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Mirages: A Primer
Parched faces look out across the desert sand as two men stagger and crawl toward what they believed to be a thirst-relieving pool of water. As they near, however, the waters disappear; the vision merely a mirage. How many times have such scenes been played out in early motion pictures? The characters may have varied -- cowboys in Death Valley of the US Southwest desert or French Legionnaires in North Africa's Sahara Desert -- but the symbolism was the same: men dying of thirst chasing an image that only existed in their minds.
My standard English dictionary defines mirage as: "an optical illusion due to atmospheric conditions by which reflected images of distant objects are seen." The word finds its origins in the French verb se mirer: to be reflected. I'll excuse the lexicographers on the use of the word reflected in the definition because it does seem more appropriate, given the word's roots, even if incorrect. Actually they were only two letters off, the proper technical term should be refracted. (I checked two other English dictionaries, and they both used the term reflected in their definition. And be careful, a number of popular books on weather have fallen into the same trap when describing mirages.)
A correct definition can be found in the American Meteorological Society's Glossary of Weather and Climate. It states:
"Mirage: A refraction phenomenon wherein an image of some distant object is made to appear displaced from its true position because of large vertical density variations near the surface; the image may appear distorted, inverted, or wavering.
The effects of these distortions, displacements, etc. of the image create many of the optical illusions we see in a mirage. Although the mind may misinterpret the mirage image it receives from our eyes, the image is no figure of the imagination -- it can be photographed. But because of the strong illusional nature of mirages, they have gained an air of magic about them, dwelling in story and legend along with gods and demons, fairies and magicians.
The desert mirage of adventure stories and movies and song (for example, the country/western classic Cool Water) is more commonly seen today as a highway mirage, those apparent pools of water lying across the pavement, which always disappear before we can reach them. Both of these forms are technically known as the inferior mirage, a form most often seen over a land surface. The other main type of mirage is the superior mirage, most often viewed around or over large bodies of water or snow/ice fields.
The terms inferior and superior are not commentaries on their quality of the mirage's appearance but refer to the perceived position of the image relative to the actual location of the object. Inferior mirages appear below the actual object's true location. Superior mirages are seen above the actual location.
Mirages form when light rays emitted from a source or reflected off an object are bent as the path of the light ray crosses air layers of different densities. The technical term for this bending is refraction. You can perform a simple experiment to illustrate refraction. Place a long pencil or straw in a clear glass filled with water, then look at the pencil in the glass from the side. It will appear to have a bend or kink where it enters the water. The degree of bend defines the medium's index of refractivity and depends on the medium's density. (Refraction also differs for the various colours (wavelengths) of the visible spectrum and is part of the process causing many atmospheric optical phenomena including rainbows.)
The index of refraction for air varies with the density of the air. Air density is strongly dependent on its pressure, temperature and water vapour content. Air density is proportional to its pressure (density increases as pressure increases) and inversely proportional to its temperature (density decreases as temperature increases) and to moisture content (decreasing as water vapour content increases).
One form of superior mirage is so common that most scientists do not even recognize it as a mirage. Have you ever seen the sun lying right on the horizon? And what was the actual position of the sun at that time? Yes, this is a trick question.
The fact is, when you see the full solar disk directly on the horizon, all or part of it is below the horizon, but the bending (refracting) of the solar rays by the atmosphere gives us the optical illusion that the sun is actually on the horizon. This happens at both sunrise and sunset each day and adds over 4 extra minutes of daylight to each day. As a result, daylight is a little longer than the night period on the date of the Equinox by about 4 minutes. [see Equal Night and Day?]
This effect on the setting/rising sun's position is mostly due to the increase in air density due to increasing atmospheric pressure as the solar rays come from the near vacuum of outer space toward the Earth's surface. (Similar effects also alter the observed position of the moon, planets and stars.) When the sun or moon are within a few degrees of the horizon, they can also lose their circular shape and appear flattened because of atmospheric refraction. There are several other refractive effects that are also of interest to sky watcher but we must leave them for a later date. In this piece I want to focus on refractive phenomena seen in the lower atmosphere under conditions of varying temperature with height which produce mirages.
The two main mirage types, superior and inferior, are caused by opposite patterns of temperature change with height -- what meteorologists call the vertical temperature gradient. They express this gradient by the number of degrees of temperature change per height increment (usually Celsius degrees per metre or per 100 metres, but in older books you will sometimes see it still expressed as either Fahrenheit degrees per foot or per 100 feet).
Meteorologists consider temperature decreasing with height a "normal" state of the atmosphere -- often using the term lapse rate for the condition. When temperature increases with height, the condition is termed a temperature inversion (or just inversion).
Inferior mirages occur under strong lapse rate conditions, and superior mirages under inversion conditions.
While the atmosphere tries to establish a uniform lapse rate of 0.98 C° per 100m (0.54 F° per 100 ft) throughout the lower atmosphere, this situation rarely occurs for long as heating and cooling establishes differing temperature gradients from the surface upward. At times there may be several layers with distinct temperature gradients including inversion layers below or between layers with lapse conditions.
Such complex temperature layer can cause some rather interesting optical situations such as the Novaya Zemlya mirage which can "carry" light rays hundreds of kilometres over the horizon. We will delve more deeply into the variations possible with mirages in separate articles on this website. For the remainder of this piece, we will focus on describing the general conditions that form the inferior and superior mirages.
In the lower layers of the atmosphere where most mirages are seen, the air refractivity is only weakly dependent upon changes in air pressure but strongly on temperature gradient changes.
Light reaching our eye, after traveling through a region of the atmosphere where the temperature gradient is constant, follows a curved (parabolic) path. (See diagrams below. In them, the dark lines indicate the actual light ray path and the white dashed lines the path our mind thinks it sees.) The degree of curvature is proportional to the temperature gradient along that path -- the stronger the temperature gradient through which the light passes, the greater the bend. When the temperature gradient is not constant but changes with height, the curvature of the light path can increase more rapidly at some heights than others, thus producing interesting effects such as object distortions and multiple images.
The light ray always bends toward the colder (and thus denser) air, so that the colder air is on the inside of the curvature. The image we see is always displaced in the direction of the warmer air. Therefore, if we have a temperature gradient with warmer air nearest the surface, the image will be displaced downward toward the surface -- forming an inferior mirage. When the air is colder near the surface (an inversion condition), the image wis displaced upward, forming a superior mirage.
Mirages are confined to small viewing angles even when they appear large, about half a degree in width -- the size of the solar disk -- and most portray objects located from half a kilometre to about five kilometres (about a quarter mile to three miles). Under strong inversion conditions, however, objects hundreds of kilometres away can be seen, including those located beyond the normal viewing horizon. (For more details on seeing beyond the horizon, see The Arctic Mirage: Aid to Discovery.)
The illusion part of the mirage generally come from our mind's interpretation of what the eye sees. When our eye sees a light ray coming from an object, our mind interprets the ray path as a perfectly straight line from the object to our eye. Only when we recognize that we are seeing an illusion can we make some mental corrections to the scene. For example, we know the pencil in the glass is not bent even if our eyes try to tell us so. But recall what happens initially when we are surprised by such a scene. We must process more information to make true sense of the scene before our eyes. Thus when we see the inferior mirage's pool of water on the ground, we expect that the "water" will actually be on the ground.
When we view an inferior-mirage "water pool" on a road or desert or other hot surface, what we are actually seeing is the image of the bluish sky being strongly refracted by the hot air near the surface so that it appears to our mind to be water lying on the surface. The appearance of the inferior mirage always indicates that the surface air is much warmer than the air above it due to the strong heating of the surface by the sun or some other heat source. This temperature structure -- very hot below and cool above -- causes light rays passing through it to be bent upward.
The superior mirage occurs under reverse atmospheric conditions from the inferior mirage. For it to be seen, the air close to the surface must be much colder than the air above it. This condition is common over snow, ice and cold water surfaces. When very cold air lies below warm air, light rays are bent downward toward the surface, thus tricking our eyes into thinking an object is located higher or is taller in appearance than it actually is.
The superior mirage can also make objects appear to be floating in the air or cause objects actually located below the horizon to appear above it (remember the setting-sun example), a condition called looming. The superior mirage can also cause objects appear to be taller than they actually are, called towering, or shorter, a condition termed stooping.
Occasionally, we can see a variation on the inferior mirage on a smaller scale over a vertical surface. In this situation, the strong heating of a vertical surface by the sun or an internal heat source (such as a motor cover) can develop a strong temperature gradient extending laterally outward from the surface. This condition can form a lateral mirage. A lateral mirage will appear as an apparent reflection of a nearby image and form just over the wall or rock face.
This "inferior" lateral mirage results from a strong temperature gradient next to the wall similar to the condition of an inferior mirage turned sideways. David K. Lynch and William Livingston in their book Color and Light in Nature suggest that there is no reason a "superior" lateral mirage could not form over a cold wall surrounded by warm air, but they had never seen one.
Interestingly, only one of the Weather Field Guides that I am familiar with ( National Audubon Society First Field Guide: Weather ) has any discussion of mirages. Therefore, I refer you to three books which can be used as guides on the subject of mirages (and a lot of other atmospheric optics topics as well) and another related volume.
1. Color and Light in Nature by David K. Lynch and William Livingston, 1995, Cambridge University Press, ISBN 0-521-46836-1.
Except for its large format which makes it awkward to carry into the field, this book could be called a Field Guide to Color and Light in Nature. The best, in my opinion, for identifying optical phenomena in the atmosphere. It really opened my weather eyes to the topic.
2. Rainbows, Halos and Glories by Robert Greenler, 1980, Cambridge University Press, ISBN 0-521-38865-1.
More in-depth scientific explanation of atmospheric optical topics, mostly involving reflection and refraction, including the author's computer simulations of some optical phenomenon.
3. The Nature of Light and Colour in the Open Air by M. Minnaert, 1948, Dover Publications; ISBN: 0486201961.
A classic with few photographs using line drawings to discuss a wide variety of visual phenomena, giving the author's (a physicist) explanation for their causes.
4. Sunsets, Twilights and Evening Skies by Aden and Marjorie Meinel, 1983, Cambridge University Press, ISBN 0-521-40647-1.
Similar in aspects to Greenler's book but focusing mostly on sky colour phenomena. Little on the inferior or superior mirages but does discuss the setting sun distortions and has a few words on the Novaya Zemlya.
For details on mirages, their causes and properties, see
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