Concentric 3rd and 4th order rainbows at Dresden-Langebrück, Aug 11th, 2020

17:27:54 CEST, Pentax K-5, smc Pentax-DA fisheye 10-17 mm at f = 10 mm, f/8, 1/1600 s at ISO 80, artifact-minimized processing by separate unsharp masking of color differences
Original image
Green minus blue color channel difference unsharp masked
Color differences unsharp masked

Taking photographs of tertiary and quaternary rainbows is difficult, as usually you won’t see what you are aiming at – theory predicts that the tertiary is just at the threshold of visibility [1], and for the quaternary the situation is even worse. I myself have been lucky only once before [2], (though having tried for almost a decade now), if one does not count experiments using artificial sprays [3]. This cannot be attributed to a lack of opportunities. Over the years, I experienced several promising situations, but afterwards no higher order rainbows could be extracted from the photographs by image processing. One problem is that cloud structures in the background mess up the unsharp mask filter. But maybe also my timing was just wrong and these rainbows did not appear when I expect them to do, because I misjudged the shower and illumination geometry.

Anyway, on Aug 11th, 2020, my instincts were right. Just before I finished work in Dresden-Langebrück, a moderate shower moved in from the northeast. The sunlight was somewhat dim, which resulted in an unspectacular primary rainbow from 17:15 CEST onwards. I could see some larger drops glint in the sunlight. I went to my car on the parking lot during the next minutes, and lost sight to the east, so I do not exactly know what happened later on this side of the sky. The rain was still ongoing, but not heavy, there were people cycling around without looking too much disturbed. I’m not entirely sure if it was still the same rain shower, or another one which had meanwhile moved in. I took three photos at the parking lot (17:23-24 CEST), and then drove about 100 m to a spot with a good view towards the west. There was nothing to be seen with the naked eye, just the sun, some glinting raindrops, a cloud, and blue sky below. A major problem is that raindrops will fall on the front lens, especially when using a fisheye objective that cannot be shielded and has to be held out of the car window to make proper use of its field of view. So one needs to be fast, otherwise the images will be spoiled by artifacts from the drops. That is why I did not do any image stacks, just a threefold exposure bracket per shot for safety (to have at least one picture with a useful exposure). In between, I had to wipe the lens dry. All of the ten shots I took there from 17:26-30 showed the tertiary rainbow after some processing, and it also appeared on the earlier pictures from the parking lot, as far as the view permitted. I was rather overwhelmed to see more than the complete upper half of the tertiary against the blue sky and cloud background when I first applied an unsharp mask to the images. The quaternary rainbow (located just outside the tertiary) can also be detected beyond any doubts, especially on the left side. I found no supernumerary arcs and no traces of the seventh order [4] (which I had missed to pay attention to during the observation, I also did not use any polarizers, and as mentioned, I did not record image stacks).

17:30:00 CEST, Pentax K-5, smc Pentax-DA fisheye 10-17 mm at f = 17 mm, f/14, 1/400 s at ISO 80, artifact-minimized processing by separate unsharp masking of color differences
Original image
Green minus blue color channel difference unsharp masked
Color differences unsharp masked

It is well known that aerodynamic flattening of larger raindrops has an impact on rainbows through the so-called Möbius shifts, but so far the consequences for higher order rainbows have only been studied theoretically. Are there any new insights from this observation? This, of course, requires an image calibration, i.e. the assignment of scattering coordinates (scattering angle and clock angle, i.e. the sun-centered azimuth, which I will count clockwise from the rainbow’s top here) to the individual pixels. The position of the sun is easily calculated from the time the respective photograph was taken (17:27:54 CEST for the top image, checked with a radio-controlled watch) and the location (51.13° N, 13.83° E), which gives in this case an elevation of 27.6° and an azimuth of 259.5°. The pixel coordinates of the sun’s center could also be reliably determined from an image version developed as dark as possible from the RAW file in Photoshop. The projection of this specific lens I had measured eight years ago (when I newly got it), but I did also a cross-check with recent starfield pictures (abundantly available from my attempts to catch Perseid meteors the following nights). In order to determine the relevant Euler angles (elevation and azimuth of the camera’s optical axis, and the rotation of the camera sensor chip around this axis), I still needed another reference mark. Luckily there was a telecommunication tower at the horizon which I could identify and then calculate under which elevation and azimuth it is seen from the observing location.

Technical sidenote: The two coordinates of the reference mark provide me indeed with one condition more than the number of available degrees of freedom, so I can check the overall consistency of the calibration. And here it initially turned out to be not very convincing. What went wrong? When checking my hidden assumptions I found that I had pinned the piercing point of the optical axis to the precise center of the CMOS sensor (in terms of pixel coordinates). This may not be realistic, and, moreover, in a Pentax K-5 camera the sensor can move several millimeters to compensate for shaking. Even with the shaking compensation turned off there is no guarantee that it will find and stay in the optical center position (plus, there are decentering errors of the lens). From the working principle of the calibration procedure I expect the decentering error to be of quadratic order, and it may turn out to be negligible for longer focal lengths. But it matters for a fisheye lens. So I used the amounts of decentering in X and Y as further degrees of freedom and achieved consistent results for a shift of 26 pixels (0.12 mm) in the horizontal (and zero in the vertical). However, a further reference mark would be needed for a truly unique determination. Then there would still remain the assumption of a rotationally symmetric lens, but this seems to be acceptable as indicated by the recent starfield test.

From an equilateral projection in scattering coordinates it can then be deduced that the tertiary does not bend significantly over the recorded range of clock angles, which also holds for the quaternary as far as it peaks out of the noise. So seemingly they appeared as perfectly concentric circles here!

Equilateral projection in scattering coordinates

This is somewhat surprising, as theory predicts that these rainbows are also subject to Möbius shifts of various amounts along their circumference, which should become noticeable if larger (more distorted) drops are involved. Interestingly, for this sun elevation the Möbius shifts will move the tops of  the 3rd and 4th order rainbows towards each other. They might even overlap for an effective drop radius of 0.5 mm [5]. However, in nature, in most cases the drop size distribution (DSD) will cover a broad range of sizes, also including small drops. Because the shape distortion sets in (at least) quadratically with rising drop radius, it is likely to see some of the traditional concentric sphere-drop rainbows shine through in the full mixture of size dependent rainbows. This I already noted in simulations using broad Marshall-Palmer DSDs (i.e. a simple decaying exponential). As mentioned, there was no heavy rainfall going on during the observation on Aug 11th, so a dominance of the less distorted smaller sizes can be reasonably assumed – regrettably there are no direct measurements of the DSD. Lee and Laven [1] argue that broad DSDs tend to wipe out the tertiary’s top and leave only the sides, but their analysis was based on much lower sun elevations than occurring here.

So in order to see how much the concentricity of the tertiary and quaternary rainbows will be affected in this specific case I did some simulations for the proper sun elevation and a (guessed) DSD which contains mostly small and moderate sized drops: A Marshall-Palmer with decaying parameter (Lambda) of 4 mm-1, as previously used [5]. There are two complementary simulation methods which I can apply: 1) GO: Geometric optic raytracing (including polarization, but neglecting interference and diffraction) for all rainbow orders up to the 7th, based on a Beard-Chuang cosine series drop shape model, with optional (2,0) quadrupole mode oscillations and Gaussian tilts of the symmetry axis from the vertical, and 2) DMK: Debye series calculations for spherical drops of various sizes, superimposed in intensity after being shifted in scattering angle by the appropriate Möbius value (depending on drop size, rainbow order, and clock angle, following Können [6]). These calculation include only rainbow orders up to the 5th. The Möbius shifts themselves are taken from a look-up table comprising earlier raytracing results. These were calculated from a simpler shape model (two conjoined half spheroids fitted to Beard-Chuang shapes) and do not include drop oscillations or tilts for the higher-order rainbows yet. However, this second method has the advantage of showing if supernumerary arcs can be expected under the given conditions.

I removed the most disturbing directly transmitted light (sometimes referred to as “zero order glow”) as well as the less important contributions from external reflection and the lowest two rainbow orders from the simulation, and show the resulting clear higher-order rainbows in the same sunward projection (and for the same sun elevation) as in the top image. As a reference, I also let simulations run for spherical drops with the same DSD. These, of course, turn out perfectly concentric (in scattering coordinates, not necessarily in the projected image). After having switched on drop distortions, it is reassuring to see that both methods agree in keeping the upper halves of the tertiary and quaternary well separated and still nearly concentric. However, a tendency to blur these parts can be noted, due to the contribution of larger drops. Two more pieces of information can be extracted here: Introducing moderate axis tilts and (2,0) oscillations (both their amplitude distributions set to the “standard values” used in [7]) does not lead to visible changes in the result (GO), and supernumeraries do not appear, neither for flattened nor spherical drops (DMK).

GO sphere reference simulation
GO distorted drops, no oscillations, no tilts
GO distorted drops, with oscillations and tilts
DMK sphere reference simulation
DMK distorted drops, no oscillations, no tilts

The latter result illustrates that in broad DSDs supernumeraries need the stabilizing “Fraser mechanism” [8] to become visible: If, with increasing drop size, the Möbius shifts grow in the opposite direction than the supernumeraries’ convergence towards the Descartes angle due to their shrinking angular width, there will be a certain critical drop size at which these effects compensate. Because of the resulting position stability against changes of drop radii, the supernumeraries of drops around the critical size will peak out from the unstructured background of superimposed non-aligned supernumeraries of other sizes. Traditionally, this argument is invoked for the primary rainbow (with a critical drop radius of about 0.25 mm for the first supernumerary), but it holds likewise for all other orders [9]. If the Möbius shifts have the wrong sign (as for the tertiary and quaternary bows at the sun elevation of my observation) or are set to zero (as in the sphere reference simulations), there exists no compensation point and the averaging of all supernumeraries results in a more or less uniform intensity gradient.

The GO simulations reproduce also the 7th order rainbow, but, under the assumed conditions, do not predict any amplification effects for it caused by drop distortions or oscillations. In fact, it is not even recognizable in the simulation pictures shown here, but can be extracted by a larger intensity-to-RGB-value scaling factor (or higher gamma value).

In conclusion, the observed concentric tertiary and quaternary rainbows without supernumeraries can be consistently interpreted in the current theoretical framework of broad raindrop size distributions and drop shapes with aerodynamically plausible amounts of flattening and oscillations. Even though shape distortions have a larger influence on higher orders, they do not forbid that traditionally shaped rainbows are formed, if enough small drops are present. Of course, any observations of genuine non-spherical drop effects such as higher order twinned bows are highly welcome as they would allow for a more challenging test of the simulation models.

A multi-split rainbow from south-east China, August 12th, 2014


Yulong river, Guangxi province, August 12th, 2014, 17:18 Chinese standard time

Twinned rainbows are rare sightings, in the sense that one may see on average only one per year in Central Europe even when paying close attention. Much rarer still, and maybe restricted to regions closer to the equator, are multi-split rainbows. Only few cases have been documented so far [1, 2, 3], though more snapshots can be found on image sharing platforms labeled as “triple rainbow” etc. It is always a very favorable situation if an archivist and analyst like myself can establish direct communication with a skilful observer, who recorded details of a rainbow display that provide some insight beyond the pretty pictures.

In April 2019 I emailed Mr. Ji Yun, who manages a Facebook group dedicated to atmospheric optical phenomena in China, asking about a spectacular photograph of a multi-split rainbow which had been shared there. He kindly relayed my request to Mr. Liu Hai-Cheng, the original observer. Mr. Liu agreed to answer a long list of questions and I also received two sets of photographs from August 12th, 2014, one from his Sony NEX-5C camera (equipped with a Nikon AF 28mm f/2.8 lens) and the other from his cell phone (Coolpad 8720L). The camera clock’s time stamps were calibrated with respect to the actual local time by comparing camera and cell phone pictures, and assuming the cell phone clock to be synchronized over the network. All time data are given here in Chinese standard time (UTC+8h).

Mr. Liu observed this rainbow rarity in the beautiful landscape of the karst mountains near the Yulong bridge (Yangshuo County, Guilin City, Guangxi province, about 400 km northwest of Hong Kong, 24.8° N, 110.4° E) during a boat trip on the Yulong river. He remembers that it was very hot that afternoon. It began to rain before he passed through the tunnel of the bridge (at about 16:50), with some heavier rain lasting for about 25 minutes. There was no lightning, thunder or strong wind.

Judging from the photos, the rainbow appeared at about 17:10 within 30 s or less. Already on the early photographs there are hints of the unusual splitting of the primary:


However, Mr. Liu’s visual impression was that the splitting became prominent only later, after the (seemingly ordinary) primary and secondary bow had appeared successively. He also noted that the visibility of the split branches changed over time, while the main primary could always be seen clearly.

Towards the end of the shower, the display reached its peak quality. The following pictures cover the full right-hand side of the rainbow and some of the left. They are presented without additional filtering to allow for a better assessment of the natural contrast conditions.

17:18 (unfiltered version of the title image)



For a deeper analysis, I chose the title picture, recorded at 17:18. In the contrast-enhanced version, three primary branches are directly visible, with the most intense one in the center. The secondary rainbow, as far as it is included in the frame, does not exhibit any anomalies. This is a typical feature in (almost) all split rainbow observations known so far. My goal was now to transform the photograph into the scattering angle vs. clock angle coordinate system (in equirectangular projection), as I did on previous occasions [1, 4]. The scattering angle is the angular distance from the sun, and the clock angle the azimuth around the rainbow’s circumference, with the 0° position corresponding to its top.

The sun’s position is easily obtained from standard astronomy software (giving an elevation of 25.4°, and azimuth of 275.4°). Additionally, the precise focal length of the lens (in pixel units) and distortion characteristics need to be known, as well as the camera pointing direction in elevation and azimuth, and the angle describing the rotation of the sensor’s pixel grid with respect to the vertical.

To precisely determine these quantities, a rather extensive calibration must be carried out. Here I had to try some reasonable guessing: There is a nominal focal length in mm, the sensor data (pixel pitch) can be looked up, as well as some distortion information for this specific lens. From aerial pictures showing the river and individual mountains, the viewing direction can be estimated. The appearance of the water surface gives some clues about the camera rotation. In combination, all these estimations allow for a plausible transformation:

Assuming this reconstruction to be not too far off, it is immediately obvious that the bright central branch does indeed fit to the conventional primary rainbow locus at a constant scattering angle of about 138°. As expected, the secondary ends up at about 129°, also as a straight line. The lower branch (i.e. at higher scattering angles) can in principle be explained by aerodynamically flattened raindrops, following a long tradition in rainbow physics [5, 6, 7, 8, 4]. However, the upper branch penetrating into Alexander’s dark band requires elongated raindrops, whose existence cannot be accounted for by aerodynamics alone. Electrostatic fields [9] can elongate raindrops, but in the absence of any lightning activity it is speculative if any higher fields were present. Elongated shapes do also occur as transitory states during oscillations of larger drops in the appropriate (axisymmetric) modes [10].

The problematic element in this explanation is, however, that in the case of the rainbow we deal with a large number of contributing raindrops and a temporal average due to the finite exposure time. So we need an argument why contributions from transitory states are not simply wiped out. The resonance frequencies of the individual drops depend on their size, so no singular event such as an acoustic shock wave from thunder (if there had been any at all) can synchronize the oscillations. The only plausible idea for a formation of stable rainbow branches by drop oscillations in a stochastic ensemble might be that the two extremal states of the oscillation (flattened and elongated) are encountered with a higher probability than intermediate ones, as the momentary velocity decreases to zero at the turning points of any classical oscillation. Admittedly, this requires a rather narrow distribution of amplitudes throughout the ensemble (at least in the dominant drop size range), as otherwise the branches will be wiped out again due to the spread in extremal axis ratios. To my knowledge, there is not enough data on the statistical properties of oscillations in large ensembles of natural raindrops published yet to draw a definitive conclusion here.

Some further details of this observation are worth to be noted: The three branches of the primary bow appear each in a distinct fashion: The lowest is broad and rather diffuse, the middle one is bright and shows the features of a typical primary rainbow, the top one is narrow with a sharp uppermost outer rim. Moreover, it gives the impression of having developed a downward sub-branch in the –10°…+5° clock angle interval, resulting in a four-fold split bow there.

Rainbows certainly go on fascinating people all over the world, and rightfully so: Even in the 21st century, some outstanding displays occur from time to time that still challenge our understanding. Maybe those in hotter climates with intense rain showers have better chances of catching such rarities. In any case, we have to go out and take a look and a picture at the right time.

Quinary rainbow in lamplight, plus a twisted primary and nice supernumeraries

In my last blogpost, I described how tertiary and quaternary rainbows in the light of a halogen lamp and made by drops from a spray bottle can be photographed. The quinary rainbow I had not been able to detect back then, so I gave it another try two weeks later (on April 14th, 2018).

I chose a more conventional wide angle lens with f = 18 mm (Pentax DA 18-55 mm at a Pentax K-5 camera) instead of a fisheye this time, so that both the peak illumination intensity and the drops can be confined to a specific rainbow sector without the need to care about the rest of the rainbow circumference. Also, I hoped that a lens hood (which cannot be applied to a fisheye objective) might help somewhat against the wetting of the front lens by drifting drops. However, this did not work out, and the wetting problem did in fact worsen due to the fact that the lens has now to be pointed upward to capture the upper sections of the rainbows against the sky. This creates a much more efficient target for falling drops.

I started with a nice shot of a primary and secondary rainbow against the night sky, which might be mistaken as a lunar rainbow at first glance – but, as mentioned, both illumination and drops were purely artificial:

(10 s, f/3.5, ISO 400)

I then took about 40 pictures, both upwards as well as pointed horizontally to the right side against the vegetation background, without any additional polarizers. A signature of the quinary rainbow appeared in only a single frame of this whole series, recorded shortly after the one shown above. I suppose that even wiping the front less does not help to much after a while, as the lens will fog up again shortly afterwards. The diffuse background resulting from even a slightly fogged lens might be enough to mask the quinary. For the next experiment I plan to install a small battery-powered hairdryer or something of that sort to keep the lens dry. Anyway, here is the picture:

(1 s, f/3.5, ISO 1600)

with increased contrast and saturation:

The arrow points to the green/blue stripe of the quinary rainbow inside Alexander’s dark band.

Ironically, I had taken this only as a fun shoot because of the twisted look of the primary, and did certainly not expect it to be the only reference image for the quinary from this series. At the location of the dark band crossing the primary, the shadow of the spray bottle was cast on the drop cloud, which suppressed part of its “rainbow response”. The remaining drops outside the shadow might have had a different size, and/or the remaining divergence of the light source did play a role. Even at a distance of 10 m from the lamp, a lateral displacement of a drop by 50 cm corresponds to a shift in the lamp position (as seen by this drop) of about 3°. So the deviation of the Minnaert cigar (which has more of an apple shape here) from an ideal cone will still have an appreciable influence. This can only be reduced by increasing the distance to the light source or by confining the drop cloud to a region closer to the camera.

As already mentioned in the last blogpost, and being also visible in the picture above, beautiful supernumeraries at both the primary and secondary rainbows can become visible for several seconds. Finally, here are several pictures that show more of their variety:

(2 s, f/3.5, ISO 200)

(2 s, f/3.5, ISO 400)

(2 s, f/3.5, ISO 100)

How you can photograph tertiary rainbows every night

After almost 7 years since the first successful documentation of higher-order rainbows, we are now aware of at least 40 photographic observations of tertiary bows, sometimes accompanied by quaternaries. It is the more surprising that so far no one seems to have tried an outdoor experiment using artificial light and drop sources to bridge between the natural observation and single-drop scattering experiments, in which caustics are projected onto a screen.

Such an outdoor setup does not only allow to test various cameras and post-processing methods, but may also help to introduce newcomers to the challenges of observing higher order bows against the intense zero order background. Also very practical issues such as drops on the front lens or wet cameras can be directly experienced.

The setup is quite similar to what is used for diamond dust halo observations in Finland. The experiment is carried out at night in order to exploit the optimal background conditions of a dark sky. A bright searchlight lamp creates an almost parallel light beam with small opening angle, in which the camera is placed. Direct illumination of the camera is blocked by a cardboard disc placed roughly halfway between lamp and camera. This also helps in the case of photographing primary and secondary rainbows (i.e. the lens is pointing away from the light source), as stray light entering through the viewfinder on the camera backside can spoil the pictures.

I tested both Xenon (HID) and halogen lamps in the power range of 50-100 W. While Xenon lamps are brighter at the same power consumption, their non-thermal emission spectrum may lead to rainbows whose color is dominated by blue and yellow only, also the emitted light can show unwanted yellowish tinges in certain emission directions. The pictures shown here were therefore taken using the 100 W halogen lamp.

Drops were created by an ordinary spray bottle and, as judged by the appearance of the rainbows, are somewhat smaller than the ones in natural rainbows. Due to wind or movements of the bottle a spatial separation of smaller and larger drops can occur, as indicated by several well formed supernumeraries on both the primary and secondary rainbows which become visible for some moments. However, I decided not study these detail here, and tried to create a more or less spatially homogeneous spray including all available drop sizes over the exposure time of 2-5 s for each picture.

This is how the primary and secondary rainbow look like:

(camera: Pentax K-5, lens: Pentax-DA fisheye 10-17 mm at f = 10 mm, f/3.5, ISO 200, 5 s)

At that time, there was also some light natural drizzling going on, which generated only a weak primary rainbow in the lamplight. The limiting factor here is not the much lesser density of drops than in the spray (this could be helped by longer exposure times or stacking), but rather the background illumination of the sky (the pictures were taken in my garden in Hörlitz, Germany, which is a rather rural, but still pretty illuminated place, and there was also the nearly full moon behind the clouds on the evening of April 1st, 2018).

(f = 10 mm, f/3.5, ISO 200, 30 s)

When reversing the camera viewing direction, the zero order glow (=light which is transmitted through the drops without reflection) is, as expected, the dominant feature in the photographs:

(f = 10 mm, f/3.5, ISO 400, 2 s)

After strong unsharp masking, the tertiary rainbow is extracted, and can be traced almost completely around its full circumference:

As the camera was directed straight to the lamp (and rainbows thus appear as circles around the image center), it is possible to apply a radial smoothing filter to enhance the visibility further:

Here is another picture, taken with the same settings and processed similarly, which clearly shows in addition the quaternary rainbow in the upper left quadrant:



A major problem is that drops on the front lens disturb the recorded rainbows massively, as becomes apparent after unsharp masking. This problem is especially severe when using a fisheye lens (which does not have a suitable lens hood), and under windy conditions which shift the drops into unexpected directions due to swirled gusts near the ground. Periodical wiping of the front lens is therefore indispensable. Of course, the camera itself should be proof against spray water.

It is known from calculations that the contrast of the tertiary rainbow lies close to the detection limit of the human eye (see here and here), at least for purely spherical water drops. Here, no traces of it could be seen directly, even when looking through a polarizer. The main problem is that the spray lifetime is only a few seconds and the observer is constantly busy to maintain a more or less constant amount of drops in the air, which is rather distracting. A garden hose may be worth testing in the future.

So far, no unambiguous traces of the quinary rainbow (see here and here) could be extracted from Alexander’s dark band, in which its green and blue parts are expected to follow immediately the red rim of the secondary. There are several reasons which make its detection difficult here. At first, the drops are generally smaller and thus the secondary rainbow wider than in a natural setting. Next, the weak but non-zero divergence of the illumination may blur the rainbow positions further. Also, the background includes green plants in some directions which hinders the detection of green rainbow features. A more detailed study using a darker background and a narrower drop size distribution (with appreciable supernumeraries) seems necessary.

Unusual Twilight Phenomena in Europe

Between August 21 and September 3, 2017, unusual twilight phenomena could be observed in widespread parts of Germany. In most cases, the sky turned into a bright yellow short after sunset. Some observers reported an increase of brightness when this yellow glow appeared. During the following 20 minutes, the colour changed into orange and later into red with the coloured part of the sky shrinking towards the western horizon. At the end, only a narrow red stripe directly above the horizon remained. Additionally, there was a very intense purple light even during the “orange phase”. Many observers reported that the landscape also appeared in a bright yellow or orange coloured light.
At daytime, the sky appeared in a pale blue as if there was a layer of thin cirrostratus clouds. At low sun elevations, stripes and ripples appeared in this layer. Some observers felt reminded of noctilucent clouds by these structures.
In the mornings, these phenomena also appeared in reversed order.

Similar phenomena were also reported from observers in Austria, Hungary, the United Kingdom, Danmark and Iceland and showed up in several pictures by webcams in the Czech Republic.

More pictures and time lapses (e.g. 12) you can find in the Forum of “Arbeitskreis Meteore e.V.

These strange twilight phenomena were caused by the smoke of huge wildfires in Canada. The plumes of these fires ascended up to the stratosphere reaching altitudes of about 15 kilometres. Then they were transported over the Atlantic Ocean by the wind.

When travelling through the northeastern parts of the USA to observe the total solar eclipse which ocurred on August 21, Andreas Möller could take photographs of these plumes of smoke.

Author: Peter Krämer, Bochum, Germany

Third and fourth order rainbow

In the late afternoon of July the 7th 2017 there were strong thunderstorms in the area around Berlin, Germany. AKM member Andreas Möller was driving trough heavy rainfall, when suddenly the sun came out. His report:

On my way home, I could observe a beautiful bright primary and secondary rainbow. It was still raining heavily and my intension was to observe the area towards the sun. Therefore I turned into a side street and stopped in front of an old industrial area.

Location details:

  • Ferdinand-Schultze-Straße 18, 13055 Berlin, Germany
  • Weather: Strong rain
  • Sun altitude: ~19°
  • Date: 2017-07-07
  • Time: 19:00 – 19:08 CEST


I took a lot of pictures in hope to get the third and fourth order rainbow. My equipment was a Nikon D750 with a Tamron SP 15-30mm f/2.8 at 15mm. The rain was strong and I had problems cleaning my lens from waterdrops. Later at home, I started to process the pictures directly. Amazingly, I could discover the third and fourth order in almost all of the pictures I took.

The image processing did clearly point out a colorful third and fourth order rainbow.

Processing details:

  1. stack of 8 frames
  2. unsharp masking (USM)
  3. contrast and light adaption with Photoshop
  4. unsharp masking with Photoshop


Here is another image processed out of a single RAW file. (USM)


Searching for Sub-Visual Atmospheric Structures in the Daytime Sky

On sunny, warm days the sun heats the Earth’s surface and the air close to it. Periodically a parcel of air will rise from this area due to the warmed air being buoyant. This parcel is thought to rise in an elongated column of fairly large size such that several hundred tons of air are lofted skyward. In doing so many of the particles generated by Earth-bound processes (pollen, smoke, dust, pollution, water vapor, etc.)  are brought with it. These particles are commonly known as aerosols. If the column reaches an altitude where the contained water vapor condenses then a cumulus cloud will form.

It is known that aerosols have a large effect on polarization of light, up to 30% or so. My first experiment in photographing these columns of air was to take 2 sequential photos of the sky with a linear polarization filter set to 90 degrees apart. Then in accordance with the article excerpt shown below and using an image processing program (Image Magik) I calculated the degree of linear polarization (DOLP) of each pixel from the formula given in the article. The resulting pictures are interesting and strange but do not show the expected structures.

I encourage others to make their own attempt at this goal as I am really a novice at image processing. No doubt there are many other ways of looking at this problem and I welcome all comments, thoughts and ideas. Thanks!

Excerpt from the article “Digital All-Sky Polarization Imaging of Partly Cloudy Skies” from Nathan J. Pust and Joseph A. Shaw

“It is our feeling that unseen aerosols and possibly thin clouds in what has recently been called the “twilight zone” between a cloud and the clear sky are reducing the DOLP in what appears to be clear sky. We believe that this effect on the sky polarization is directly related to the recently described observations of enhanced optical depth near clouds. In partially cloudy skies, we see DOLP reductions in clear sky areas between clouds that appear to be caused by subvisual aerosols and/or clouds. (Even though clouds appear to have hard edges, they are in fact surrounded by thin clouds.) Furthermore, these DOLP reductions show up in the clear sky long before we can physically see clouds in the sky.”

To determine Degree of Linear Polarization (DOLP) in each pixel he uses this formula:
(Image1pixel value – Image2pixelvalue) / (Image1pixel value + Image2pixelvalue)

Then he normalizes and stretches the result so it fills the whole 8 bit range of 0 to 255 pixel brightness values.

Some of my resulting pictures:

Author: Deane Williams, Connecticut, USA

Green-rimmed cloud at sunrise


On June 14th, 2014, I could observe green flamelets at the upper rim of an altocumulus cloud from Mt. Zugspitze (2963 m above sea level). The cloud was located left from the rising sun, and the phenomenon lasted from two minutes before the visible sunrise until shortly after it. At the moment of the astronomical sunrise the green flamelets at the cloud vanished. Additionally, green and blue rims appeared at the sun’s disk (see pictures  1 – 2).

I already observed a similar phenomenon a few seconds after sunset on September 24th, 2013, from Mt. Zugspitze. However, I could only take a single photograph of it. As there were seemingly no other reports about green cloud rims I decided to let the matter rest at that time. It was only after the second occurrence that I re-visited the case of the older observation.


When doing a new search for similar reports I encountered an observation from by Robert Wagner, January 7th, 2008, who also recorded green cloud rims during sunset on La Palma (2136 m above sea level).


No other documented observations could be found on the internet so far.

We cannot offer a complete explanation yet. It may be that the cloud edge, when illuminated from behind, acts as a separate light source and the green flamelets are then caused by the refractive dispersion of a weak mirage effect. This is consistent with the presence of blue and green rims at the sun, which indeed have been observed in all three cases. Furthermore, all observations were carried out from high mountains, from where the true geographic horizon already lies below zero elevation, and even the ordinary elevation shift due to refraction is already pretty high due to the long light path through the atmosphere.

More ideas and reports of similar observations are welcome in any case.

Author: Claudia Hinz

Edit 21th March, 2017: 

I would like to add a video to this article, in which I was record the green rimmed clouds on the Mt. Fichtelberg/Ore Mountains on 20-12-2016.

Gloridescent clouds


As “Gloridescence” I define colored clouds in the antisolar area, where there is no visible connection to a glory.

The first observation of colored clouds at the antisolar point was made by Stefan Rubach on Mt. Großer Arber at Jan. 26, 2007. We suspected fragments of a glory, but we were not sure.


Jan. 26, 2007: Glorydescence on Mt. Großer Arber. Photo: Stefan Rubach

On Nov. 18, 2007, I made the first observation of my own and on Mar. 1, 2010 my second observation at Mt. Wendelstein (1835m).

At Mt. Zugspitze (2963m) I observed these colored clouds a few times and named them „gloridescent clouds“ (and so far no one ever challenged this name).

On Apr. 25, 2015 I made my first observation of „gloridescent clouds“ at Mt. Fichtelberg (1215m). Meanwhile we received more observations, one from the valley of Neckar river, one photo by Eva Beatrix Bora from Stavanger, Norway and some from an aircraft (12). From these we conclude that:

  • Just as glories become more frequent with increasing observing levels (see this article), the frequency of “Gloridescence” also increases.
  • At lower altitudes (i.e. in the area of low clouds), “Gloridescence” originates mainly from underneath of stratocumulus clouds.
  • At higher mountains (e.g. Zugspitze, 2963m) and on airplanes, “gloridescent clouds” are more frequent and appear mainly in deeper cloud layers or single shreds of clouds.


Author: Claudia Hinz, Schwarzenberg, Germany

Frequency of glories from different observation levels


Glory and Fogbow with interferences at Mt. Zugspitze

The combination of spectre of Brocken with glory and fog bow is named after the German Brocken mountain, even though it cannot be observed there too often. My colleagues from the weather station estimated a frequency of 2 or 3 observations per year at the top of the mountain. The phenomena much more frequently observed at higher mountains.

Since there is no reliable statistics about the frequency of Glories to date, I tried to obtain some tendencies from my own observations on various mountain tops.

I observed at three different mountain tops where I worked for a longer amount of time:

  1. Mount Fichtelberg, Ore mountains, 1214m (similar height as Mt. Brocken)
  2. Mount Wendelstein, Alps, 1838m (standalone rock)
  3. Mount Zugspitze, Alps, 2963m (main mountain chain of the Alps)

Fichtelberg I observed most frequently in the early morning hours without interferences. On Mt. Wendelstein the Glories often long duration phenomena, sometimes very colorful with impressive interferences. On top of Mt. Zugspitze the Glory was visible at every solar altitude, in most cases long duration, with impressive interferences an colors.

I tried to capture the frequency of glory statistically. Since I could not look at the same time periods, the statistics is an approximation.


These observations lead to the following conclusions:

  • The frequency of glories increases with altitude (at my observing sites the number of glories increased by a factor of three for every 1000m altitude)
  • The higher the altitude of the observation point, the more impressive are the glories! With increasing altitude of the cloud, the size of the droplet in the clouds decreases and interferences become more frequent. Because the smaller and more uniform the droplet size, the more impressive becomes the glory (Simulation of Les Cowley). In the best case, the glory transforms into interferences of a cloud bow.
  • The duration of the phenomenon increases with the altitude, too. If the local conditions allow observations well below the horizon, the glory is possible at every solar altitude.

Author: Claudia Hinz, Schwarzenberg, Germany