# Viewshed analysis distance [closed]

If you were to make viewshed analysis for a point in the landscape and whether you can see a smoke in the distance, what would be the total area that you would calculate? 20 km from the observer point, 30 km? Or less?

Elevation of observer point is 400m, the source fire is on a mountain, below it's peak, on 950m. Distance is 25km, between them there is flat ground and clear atmosphere. Obviously, the viewshed analysis shows that it's visible. But how clearly visible? That's what I'm wondering.

• What assumptions are you making about the height of the observer, the height of the plume of smoke, the height of the source of the fire, the type of smoke, and the clarity of the atmosphere? – nmtoken Sep 27 '16 at 17:22
• Elevation of observer point is 400m, the source fire is on a mountain, below it's peak, on 950m. Distance is 25km, between them there is flat ground and clear atmosphere. Obviosly, the viewshed analysis shows that it's visible. But how clearly visible? That's what I'm wondering. – birdybird03 Sep 27 '16 at 17:26
• @BlueBird03 please edit your question to include the extra information rather than as a comment – Midavalo Sep 27 '16 at 17:56

Viewshed analysis generally only checks the theoretical line of sight - can a cell be seen from another cell, without any higher terrain standing in the way?

It doesn't take into account whether or not the human eye can make out an object at that distance. It will (if you choose) take refraction into account (the slight bending of light through the atmosphere over large distances) but not visual acuity.

The actual visibility depends on the size of the object and its distance, and the angular size - this site here has a useful calculator.

The formula is fairly straightfoward and can be found here

``````angle = 57.3 * (size/distance)  where distance >> size
``````

For example, a 1m wide telegraph pole 1km away has an angular size of 0.057296 Degrees. A 10m wide building 12km away has a similar angular size of 0.04775

According to wikipedia, the human eye can resolve at a resolution of 0.02 degrees, so you'd be able to make it out, assuming normal vision. According to that site I posted, the telegraph pole would hit that 0.02 degree limit at around 2.8 km.

If you assume the smoke is an opaque column and can estimate its width, you could measure the distance and use that formula.

I think SAGA GIS can produce a distance raster as part of its viewshed output. By using raster calculator and that formula, you could find - for each cell - whether or not the smoke would be visible. That would also tell you the distance you would need to extend your viewshed analysis to.

• Excellent answer! Just one more thing before I wrap it up: "width" in the context of the smoke column would be the "size" parameter in the formula? – birdybird03 Sep 27 '16 at 20:26
• cheers! yes.. width equals size. Assumed distance and size are in the same units (e.g. meters). The 57.3 "magic number" is to convert radians to degrees... a slightly more accurate figure is 57.29577951308232 :) – Steven Kay Sep 27 '16 at 20:35