A green-flash reading list

Here are a few books and magazine articles that have interesting and/or useful information about green flashes. I have some reservations about most; so there will be many critical comments. Don't believe everything you read, especially about green flashes. A look at my page of fallacies and misconceptions may be useful.

Please note that the references listed here are a tiny fraction of the full green-flash literature. At the end of this page, you will find links to my full GF bibliography, which contains over a thousand references. The purpose of the present page is to recommend the cream of the crop to anyone who is interested in learning more about these beautiful phenomena.

Note: Italicized  links lead to the Glossary ; boldface links lead to the bibliography, and will take a while to load. To see why I am trying this system, see the discussion of typographical conventions.


M. E. Mulder
The ”Green Ray” or ”Green Flash” (Rayon Vert) at Rising and Setting of the Sun
(T.Fisher Unwin, Ltd.; London; 1922)

The first-ever book on the green flash. Mulder was an emeritus Professor of Ophthalmology, so his remarks about the safety of looking at the setting Sun are authoritative. He quotes most earlier writers in extenso and verbatim, translating only the Dutch, and leaving the French and German articles in the original, “because I suppose that those, who read this booklet, will be able to read these modern languages. Therefore I think it better to quote them in the original.”

Mulder's book is important because it was he who first introduced the three-fold classification of the observations into the green rim , the green segment , and the green ray  that shoots up from the horizon. This trinity was propagated widely by Minnaert (see below), who relied chiefly on Mulder's book for his own better-known treatment. Unfortunately, O'Connell (see below) was unable to obtain a copy of Mulder's book, and so misunderstood some of the earlier literature (particularly regarding the “green ray”).

If you read Mulder, be aware that green flashes come in more flavors than he supposed. Most of the observations he reviews were made near sea level, so his “green segment” category is mostly made up of inferior-mirage  flashes. But there are also mock-mirage  flashes, and other kinds. However, his recognition of a “green ray” category remains valid.

Mulder's book is frustrating to use because it lacks an index. This lack has now been partly rectified by Stephen Williams, who made a list of all the references in the book; I have converted this to a rough author index. The book is also irritating to use because of many incomplete references and (mostly) minor typos; these are detailed in the errata.

Mulder was one of the first technical writers to be taken in by Jules Verne's fictitious “legend”, which was picked up from him by Feenstra Kuiper, and from both by Minnaert; and almost every writer since has continued to propagate this “urban legend”. Shame on them all!

Walter Nissen has managed to get Mulder's book included in Google Books; the URLs are included at the end of its bibliography entry.

M. Minnaert
The Nature of Light & Colour in the Open Air
(Dover Publications, New York, 1954)

Minnaert's book had been translated from the original Dutch much earlier, but the Dover paperback reprint of the 1940 London edition disseminated it very widely; and it is probably from Minnaert that most people have first learned of the green flash. Minnaert had obviously not seen very many flashes, for he confuses forms that had been recognized as separate by Joule in 1869, and (by his own admission) his account is based almost entirely on Mulder's book and Pieter Feenstra Kuiper's dissertation. For example, Lagaaij's drawing in Minnaert is reproduced from Feenstra Kuiper's thesis. (It is reproduced in color by Meyer (1942–1961) in his review in Handbuch der Geophysik .)

Because of his obvious lack of familiarity with green flashes, I cannot recommend Minnaert's account. The illustrations are all in black and white in the Dover edition. A newer translation,

M. Minnaert
Light and Color in the Outdoors
(Springer-Verlag, New York, 1993)

is available, but it hardly seems an improvement — especially as most of the few useful green-flash references given in the Dover edition have vanished entirely in the newer one, having been replaced by such useless citations as Jacobsen's rather misguided efforts. Dietze's important paper is overlooked entirely. However, the new edition has illustrations in color, including one nice GF photo by Pekka Parviainen, and has fairly good coverage of mirages . Still, the text is still rooted in the 1920s and shows little comprehension of the physics of green flashes. And he believes Jules Verne's phony “legend” as well.

Both the old and the new editions have some errors that should be corrected.

Despite all the critical remarks above, Minnaert's book is generally a delight to read. I was pleased to see from a recent Dover catalog that the old Dover edition is still available for only $9.95 — so anyone with any interest in the phenomena of atmospheric optics can still obtain a copy very inexpensively. If you don't have one, buy it.

I was also happy to see that Leo Molenaar is writing a biography of Minnaert.

D. J. K. O'Connell
The Green Flash and Other Low Sun Phenomena
(North Holland, Amsterdam, 1958)

The text is not very informative, though this is the “standard” work today on the subject. It is an uncritical recounting of previous works, without much physical insight. But the main aim of the book was to publish the pictures taken from the Vatican Observatory at Castel Gandolfo, 450 m above the sea. Thus the phenomena shown here are not  those seen from near sea level, and the view is somewhat parochial. Given these limitations, it remains the best published collection of green-flash observations today.

Unfortunately the colors are often rather poorly reproduced, so even the color photos do not prepare the visual observer for the vividness of real green flashes. These seem to be the first pictures reproduced  in color; some earlier color photographs are mentioned on p. 24.

Two major weaknesses to beware of here: (1) O'Connell erred in supposing the solar distortions in the pictures arose in the upper atmosphere; actually, they are all produced in the marine boundary  layer. (2) O'Connell copied Feenstra Kuiper's misunderstanding of Wegener's theory of thermal inversions . Consequently, all the phenomena called “blind strips” in the photo captions are in fact mock mirages ; see our paper in Applied Optics  36, 2689 (1997) for an explanation of the differences.

O'Connell's references are very incomplete, as he did not search the meteorological literature. They also contain a surprising number of errors; see the errata.

Jim Mosher points out to me that the ADS has digitized O'Connell's book — but alas! they have turned all the colored plates into high-contrast black-and-white images, almost completely without a gray scale. All that survives is the text, which is nearly useless — especially without the photographs in usable form.

Many people recall seeing O'Connell's much shorter article in Scientific American  202, 112–122 (1960), which presents just a few of the pictures from the book. Despite the popularity of the Scientific American  article, I strongly recommend the book, which shows many more of the Vatican Observatory photographs. The strength of the Vatican work lies in the variety of the observational data they have published, not in the text. The pictures are so useful that I have a special page to explain them in detail.

Robert Greenler
Rainbows, Halos, and Glories
(Cambridge Univ. Press, Cambridge, 1980)

One of the best books on atmospheric optics around. The treatment of green flashes isn't bad, but I disagree with his statement (p.177) that “All are variations of the same effect and all, in my judgment, may appropriately be given the same name.” The use of a single name (“the green flash”) for several quite different phenomena has fostered untold confusion; the detailed optics of the various kinds of flash are really quite disparate. Fooled by Jules Verne; he even has a section called “The green flash legend”! Nice pictures, though. Ch. 7 and Plates 7–10 and 7–11 show distorted sunsets.

It's hard to believe that Cambridge University Press was dumb enough to let this go out of print! Fortunately, Greenler has acquired the rights to his book and has re-published it under another imprint.

A. Meinel, M. Meinel
Sunsets, Twilights, and Evening Skies
(Cambridge University Press, Cambridge, 1983)

Probably as good a treatment of the green flash as any in print today, though it's marred by numerous errors in references (and by the authors' very haphazard reading of the literature). They recognize the importance of visual adaptation in sunset flashes. There are some good GF photographs; the Vatican Observatory pictures shown here are much better reproduced than in O'Connell's book.

The Meinels have dug up the second-oldest reference to a green flash known. Unfortunately, their citation is so garbled one can hardly find it in a library without help; the correct reference is

Sir George Back
Narrative of an expedition in H. M. S. Terror, undertaken with a view to geographical discovery on the Arctic shores, in the years 1836–7
(J. Murray, London, 1838) p.191

While Sir George Back's account is the earliest known specific account of a green flash, it isn't the earliest account published. Currently, that record is held by a rather vague 1829 report by a British sailor, known only by his initials. “W. H.,  R. N.” recalled having once

… noticed the last ray of the setting sun, … which was of a bright emerald green.

He also mentions “the green appearance sometimes observable on each side of the setting sun”, so I suppose he had made sextant sights on the setting Sun. These observations at sea are the earliest ones I know of.

D. K. Lynch, W. C. Livingston
Color and Light in Nature , 2nd ed.
(Cambridge Univ. Press, Cambridge, 2001)

More pictures, but less explanation, than Greenler's book. The illustrations are gorgeous; the text of the 1995 edition suffers from many small errors, A revised (2001) edition is available, with better coverage of green flashes, and improved text. Worth buying in any case.

These last three books show how good Cambridge University Press is at color printing; none of the other books can touch them. The illustrations in all 3 are superb!

You may think I've overlooked your favorite textbook reference on green flashes. Before complaining to me about this, please take a look at the list of textbooks in the full list of references. In particular, I do know about Bowditch. If, after checking the full bibliography, you find I really have missed something you know about, please let me know.

Popular Articles

The articles listed here have been chosen mainly because they show good color photographs of green flashes. The text ranges from fair to poor, as it is generally derived from the (already unreliable) secondary sources mentioned above.

P. W. Kemp
“The elusive green flash”
Pacific Discovery , 42 (3), 16–21 (Summer 1989)

Very nice color photos showing the two main kinds of green flash. Misled by the secondary sources into believing Verne's “legend.”

Mark J. Coco
“Stalking the Green Flash”
Weatherwise  49, no.6 (Dec. 1996/Jan. 1997) 31–34 (1996)

Beautiful photographs of green flashes in a variety of geographical settings taken by Kenneth Langford. There is some discussion of how to photograph GFs in the text, but also some errors.

A. T. Young
“Sunset spectacular”
Ocean Navigator  No. 83, 86–91 (July/August 1997)

OK, I'll add some of my own pictures to the list. You may not find Ocean Navigator  easily; it's a magazine for yacht owners, and few libraries seem to carry it. But they did a good job of reproducing my pictures. A slightly shorter version of this article has been reprinted as

“Green flash: sunset spectacular”
Professional Mariner  No. 30, 79–82 (Feb./March 1998)

in Ocean Navigator 's sister magazine for the maritime industry, published by the same company.

My best GF photo also appeared on the cover of the June, 1998, issue of Weather , with a short (500 words) writeup telling some of what I knew at the start of 1998. This magazine is probably more widely available than the other two.

That picture, along with my inferior-mirage  GF photo that's here on the Web, was also published in my article

“Green flashes and mirages”
Optics and Photonics News  10, no.3, 31–37 (March 1999)

together with a brief explanation of the optics of green flashes and some simulations. This is a semi-technical article intended for an optics audience, but anyone with a little technical background can probably follow most of it.

If you read Dutch, an article of mine also appeared in the June, 1999, issue of Zenit , containing both photographs and simulations of inferior-mirage and mock-mirage flashes. The reference is

“De groene flits, hemelsverschijnsel tussen wal en schip”
Zenit  26, nr. 6, 248–254 (Juni, 1999)

I'm pleased to say the pictures turned out well. Though I have placed an approximate English translation on the Web, the photographs (not to mention the whole layout) look much better in the printed version; so — as you are unlikely to be near a library that carries the magazine — you might want to write to their publisher and buy a copy of the June, 1999, issue, even if you don't read Dutch.

This article also prompted Mr. C. Booy to write a most interesting letter to Zenit, in which he tells a wonderful story about P. Feenstra Kuiper. He was privileged to hear Feenstra Kuiper talk on our subject, half a century ago. I have added a translation of this letter to my pages.

I finally got my technical paper on visual effects in green flashes published:

A. T. Young
“Sunset science. III. Visual adaptation and green flashes”
JOSA A 17, 2129–2139 (Dec. 2000)

You can see the preprint version here. It contains a couple of my more recent GF photographs.

The articles given above show a variety of green flashes. The ones below typically show just one or two, but are cited here to provide additional examples. Let's start with some movie frames taken by Dennis di Cicco at Cape Velas, Costa Rica:

(editorial summary)
“Observations of the Green Flash”
Sky & Telescope  48, 61–63 (1974)

There are also images of the green rim photographed by George Ripley, and an inferior-mirage  GF photographed by Paul Travers at Puerto Vallarta , Mexico.

Elizabeth Stone
“The Green Flash”
Oceans  16, no.5, 13 (Sept./Oct. 1983)

This shows a nice inferior-mirage  flash flanked by tropical cumuli limned in red — a very pretty picture. For a similar picture, see Aqua (1997), cited below.

(editorial summary)
“Bidding the day adieu”
Sky & Tel.  74, 680 (1987)

Sunset photographs and green flashes by Pekka Parviainen, and sunset photographs by Lee Coombs, Los Osos, CA, showing a good hourglass and extinction  effects.

Photographs by Kenneth A. Barbone at Pismo Beach and Rincon Point, CA. The inferior mirage  is plainly visible in the first photo.

[Observer's Notebook]
“The green and blue flash”
Sky & Tel.  87, No.2, 110–111 (1994)

A. M. MacRobert
“Beating the seeing”
Sky & Tel.  89, No.4, 40–43 (1995)

A sunset photograph by Marc J. Coco — green corners on a small segment. This seems to be a weak mock-mirage flash.

You'll notice that Sky and Telescope  publishes green-flash pictures fairly often.

“Take This, You Green Flash Skeptics” (in Flotsam & Jetsam Dept.)
Aqua (Premier issue) 1, p. 22 (1997)

A picture remarkably like the Stone photograph in Oceans  (1983); see above. Here one clearly sees the miraging of the clouds beyond the horizon, at the same altitude in the sky as the flash. Taken by Steven Businger.

Technical Articles

If you have a technical background, and want to learn the nuts and bolts of green flashes, here are a few basic references. Anyone who wants to be a green-flash expert needs to read all  of them. This list is by no means complete, but at least it provides pointers to the most essential works in the field.

Before giving the list, I must say that anyone who wants to understand green flashes needs to see several dozen flashes personally, from at least three widely different heights above sea level, to have some appreciation of the variety of phenomena under discussion. Many observers are rather inept with words, and give verbal descriptions of what they have seen that are nearly impossible to understand until you have seen similar displays yourself. The pictures on the Web, and in the books and popular articles cited above, are also helpful.

I suppose you will have read everything cited above before venturing into the territory charted below. Start with Mulder's book, which is very readable, but deals only with flashes seen from near sea level. Then read O'Connell, paying more attention to the pictures than the text. The Vatican photographs show what can be seen from a considerable height, and complement the sea-level reports.

Next, read the “anomalous” reports singled out by

Rare Halos, Mirages, Anomalous Rainbows and Related Electromagnetic Phenomena
(Sourcebook Project, Glen Arm, MD, 1984)

His method, like Mulder's, is to quote items he has found, and comment on them briefly. He lists 42 references (without a single error that I can find), thus (roughly) bringing Mulder's approach up to 1984. As Mulder's theme was that the afterimage explanation was wrong, Corliss's is that the simple textbook explanation is inadequate. He has many good examples (and a couple of duds.)

Then look at the rest of the pictures mentioned above, and you are ready for some serious reading.

NOTE: Green flashes are interdisciplinary phenomena. This means that you must be willing to read technical literature outside your field, whatever it may be. Astronomy, boundary-layer meteorology, hydrography, atmospheric optics, visual physiology, and other fields are involved. Some hard work will be required!

Probably the best place to start is Willard J. Fisher's review article

Low-Sun phenomena — IV. The “Green Flash”
Popular Astronomy  29, 251–265 and 382–392 (1921).

Fisher had already drawn the distinction between sunsets with inferior mirages (when the water is warmer than the air), and cold-water sunsets (which involve thermal inversions). He found that the first kind, which he called type A, is associated with the flashes seen from near sea level.

Ignore Fisher's fascination with the colors of individual flashes, and concentrate on his distinction between “Type A” and “Type B” sunsets. Pay attention to his comments about mirages (these are the inferior mirage and not, as Feenstra Kuiper thought, Wegener's superior-mirage  phenomena.) Fisher's work is insightful, but not very clearly presented.

There are about a dozen errors in Fisher's references.

S. W. Visser's very clearly written article

Dutch observations of the green flash
Pub. Astronomical Soc. Pacific  42, 336–339 (1930)

gives a better summary of Feenstra Kuiper's thesis than F.K. did himself in JBAA, partly because it omits the parts that are wrong. It also gives a brief synopsis of Nijland's crucial solicitation of observations from Dutch seamen. This essentially completes the observational side of the matter as far as the classical “last glimpse” (inferior-mirage flash) is concerned.

A remarkably insightful discussion of green flashes was given by

Carlo Bonacini
Sul fenomeno del “Raggio Verde„
Pubblicazioni dell'Osservatorio Geofisico dell'Università di Modena  No. 39, 115–130 (1927)

(No.39 of the Pubblicazioni is entitled NEL PRIMO CENTENARIO DALLA FONDAZIONE DELL'OSSERVATORIO - 1827 – 1927, according to Luca Lombroso.)

Bonacini recognized the connection between thermal inversions and mock-mirage flashes. He also observed the spectrum of the green rim visually; realized that the phenomena are complex and depend on several factors, so that the textbook explanation is inadequate; realized the contribution of visual effects to what is seen; and connected sunset distortions, green flashes, and mirages. This is a thoughtful and insightful discussion, even though he believed that water vapor played an important part in producing the green color, and laid heavy emphasis on the variability of the rain bands in connection with his GF observations. Note that he discovered that "spikes" on the upper limb occur at the same altitudes as indentations in the lower limb, and associated these with inversion layers, 30 years before O'Connell! (Compare his Fig. 3 with O'Connell's pp. 135 and 137.)

Carlo Bonacini realized that the conventional explanations were too simplistic; so he wisely refrained from trying to explain all this complexity himself. He was fortunate in making most of his observations from heights around 40 meters above sea level, which allowed him to observe both inferior-mirage and mock-mirage flashes. This is really one of the finest papers ever published on green flashes, and was far ahead of its time. Even today, few people understand as much about green flashes as Bonacini did. This paper needs to be rescued from its undeserved obscurity.

I have listed the observational papers first, because — particularly for such a poorly understood matter as green flashes — it is best to be aware of the facts  before engaging in speculation. In any case, observations are reality, and theories are often little more than speculation.

I suppose you will have read a textbook account of astronomical refraction, such as Newcomb or Smart, before venturing into the theory. (Newcomb is more detailed; Smart is easier for novices; so I suggest reading Smart first, then Newcomb. Unfortunately, I no longer regard these accounts as favorably as I once did: Newcomb's contains some errors, and Smart's traditional approach is not as illuminating as one would like. So I have written a tutorial introduction of my own, which I would suggest reading before either of these standard references. It's a more formal version of my Web page aimed at understanding refraction better.) But these are aimed at astronomers, who seldom work near the horizon; therefore, they should be supplemented by reading

A. Fletcher
Astronomical refraction at low altitudes in marine navigation
J. Inst. Navigation (London)  5, 307–330 (1952)

This is a really superb review of refraction near the horizon . Furthermore, Fletcher is concerned with navigational accuracy, which is a couple of tenths of a minute of arc — similar to the 0.1 minute suggested by Wegener as the useful accuracy in mirage work. There is no mention of mirages, or green flashes; but the clarity and thoroughness of the presentation make this paper a necessity.

Arthur Rambaut's article in Symons's Met. Mag.  41, pp. 21 and 41 (1906) was largely quoted by Mulder; but if you (like O'Connell) were unable to lay hands on Mulder, go and read it to see the standard “straw-man” theory. Note that Rambaut did not cite any works published outside Great Britain; nor did he know of Winstanley's work, which he duplicated (less well than Winstanley had done, however).

This curiously insular paper was the basis for the younger Rayleigh's papers, written before he had ever seen a green flash. Rayleigh's 1930 paper was cited by Minnaert, and so forms the basis for the widespread (but incorrect) impression that normal refraction alone might explain the phenomena. (See my simulations of this model to see that it can't.)

The inadequacies of this standard theory were thoroughly exposed by Gerhard Dietze in his excellent paper

Die Sichtbarkeit des „grünen Strahls”,
Zeitschr. f. Meteorologie  9, 169–178 (1955).

Dietze showed quantitatively  that the simple model produces a flash too small and faint to be seen by the unaided eye. The obvious implication (supported by careful observations by John Evershed in the 1920s — see his letters to Nature  cited by O'Connell — as well as by Fisher's careful study) is that mirages or mirage-like phenomena must be involved in all naked-eye flashes seen at or below the astronomical horizon. Indeed, this is evident when you go back and study the photographs of green flashes, all of which involve double images of the Sun's upper limb. In many cases, the miraging of terrestrial objects, or of clouds near the Sun, is also apparent.

Dietze's paper is by far the most careful examination of the normal-refraction model ever published. It is required reading for anyone who wants to advance the field. Subsequent papers along the same line by Shaw (1973) (cited by Greenler and later writers), and especially that by Menat (1980), are quite deficient by comparison.

Having established that mirages are important, let's take a look at the mirage literature, which is also very extensive. Two papers of particular significance for the green flash are those by Alfred Wegener, the father of continental drift:

A. Wegener
“Über die Ursache der Zerrbilder bei Sonnenuntergängen”
Beitr. Physik d. freien Atmos.  4, 26–34 (1912)

A. Wegener
“Elementare Theorie der atmosphärischen Spiegelungen”
Annalen der Physik  (4) 57, 203–230 (1918)

These are both very readable papers; so clearly is the material presented that I would have thought it impossible for anyone to misunderstand. Alas, I was wrong: Feenstra Kuiper got the business of the “reflecting strip” due to an overhead thermal inversion completely screwed up, somehow got the notion that it could reflect the Sun instead of the Earth, and proceeded to develop a completely mistaken picture of sunset phenomena from it.

From Feenstra Kuiper, both Minnaert and O'Connell picked up the error, evidently without ever bothering to read Wegener's papers. So the phenomena O'Connell identifies as Wegener's “blind strips” (a better translation might be “obscured strip”) are in fact all  mock mirages; see

A. T. Young, G. W. Kattawar, P. Parviainen
“Sunset Science. I. The Mock Mirage”
Appl. Opt.  36, 2689–2700 (1997)

for details. This episode should serve as an object lesson to people who merely copy references from other people's papers, instead of actually reading  the papers they cite.

This brings us to Pieter Feenstra Kuiper's dissertation:

P. Feenstra Kuiper
De Groene Straal
(C. de Boer Jr., Helder, 1926)

This is hard to obtain; evidently only a few copies were originally printed. It is noteworthy for the colored version of Lagaaij's “green-ray” observation (also reproduced in color by Rudolf Meyer in his Handbuch der Geophysik  review, but only in black and white in the old edition of Minnaert's book — and not at all in the newer one.)

However, for the serious student of green flashes, it is an essential reference. Not only is it a pivotal work, having influenced Minnaert and O'Connell (and through them, many others); it is the largest single repository of green-flash observations, numbering many hundreds in all.

He also has combed through Mulder's book for references, and combined them with those listed by Fisher. However, be careful: the reference list is full of errors; see the errata.

Dutch isn't a language much taught in schools outside Holland and Belgium; but it can be read (with the help of a dictionary) by anyone with a good knowledge of English and German. The grammar is like German, but simpler; the spelling is often closer to English, for words with common roots. Not only this thesis, but the numerous important GF papers that have appeared in Hemel en Dampkring  over the years, make the effort to learn some Dutch well worth while for anyone who is serious about understanding green flashes.

Please note, by the way, that Feenstra Kuiper's last name really is “Feenstra Kuiper” (as his compatriots Minnaert and Visser correctly call him), and not just “Kuiper” (as O'Connell and nearly everyone else calls him); and certainly  not “Keuper” as the Meinels have him in their book — an error they obviously picked up from the unreliable Miss Botley's article in Weather  26, 354 (1971). This is yet another example of the sloppy scholarship of people who don't take the trouble to look up the actual references, but copy the mistakes of others.

While we're thinking about Dutch and Feenstra Kuiper's thesis, it's worth taking a look at

B. G. Escher
“De Groene Straal”
Tijdschr. Kon. Ned. Aardr. Gen. (2) 47, 602–609 (1930)

who comments (in Dutch, of course) on Feenstra Kuiper's work. This paper supplements F.K.'s thesis in two interesting ways: first, by actually plotting the geographic distribution of the Dutch sailors' GF observations; and second, by adding a remarkably detailed “green ray” observation of his own (which he classifies as a “green column.”)

Escher (brother of the well-known artist M. C. Escher) also makes some very sensible comments. For example, he attempts to re-classify the various types of flashes, drawing the important distinction “between the phenomena that are seen on the Sun itself, while it still (or already) stands above the horizon, and the phenomena that appear immediately after the Sun has set or just before it has risen;” although he prefaces this attempt by saying that only “someone who has made very many observations himself and moreover is sufficiently educated in the natural sciences” should undertake a complete classification. (As he himself was a geologist who had made only 4 GF observations, I took this comment to be a modest apology for his essay in classification).

Finally, as the map shows that most of the observations in Feenstra Kuiper's thesis were concentrated in the Red Sea, the Gulf of Aden, and the south-eastern Mediterranean, Escher draws the very reasonable inference that “the frequency of the green ray observations is greatest in the regions where the precipitation is the least, that is, where the shipping routes pass near or between deserts.” So he concludes that “a dry climate is favorable for the appearance of this very remarkable phenomenon.” This is contrary to Feenstra Kuiper's conclusion that absolute humidity favors the flash (a conclusion I think is quite weak); but perfectly reasonable, given what we now know about green flashes — namely, that they are associated with mirages and hence are favored by conditions that offer large variations in air temperature.

Well! You won't believe the vehemence of Feenstra Kuiper's reply to this (on p. 868 of the same volume). He must defend himself against this unreasonable criticism; who is this geologist  to criticise the works of astronomers; how can he criticise a work containing hundreds of observations when he himself has made only four; and besides, I proved  that humidity was the most important factor in my thesis; etc., etc. You never saw such a wounded ego in print in your life. Maybe this over-reaction helps explain why we never seem to hear from Feenstra Kuiper again. Anyway, it is an interesting as well as a dramatic exchange; read these papers and judge for yourself. And, for an additional view of Feenstra Kuiper, see Cor Booy's letter to Zenit; I have provided an English translation of it here.

Now, back to mirages for a bit. There are no really good reviews of mirage theory. There are fairly good introductions to the observational side of mirages, however. Perhaps

W. J. Humphreys
Physics of the Air , Third Edition
(McGraw-Hill, New York, 1940)

gives the best descriptive introduction in English, and the articles by Bravais (1853) and Bonnelance (1929) are the best in French; though

J. M. Pernter, F. M. Exner
Meteorologische Optik  (second edition)
(Wilhelm Braumüller, Wien und Leipzig, 1922)

is the canonical treatment of the subject, with a little basic theory. I have already mentioned Wegener's papers, which give good insight into the simple view of inferior mirages and simple superior mirages as reflection phenomena. But be careful: these mirages really are not reflection phenomena, as Pernter & Exner (among many others) show.

An equally lucid treatment of a 3-image mirage is given by

A. Schmidt
Die cyklische Refraction
Programm des Königl. Realgym. Stuttgart , pp. 1–31 (1878)

which refers to Kummer's marvelously original paper. A more detailed, though less pedagogical treatment, is contained in two major works by Hillers:

W. Hillers
Einigie experimentelle Beiträge zum Phänomen der dreifachen Luftspiegelung nach Vince
Physik. Zeitschr.  15, 304–308 (1914)


W. Hillers
Theoretische und experimentelle Beiträge zur Aufklärung des dreifachen Bildes einer Luftspiegelung
    = Abhandlungen aus dem Gebiete der Naturwissenschaften  20, No. 2, 1–55 (1914)
(L. Friedrichsen & Co., Hamburg, 1914) pp. 1–55

Papers since then have been either superficial, or highly specialized. The complete bibliography contains over 400 papers on mirages, mostly observational; but there is a section on Mirage Theory as well.

Because there are many inaccurate explanations of mirages on the Web, I have added a mirage page here.

And because the most vivid mirage displays have attracted the most attention, I have also added a long page devoted to the Fata Morgana..

Spectra of the green rim (but not of green flashes per se ) were extensively photographed by Danjon and Rougier:

A. Danjon, G. Rougier
“Le rayon vert, étude spectroscopique et théorie”
Ann. Obs. Strasbourg  1, 105–115 (1926)

Unfortunately, their study led them to disbelieve the existence of flashes longer than a few seconds; actually, several over 10 sec are very well substantiated.

For actual green-flash spectra, one must turn to those observed visually and accurately drawn by Dijkwel:

N. Dijkwel
“Enige waarnemingen van de Groene Straal, verricht op een heen- en terugreis naar Ned. Indié”
Hemel en Dampkring  34, 235–239 and 258–262 (1936)

Dijkwel's spectra accord well with those of Danjon and Rougier, however. One can clearly identify the telluric absorptions Dijkwel documents with increasing airmass. Dijkwel's spectra clearly show that the orange part of the spectrum is attenuated by ozone — a fact O'Connell seems to have been reluctant to accept. Note that Dijkwel's drawings were reproduced and cited by Minnaert.

Reading the references given above will give you the basis for contributing something to the study of green flashes. They should at least provide a decent perspective from which you can read the remaining hundreds of papers cited by Mulder, Fisher, Feenstra Kuiper , and O'Connell.

I have not touched upon a number of side issues, such as the recurrent futile attempts to explain GFs as afterimages. The matter of visual-system effects in sunset flashes is dealt with in some detail in a paper published in December, 2000; you can read the Web version here if you like.

There is also the interesting story of Prof. A. A. Nijland's solicitation of observations from Dutch seamen, which elicited hundreds of observations from E. E. Havinga alone. These observations formed the core of Feenstra Kuiper's thesis. I have published the story of Nijland, Mulder, and Feenstra Kuiper in the Dutch magazine Zenit , which is basically the modern version of Hemel en Dampkring . Something approximating an English translation of this article is now available here.

Full Bibliography

Want more? My whole bibliography of references on atmospheric refraction, mirages, green flashes, etc. is now available. Please read its introduction before you try to use it; the intro will lead you to the whole bibliography, which is now over 2.2 MB long and contains more than 1000 green-flash references, and hundreds more on related topics, such as dip of the horizon, and terrestrial refraction.

If you find this information useful, I'd appreciate an acknowledgment in any published work that makes use of it.

You can help!

You might think I've found everything there is to find that has been published about green flashes. Wrong. There's a lot I haven't been able to locate. If you are near a good library, and would like to help, I have a wish list available.

There are also many additional reports and articles on green flashes in a host of popular and semi-technical magazines on astronomy, meteorology, navigation, travel, etc. that are not indexed by the abstracting services I have been able to use. For example, I don't have access to a library that has complete runs of journals like De Zee  or Hemel en Dampkring ; I haven't been able to search through all volumes of Symons's Met. Mag.  or Sterne und Weltraum . Another likely source of reports is the 19th-Century Nautical Magazine ; no library near me seems to own a set of it. There must also be many reports in travelers' accounts of sea voyages that have been published in hard covers and forgotten.

If you come across any item that isn't in the bibliography but ought to be there, please at least send me an email giving (if possible) the full citation, so I can try to get it through Inter-Library Loan.

Better yet, make a photocopy, or a PDF, and send it to me. I'm

Dr. Andrew T. Young
Astronomy Dept.
San Diego State University
San Diego, CA 92182–1221

I'll add it to my files, and the on-line bibliography, and add your name to the list of benefactors who have made all this possible.

If you have other suggestions, please email me.

© 1999 – 2010, 2012, 2016, 2017, 2020 Andrew T. Young

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