Chapter 13 - Halos and Rainbows
Probably the best place in the world to view halos and other ice crystal reflection and refraction phenomena in the world is the front seat of a jet. The second best place is in first class next to the window. But the best place for the pilot to view rainbows is from the ground. That's because rainbows are often seen just after a thunderstorm has just gone past, and thunderstorms - well, that's another story. Often, pilots have seen halos and other similar phenomena and not recognized what they are. Infrequently, they have been reported as UFOs. Since halos are more visible to pilots than they are to ground dwellers, there is some justification for a separate chapter on them. A better reason is that they are just fun to see, and a little explanation has helped me feel more comfortable. On the right occasion, they also form good gist for cocktail party conversation.
Rainbows come in one shape and sort of two sizes. The two major rainbows are called the primary and secondary bows. I say "sort of" because a primary or secondary bow may contain two or more cycles of color called supernumerary bows. Usually the primary bow is the brightest of the bows, and the secondary bow is usually much fainter. Third and fourth order rainbows are theoretically possible, but I've never seen one. However, one of my readers has. If you do see one and take a picture of one, get some shadows from a tree or post in the picture so you can confirm that it is a true third or fourth order bow. That's because the order of the bow is determined by its angle from the antisolar point, the point in the sky or on the ground which is exactly opposite the sun. It's also called the shadow of your head, but antisolar point sounds more profound.
Some sunny summer's day, when you need to sprinkle your lawn, spend some time looking at the rainbow which will probably be in the spray from the sprinkler. If the spray is in the shade, no bow, but bring it out into the sunlight and there will almost always be a bow. Look at your shadow, and find the antisolar point, the shadow of your eyes. Then look outward from the antisolar point to the rainbow. The angle will be around 23 degrees. If you found the secondary bow, the angle will be around 35 degrees from the antisolar point. If you look for the third order bow, it should be at 120 degrees from the shadow or on the sunny side. The fourth order bow should be at 160 degrees from the shadow.
Going back to the first order bow, the reason it is seen away from the sun is because there is a reflection in the drop. Figure 13-1 shows a diagram of a smallish raindrop, smallish because it is round, not oblate as larger drops are. The sunlight is represented by an arrow coming in from the left. As the light enters at an angle, the light separates into colors just as it did in that prism back in science class. Most of it goes on through the back wall of the drop.
As with any surface of a transparent material, some of the light goes through, and some is reflected. The amount depends on the angle at which the light strikes the surface.
The back wall of a raindrop is a curved surface. Some of the light that hits this curved surface will strike it at the critical angle where all of the light is reflected and none goes on through the back wall. All of the reflected light is headed back towards the side it came in on, and all the light of the same color emerges at the same angle.
The sunlight which went on through is, of course, split into colors; however, the mixing of the light from all of the other drops from different directions causes the mixed light to be white again. This is why the area of the sky outside the primary rainbow is lighter than inside the rainbow. When you are looking at the bow, you are looking at all of the light which has been reflected just at the critical angle, and each drop along that angle contributes to the bow.
Supernumeraries, that is, repetitions of the bows within each bow are caused by interference effects. Although they are not difficult to understand, the discussion is tedious. I'll simply refer you to Minnaret's book Light and Color in the Open Air or to Physics of the Air by Humphreys.
Probably the reason why rainbows are noticed is that they occur in stormy weather when people naturally look at the sky. The reasoning behind the old proverb that - if you see a rainbow in the east, the weather will clear but if you see the rainbow in the west expect storms all day - is simple. To see a bow in the west means that the day is young, and the storms are to the west and probably are headed towards you. A rainbow in the east means the day is nearing sunset and the storms are east of you, probably headed east, and the worst is over.
I have been told that in the central part of the U.S., rainbows are fairly common to see aloft. All you need is sunlight and rain to get them. Of course, the bottom of the circular bow is fully visible from a vantage point of a few thousand feet above the ground, something that is almost never seen from the ground. If you go out to look for them, be careful. The brightest bows (and halos) are those which are formed by drops (ice crystals) closest to you, with the least amount of intervening atmosphere.
This is perhaps why rainbows are more colorful than halos to people on the ground. But halos come in many different shapes, some of which have a little color.
That's because they are caused by the action of sunlight on two different phases of water, ice and liquid. It takes both sunlight and raindrops to produce a rainbow. It takes both sunlight and ice crystals to produce a halo. So when you see a halo you know that ice crystals have already formed and that rime icing is not likely.
There are a number of different types of ice crystals, all of them being in the hexagonal crystal system. Figure 13-2 shows the schematic diagrams of the various forms of snow that have been observed. Snow crystals which occur during lake effect snows are really a number of needles which start from a single point.
The most common are the dendrites, the six-armed frilly ones often drawn on advertisements, the type you normally think about when snow is mentioned. The six (occasionally 12) arms are almost perfectly symmetrical, and the faces are frequently perfectly flat, giving rise to sparkles on newly fallen snow.
The dendrites are the most common type of snow simply because they grow at the range where the difference in vapor pressure over ice and liquid water is the maximum. At -12 degrees C, the most energy is released when liquid water evaporates and the vapor condenses on ice crystals. This probably accounts for the many frilly surfaces which grow on the crystal.
The other types of crystals are less frequently seen in pictures, primarily because they don't sell as well as the dendrites. When photographers work on snowflakes, they tend to take pictures which people will buy. Since advertisers aren't interested in the others, as people will probably not recognize ice needles or columns, photographers tend to use their expensive film on dendritic snowflakes. However, the other types are quite common but do not grow as big as fast as the dendrites.
Platelets resemble a dinner plate with the edges chipped into a hexagonal pattern. Because of their disk-like shape, dendritic snowflakes and platelets fall with their flat faces parallel to the ground, much like a sheet of paper falling. Figure 13-3 shows a single platelet falling the way it does normally. It actually oscillates around somewhat. I have drawn in the dotted lines to indicate that it really is a portion of a prism made of ice and a typical ray of light coming from the sun.
The six edges are frequently very flat crystal faces, especially the smaller ones, and these crystal faces are probably flatter than a sheet of glass. The effect is one of a spinning fluttering prism slowly falling towards earth. The prism-like color separation is what makes up the halo; however, there's more to it than a set of simple prisms.
With a lot of these platelets, the red light from one platelet which reaches your eye would be mixed with the orange from another nearby, with the yellow from still another, and the green from another, and so forth. The result of all of this mixing would be white light, a simple hazy sky. The halo is the result of another property of prisms, the minimum angle of refraction.
If you take a prism of glass or ice and rotate it, the best spectrum is found by stopping it at just the right angle between the incoming light and the prism surface. Turn it a little bit either way and the color separation is weaker and the angles increase. The geometry and physics of light through ice platelets gives this minimum angle at 22 degrees. Any other refracted rays come out at angles of more than 22 degrees. So, as the platelets fall and spin at the same time, the angle of maximum color separation is 22 degrees from the sun.
Any platelets between the halo and the sun are refracting their colors at an angle larger than 22 degrees, so the inside of the halo is "darker" than that outside the halo. Figure 13-4 shows the two most common of these halos. The halo of 22o is formed in ice crystals fairly close to the observer. Generally, the brighter the halo, the closer are the ice crystals. The ring around the sun close in is called the corona which is caused by a few water droplets the size of fog or haze. Between the sun and a halo of 22o the sky is often perceptibly clearer or bluer than normal. Just outside the halo, the sky is slightly lighter than the rest of the sky with the light being produced by the poorer spectra from the platelets not at just the right angle. To the ground dweller, the most common halo is the halo of 22 degrees. This "ring around the sun or moon" is often quite striking. The forecasters aren't surprised if they get calls about these slightly colored circles around the sun or moon when stratus clouds are around.
The 22 degree halo should not be confused with a corona (caused by cloud droplets, not ice crystals) which is right next to the sun or moon. The 22 degrees refers to the angle the halo makes with the sun or moon. Stretch out your hand wide and extend your arm out, then cover the moon with your thumb. Your little finger will then be about 20 degrees away from the moon. Figure 13-4 shows both and their relative scale.
Most winter travelers to Alaska have felt the sharp points of the needles for they are common in ice fogs in the more northern climates. Ice also forms in hollow and solid columns, much like needles but thicker. Composite columns with dendrites growing from each end are infrequently found.
Since most people don't look at the sky - either they are urban geologists intent on discovering a new form of concrete, or they are looking for dollar bills - only relatively bright sky phenomena catch the eye. Those of us who look at the sky have probably seen these phenomena. They are most common in the cooler months because the best halos come from ice crystals which are close to the observer and the freezing level is lower in winter. In fact, the closer you are to the ice crystals, the more distinct and colorful they'll be. The halo of 22 degrees is caused by refraction of light through small platelets which are falling and oscillating through a large angle when they fall.
Contrary to the belief of the Roman general Constantine when he saw one of these and converted to Christianity, the halos do not have any metaphysical origin. They come from stratus clouds with ice crystals of the various crystal types of Figure 13- 2 in them. Looking back at the model of a cyclone, the most likely place for stratus clouds is at the leading edge of a warm front when the storm is following. Because of this, it should be no surprise that in the Northeast U.S., rain or snow follows these between 85 and 90 percent of the time when viewed from the ground. But be careful with statistics; the lack of a halo in stratus clouds doesn't mean rain or snow will not fall. The sun's size is exaggerated in this figure.
There are a lot of these phenomena, most of which are rarely seen from the ground. They are much more commonly seen from the flight levels which are frequently the sub-freezing parts of the atmosphere. Figure 13-5 shows a composite of many different types of halos which have been described over the years and named but there are more, especially near the part of the sky which is exactly opposite the sun. A very senior professor once told me that there are others theoretically possible; however, they haven't been photographed or even described in the literature. I don't know if all of them can appear at once. I do know that they appear separately or with a few others.
Next to the halo of 22o, the next most commonly seen haloes are the parhelion. These often appear in pairs but sometimes appear on either one side or the other of the sun. They aren't usually circular like the sun but most likely elongated like a teardrop with the points away from the sun. Often, the points will extend outward from the sun a good ways, infrequently going all around the sky as the parhelic circle. Frequently the parhelion, also called "mock suns" or "sun dogs" will be seen late in the afternoon or early morning. I often see them during commuting in the cool of late autumn, during winter and in early spring. In Alaska, these are frequently seen at dawn or sunset in ice fog situations. Since dawn lasts a few weeks, they may be around a while. Parhelion are caused by refraction of light through larger platelets which are found in cirrus and cirrostratus clouds. The rain/snow prediction (if you see one expect rain or snow within 24 hours) doesn't work as well with parhelion although the percentage is higher than 50%. When the sun is nearly on the horizon, the sun dogs are usually found around 22 degrees on either side of the sun at the same elevation as the sun. When the sun is higher in the sky, the angles between the sun dogs and the sun are larger.
The rest of the phenomena are rarely seen from the ground. They are much more frequent when flying through cirrus clouds. Probably the most frequently seen from the cockpit are the lower tangent arcs, usually filled in. These are caused by reflection from flat platelets which are slowly fluttering as they fall. The rocking motion of the very flat and distinct surfaces causes them to appear to be a bright teardrop shape directly under the sun.
The halo of 46 degrees is caused by light refracted through the ends of columns which form at different temperatures than platelets. The lower tangent arcs and Parry's arc are rare as seen from the ground. I've seen the lower tangent arcs a couple of times from my perch at the window during a commercial flight.
Look for these phenomena when you are flying. If you are at the top of your service ceiling and in light IFR, these tell you something about the air you are flying in. If you are in and out of clouds and see halo phenomena, you are seeing ice crystal phenomena. If you see a lot of it, you can breathe a little easier than if you see only a hint or two. In cumulo-stratus type clouds, when ice crystals are present, the likelihood of heavy aircraft icing is low. The ice crystals scour water vapor from the cloud, causing the droplets to evaporate rapidly. Since the clouds are rapidly depleted of droplets which form rime icing on the various appendages of airframes, the likelihood of buildups of rime icing is small. Flying in ice crystals won't rapidly reduce any load of ice you have existing on your airframe; you need warm air for that. But, at least the load won't get worse.
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