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At 9:30 PM on July 13, 2015, I was looking due south from Oshkosh, WI. I saw very clearly a large storm with 1-2 lightning strikes per second. I could see cloud-to-cloud lightning traces, as well as the cloud lit up from within.

Looking at the radar, the only storm in that direction was near Rockford, IL, 125 miles away as the crow flies.

Is it possible to see the top of a thunderstorm from that far away?

Weather radar July 13, 2015

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The top of a cumulonimbus cloud is usually about 40,000 feet and can reach heights of over 60,000 feet, which would be visible for a distance of 245 or 300 miles, respectively. Of course, that would be the very top that would be visible at those distances, but it puts it well within the 125 mile distance from which you saw the storm.

The following formula was used:

$$\text{distance} = 3958.8 * \arccos(3958.8/(3958.8+\text{height}))$$

where $3958.8 \ \mathrm{mi}$ is the mean radius of earth.

This formula calculates the distance from an observer to the horizon, which for a six-foot tall person is close enough. If you wanted to calculate the distance an object would be visible from (given absolute atmospheric clarity) you'd have to calculate this twice (from observer to horizon and horizon to object) and add the results.

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    $\begingroup$ This is only a geometrical limit. More relevant to the problem in question is the visibility limit due to light scattering. This is most often < 100 miles, but in exceptionally clean and dry atmosphere, it may exceed that distance. $\endgroup$ – milancurcic Jul 26 '15 at 0:58
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    $\begingroup$ @milancurcic, you're right. When I first looked at this question, I thought of it as a geometry problem. That having been said, the tops of thunderstorms are high enough to be above most atmospheric haze and dust (higher than any mountain), so as long as the air is pretty clear, one ought to be able to see the tops of them from nearly their mathematically possible distance. Of course, if there's a lot of smog and haze in the air, then all bets are off. $\endgroup$ – BillDOe Jul 26 '15 at 1:32
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    $\begingroup$ Miles? Feet? What is happening here? $\endgroup$ – Gimelist Jul 26 '15 at 7:24
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I had the exact same experience as the original poster, just this evening Sept 1, 2018, coincidentally right by Wittman Airport in Oshkosh. It's flat without trees across the EAA grounds there, so I could see to the horizon. There were lightning strikes going on almost directly south, and the lightning was colored orange by the humid air and distance. I seriously underestimated the distance of the storms; I thought they were between Fond Du Lac and Milwaukee.

When I got home, I got on the computer and looked at weather radar. To my amazement, the storm line was in northern Illinois, a little bit south of Rockford, a good 150 miles (240 km) away as the crow flies. That had to be some huge storms and cloudtop to ground type lightning to be visible so far away.

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Same experience two weeks ago north of Charleston, SC: could very clearly see abundant lightning in the top of a distant bank of clouds east over the ocean at nighttime with no moon. It was spectacular. But the radar showed that storm to be a little over 150 miles out to sea...

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