1. What a moonbow is
A moonbow is a rainbow whose light source is the moon. Nothing else about it is different. Sunlight or moonlight enters a water droplet, refracts, reflects once off the back wall, and refracts again on the way out. Because the refractive index of water varies slightly with wavelength, each color exits at a slightly different angle, and because a sphere concentrates the exiting light near a particular angle (the "rainbow angle"), you see a bright ring at about 42° from the anti-light point for red, 40° for violet.
Three things make Cumberland Falls unusual. The drop (68 ft) and the flow (a median around 1,200 cubic feet per second at the Williamsburg gauge, from a typical 300 in September to about 3,500 in March, and far more after a big rain) produce a persistent cloud of spray. The gorge is wide enough to the east and south that the rising moon clears the rim early in the night. And there is almost no artificial light. Niagara had all three until the city lit up. Yosemite has a seasonal moonbow at spring runoff, and a handful of falls in Africa and Iceland get them, but for a moonbow you can put on a calendar, this is it.
2. Why it looks white
Your retina has two kinds of light detectors. Cones see color and need a fair amount of light. Rods are about a thousand times more sensitive but see only in grayscale, and they take ten to thirty minutes to reach full sensitivity in the dark. A full moon is roughly 400,000 times dimmer than the sun, so the moonbow lands almost entirely on your rods: a pale white arc. A camera on a long exposure keeps collecting photons until the color signal is there, which is why the photos are vivid. Both are honest.
3. The Moonbow Index
The Index is a number from 0 to 100 computed for every hour of a night, from 7 PM to 5 AM Eastern. The night's headline number is its best hour, and the "window" is the run of hours scoring at least 75% of that best. Each hour is:
The four G terms are gates, each between 0 and 1. If any is zero, the hour is zero; no amount of clear sky helps when the moon is down. The four S terms are weather scores, also 0 to 1, combined by weight. All the ramps use a smoothstep so nothing jumps.
Gates
| Gate | Input | Shape |
|---|---|---|
| G_dark | Sun altitude | 1 when the sun is 12° or more below the horizon (nautical twilight over); 0 at −6°; linear between |
| G_moon | Illuminated fraction | smoothstep from 0 at 84% lit to 1 at 97%. That reproduces the park's "two nights either side of full" without a hard edge |
| G_light | Total cloud cover | 1 up to 60% cloud (gaps let moonlight through); smoothstep down to 0 at 95%. An overcast sky is a zero no matter what the river is doing |
| G_alt | Moon altitude | smoothstep from 0 at 2° to 1 at 8° (trees and the gorge rim); above 55° it fades gently toward 0.4 by 72°, never to zero. See section 5 |
Weather scores
| Score | Weight | Inputs | Shape |
|---|---|---|---|
| S_sky | 0.45 | Total cloud cover, precipitation probability, precipitation | 1 − smoothstep(10%, 70%) of cloud; then × (1 − 0.6·smoothstep(20%, 70%) of rain chance); × 0.3 if measurable rain that hour |
| S_mist | 0.30 | River discharge at Williamsburg (cfs) | 0.25 + 0.75·smoothstep(150, 1200). The floor is there because the falls make some mist even at record low flow |
| S_haze | 0.15 | Visibility, relative humidity | smoothstep(1.5 km, 12 km) of visibility × (1 − 0.6·smoothstep(94%, 100%) of humidity), the second term being a stand-in for valley fog |
| S_wind | 0.10 | 10 m wind speed | 1 − 0.7·smoothstep(8, 25 mph). Light wind is fine; strong wind shreds the mist |
When the sky forecast doesn't reach a night yet (Open-Meteo goes out 16 days), the site shows the gates alone, labeled "moon only," which is an upper bound. When the river gauge is down, S_mist is assumed to be 0.6.
Why a night reads zero, and how much to trust it
A zero almost always means one gate slammed: the moon isn't full enough, or the moon is below the ridge for every dark hour, or the forecast says overcast (95%+ cloud) for every hour the moon is up. That last one surprises people, because the river and wind might be perfect. It doesn't matter. A moonbow is moonlight refracted through spray, and a solid cloud deck removes the moonlight. Each night on the home page now says which gate did it.
The catch is that a cloud forecast is only as good as its lead time. Out to about three days it's reliable to the hour. Four to seven days out it usually gets the pattern right and the timing wrong. Beyond a week it is closer to a coin flip, and the Index will swing wildly as the models change their minds. A full-moon night that reads 0 ten days out has not been ruled out; it has been guessed at. The site labels these as low confidence and the right move is to check back within a week of the night, and again the afternoon of. The moon and river parts of the score don't have this problem: the moon is known to the minute years ahead, and the river changes slowly.
The other thing that quietly caps scores is a low river. In a dry stretch the Cumberland at Williamsburg can drop under 300 cfs, which puts S_mist near 0.3. At 30% of the score, that means a night with a perfect moon and a perfectly clear sky tops out around 78, not 100. The factor panel shows the flow against the median for that date so you can see when the river, not the sky, is the limit.
Where the numbers come from
| Quantity | Source | Notes |
|---|---|---|
| Moon position, phase, sun altitude | Computed in your browser (SunCalc) | Accuracy a fraction of a degree, which is plenty |
| Full-moon instants | Computed (Meeus, Astronomical Algorithms, ch. 49) | Agrees with ephemeris tables to about a minute |
| Cloud, rain, wind, humidity, visibility | Open-Meteo hourly forecast for 36.838°N, 84.344°W | Blend of national weather models; 16-day horizon; CC BY 4.0 |
| Second opinion on cloud | National Weather Service, Jackson KY gridpoint | Shown as "forecast agreement," not folded into the score |
| River discharge | USGS 03404000, Cumberland River at Williamsburg | Upstream of the falls, so it leads them by a few hours; daily records since 1950 |
4. Backtesting
The same formula, run against reanalysis weather (ERA5, via Open-Meteo's archive) and the USGS daily record, gives an Index for every full-moon night since 1950. That's what the 76 years of data page is. It's a hindcast, not a record of sightings: it says what the instrument would have said, and it's the best available answer to "which month is best" until enough field reports come in to do better.
5. What we don't know
The altitude question. Textbook geometry says a rainbow disappears below the horizon when the light source is above 42°. The park's own guidance says midnight to 2 AM is best, which is when the moon is highest. Both can be true because at the overlook the mist is below you, so the "horizon" for the bow is the gorge floor. The Index therefore fades the altitude gate gently rather than cutting it off, and the exact shape of that fade is the single most uncertain number on this page. Field reports will settle it.
The mist threshold. The relationship between gauge flow and usable spray is guessed. 150 cfs is around the lowest the river gets; 1,200 is a comfortable winter flow. The truth is probably a curve that also depends on wind direction in the gorge, which we don't model.
Direction. The bow is only visible from a spot with the moon behind you. The overlook's orientation relative to the mist plume, and how the plume shifts with wind, would let the Index say "stand here" instead of "go." Not modeled yet.
Weights. 45/30/15/10 are starting guesses informed by the physics, not fitted to anything. Once there are a few hundred field reports, the plan is to fit them and publish the change here.
If you know something we don't, [email protected]. Corrections are welcome, especially the kind that come with a citation.
Weather data by Open-Meteo.com (CC BY 4.0). River data from the U.S. Geological Survey. Astronomy by SunCalc (MIT) and the Meeus algorithms. Not affiliated with Kentucky State Parks. Contains no cookies, trackers, or analytics; the only thing this site stores is what you type into the field-report form.