A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2016 Aug 1, 11:12 -0700
Bob, in your Aldebaran post earlier today you asked about visibility distance:
"On a completely separate topic, we had tornado warnings for a community 20 miles west of my house last night. I was looking to the west, and wondering whether the thunderclouds that triggered the warning were visible to me or below my horizon. That will be related to the height of the clouds I am looking at, of course. But Bowditch's Table 15 was not really designed with clouds in mind. Are there any rules of thumb for how far away I can see clouds of various sorts?"
The square root of height approximation is reasonably accurate even in LEO (Low Earth Orbit) but near the breaking point at that altitude. Within the denser parts of the atmosphere and especially within the troposphere, where the vast majority of clouds are found, the square root of height approximation is as accurate as most needs require. The standard distance to the horizon is somewhat greater than the straight line distance since it includes terrestrial refraction, but that matters less for higher altitudes so you can use d(n.m.) = 1.06·sqrt[h(in feet)]. Mid-level clouds are on the order of 10,000 feet high which implies they have a maximum range of visibility of 106 nautical miles, close enough to 100 miles. The tops of thunderstorms generally extend to, and often slightly above, the tropopause so you can use 40,000 feet for altitude implying a visibility range of 200 nautical miles. Of course, in order to see some portion of the storm poking above the horizon, you probably couldn't detect a storm beyond 150 miles even with perfect conditions. At this range, perfect conditions exist only in theory, and extinction in the atmosphere will normally prevent you from seeing anything. I would count 50 to 75 miles as a reasonable maximum. To emphasize, for very distant thunderstorm tops, it's not that they're beyond the horizon. Rather, they're lost in the "haze" at greater distances.
Setting aside computation, estimating distances to clouds is a visual task beyond our natural skills --we didn't evolve for that. I find that most people can't estimate the distance to a thunderstorm to better than a factor of five. They may think 'two miles' when a storm is actually ten miles away, or vice versa. Thanks to our networked pocket supercomputers, there is now a way to "train" ourselves as observers to estimate distances to certain types of clouds, in particular fully-developed thunderstorms. Next time you see some distant thunderstorms, call up the weather radar on your smartphone. Making allowances for the usual delays, you can often determine the distance to storms within a few miles. I find that I can now estimate distances to storms far better than I could fifteen years ago (before my first portable networked device with live weather radar). There are clear practical advantages to such distant estimation skills. Don't forget that storms travel with a wide range of speeds; for one storm 20 miles may mean three hours travel time, for another it may be twenty minutes. And don't forget that storms grow as well as travel, sometimes very rapidly!