I Can See For Miles, And Miles, And Miles…
2015-01-16 19:55:48.000 – Ryan Knapp, Weather Observer/Meteorologist
On Wednesday, January 14, we posted a picture to our Facebook page that described how we could see 120 miles in all directions that day. Since then we have had a few emails, Facebook comments, and private messages asking what the farthest distance is we can see, and what might be the farthest distance you can see in general. For weather stations like ours, we use visibility markers with known distances around the horizon (in the past using geometry and trigonometry but more recently using computer software). Using these points as reference, the farthest distance that we report is 130 miles. For example, on a clear day we can easily see Mt. Marcy (131 miles) and Whiteface (129 miles) in NY state. While weather stations at airports might use buildings as their markers, here we use mountain peaks, cities, oceans, lakes, etc as our visibility markers. So, that is how far we can see and what we use to report it.But what about using math? Well, it becomes a bit more complicated because you then have to define which horizon you are looking at or for: astronomical horizon, true horizon, or visible horizon.
If we were to strip the Earth of its atmosphere and make the Earth a perfectly round sphere (no mountains or valleys), the distance to the horizon (after a few derivations) would be whittled down to: d = 1.22*(sqrt[h]) where d is in miles and h is in feet. The summit of Mt Washington is 6288 feet so if we were the only high point on this theoretical Earth and using this simple equation, the true horizon would be approximately 96.7 miles away. If we were to use an Earth with an atmosphere (but again assuming a nearly flat, round surface) the equation would then become: d= 1.32*sqrt(h) where d is the distance to the horizon in miles and h would be your height in feet. So from our elevation of 6288ft (and not factoring in any of our Observers’ heights), we would be able to see the true horizon about 105 miles away. However, the earth is not perfectly flat and there are points sticking up all around us. So using standards set in place by NOAA we use our visible horizon which, as I defined previously, extends out to a reported 130 miles. While we limit our reporting to 130 miles, if we get a clear day with clean northern air or clouds popping up to 30000 feet in the atmosphere, our visibility towards the astronomical horizon could go on for hundreds of miles.
So what about your horizon?Well, for most people standing on a perfectly “flat” surface (the shore of an ocean on a day with “flat” waves), the Earth would typically curve out of sight at approx. 3 miles away. However, the Earth is not perfectly flat for most people and then buildings, trees, hills, mountains, etc start to limit this distance even further. But climb up a tree, scramble to your roof, take a hike, etc and your visibility increases. So you can use the equations above to calculate what your true horizon should be then look around you and figure out what your visible horizon actually is. And if you would like to delve into the geometry and trigonometry behind calculating the distance to a horizon, I will add a few useful links (below) that I found which match what is in the textbook I referenced for this comment.
http://mintaka.sdsu.edu/GF/explain/atmos_refr/horizon.html (there are several embedded links on this page which will allow you to explore even deeper)
http://en.wikipedia.org/wiki/Horizon#cite_note-ATYoungDistToHoriz-5 (there are several embedded links as well as reference at the bottom that can expand your exploration even further).
Ryan Knapp, Weather Observer/Meteorologist