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Twinned rainbow over Dresden, May 11th, 2012

During the late afternoon of May 11th, 2012, a mild thunderstorm moved from west to east over Dresden. I was located at the University campus (51° 02′ N, 13° 44′ E) south of the city and seemingly at the southern edge of the cloud. At 17:30 CEST I noticed the beginning of rainfall, and at 17:32 the cloud already gave way for the sun again in the west, while the peak intensity of the rainfall was just reached at my place. I could trace the primary rainbow in the glittering of nearby drops at this time, similar to the appearance of halos in close ice crystals which are frequently observed at cold placed during winter. Already at this stage, the primary looked unusual, and the idea of twinning occurred to me. So I rushed through the building to fetch my camera and find a suitable location to take photos. I arrived at my preferential observation window at 17:36. At this time, local rainfall had almost completely ceased, and a beautiful double rainbow display could be seen in the east (Fig. 1, 17:37:44, Pentax K-5 + Zenitar 16 mm).

The primary rainbow showed a rather broad single supernumerary around its top, which could be interpreted as a weak form of twinning. Within the next minute, some cloud (maybe a part of the cumulonimbus that was still above my place, though not producing rain anymore) did cast a localized shadow on a part of the veil of raindrops in the east, and a very distinct twinning of the primary bow near its top became visible (Fig. 2, 17.39.06, Pentax K-5 + Pentax DA 18-55 mm at 18 mm, with boosted contrast and unsharp masking)

The most convincing theory for twinned bows so far is the assumption of a mixture of smaller and larger raindrops within the shower, with the larger ones being more flattened or squeezed in the vertical due to the resistance of air during falling [1]. According to this, the primary rainbow produced by the larger drops is shifted inwards (i.e. towards the antisolar point), especially near the top. However, as calculations show, the secondary rainbow remains almost undisturbed. This behavior of the secondary was exactly what I could record during my observation (Fig. 3, 17:39:12, Pentax K-5 + Pentax DA 18-55 mm at 40 mm, with boosted contrast)

The twinning was visible up to 17:41, when the top of the rainbow faded away due to the growing shadow of larger clouds in the west. The left part remained visible for some more minutes (Fig. 4, 17:43:44, Pentax K-5 + Pentax DA 18-55 mm, single frame extracted from video file). At 17:42, a complete and intense double rainbow could be observed also from a location 5 km north of my place, with a well-developed supernumerary inside the primary but without any signs of twinning [2].

For the image taken at 17:39:06, I performed a detailed analysis of the position of the twinned primary and the un-twinned secondary rainbow. The sun was located at this very moment at 26,9° in elevation and 265,9° in azimuth. To calibrate the photo with respect to focal length, elevation and azimuth of the image center as well as rotation around the optical axis, I took a star field image in the late evening of May 14th, 2012 from the very same place. From the position of two stars, the star field photo can easily be calibrated, which allows to calculate the positions of two landmarks at the horizon. Their positions allow in a second step the calibration of the original rainbow image [3]. Lens distortion was not considered, i.e. perfect rectilinear projection was assumed, since all pictures with the zoom lens were taken with activated real-time distortion compensation (camera feature). The results are very convincing, indicating the high accuracy of this calibration method when carried out carefully. This can be illustrated nicely by an overlay of the actual image with the theoretical positions of rainbows made by spheres (Fig. 5)

Only geometric optics was used here, and from it only the Descartes angles for the monochromatic wavelengths of 600 nm (red), 530 nm (green), and 460 nm (blue). Furthermore, I transformed the image into a sun-centered equirectangular projection, in which the rainbows from spherical drops have to appear as straight horizontal lines, indicated by the marks on both the left and right side of the image (Fig. 6)

The inward shift of the lower branch of the primary is obvious, with no part of it extending into Alexander’s dark band, i.e. beyond the Descartes angle. This is in accordance with the theory for flattened drops, as well as the secondary not showing any measurable shift or distortion and furthermore sticking closely to the Descartes angle all along its visible extension. It should be noted that more exotic splittings of the primary have been observed [4] whose explanation requires a different theoretical approach.

Taking a closer look at the shadow edge near the top of the primary, it seems that coming from the left the “ordinary” rainbow, i.e. the upper branch, is dimmed in the shadow region, but can be traced up to +20° in clock angle. On the other hand, one marks a smooth transition from the supernumerary in the bright region on the left into the inner branch of the twinned bow in the shadow region on the right. It is obvious that this localized shadow which is cast by a smaller cloud segment will prevent a certain set of drops in this very direction from contributing to the primary rainbow, and that the remaining sunlit drops are in the right mixture to give rise to a clear twinned bow. Very likely the drops a few degrees to the left will not exhibit a drastically changed size distribution. However, the drops in the foreground are illuminated there and add to the overall primary brightness, thus covering unfortunately the twinned bow. One can speculate that there might be many twinned bows in nature that are hidden from us due to the contribution of “ordinary” drops in front or behind the interesting region along the rainbow cone.



Author: Alexander Haußmann, Dresden, Germany

Cloud bow

On December 23, I observed on Mt. Wendelstein (1838m, Bavarian Alps) my first real cloud bow which formed on the rim of a cumulus – or might be even a cumulonimbus – cloud. Although a snow shower had formed in the centre of the cloud, the bow clearly did not appear in the shower itself but on the outermost rim of the cloud. There, the cloud droplets must have been even big enough to make the bow show faint colours.

When the phenomenon started to appear, there was the left end of a rainbow visible at the rim of the shower, so it might have rained there. But the picture clearly shows how the droplets become rapidly smaller as the bow extends into the cloud. Even its diameter seems to be smaller in its upper part (123).

The crossed bows

What kind of rainbow is that? This is no fake this is real! Ok…it’s a little trick with an open window and the right angle to the sun.

The rainbow are produced with a water spray bottle. The right bow is the “real one” and the left bow is the reflected one.

The reflected surface in this example is the window in vertical direction, so the bows looks like a “x”. (2)

Place : Pforzheim, Germany
Time : 18 May 2011
Digital Camera : Panasonic DMC-FZ50
Exposure : 1/200 sec , f/3.6 , ISO 100

Author: Michael Großmann, Kämpfelbach, Germany

A single water drop

A slight-projector and a singel water drop shows a lot of bows. Here you can see the primary, secondary and tertiary bow.

The distance between the water drop an the projection backside (white paper) is 30 mm, waterdrop an light source has an diameter of 2 mm.

Photo taken on 28.07.2011 on my desktop 🙂

Author: Michael Großmann, Kämpfelbach, Germany

Discontinuous Rainbow in Front of Ridge

There have already been observed discontinuous rainbows above a ridge for several times. (For example by H. Edens and C. Hinz). Explanations range from an optical illusion via burst raindrops up to the assumption that there are only large flattened raindrops in front of the ridge which reduce the radius.

This is why during my latest observation on June 16, 2011, on Mt. Wendelstein (1838 m), I made the effort to also watching the raindrops. During my observation, there were wind gusts of up to 34 m/sec (122 km/h). In addition, on (my) mountain slope, there were heavy turbulences making the large raindrops come from all directions, even upwards the steep northern slope. These were most deformed of all, some had the shape of vertical ellipses, and some were even almost triangular. Unfortunately, due to the storm I was unable to take valid photographs of the raindrops.

From Physical Review Letters (DOI: 10.1103/PhysRevLett. 101.234501) I learned that raindrops of a diameter of about 1 cm and making 3 rotations per second take a triangular shape. Such kind of rotations must have occurred on my mountain as well as on the neighbouring one where the rainbow appeared.

I am sure that such deformations alter the diameter of the rainbow causing those breaks. Does someone have the occasion to simulate rainbows on such raindrops?

Author: Claudia Hinz, Brannenburg, Germany

Near Infrared rainbow

Since Newton specified rainbow colors in 1672, we have been told that a rainbow has 7 colors : red, orange, yellow, green, blue, indigo and violet. These colors are thought to be a representative of how humans see rainbows everywhere. In fact, a rainbow spans a continuous spectrum of colors (no bands).

If there are rainbow bands in the visible spectrum, then there should be rainbow bands in the rest of the spectrum as well, but we just couldn’t see them directly. A near IR sensitive digital camera and a near infrared pass filter allow the near infrared rainbow to be captured.

A near infrared rainbow lies next to a red band of any rainbow, simply because the near infrared region lies right next to the visible red region of the electromagnetic spectrum.

The visible and near infrared rainbows were captured in the evening of June 18, 2011 at approximately 5:24 PM in Bangkok, Thailand. The rainbow showed up after a quick rain and last for about half an hour

(see time-lapse video :

Camera and filter used :
Camera : FujiFilm IS-1
Near IR Pass Filter : Hoya R72 IR Filter
UV/IR Block Filter : Heliopan Digital UV/Infrared Lichtfilter Slim version

FaceBook Album:

Author: Pitan Singhasaneh, Bangkok, Thailand

Valley rainbows

When working on a mountain top, one very soon breaks the habit of looking for rainbows only in the sky. Here rainbows can appear at all sun elevations, even when one really does not reckon with them. Last year I could watch rainbows at sun elevations of more than 60° on Mt. Wendelstein. The most beautiful ones appeared when several rain showers passed on May 31, 2010. The maximum sun elevation during this observation was 63.6°.

Photos: 123

Later the same day (sun elevation now was “only” 41.8°) i had the rare opportunity to see a part of a rainbow on the left side of the mountain, while at the same time there was a fogbow on the right side, which soon was replaced by a glory. Unfortunately, it was impossible to look from the northeastern part of the mountain at the same time, so I could not see the transition from rainbow to fogbow.

On this day, rainbows appeared 6 times, the last one was a double reddish rainbow over the Inn valley.

Author: Claudia Hinz, Brannenburg, Germany

3rd and 4th order rainbows

Last evening (11 June 2011) thunderstorms approached my home town Schiffdorf near Bremerhaven in Northern Germany. I went to a field road by car to take some photos of the storm clouds. Just after I had arrived (about 18:00 UTC), heavy rain started which lasted for nearly 20 minutes. To my disappointment, the rain covered the gust front and most of the interesting features of the storm. So I waited and hoped that the sun would come out soon and produce some nice rainbows. When it did I realized that the dark clouds covered the sky to the right of the Sun – just the situation Michael Großmann had had when he took the the first image of a 3rd order rainbow only four weeks ago. I decided to try this out as well. Instead of one image I took sequences of five to stack them and, thus, increase the signal-to-noise ratio. I hoped this would increase my chances to detect the 3rd order bow. I took the images from my car through the open window to protect my camera (Canon 40D) from the rain. Visually, I did not see a 3rd order rainbow. However, in my back, the 1st and 2nd order bow developed nicely.

Back home I converted the raw images to 16-bit-Tiff and stacked them in Photoshop. Adjusting saturation already showed the 3rd order bow in the image sequences taken between 18:17 and 18:22 UTC (first image).  Applying unsharp masking revealed something unexpected in one of the stacked images (from 18:19 UTC): There seemed to be another rainbow close to the 3rd order bow, but, with reversed colors (second image). I checked Les Cowley’s website and realized that my image likely showed the 4th order rainbow!

After some more sophisticated processing including denoising (Neat Image), unsharp masking and increasing saturation, the 3rd and 4th order rainbows both were clearly visible. Finally, I created a composite using masks to retain the natural look of the foreground while still showing the 3rd and 4th order rainbows (third image).

Author:  Michael Theusner, Bremerhaven, Germany

Full circle rainbow

Partly because of my embarrassment to capture any pictures of rainbow this year, I dug up my old idea about how to create a circular rainbow and went to a local shop.

After few hours with some assistance, a bent-looking sprinklers frame was completed (1). The first test on 2 June 2011 was somewhat unsuccessful because the sun was too high and I could not find a right angle to see the whole rainbow circle.

For a few days, rain storm after rain storm poured down over Bangkok, with no sunlight in the morning. On 5 June 2011, a heavy rain hit Bangkok again before sunrise, but the sun appeared around 7:30 AM. Many rainbow shots were taken (2) and the photos were stitched together by “AutoStitch” on a PC.

Place : Bangkok, Thailand
Time : Sunday 6 June 2011, approx. 7:44 AM
Rainbow Equipments : A row of sprinklers placed approximately 4 meters above the street
Digital Camera : Ricoh GX200 + 19 mm. wide angle lens
Exposure : 1/200 sec , f/4.1 , ISO 64, Daylight setting
Photo Processing : 4 pictures, stitched together by ‘AutoStitch’ on a PC, no image enhancement

Author: Pitan Singhasaneh, Bangkok, Thailand

Natural tertiary rainbow 3rd order

On May 15, 2011, a rain area moved from north to south. When it started to rain at my position, I immediately rushed to my observing site which is reachable within 2 minutes for me.

Once there, I saw beautiful specimen of the primary and secondary rainbow. During my observation,  the rain intensified, and now I knew hat I had to look for!

On the left side of the sun there was a relatively dark cloud bank providing ideal conditions for a possible sighting of the 3rd order rainbow.

In fact, I had the idea of seeing a very faint arc at the expected position of about 40° away from the sun. It is really exaggerated to say that I saw it, but there seemed to be something.

I went into the shadow of a tree in order not to be blinded by the sun.

Now I did not take any care to protect the camera from the rain, I just had a little box with me to put the camera into. The arc could not be seen for more than 30 seconds, but I´m sure there was something at that position.

As under those lighting conditions a correct exposure is hard to get, I took my photographs in RAW mode. All the “little helpers” of the camera had to be set off.

To my disappointment, I did not find anything at the expected position when examining my pictures on the PC screen. But when putting an unsharp mask over the pictures, I saw it immediately. A bow! You can see that the outer part of the bow is slightly red and the inner part is light green.

Here is an animation showing the original image and three different settings: Unsharp mask, intensified colours and inverted.

If you need more information about the measurements of this tertiary rainbow, take a look at this pdf-file written by Dr.Alexander Haußmann. Thank you very much for your calculation!

Author: Michael Großmann, Kämpfelbach, Germany