From which Munro can you see the most other Munros?

 (Munro = Scottish mountain over 3000ft. There are 282 Munro)

This question was posed during a few day's walking in Knoydart in September 2021. There wasn't any sort of answer online, so I set about finding it.

There are two factors to whether you can see a hill from another hill:

1. If there is another hill in the way (taking into account the curvature of the earth)
2. If the atmosphere is clear enough - even if there are no clouds in the sky, after some distance there becomes too much haze

It is clear from (2) that the answer will vary day to day! So I suppose the question then becomes two questions:

• From which Munro can you see the most other Munros if distance is no object
• From which Munro can you see the most other Munros given the viewing distance is x kilometres

Clearly if a way of answering the first can be found, the second will easily follow by filtering.

To attack the first part I used QGIS, a free geographical information system application, to analyse a DEM (digital elevation model) file of Scotland. A CSV file listing the locations of the Munros was obtained from this website https://www.haroldstreet.org.uk/munros/, and loaded into QGIS. I then used a plugin called  QGIS Visibility Analysis (https://landscapearchaeology.org/qgis-visibility-analysis-manual/) to perform an inter-visibility analysis on the list of Munros. This took each Munro in turn, and checked if there was a line of sight to each other Munro, taking into account the curvature of the earth, and refraction in the atmosphere.

As there are 282 Munros this meant 282*281 = 79,242 calculations needed performed (theoretically you could get away with half this number, as if you can see from point a to point b it means you can see from point b to point a, but the plugin simply iterated through all the Munros). 

The inter-visibility network: green indicates line of sight; red indicates no line of sight.

This produced a database of all the views between Munros and whether they were lines of sight. It was then simply a case of filtering for a given viewing distance, and count up for each Munro.

The ranking was obtained for 10km viewing intervals, starting at 10km, and is displayed in the graph below.

The top ranked Munros, as a function of viewing distance 

The location of the top ranked Munros.

For low viewing distances, the top ranked Munros are in the West - which makes sense; this is where the hills are most densely packed. Indeed Mullach Fraoch-choire sits right between Glen Shiel and Glen Affric, probably the densest area of Munro in the country. However as the viewing distance increases, this becomes a hindrance - hills begin to block other Munros. And so the best viewpoint becomes somewhere with more of a side on view to the dense regions, as well as being tall. This role is first taken up by Geal-charn and Ben Alder, and then Ben Macdui, which is the Munro from which Munro can you see the most other Munros if distance is no object. Being the second tallest in the country, and positioned in the East, it has a great panoramic view of the spine of Munros that run up the West coast - and most of the glens running East-West means there are lots of viewing corridors for further afield views, even, amazingly, to Skye.

The number of Munros visible from the top ranked Munros, as a function of distance

Below is a map of the lines of sight from Ben Macdui. Open it in a new tab to zoom in!