Supernumerary bows over Oahu

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Primary rainbow with supernumerary bows and a faint secondary bow. Photo from Noboru Chikira, 21 Apr 2016, Oahu, Hawaii.

 

No, your vision isn’t blurred. There are actually additional colored bands bordering the bright primary rainbow in this picture from the Hawaiian Island of Oahu. These faint, pastel bands of light are referred to as supernumerary bows. “Supernumerary” means “more numerous” and is an adjective used not only for describing this optical phenomenon, but also for everything from teeth to military officers. To understand how these bands form, we first need to consider what creates a rainbow in the first place.

Rain showers over the tropical Hawaiian Islands, and elsewhere, can lead to vibrant rainbows. How does this occur? First, consider the energy emitted by the sun, which includes waves of energy in the UV, infrared, and visible portions of the electromagnetic spectrum. Most of the sun’s energy is emitted as visible light, which includes a range of colors (ROYGBIV).

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In 1665 Isaac Newton, through his infamous prism experiment, was able to prove that the white light of the sun was actually composed of a color spectrum. The sun’s visible light entered the prism and was refracted (bent) through the prism, with the red (longest wavelength) bending the least and the shorter wavelength violet bending the most.

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A raindrop falling from a cloud can act as a prism, bending and reflecting the light to produce the colors of the rainbow. When the sunlight encounters a raindrop, some of the light is bent as it enters the drop. This refracted light hits the back of the raindrop, is reflected internally within the drop, then is bent (refracted) once again as it exits the drop.

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Because the different colors of the sunlight bends at different angles, the result of one internal reflection means the primary rainbow will have red on the outside and blue on the inside. This process happens to an assortment of raindrops falling from the sky leading to the existence of many rainbows at the same time; however, which one you see (and how much of one you see) depends on your viewpoint relative to the angle of the sun above the horizon behind you.

Sometimes, a second, fainter rainbow can be seen in the sky. This secondary rainbow results from two internal reflections (instead of one) inside the raindrop, leading to the colors appearing in the opposite order as the primary bow. In the following picture, you can see the faint secondary bow in the upper right.

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Primary rainbow with supernumerary bows and a faint secondary bow. Photo from Noboru Chikira, 21 Apr 2016, Oahu, Hawaii.

 

The key to the formation of rainbows, is therefore dependent on the sunlight, raindrops, and how much and how many times the sunlight bends and reflects within the drop. To understand supernumerary bows, the feature of this post, it’s important to remember that rays of light are waves of energy. Think of the ripples and waves that form on a water surface and what happens when they interact with each other. Some can counteract and destroy each other, while others can join to make a bigger wave. A similar description can be applied to waves of light.

The distance between the crests of these waves of energy is referred to as the wavelength (recall red light has a longer wavelength than blue).

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If the waves are in sync with each other, they can constructively interfere to amplify the wave. If they are out of sync (out of phase) with each other, they can destructively interfere to cancel each other out.

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So with this in mind, given the different angles of refraction for the different colors of the sun’s rays when sunlight encounters and is bent through and around a raindrop, there is bright light where the crests of waves are aligned (and therefore constructively interfere); similarly, there is darkness where the waves of light destructively interfere. Each of the bright fringes is a supernumerary bow, created by interference between different portions (colors) of the same light wave.

Why can’t we always see supernumerary bows? Well, their presence depends on the size of the raindrops. Supernumerary bows can only be seen when the sunlight encounters small raindrops that are all nearly the same size. In a typical rain storm, there are drops falling of many different shapes and sizes, which would wash out the colors of the supernumerary bows. Basically each differently sized raindrop would produce differently spaced, overlapping fringes that would blur. There is a sweet spot, though, because as the drops become even smaller, the bow broadens, the colors become less saturated, and eventually there is no longer a vibrant rainbow but a faint cloudbow or fogbow. An excellent description of these bows and their dependence on drop size can be found here: http://www.atoptics.co.uk/rainbows/supdrsz.htm

The first explanation for supernumerary bows was provided by the English physician and scientist Thomas Young in 1804.

Vog in paradise

Vog? What is that? Well, fog is tiny suspended droplets in the air, while vog are suspended particulates from volcanoes. This volcanic air pollution casts a hazy scene near the Hawaiian Islands as sulfur dioxide from the volcanoes mix with oxygen and water vapor in the atmosphere to form tiny sulfate particles. These particles can reflect the sunlight, making the extent of vog detectable by satellites, such as in this example from 2008.

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Image from MODIS on 2 December 2008 showing the milky haze around the Hawaiian Islands indicating vog. Image courtesy of NASA’s Earth Observatory: http://earthobservatory.nasa.gov/IOTD/view.php?id=36089

While the vog in this example was an extreme case, from the ground, these particulates can create a hazy view. This picture was taken by Stephen Green on a plane near the Kona airport on the Big Island of Hawaii, showing an example of the haze.

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Stephen Green (Imaginscape Photography), Kona, Hawaii, 1 Apr 2015

Notice how the haze is trapped in a shallow layer near the ground. This happens because of what’s called an inversion, where the temperature increases with height instead of typical decreasing. This “trade inversion” provides a cap to the vertical growth of clouds, which is why the cumulus clouds in this photo remain shallow in this layer. This stable scenario forms when winds are weak, so the vog persists in this shallow layer of stagnant air near the surface. Balloons launched twice a day from locations around the U.S., including Hawaii, carry instruments into the atmosphere that measure the vertical profile of temperature, moisture, pressure, and winds. An example of these measurements from Hilo, on the day this photo was taken (1 April 2015), shows the existence of this temperature inversion, with dry air above it and moist, relatively calm conditions below.

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A study by Guanxia et al. [Guangxia Cao, Thomas W. Giambelluca, Duane E. Stevens, and Thomas A. Schroeder, 2007: Inversion Variability in the Hawaiian Trade Wind Regime. J. Climate20, 1145–1160. http://journals.ametsoc.org/doi/full/10.1175/JCLI4033.1] used these observations from Hilo and from another location on the island to determine how often this trade wind inversion occurred. They found that the inversion occurs approximately 82% of the time at each station. The following figure from their paper also shows the height and strength (determined by temperature) of the inversion varies based on time of the year.

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Annual cycles of the (a) inversion base height and (b) inversion strength at Hilo and Līhu‘e, Hawai‘i, based on data from 1979–2003. (Figure 6 from Guangxia et al. 2007)

Here is another picture from Stephen of an obstructed view of the sky due to vog. In this example, haze from the Pu’u O’o eruption limited the view of lenticular clouds near Mauna Kea on the big island on 8 February 2015.

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Stephen Green (Imaginscape Photography), Hawaii, Feb 2015

These inversions aren’t present all of the time as weather systems can move through and eliminate the stable layer, provide moisture, and remove the vog particulates. In these cases, the view on the big island is clearly stunning.

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Stephen Green (Imaginscape Photography), Hawaii, March 2015

The upside to this inversion is that the vog and clouds are trapped in the lower part of the atmosphere, leaving a crystal clear view of the sky above. The Mauna Kea observatory is truly a sight to behold and we’ve had the fortune to gaze at the stars from that location on one of these clear nights.

Check out more of Stephen’s pictures on his Facebook page: https://www.facebook.com/stephengreenimages?fref=ts

Altocumulus stratiformis translucidus

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This is an example of Altocumulus stratiformis translucidus. Wow, that’s a mouthful! Let’s break it down a bit. Altocumulus are mid-level patches of clouds (cloudlets), existing between 6500 and 20,000 ft, that are mostly made of water droplets. They indicate some instability at that level. Stratiformis is its species because they are spread out over a large area. Note how they are different from the layered altostratus clouds because you can still make out the individual cloudlets. The variety Translucidus means that you the clouds are thin enough to see the sun through. If these were to continue to spread out and thicken to altostratus, it would be an indication of more inclement weather to come.

Angela Rowe
Location: Oahu
Date: February 2011

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