As the weary traveller sees
In desert or prairie vast,
Blue lakes, overhung with trees,
That a pleasant shadow cast;

Fair towns with turrets high,
And shining roofs of gold,
That vanish as he draws nigh,
Like mists together rolled,—

Henry Longfellow “Fata Morgana” (1873)

I took the photograph above in Kolyuchin Inlet, in the Russian Far East, one evening in September 2016. The curious “objects” on the horizon are not clouds, as you might at first guess, but are an example of a kind of mirage called the Fata Morgana. Here’s a time-lapse film of the same phenomenon at Lake Michigan:

In both cases, we’re seeing distant land distorted by a complex mirage effect. The ice floes in the foreground of the video give a clue to the atmospheric conditions required for the Fata Morgana—there must be a layer of air at the surface that is considerably colder than the air aloft. This situation, the reverse of the usual condition in which the air becomes progressively cooler as one climbs higher, is called a temperature inversion. In Kolyuchin Inlet and Lake Michigan, the surface air was close to freezing point, but that’s not necessary for a Fata Morgana to appear. The important thing is the change in temperature with altitude, not the absolute temperature. Indeed, the Fata Morgana got its name in the Strait of Messina, the narrow channel that separates the island of Sicily from the “toe” of the Italian mainland. It’s not an area known for its ice-floes, but it is prone to temperature inversions. The proximity of two warm landmasses separated by a narrow channel of relatively cool water means that Sicilians can often observe this mirage effect distorting the mainland hills, while the residents of Reggio Calabria can watch the same thing happen to the Sicilian coastline.

La Fata Morgana is the Italian name of Morgan le Fay, a mythical adversary of King Arthur. From her origin in the Arthurian legends of Britain and France, she arrived in southern Italy along with the Normans, who established a short-lived kingdom in the region during the twelfth century. In her new Mediterranean home, Morgan was said to inhabit a castle that floated in the air. And so her name became attached to an optical phenomenon that occasionally produces the appearance of towers and battlements where none exist.

Here’s an example from Antarctica that shows how the Fata Morgana can convert the appearance of rounded hills into flat-topped towers:

Everyone probably knows that mirages, of which the Fata Morgana is a particularly complex example, occur because light rays are following unusually curved paths through the atmosphere. It’s perhaps less well known that light generally follows a curved path through the atmosphere, induced by the drop in atmospheric pressure with height, which produces a corresponding change in the refractive index of air. This normal curvature of light rays is concave downwards, so it routinely brings into view objects that are actually below the level of the geometrical horizon. In particular, if we were to wait until the setting sun appeared to be resting exactly on the sea-level horizon, and then removed all the intervening air, we’d discover that the sun was already entirely below the “real” horizon. I’ve written a lot more about that in my post on the Shape Of The Low Sun. The curving rays also make visible distant landscape features that would be invisible below the horizon in the absence of the atmosphere.

A temperature inversion, in its simplest form, simply accentuates this natural concave curvature of light rays, as increasingly warmer air aloft further reduces the atmospheric pressure and the refractive index of the air. Such temperature inversions further delay the setting of the sun, and lift even more distant geographical features into view—for instance, the towers of Chicago occasionally pop into view from the opposite shore of Lake Michigan, a good 60 miles away. It’s been calculated that a rise in temperature of 0.11°C for every metre of altitude induces horizontal light rays to follow a path with a curvature equal to the curvature of the Earth. Under such conditions, the surface of the Earth appears flat, and an observer can see as far as atmospheric haze and intervening topography allow. There have long been speculations that this sort of “Arctic mirage” informed the early voyages of discovery in the North Atlantic—allowing the first inhabitants of the Faroes to glimpse Iceland, and the early Icelanders to occasionally discern Greenland.

But temperature gradients much steeper than the critical 0.11°C/m exist, locally and over a few tens of metres altitude, at times when the Fata Morgana is visible. Under these circumstances, light rays emitted upwards by an object on the surface of the Earth can follow an arching course that brings them down to meet the eye of an observer some kilometres away. Like this:

The vertical scale of my diagram is typically a few tens of metres; the horizontal a few tens of kilometres—so you must imagine these trajectories stretched out a thousandfold from side to side.

If the temperature increases in a roughly linear way with altitude, the trajectories of the emitted light rays are all roughly the same shape. As a result, only one ray (the red one in my diagram) connects the object to the observer’s eye. So this sort of mirage merely lifts the image of the distant object so that it appears to sit higher in the sky than usual. At the extreme, sailors traversing a cold sea with warm air aloft can get the visual impression that their ship is sitting at the bottom of a bowl. In the parlance of English-speaking mariners, this effect was aptly named looming. And it was also known to those archetypal cold-water sailors, the Vikings, who called it hillingar. (Cleasby and Vigfusson’s dictionary of Old Icelandic translates this word as “an upheaving”.) So the general phenomenon is sometimes referred to as the hillingar effect.

The Fata Morgana requires a rather more dramatic temperature gradient, however—one in which the temperature changes abruptly over a short change of altitude, at a junction called a thermocline. Like this:

The thermocline provides such a range of temperature gradients in a relatively short span of altitudes, it can deflect a correspondingly wide range of ascending light-rays downwards towards a ground-level observer, acting like a sort of mirror in the sky. Like this:

So now our observer sees two images of the same object. The lower ray (let’s call it the direct ray) may or may not produce a noticeable hillingar effect, but the upper ray (call it the reflected ray) certainly produces an out-of-place image floating above the first.

And the thermocline really does act like a mirror. Here’s a diagrammatic plot adding the trajectories of light rays originating from a higher position on our distant object (marked in red):

The direct rays maintain their relative positions on their way to the observer’s eye, so that the higher parts of a distant object appear above its lower parts, in the usual way. But the reflected rays cross each other, so that the image of the higher parts arrive at the observer’s eye from a direction lower than the image of its lower parts. So we see an inverted image hovering disconcertingly above an upright image, like this:

But there’s more. For objects at a specific distance and height above the horizon, the range of temperature gradients associated with the thermocline can deflect multiple rays from the same source into the observer’s eye. Like this:

That means that part of the direct image can appear to be smeared vertically:

This phenomenon has another name that comes to us from the Vikings—the hafgerdingar effect. The original Norse word is haf-gerðingar, variously translated as “sea-fences” or “sea-hedges*”, which certainly fits the mirage appearance. But the Vikings may not actually have been referring to the mirage that now has this name; it’s possible they were talking about some sort of real, dangerous oceanic wave. The phenomenon is only ever discussed in an Old Norse text called Konungs skuggsjá (“The King’s Mirror”), which is far from clear:

Now there is still another marvel in the seas of Greenland, the facts of which I do not know precisely. It is called “sea hedges,” and it has the appearance as if all the waves and tempests of the ocean have been collected into three heaps, out of which three billows are formed. These hedge in the entire sea, so that no opening can be seen anywhere; they are higher than lofty mountains and resemble steep, overhanging cliffs. In a few cases only have the men been known to escape who were upon the seas when such a thing occurred. But the stories of these happenings must have arisen from the fact that God has always preserved some of those who have been placed in these perils, and their accounts have afterwards spread abroad, passing from man to man. It may be that the tales are told as the first ones related them, or the stories may have grown larger or shrunk somewhat. Consequently, we have to speak cautiously about this matter, for of late we have met but very few who have escaped this peril and are able to give us tidings about it.

But whatever the original haf-gerðingar was, it’s the merging of the hafgerdingar effect with the inverted reflected image that produces the full Fata Morgana appearance, like this:

Added to this appearance of distant, fluted towers and battlements, there’s a degree of animation to the Fata Morgana, because the thermocline is never entirely still. If you watch the time-lapse video near the head of this post carefully, you’ll be able to see the occasional wave running along the top of the mirage, produced by real wind-driven waves in the thermocline itself. These produce a gentle billowing effect at the upper margin of the miraged image, which on occasion can look like banners wafting gently in the wind.

So that’s an “edited highlights” explanation of the appearance of the Fata Morgana. Proper detailed treatments are hard to come by, I find, and much of the early mathematical analysis was published in German. So my primary reference has been one of the documents published in English by the Norwegian Polar Institute in 1964, reporting the scientific findings of the Norwegian-British-Swedish Antarctic Expedition of 1949-1952. It’s entitled Refraction Phenomena In The Polar Atmosphere (Maudheim 71° 03´S, 10° 56´W), and written by G.H. Liljequist.

* I’m somewhat surprised that there’s an Old Norse word for “hedge”. It’s like discovering that the Vikings had words for “herbaceous border” and “ornamental water feature”.

---