Multiple Bows, Statesville North Carolina


Multiple Bows

Charles Tilley saw this very rare display in the early evening of July 29, 2006 at Statesville, North Carolina.
Mouse over the image for labeled features.

Image ©Charles Tilley, shown
with permission.



The display occurred for a few minutes before sunset and the bows are consequently reddened. The unusual aspects were (1) the two diverging fans of up to 3-4 narrow coloured arcs inside the primary, (2) Indents in the primary at the levels where the sets of multiple arcs were most widely separated and (3) a very faint coloured arc outside the secondary bow.

What was happening?

Multiple bows, reflection bows, are sometimes produced by sunlight reflected off sheets of water. However, the nearest water was 28 km to the West and 56 km to the SouthEast. The multiple bows were also too narrow and wrongly placed for reflection bows. Violent showers sometimes produce the enigmatic ‘twinned bows’ but Statesville bows do not look like them and there were no violent showers or hail.

The clue is the faint and broad arc outside the secondary bow. It is a secondary supernumerary. Supernumeraries inside the primary bow are not unusual but a supernumerary to the secondary is very rare. That it is present and so bright tells us that in that region the raindrops (1) had a narrow range of sizes and (2) they were less than 0.4mm (400 micron) diameter [G.P. Konnen, ''Appearance of the supernumeraries of the secondary rainbow in rainshowers, J Opt Soc Am A, 4, 810-816 (1987)].

The existence of small raindrops with a narrow range of sizes also explains the multiple arcs inside the primary. They are supernumeraries to the primary bow. They are not their usual colours because they are produced by sunset reddened rays.

Why the fan-like spacing? When raindrops are less than ~0.4mm dia the spacing of supernumeraries widens as the drops get smaller. Usually showers have their smallest drops at their edges. What we have here are localised showers in which the drop size varied smoothly from small drops to larger ones across a small part of the sky and so produced the fan-like structure.

We can estimate the sizes of the drops involved. The angular scale of the image can be found from the red, orange, and green separations of the main primary and secondary bows. That then allows rainbows simulations by Airy scattering theory to be superimposed and compared with the actual supernumerary spacings.

The simulations used a distribution of drop sizes around each mean value characterised by a standard deviation of 15%. The simulations match the spacings of the upper and lower parts of the ‘fan’ reasonably.

The upper simulation tells us more. As the drop size decreases the main primary bow shrinks slightly. This is the reason for the two indents.

Why were so many supernumeraries visible? Usually you see one or two. Here, the arcs were widely spaced because of the small drop sizes. The reddened light stopped blue light from reducing the contrast. And the drops were of closely similar size. When the size spread in the simulations was increased to 20% the outer arcs were not visible.

In summary: That evening over Statesville there were several localised showers that produced fragments of a primary and secondary rainbow. Some showers had raindrops smaller than 0.4mm with a very narrow range of sizes. These produced bright primary supernumeraries and a very rare secondary supernumerary. The drop size varied smoothly across two areas of sky and so produced supernumeraries of smoothly changing spacing that gave them a unique fan-like structure. A sight like this does not occur very often!


Secondary supernumerary