AEROSOL refers to small particles suspended in the air, as opposed to big “hydrometeors” like snowflakes and raindrops. Aerosols make the air look hazy by scattering light; the loss of light by scattering increases the atmosphericextinction. The relative AIRMASS is the ratio of the amount of air in the line of sight (at some zenith distance Z) to the amount in the zenith. It gives the relative amounts of molecular extinction at different zenith distances.

ALTITUDE: Angular distance above (positive) or below (negative) the horizontal (i.e., the astronomical horizon.) Altitude is usually measured in degrees and minutes of arc.

This is the astronomical definition of the term. In common usage, “altitude”, “elevation”, “height” and the like are used indiscriminately for both angular and linear measurements; and the technical usage varies from one field to another. Be aware of possible confusion here.

Because altitude is the coordinate affected by refraction, it's usual to distinguish between apparent altitude (the observed quantity, affected by atmospheric refraction) and true or geometric altitude (where an object would appear without the effect of refraction).

APPARENT HORIZON: Where the sky appears to meet the Earth. (See also sea horizon.) Because of perspective effects, different observers generally have different apparent horizons. Because of refraction, even the sea horizonusually lies above the geometric horizon.

ARCSECOND Seconds of arc as units of angular measurement. An arcsecond is equal to 1/3600 of a degree. An arcminute is equal to 1/60 of a degree.

ASTRONOMICAL HORIZON: the intersection of a horizontal plane through the eye with the celestial sphere (because the celestial sphere has an infinite radius, two observers at different heights above sea level, but placed on the same vertical line, have the same astronomical horizon.) Because of dip, the astronomical horizon always lies above the sea horizon. But it usually is hidden by trees, hills, and buildings on land. These objects then determine the observer's apparent horizon.

ASTRONOMICAL REFRACTION: The displacements of astronomical objects by atmospheric refraction. The effect is about a minute of arc at 45° from the zenith, and increases roughly with the tangent of the zenith distance; at the horizon, it is typically about half a degree, and quite variable. These effects are many orders of magnitude larger than the accuracy of the best astronomical position measurements, and so large that the mountings of most astronomical telescopes are adjusted to minimize the effects of refraction. See also terrestrial refraction.

ASTRONOMICAL UNIT (AU) A measure of distance moste often used in the solar system. It is the lenght of the semimajor axis of earth’s orbit. One AU is equal to approximetaly 149.597.870 Kilometers or 499.005 light seconds.


BOUNDARY LAYER: A relatively thin layer of fluid next to a boundary (such as a solid surface). Example: the layer of air next to the Earth's surface (the “planetary boundary layer”). Ordinarily, only the boundary layer is appreciably affected by the properties of the surface. The rest of the fluid is unaffected; so the part of the atmosphere above the boundary layer (which is typically a few hundred meters thick) is called the “free atmosphere.”

BOUNDARY LAYER METEOROLOGY is the name of the discipline that studies atmospheric boundary layers, as well as the name of a leading journal in this field.


CELESTIAL SPHERE: An imaginary sphere of infinite radius, centered at the observer. A point on the celestial sphere is really only a direction in space; parallel lines meet the celestial sphere in the same point.

CREPUSCULAR RAYS: When the lower atmosphere is hazy, light passing through gaps between broken clouds can produce bright “beams” that are made visible by scattering by aerosol particles. These are usually seen best when the Sun is low, or at twilight (hence the term “crepuscular.”)


DEGREE OF ARC (º) A unit of angular measurement that is 60 arcminutes. The full moon subtends an angle of about one-half a degree (30 arcminutes) in the sky.

DENSITY: How much stuff there is in how much space. The density of water is 1 gram per cubic centimeter, or one (metric) ton per cubic meter. The density of air is about 1 kilogram per cubic meter — about a thousand times less dense than water. The density of air is proportional to its pressure, and inversely proportional to its (absolute) temperature.

DIP: The dip of the apparent (or sea) horizon is its angular distance below the astronomical horizon. See the dip pagefor details.

DISPERSION: The variation of refraction, or refractive index, with the wavelength or color of light. All transparent media — air, water, glass, etc. — are dispersive. Normally, the refraction is greater for the short wavelengths (blue and violet) and least for the long ones (red light). See my dispersion page for details.

DUCT: If the ray curvature within a thermal inversion is stronger than the curvature of the Earth's surface, rays can becontinuously guided along the surface of the Earth without ever escaping to space. This region in which rays are trapped is called a duct. An observer within the duct sees a superior mirage of distant objects within the duct. Ducting occurs when the temperature gradient within the inversion is steeper than about 10 K in 100 meters (1 degree in 10 m). See the duct page for details.


EXTINCTION: loss of light in the atmosphere. Extinction is the sum of actual absorption, and scattering.


FATA MORGANA: A complex mirage display that involves multiple images, alternately expanded and compressed vertically, often giving the impression of buildings, cliffs, etc. where no such objects exist. The name is traditionally used in Italy for the vivid mirages seen across the Strait of Messina.


GEODESY is the study of the size and shape of the Earth. The corresponding adjective is geodetic.

GEOID is the equipotential surface corresponding to mean sea level.

GEOMETRIC HORIZON: Where the apparent sea horizon would be if there were no refraction; equivalently, where the cone with vertex at the observer's eye and tangent to the sea surface would meet the celestial sphere.

GRADIENT: the rate at which something changes; here, we are talking about temperature gradients: how fast the temperature changes with height in the atmosphere. The bending of rays in the atmosphere depends on the temperature gradient.

GREEN FLASHes are phenomena seen at sunrise and sunset, when some part of the Sun suddenly changes color (at sunset, from red or orange to green or blue). There are several quite different phenomena commonly lumped together under the name of “the green flash”, and this intermingling of disparate phenomena has fostered confusion.

GREEN RAY: a rare kind of green flash, in which an actual beam of green light is seen shooting up from the horizon where the Sun has just set, or from the Sun itself. Usually this beam or ray is only a few times larger than the Sun itself; sometimes, it appears as a diffuse glow. Unfortunately, the term “green ray” has often been used for green flashes in general — a confusing practice that should be discouraged.

GREEN RIM: When the Sun is low, normal atmospheric dispersion raises the short-wavelength images of the Sun more than the long-wavelength images; but atmospheric extinction attenuates the blue so much that the upper edge usually appears green, not blue or violet. The green rim is so narrow that it can only be seen telescopically.

GREEN SEGMENT: Mulder's term (popularized by his followers Minnaert and O'Connell) for all the common kinds of green flash together. This catch-all category is no longer useful, and should be avoided.


HEIGHT: Linear distance (usually measured in meters) above sea level; as contrasted with altitude, which is angular distance above the astronomical horizon. Usually called “elevation” by geographers.

HORIZON: An ill-defined term, used in many ways: see apparent horizon, astronomical horizon, and geometric horizon. To an astronomer, one of these horizons is a collection of directions in space, and in fact a circle on thecelestial sphere. To most other people, “horizon” means the edge of some physical object; then it makes sense to speak of the “distance to the horizon,” a usage that seems absurd astronomically.

HORIZONTAL REFRACTION: The astronomical refraction at the astronomical horizon — not refraction parallel to the horizon, as non-astronomers might suppose.


ILLUMINANCE: The amount of visible light per unit area. This is the visual quantity analogous to the radiometric quantity irradiance.

INDEX OF REFRACTION: See refraction.

INFERIOR MIRAGE: "Inferior" means "lower"; this is the mirage in which the inverted image is below the normal one. The common example is the hot-road mirage seen on sunny days.

INVERSION refers to something being upside down. Don't confuse inversion of an image with inversion of the temperature gradient (a thermal inversion).

IRRADIANCE: The amount of power per unit area in a beam of light. Sometimes also called flux. Units: W m-2


JORDAN SUNSHINE RECORDER A sunshine recorder of the type in which the timescale is supplied by the motion of the sun.

It consists of two opaque metal semicylinders mounted with their curved surfaces facing each other. Each of the semicylinders has a short narrow slit in its flat side. Sunlight entering one of the slits falls on light-sensitive paper (blueprint paper) that lines the curved side of the semicylinder. One semicylinder covers morning hours, the other afternoon hours. The sensitivity of the recording paper is variable, and this introduces an uncertainty in the evaluation of the record.


KINETIC THEORY The theory that bulk matter, to outward appearances motionless, is composed of huge numbers of atoms and molecules in rapid and incessant motion.


LAPSE RATE: The rate at which temperature decreases with height in the atmosphere. This has the opposite sign from the temperature gradient a physicist would use, so be careful.

LATERAL MIRAGE: A much mis-used term. Refraction in the horizontal direction is appreciable only when a boundary layer is stabilized by a wall or other near-vertical surface; in such cases, the term “mural mirage” is more descriptive.

Unfortunately, the existence of the term “lateral mirage” has encouraged uncritical observers to think they have seen images separated by many degrees in azimuth from the actual direction to the object. These are always cases of mis-identification; atmospheric refraction cannot produce such effects.

LOOMING: The appearance above the horizon of a distant object that would normally be hidden below it. This effect is caused by unusually large terrestrial refraction, usually due to a thermal inversion. Looming is the opposite of sinking. Both are refraction phenomena, but not mirages.

LUMINANCE: The amount of visible light per unit area and per unit solid angle. Often called “surface brightness”. This is the visual quantity analogous to the radiometric quantity radiance.


MINUTE: A minute of time is 1/60 of an hour; a minute of arc is 1/60 of a degree.

MIRAGE: An inverted image caused by atmospheric refraction.

A mirage may be defined as any display of atmospheric refraction that produces either multiple images of an object, or at least one inverted image. There are many kinds, including the classical inferior and superior mirages, the mock mirage, and Wegener's Nachspiegelung.

MOCK MIRAGE: an inverted image produced by a thermal inversion below eye level. While the classical inferior and superior mirages can be regarded, for some purposes, as due to internal reflections, no such interpretation is possible for the others, which might well be called “pseudo-mirages.”

Terms like “mock mirage” and “pseudo-mirage” should not be taken to mean that these phenomena are any less real than the classical inferior and superior mirages. The names are chosen simply to distinguish the recently-understood mirages from the classical ones, which involve different optical mechanisms.

MURAL MIRAGE: A mirage produced by the boundary layer of hot air next to a heated or sunlit wall. It is essentially an inferior mirage turned on its side.


NACHSPIEGELUNG: Alfred Wegener's term for the “late mirage” seen by an observer within a duct after the Sun has passed the “reflecting” or “obscured” strip (i.e., the superior mirage) produced by a duct.


OPTICAL DEPTH: If the transmission of a slab of material is   t = exp(-τ) then we say that τ is the optical depth of the material. So the optical depth is the negative of the natural logarithm of the transmission. (Note that it is a dimensionless number.)

A similar measure of opacity, called optical density, which is used in photography, uses the common (base 10) logarithm instead of the natural (base e) one.

ORIANI'S THEOREM: A proof that astronomical refraction is independent of atmospheric structure above the observer, from the zenith to about 70° zenith distance.


PERIGEE: The point on a trajectory, or the path of a refracted ray, that is nearest the center of the Earth.

PSEUDO-MIRAGE: A mirage that cannot be explained, even approximately, as due to internal reflection at the interface between warm and cool air. The mock mirage and Wegener's Nachspiegelung are examples of pseudo-mirages.


QUASIPERIODIC A term with a variety of meanings usually used to describe motion, a series of data, or a mathematical function the behavior of which suggests a recurring pattern but fails to conform to the strict meaning of periodicity in that an ordered set of values does not repeat at regular intervals of time or space.


RADIANCE: The amount of power per unit area and per unit solid angle in a beam of light. Units: W m-2 sterad-1

RED FLASH: the less-conspicuous complement of a green flash. There are a few in the list of pictures, and somesimulations.

REFRACTION: the bending of rays of light in passing from one medium to another (e.g., air to water), or between parts of the same medium with different densities (e.g., different levels in the atmosphere). The amount of refraction is given by Snel's law, which is expressed in terms of the medium's refractive index, which is just the ratio of the speed of light in a vacuum to that in the medium. 

Diffraction is purely a wave-optical phenomenon, and is appreciable only when the lateral dimension of an object in the path of the light is only a few wavelengths. Refraction is a ray-optical phenomenon that strictly is useful only when objects are many wavelengths across. So the two phenomena are usually important only in mutually exclusive situations.


SCATTERING: When light passes through a medium that is not perfectly homogeneous, the irregularities in the medium scatter some of the light in all directions. Even the molecules of air are large enough to scatter light; in 1871, Lord Rayleigh showed that this accounts for the blue sky. (Since then, molecular scattering has been called “Rayleigh scattering.”)

SEA HORIZON: The apparent horizon formed by the sea.

SINKING: The disappearance below the horizon of distant objects normally visible; the reverse of looming.

SNEL'S LAW gives the quantitative change of direction of a ray of light in passing from one medium to another. The product n sin z is the same on both sides of a plane interface between two media, where n is the local refractive index, and z is the local angle the ray makes with the normal to the interface. In the curved atmosphere, Snel's law becomes nR sin z = constant, where R is distance from the local center of curvature; see the page especially devoted to this refractive invariant.

STANDARD ATMOSPHERE: The STANDARD ATMOSPHERE is defined in: U.S. Standard Atmosphere, 1976 and U.S. Government Printing Office, Washington, D.C., 1976

but is very similar to its 1962 predecessor, and to the 1958 ICAO Standard Atmosphere in the lower parts that are important for refraction. Its most important property, for present purposes, is its constant lapse rate of 6.5 K/km.

This “model atmosphere” is a highly idealized version of the average of many measurements made in the real atmosphere. Thus, it lacks the fine structure that is always present in the real world.

STOOPING: Vertical compression of the refracted image of a distant object; the opposite of towering.

SUPERIOR MIRAGE: "Superior" means "higher"; this is the mirage in which the inverted image is above the normal one. These are somewhat uncommon, and are associated with ducting.


TERRESTRIAL REFRACTION: The displacement of terrestrial objects from their geometric directions by atmospheric refraction.

THERMAL INVERSION: On the average, the temperature in the lower atmosphere decreases with increasing height. (The average gradient is about 6.5 K per kilometer.) A region in which the warmer air lies above the colder air is said to have an “inverted” temperature gradient, and is called a “thermal inversion,” or “inversion layer.” A thermal inversion is required to produce a superior mirage.

TOWERING: Abnormal vertical stretching of the image of a distant object; the opposite of stooping. Towering and stooping are refraction phenomena that distort but do not invert images; hence, they are not mirages.

TWILIGHT WEDGE it is the visible shadow to the earth cast upon the sky by the setting sun. It can be seen as a blue-gray line or wall which rises in the east after a clear sunset. It is often tinged with pink.


ULTRAVIOLET RADIATION  Electromagnetic radiation of shorter wavelength than  visible radiation but longer than x-rays.


VECTOR FIELD In its restricted physical sense, any physical quantity that varies in three-dimensional space (and possibly time), usually continuously except possibly on surfaces or curves.


WATER SKY The dark appearance of the underside of a cloud layer when it is over a surface of open water.

WHITEOUT An atmospheric optical phenomenon in which the observer appears to be engulfed in a uniformly white glow.

Neither shadows, horizon, nor clouds are discernible; sense of depth and orientation is lost; only very dark, nearby objects can be seen. Whiteout occurs over an unbroken snow cover and beneath a uniformly overcast sky, when, with the aid of the snow blink effect, the light from the sky is about equal to that from the snow surface. Blowing snow may be an additional cause. This phenomenon is experienced in the air as well as on the ground.


X-RAY Electromagnetic radiation with wavelengths shorter than that of ultraviolet radiation and greater than that of gamma radiation.


YAW Oscillation of a ship about the vertical axis.


Z0 The internationally accepted symbol for the elevation of mean sea level above chart datum.

ZENITH an imaginary point vertically aligned with a particular location, on the celestial sphere