Supernumeracy Rainbows and Drop Size

Last updated on September 16, 2023

Supernumerary Rainbows and Drop Size: Exploring the Intricacies of Atmospheric Optics

Rainbows have long captivated our imaginations with their vibrant colors and ethereal beauty. But did you know that there is more to rainbows than meets the eye? In this article, we will delve into the fascinating world of supernumerary rainbows and their relationship with drop size.

As drops of rain become smaller, several interesting phenomena unfold. First, supernumeraries, those delicate fringes of light that appear just inside the primary rainbow, become more widely spaced. This means that the colorful bands of light become more distinct from each other, creating a mesmerizing display. However, the primary bow itself begins to broaden, and its colors become less saturated. Eventually, as the drops continue to decrease in size, the rainbow gives way to a cloudbow or fogbow, characterized by a diffused and pale appearance.

The visibility of supernumeraries is also influenced by the size distribution of raindrops. When the rain contains drops of widely different sizes, the fringes produced by each drop size overlap and blur together, making the supernumeraries less obvious. Interestingly, smaller drops create broader supernumeraries that are more tolerant of variations in drop size. This means that even if the rain consists of drops of varying sizes, the broader supernumeraries from smaller drops can still be discerned amidst the chaos.

Another intriguing observation is that the top of a rainbow often exhibits more distinct supernumeraries compared to lower sections. This phenomenon can be attributed to the size variation of raindrops along the rainbow's arc. Drops higher up in the atmosphere are possibly smaller, and their size variation has a less critical effect on the visibility of supernumerary bows. On the other hand, larger drops lower down are more susceptible to changes in drop size, making the supernumeraries less pronounced.

At the upper parts of a rainbow, there is an additional effect caused by the shape of raindrops. Larger raindrops tend to flatten slightly, creating a vertical cross-section that rays of light must pass through. When the drop size distribution is broad, such as during a shower, the combination of flattening and supernumerary spacing produces a consistent fringe spacing of about 0.7°. However, this comes at a cost - the fringes provide little information about the raindrop size. This effect is not observed at the base of the rainbow because the rays pass through the horizontal circular section of the flattened drops, causing the fringes from drops of various sizes to overlap and become indistinguishable.

To gain further insight into the relationship between supernumeraries and drop size, simulations were conducted using different drop size distributions. These simulations aimed to preserve the visibility of approximately three supernumerary bows. The results revealed that drops with a mean diameter of 0.40 mm had a standard deviation of 14%, while drops with diameters of 0.86 mm and 1.50 mm had standard deviations of 6% and 4%, respectively. These findings highlight the importance of drop size distribution in determining the visibility and characteristics of supernumerary rainbows.

In natural phenomena like showers, where drop size distributions are often wide-ranging, the effects of droplet flattening described earlier become more prominent, particularly at the top of the rainbow. The interplay between droplet shape and supernumerary spacing creates captivating visual displays, adding yet another layer of complexity to atmospheric optics.

In conclusion, supernumerary rainbows offer a captivating glimpse into the intricate relationship between drop size and atmospheric optics. As raindrops vary in size, supernumeraries become more distinct or fade away, revealing nature's ever-changing canvas of colors. Whether it's observing the widely spaced fringes or marveling at the subtle flattening of raindrops, there is always more to discover about the enchanting world of rainbows. So, the next time you witness a rainbow, take a moment to appreciate the hidden wonders that lie within its celestial arc.

Supernumerary bows and raindrop size. Mouse over the slider to see the effect of changing raindrop size when the droplet size distribution is narrow... The simulations were calculated by AirySim. The scale has steps of 1º.

As drops become smaller, several things happen: supernumeraries become more widely spaced, the primary bow broadens, its colours become less saturated. Eventually there is no longer rainbow but instead a cloudbow or fogbow.

Supernumeraries are less obvious when the rain has drops of widely different sizes. Each drop size produces differently spaced fringes which overlap to a blur. The broader supernumeraries from smaller drops are more tolerant of variations in drop size..

The top of a rainbow often has more distinct supernumeraries than lower down. The drops higher up are possibly smaller and their size variation then has a less critical effect on the supernumerary bows' visibility than does the same percentage size variation in the larger drops lower down.

There is another another effect at the upper parts of a bow. Larger raindrops are slightly flattened and rays forming the top of a rainbow have to pass through the flattened vertical cross section. It so happens that when the drop size distribution is very broad, as in a shower, the combination of flattening and supernumerary spacing versus drop size produces a persistent fringe spacing of about 0.7°. The downside is that little information about the raindrop size can then be gained from the fringes. The effect does not occur at the base of the bow because those rays pass through the horizontal circular section of the flattened drops and the fringes of different spacings from the many sized drops overlap and cease to be visible.

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The drop size distributions in the simulations above were set to preserve the visibility of about three supernumerary bows. Drops of 0.40 mm mean diameter had a standard deviation of 14%, drops of 0.86 mm diameter 6% and 1.50 mm drops 4%.

.. Showers often have very wide drop size distributions and then, particularly at the top of the bow the droplet flattening effects described in the last paragraph operate.

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