Basic Principles for understanding atmospheric refraction phenomena

Introduction

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.)

Overview

One principle is to realize how all these pieces fit together:

• Astronomical refraction is all the atmospheric refraction between the observer and some point outside the atmosphere.
• Terrestrial refraction is just the part between the observer and some object inside the atmosphere.
• Mirages are extreme examples of terrestrial refraction that sometimes occur for objects that are (usually) beyond the horizon.
• Dip involves just the refraction between the observer and the apparent horizon (usually, the sea horizon).

Astronomical and apparent horizons

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.

Compression

Because refraction raises a small part 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 appreciable 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 normal flattening of the setting Sun. See the Standard-Atmosphere sunset simulation, for 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 produce the quasi-rectangular features of the Fata Morgana display that fool observers into thinking they see architectural features such as castles, aqueducts, and cities where no such things exist.

Alternation of erect and inverted images

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 those 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.

Symmetry

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).

Density gradients and ray curvature

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.

Refractive Invariant

An important basic idea in this business, which applies to all of these phenomena, is the refractive invariant. Again, it is so important that it has its own page. Warning: a little math is required here.

Ducting

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.

Upper vs. lower atmosphere

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 Andrew T. Young

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