scale of print will depend on the print resolution (usually in dots per inch), because when you say 1:10000, you have to make sure you have the correct print resolution. For a pixel size of 30m, and a 300dpi print resolution, your correct image will need a scale of around 1:350000. However, if you will print with a 150dpi, you can use a 1:175000 scale. A correct formula for knowing the scale by resolution will be: scale=photographic resolution*print resolution*100 (ex.: 30m*(150dpi*0.393700787)*100, will be a scale of around 1:177165) note the factor of conversion of inches to cm

• The question is not about printing maps though. – lynxlynxlynx Nov 18 '17 at 12:54
• Only on a printed map is scale relevant... – MCunha Nov 18 '17 at 21:11