Wegener's Blank (or Reflecting) Strip


Because rays that are trapped in a duct  cannot leave the Earth's atmosphere, an observer within the duct cannot see the Sun or other astronomical  objects in a zone of the sky, containing the ducted rays, that is centered on the astronomical horizon. Instead, this strip of sky is filled with miraged images of distant terrestrial  objects, if there are any in the duct.

This horizontal “blank strip” or “forbidden zone” was pointed out by Alfred Wegener in 1918. Wegener called it a “reflecting” or “miraging” strip when he was discussing mirages, and a “blank strip” when discussing sunsets; he says:

The reflecting strip of the terrestrial mirage … becomes a blank strip  in the solar image.

Because most of the atmosphere that scatters the light of the daytime sky is also above the duct, it too is hidden by Wegener's blank strip. Consequently, the strip usually looks dark at sunset, and is often mistaken for a cloud or fog-bank by observers.

Examples and explanations


It's hard to find good pictures of blank strips on the Web, but there are some published photographs. A particularly good example is in my paper with George Kattawar and Pekka Parviainen; we made a point of showing the difference between a real blank strip (which has constant width during the sunset, and never closes up) and a mock-mirage gap in a different sunset.

Pekka's blank-strip sunset appears on his Web pages, but you have to dig down through the menus to find them. Start with “SUN involved” images, then look for image su08032 on “Sun distortion page 2”. Or go to “Solar sequence page 2” and pick sunseq15. Because the duct was of finite length, the Sun eventually appears (seen through the far end of the duct) in the blank strip as a very dim, red image. In such cases, the duct is often described as “leaky”.

In 2016, Mila Zinkova posted a video of a blank-strip sunset at https://www.youtube.com/watch?v=38rXMlcTIB4. It nicely shows that the strip contains a superior mirage of something terrestrial — in this case, the sea surface. That mirage shows that the camera was below a strong thermal inversion, and that the duct produced by the inversion extended down to the sea surface. In addition, one can see the actual sea horizon; so the camera was in a region of normal, rather than super-refracting , ray curvature, below the inversion.

And I should emphasize that the two highly-flattened images of the Sun, starting about 3 minutes into the video, are complete (but greatly flattened) images of the whole solar disk. Notice that the image beneath the strip first appears as a double image of the lower limb, and disappears as an inverted image of the upper limb; this mirage is Wegener's Nachspiegelung . The Sun finally disappears at the top of the duct, which is Hasse's horizon surface — the upper edge of Wegener's strip.

In a sense, the strip can be thought of as an image of the duct — or, more precisely, an image of the scattering air inside the duct. At sunset, the duct is only dimly illuminated by the Sun, whose image is partly or completely blocked; then the strip looks dark. In Mila's video, the strip also includes a mirage of the low Sun's “speckle path” on the sea surface; those parts of the strip appear bright.



An animation of a ducted sunset with a prominent blank strip is here. The effects of ducting on a sunset are explained further on the Introduction to Ducts page, which shows simulated images of a ducted sunset as seen from several different heights (not just from within the duct, where the blank strip is seen).


The simulations of superior mirages contain many examples of Wegener's strip, if the target is sufficiently far from the observer. Good examples occur when the observer is in a duct, and the target distance is at least 40 km.

Ray diagrams and transfer curves

There are ray diagrams on the mirage page, including one that shows just the rays trapped in the duct. Another ray diagram, on the duct page, shows the gap between rays that pass above and below the strip. Numerous ray diagrams and transfer curves for terrestrial mirages are on the mirage simulation pages.

However, ducted sunsets present complex phenomena that are not easily explained by means of ray diagrams alone. I find it more useful to look at their transfer curves to understand them. The transfer curves used to explain the sub-duct flash are particularly interesting.


Wegener offered a highly simplified treatment of ducting, though his papers are a good place to start. However, he treated the temperature profile as discontinuous; in reality, it's not only continuous, but smooth. The smooth corners in the temperature profile guarantee that there will be heights at which the ray curvature exactly matches the Earth's curvature.

At these heights, the rays orbit the Earth, and the astronomical refraction becomes nearly infinite. The infinite refraction produces infinitely-compressed (line-like) images of the Sun, and other phenomena not foreseen by Wegener. Laplace's extinction theorem means that the extinction (and atmospheric reddening) also become very large at the edges of the blank strip. The large reddening and great compression both act to suppress the visibility of green flashes in sunsets that show blank strips.

In the real world, the atmosphere is not perfectly uniform horizontally; so real ducts have only a finite extent. If the duct is short, the observer sees a dim, strongly reddened image of the Sun appear in the strip when the true zenith distance of the Sun is large enough to shine into the far end of the leaky duct. (That's the case in Pekka's sunset mentioned above.) If the leaky duct is longer, the images of the Sun above and below the strip may have disappeared before the dim red image becomes visible in the strip. Then the isolated image seen through the duct is referred to as the Novaya Zemlya effect.

Another complication occurs when the duct is so deep that it reaches the surface of the Earth. This situation guarantees that there are terrestrial objects (though perhaps only a sea horizon) within the duct, so a superior mirage will certainly be seen. So the classical superior mirage is an example of Wegener's blank strip; the strip is often recognizable as a dark band in mirage photographs.

If the strip is so wide that its lower edge is occulted by the apparent horizon, the normal symmetry of the strip is destroyed. Then there is no Nachspiegelung  at sunset, which occurs only at the upper edge of the strip. In this case, the strip contains a loomed (raised) image of the nearby surface, and its upper part may contain an inverted image (a superior mirage) of the distant surface.

A note on terminology

Wegener called the strip ein blinder Streifen , a phrase that some people (like O'Connell) have translated literally as “blind strip”. But Wegener meant “blind” in the sense we use the word in English in phrases like a “blind hole” — i.e., one that's blocked instead of clear through: you can't see through it.

Sometimes Wegener calls the strip ein spiegelnder Streifen , which could equally well be translated as a miraging strip, or a reflecting strip, as the word spiegelnd  means both “reflecting” and “miraging”. This makes sense when talking about superior mirages, but it's not useful when discussing sunsets.

I think “blank strip” conveys the idea that the strip lacks all astronomical objects. But of course it fails to indicate the strip's action in producing mirages. There doesn't really seem to be a good English term to describe both the appearance and the actions of Wegener's strip.


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