Green flashes, mirages, astronomical refraction, dip of the horizon: these are all related phenomena. But there are some basic ideas that are helpful in understanding all of them. The purpose of this page is to point these out. (A more technical page is also available.)
One principle is to realize how all these pieces fit together:
The apparent horizon is “where the sky meets the sea [or land]”. It's a visible feature that everyone is familiar with. Because the Earth is convex, the sea horizon is always below the astronomical horizon; this depression of the sea horizon is the dip .
The astronomical horizon divides the sky into two regions. Below it, a ray passing through your eye can be horizontal — a fact that has profound consequences. Above it, a ray passing through your eye is (ordinarily) always inclined to the horizontal. The astronomical horizon is a conceptual, not a visible, feature of the sky; non-astronomers are usually unaware of its importance.
All transparent media refract light. The refractivity of common media like air and water is roughly proportional to their density. As air is nearly a thousand times less dense than water, its refractivity is also about a thousand times smaller; but this still is enough to produce visible effects near grazing incidence (i.e., for nearly horizontal rays).
Continuous media like air bend light rays into nearly circular arcs, whose curvature is nearly proportional to the local density gradient. (See the bending page for details.) In the atmosphere, this bending is visible to the naked eye only near the horizon, where the curvature is nearly constant with angular altitude.
So a constant vertical density gradient changes the directions of all nearly horizontal rays by the same amount: the image of a distant object is displaced, but not appreciably distorted. The density gradient is primarily due to the change in pressure with height; so unless the vertical temperature gradient changes rapidly with height, there is no mirage.
However, the dip of the horizon depends on the temperature gradient (the negative of the meteorologists' “lapse rate”). The steep decrease in temperature with height on a sunny day depresses the horizon (i.e., increases the dip and lowers images); the nocturnal thermal inversion on a clear night, or the inversion above cold water during the day, raises the apparent horizon and reduces its dip.
But if the lapse rate itself changes with height, the dips of distant objects change with their height.
When the dip increases with height, the tops of distant targets are depressed more than their bases: the images of the objects are compressed vertically. The towering effect is larger for more distant objects; if their tops are depressed strongly enough, an observer sees the images inverted, and we have an inferior mirage. This happens when a large surface lapse rate decreases rapidly with height, as it does over smooth ground on a sunny afternoon. Distant objects are hidden by the inverted image of the mirage, so the apparent horizon is closer to the observer than usual, and the convexity of the Earth is exaggerated.
Conversely, when the dip decreases with height, as it does when hot air from the land flows out over cold water, the steeper thermal inversion near the surface raises the images of the lowest parts of an image more than the upper parts, and the images of distant objects are vertically compressed — sometimes to the point of invisibility. (This compression is called stooping.) Images of distant objects are raised more than closer ones, so the cold surface sometimes appears concave. The apparent horizon is farther than usual from the observer, which produces looming.
Because refraction raises a small zone of the sky just below the astronomical horizon into the part just above it, the image of this strip of sky at the horizon is, on the average, compressed vertically. The obvious compression is confined to a narrow band that extends only 2 or 3 degrees above the astronomical horizon. As the refraction at the astronomical horizon is typically about half a degree, that means the usual compression is about 1/6 of the vertical size of an object at the horizon. (This is, for example, about the usual flattening of the setting Sun. See the Standard-Atmosphere sunset simulation, for an example.)
But when refraction is unusually large, a bigger zone of sky that would normally have been below the horizon is crammed into this compressed region. Then the average flattening is greatly increased; the Sun can flatten out into a thin line.
Note that the average compression does not exclude a vertical expansion of some part of the image. If one part is expanded, other parts must be even more compressed to fit into the available image space. Alternating bands of compression and expansion can produce the quasi-rectangular features of the Fata_Morgana displays that fool observers into thinking they see architectural features such as castles, aqueducts, and cities where no such things exist.
If the image is unbroken and continuous, multiple images are alternately erect and inverted. This applies to all mirages (which involve at least one inverted image) except some that are produced by ducting (see below). Ducts can produce discontinuities in the images; then one erect image is often seen directly on top of another.
I have a separate page devoted to symmetry principles. Some of them involve the astronomical horizon (see above).
The most important symmetry in atmospheric refraction is that a ray in a horizontally stratified atmosphere is symmetrical about its lowest point (where it is horizontal).
Again, I have a separate page on the subject of ray bending. Because density gradients are closely related to temperature gradients, I have another page devoted to the thermal structure of the atmosphere. The important point is that mirages involve the difference between the curvature of the ray and the curvature of the Earth.
Specifically, because mirages always have inverted images, rays between the observer's eye and different parts of a miraged object must cross, so that rays from the top of the object reach the eye from lower directions than rays from the lower parts. And because
An important special case of ray bending occurs when the curvature of a horizontal ray exceeds the curvature of the Earth. Then the ray bends back toward the Earth in both directions, and can be trapped in a duct . Some of the most spectacular mirages and green flashes are produced by ducts.
Because the thermal structures that produce the most interesting phenomena are usually the result of temperature differences between the air and the surface of the Earth, temperature gradients tend to be biggest near the surface. Moreover, because the part of the atmosphere in which you can see rays that are horizontal is always near or below eye level, the lowest part of the atmosphere — at and below eye level — is the most important for these phenomena.
That means this region is where all the action is; the air above eye level (except in cases of ducting) is really unimportant. (Even in ducts, the top of the duct is never very far above the eye.) This means it's very useful to divide the atmosphere into two regions: the lower part (near and below eye level) that produces the spectacular phenomena, and everything above that — which is really most of the atmosphere! The idea of cutting the problem into two pieces this way was first suggested by Alfred Wegener, so I call it “Wegener's Principle” and have devoted a special page to it.
The lower atmosphere is so important that most of the refraction at the sea horizon seen by an observer more than a kilometer above sea level comes from the air below eye level, even for the Standard Atmosphere. When there are thermal inversions nearer the surface, as happens when there are superior mirages, this halfway-point is even lower in the atmosphere.
If you want a more technical and systematic presentation of these matters, see the page on understanding atmospheric refraction.
Copyright © 2003, 2005, 2006, 2012, 2026 Andrew T. Young
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