Mirages and “Fog”

Introduction

A common illusion is the appearance of “fog” in superior mirages. The cause is the very long air-path of the strongly-refracted rays, particularly when ducting is involved. This appearance is so well known to mirage researchers that Pernter and Exner devote a few (rather confused) pages to it; a better discussion is given by Bonnelance (1929). Here's a good example, selected from Wim van Bochoven's mirage pictures: Bochoven mirage image

Image © Wim van Bochoven 2002

You'll notice the horizontal haze-like band that contains the miraged zone of the image. This band is just Wegener's blank strip, which contains superior mirages (if there is any scenery available to be reflected within the strip).

Although the strip appears lighter than the background islands in this image, notice that the reddish patch of sky visible in the “keyhole” here is darker than the sky above the strip. That's additional evidence of the increased aerosol scattering and consequent extinction within the miraged strip. Depending on the direction of viewing and the angular properties of the scattering, the strip may appear either lighter or darker than its surroundings; when it's darker, it may be perceived as a “cloud” instead of a bank of fog.

Mistaking a blank strip for a bank of fog is a common misperception suffered by mirage observers, who tend to force the distorted images of mirages into the Procrustean bed of everyday experience. So, in the examples that follow, don't take their comments about mysterious cities and impossible landscapes literally.

Examples from the literature

At sea

Let's start off with two entries from a seaman's journal:

[Jan. 26, 1774:] At nine in the morning every body on deck imagined they saw land; and accordingly preparations were made for getting all things in readiness to cast anchor. At eleven crossed the antarctic circle to the southward for the 2d time, and hauled up S. E. by E. where they were persuaded land was. But to their great disappointment, the farther they sailed, the farther the land seemed to bear from them; and at length it wholly vanished.
[Jan. 30, 1774:] Came in sight of a fog bank, which had a great appearance of land, and many who were thought the best judges asserted that it was land; however it proved upon trial a deception, as well as the former. … Taking a view from the mast-head nothing was to be seen but a dreary prospect of ice and sea. Of the former might be seen a whole country as far as the eye could carry one, diversified with hills and dales, and fields and imaginary plantations, that had all the appearance of cultivation; yet was nothing more than the sports of chance in the formation of those immense bodies of congregated ice.

Now, a few years later (in June, 1787), we find Jean François Galaup de La Pérouse sailing at a latitude of about 44° off the coast of the Sikhote-Alin mountain range, ENE of present-day Vladivostok, looking for the Northwest Passage. Here's his report, in the official English translation:

The 15th and 16th were very foggy. We sailed along the coast of Tartary at no great distance, and had sight of it at intervals, when the fog dispersed a little; but the 16th will be distinguished in our journal by the most complete illusion that I ever witnessed since I have been at sea.
At four in the evening the most beautifully clear sky succeeded the thickest fog. We discovered the continent, which extended from west by south to north by east; and very soon after, to the south, an extensive land, running west towards Tartary, so as not to leave an opening of 15° between it and the continent. We distinguished the mountains, the valleys, and all the particulars of the land; and could not conceive how we had entered into this strait, which could be no other than that of Tessoy, the search after which we had given up. In this situation I thought it advisable to haul our wind, and steer south-south-east. But soon these hills and valleys disappeared. The most extraordinary fog-bank I had ever beheld was the cause of our illusion. We saw it disperse; it's shapes, it's colours, ascended, and vanished in the region of clouds; and we still had day-light enough left to remove every doubt about the existence of this fantastic land. I sailed all night over the space of sea it had appeared to occupy, and at day-break nothing of it was visible, though our horizon was so extensive, that we distinctly saw the coast of Tartary upwards of fifteen leagues distant.

A little later, in 1802, we find William Beauford commenting on the Fata Morgana:

Also far out at sea, in the midst of the Atlantic and Pacific oceans, the adventurous mariner sometimes observes them; and though well known under the name of fog banks, yet has their appearance been so imposing as to illude the nicest scrutiny, and to promise refreshments to the fatigued and sea-worn mariner which he could not obtain.

Thirty years later, in the first of a series of perceptive papers on mirages, Dr. William Kelly noticed that “There was generally with the mirage an appearance of a fog bank on the horizon … . The air within the horizon was at the same time perfectly clear.”

Skipping ahead a century, we have another nice mirage tied to “fog”:

At 8h. on August 17th, … although it was perfectly clear and sunny where I stood on the shore, there was an extensive layer of fog at the scene of operations, about three miles out, and only the smoke of the Empress was visible above the layer. … I was startled to see the Empress above the fog completely upside down with her hull pointing skywards and her masts apparently resting on the layer of fog. The illusion lasted for about one minute and was perfectly clear in every detail when it finally disappeared and the ship came out of the fog in its normal position.

On land

Similar reports come from land-locked observers. Here's one from the Red River, on the border between Minnesota and North Dakota, thousands of kilometers from the sea (Upham, 1895):

A more complex and astonishing effect of mirage is often seen from the somewhat higher land that forms the slopes on either side of the plain. There, in looking across the flat valley a half hour to two hours after sunrise of a hot day following a cool night, the groves and houses, villages and grain elevators, loom up to twice or thrice their true height, and places ordinarily hidden from sight by the earth's curvature are brought into view. Occasionally, too, these objects, as trees and houses, are seen double, being repeated in an inverted position close above their real places, from which they are separated by a very narrow, fog-like belt. In its most perfect development the mirage shows the true upper and topsy-turvy portion of the view quite as distinctly as the lower and true portion; and the two are separated, when seen from land about a hundred feet above the plain, by an apparent vertical distance of 75 or 100 feet for objects at a distance of 6 or 8 miles, and 300 to 500 feet if the view is 15 to 20 miles away. Immediately above the inverted images there runs a level false horizon, which rises slightly as the view grows less distinct, until, as it fades and vanishes, the inverted groves, lone trees, church spires, elevators, and houses at last resemble rags and tatters hung along a taut line.

(These dimensions correspond to angular heights of 8 to 16 minutes of arc — very typical for superior mirages.)

Here's another from Nebraska, in the middle of the North American continent (Skelton, 1941):

When a gray, rather smoky and unnatural-appearing cloud lies along the horizon in the early morning, it is generally mirage material. Such a cloud will usually form into a clear cut mirage before the morning passes.

Terminology

The illusion of fog is so common that Hurd, on the back of a 1937 Pilot Chart for mariners, devotes considerable attention to what he aptly calls “mock fog and haze bands”. Hurd's term “mock fog” is certainly preferable to the expression “dry fog” that one often encounters — as in Antoine d'Abbadie's interesting account of it in the Ethiopian desert:

All the Ethiopian languages have a special word to designate it and to avoid paraphrases. We take from one of the most ancient of these languages the specific name of qobar. … The people of Ethiopia compare it to smoke, and, in fact, it is almost always accompanied by a great dryness … . Seen from afar, at the limits of the horizon, the qobar seems disposed in layers, most often horizontal, with sharp edges, without irregularities, and so dense that the sun is eclipsed by it as behind the most opaque screen. Thus, in Ynarya we saw, on the 24th of January 1844, the setting sun disappear completely behind a bank of qobar which thus became negatively visible.

This is evidently just the blank strip occulting the Sun. He continues: “This layer of dry vapors had a slight refraction of red light on its upper surface while the star was hidden behind it,” — a phenomenon shown in some of my simulations. He adds:

The most striking character of our meteorological phenomenon, aside from the enormous dryness that always accompanys it, is its ability to extinguish light. …
In the twilight one sees the qobar at the horizon, sometimes at isolated points, sometimes all around it, and producing the appearance of an opaque livid and motionless cloud … . In its lower part, the qobar is so dispersed on the ground that the eye cannot suspect the place of the natural horizon. A mountain 15 miles distant, with a large head, … disappears under a weak qobar, not only in the telescope, but even to the naked eye, which penetrates this phenomenon much better than the best instruments of optics. With a stronger qobar we see confusedly, at the feeble distance of a mile, and the landscape becomes veiled as by a distant fall of snow.

He also says that a qobar seen over a lake “resembled a white powder, like that which follows a cavalry charge.” Evidently the extinction in Ethiopia was greatly enhanced by dust.

Explanation

Why does the blank strip often look like fog? Take a look at the paths of the ducted rays: they follow the curve of the Earth as far as the duct extends — often hundreds of kilometers. Ducted-ray diagram

If there's an object, such as a mountain, in the duct, it may lie well beyond the observer's normal horizon. So there's enough path length between the observer and the mirage to make even a little aerosol scattering in these low-lying layers obvious.

Furthermore, the rays oscillate up and down within the duct, and may pass close to the Earth's surface at their perigee points. But the aerosol tends to be concentrated toward the surface; so these ducted rays tend to pass through some of the haziest layers along the way.

For example, take another look at Wim van Bochoven's pictures: the very first one clearly shows how the aerosol is concentrated toward the surface of the sea. The ducted rays have to pass through this hazy layer on their way from the miraged objects to the observer's eye. In fact, because a ray that reaches the top of the duct also reaches the bottom of the duct, well below the inversion that produces it, the top edge of the blank strip (i.e., the top of the miraged zone) is likely to be the haziest part of the scene. In any case, the sharp discontinuity at the top of the strip tends to make the contrast between the hazy strip and the clearer air above it quite obvious, if the path length is long enough.

If the observer is high enough to make the bottom edge of the blank strip visible (as in the ray diagram above), the discontinuity between that edge and the relatively nearby landscape visible below it again emphasizes the opacity visible in the strip. If, as in the picture shown at the top of this page, the observer is so low that the lower edge of the strip is occulted by the sea horizon, there is still some contrast there. In either case, the opacity visible in the strip contrasts with the region below it, as well as above it. Either way, it's easy to mistake the hazy blank strip for a bank of fog.

We don't see these effects in inferior mirages, because there (a) the horizon is nearer than normal, rather than farther away; and (b) the image has no sharp discontinuity like that at the top of the blank strip. Furthermore, the inferior-mirage rays rapidly separate from the Earth's surface beyond the apparent horizon, so there isn't the long path available at low elevations for scattering to make its presence obvious, as there is in superior mirages.